0% found this document useful (0 votes)

46 views541 pages

Mathematics A: Paper 3H Higher Tier

This document is an examination paper for the Pearson Edexcel International GCSE Mathematics A, Higher Tier, dated May 26, 2016. It includes instructions, information about the total marks, and a formulae sheet, followed by a series of mathematical questions covering various topics such as algebra, geometry, and statistics. The paper consists of 22 questions, requiring candidates to show their working and answer all questions within a 2-hour time limit.

Uploaded by

daniel.whelan

We take content rights seriously. If you suspect this is your content, claim it here.

Available Formats

Download as PDF, TXT or read online on Scribd

0% found this document useful (0 votes)

46 views541 pages

Mathematics A: Paper 3H Higher Tier

Uploaded by

daniel.whelan

We take content rights seriously. If you suspect this is your content, claim it here.

Available Formats

Download as PDF, TXT or read online on Scribd

You are on page 1/ 541

Write your name here

Surname Other names

Centre Number Candidate Number

Pearson Edexcel Certificate
Pearson Edexcel
International GCSE

Mathematics A
Paper 3H

Higher Tier
Thursday 26 May 2016 – Morning Paper Reference
4MA0/3H
Time: 2 hours KMA0/3H

You must have: Total Marks

Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser, calculator. Tracing paper may be used.

Instructions
• Use black ink or ball-point pen.
• centre
Fill in the boxes at the top of this page with your name,
number and candidate number.
• Withoutallsufficient
Answer questions.
• Answer the questions working, correct answers may be awarded no marks.
• – there may be more spacein the spaces provided
than you need.
• You must NOT write anything on the formulae page.
Calculators may be used.
• Anything you write on the formulae page will gain NO credit.
Information
• The total mark for this paper is 100.
• –Theusemarks for each question are shown in brackets
this as a guide as to how much time to spend on each question.

Advice
• Check
Read each question carefully before you start to answer it.
• your answers if you have time at the end.
Turn over

P45841A
©2016 Pearson Education Ltd.
*P45841A0124*
1/1/1/1/1/
International GCSE MATHEMATICS
FORMULAE SHEET – HIGHER TIER

DO NOT WRITE IN THIS AREA

Pythagoras’ Volume of cone = 1
r 2h Volume of sphere = 4
r3
3 3
Theorem
c Curved surface area of cone = rl Surface area of sphere = 4 r 2
b
r
a l
h
a + b2 = c2
2
r

adj = hyp cos

hyp opp = hyp sin
opp opp = adj tan In any triangle ABC
C
adj opp
or sin b a
hyp

DO NOT WRITE IN THIS AREA

adj A B
cos c
hyp

opp a b c
tan Sine rule:
adj sin A sin B sin C

Cosine rule: a2 b2 + c 2 2bc cos A

1
Area of triangle 2 ab sin C
cross
section
h
lengt
Volume of prism = area of cross section length

Area of a trapezium = 12 (a + b)h

r Circumference of circle = 2 r a
DO NOT WRITE IN THIS AREA

Area of circle = r 2 h

r
The Quadratic Equation
Volume of cylinder = r h 2 The solutions of ax2 + bx + c 0,
h where a 0, are given by
Curved surface area
of cylinder = 2 rh b + b2 4ac
x
2a

2
*P45841A0224*
Answer ALL TWENTY TWO questions.

Write your answers in the spaces provided.

DO NOT WRITE IN THIS AREA

You must write down all the stages in your working.

1 Here are the ingredients needed to make 12 muffins.

Ingredients to make 12 muffins

300g flour
150g sugar
250ml milk
100g butter
2 eggs

Sarah makes 60 muffins.

DO NOT WRITE IN THIS AREA

(a) Work out how much sugar she uses.

....................................................... g
(2)
James makes some muffins.
He uses 625 ml of milk.
(b) How many muffins did he make?
DO NOT WRITE IN THIS AREA

.......................................................

(2)

(Total for Question 1 is 4 marks)

3
*P45841A0324* Turn over
2 a í
c í

DO NOT WRITE IN THIS AREA

(a) Work out the value of 2a2 + 6c

.......................................................

(2)
There are 4 pens in a small box of pens.
There are 10 pens in a large box of pens.
Ami buys x small boxes of pens and y large boxes of pens.
She buys a total of T pens.
(b) Write down a formula for T in terms of x and y.

DO NOT WRITE IN THIS AREA

.......................................................

(3)

(Total for Question 2 is 5 marks)

DO NOT WRITE IN THIS AREA

4
*P45841A0424*
3 The table shows information about the number of visits each of 40 adults made to the
gym last week.
DO NOT WRITE IN THIS AREA

Number of visits to the gym Frequency

0 4
1 3
2 12
3 5
4 8
5 5
6 2
7 1

Work out the mean of the number of visits to the gym.

DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 3 is 3 marks)

4 A = {2, 4, 6, 8, 10, 12, 14}

B = {1, 3, 5, 7, 9, 11, 13}
C = {3, 6, 9, 12}
(a) List the members of the set
(i) A C
DO NOT WRITE IN THIS AREA

..................................................................................

(ii) A C

..................................................................................

(2)
(b) Explain why A B = Ø

. . . . . . . . . . ............................... .............................................................. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)
(Total for Question 4 is 3 marks)

5
*P45841A0524* Turn over
5 On the grid, draw the graph of y = 3x – 5 for values of xIURPíWR

DO NOT WRITE IN THIS AREA

y
6

DO NOT WRITE IN THIS AREA

–2 –1 O 1 2 3 4 x
–1

–2

–3

–4

–5

–6

–7 DO NOT WRITE IN THIS AREA

–8

–9

–10

–11

–12

(Total for Question 5 is 4 marks)

6
*P45841A0624*
3 2 13
6 (a) Show that + =
10 15 30
DO NOT WRITE IN THIS AREA

(2)
5 1 1
(b) Show that 2 ÷1 = 2
8 6 4
DO NOT WRITE IN THIS AREA

(3)
DO NOT WRITE IN THIS AREA

(Total for Question 6 is 5 marks)

7
*P45841A0724* Turn over
7 (a) Factorise 3y2 + 2y

DO NOT WRITE IN THIS AREA

..................................................................................

(1)
(b) Expand and simplify (x – 9)(x + 2)

..................................................................................

(2)
(c) (i) Solve 6k + 5 < 20

DO NOT WRITE IN THIS AREA

.......................................................

(ii) n is an integer and 6n + 5 < 20

Write down the largest possible value of n

.......................................................

(3)
DO NOT WRITE IN THIS AREA

5 3
28 x y
(d) Simplify fully
4 xy 2

.......................................................

(2)

(Total for Question 7 is 8 marks)

8
*P45841A0824*
8 A B Diagram NOT
accurately drawn
DO NOT WRITE IN THIS AREA

13.4 cm
53°

Work out the length of AB.

Give your answer correct to 1 decimal place.
DO NOT WRITE IN THIS AREA

....................................................... cm

(Total for Question 8 is 3 marks)

DO NOT WRITE IN THIS AREA

9
*P45841A0924* Turn over
9 Bhavin, Max and Imran share 6000 rupees in the ratios 2 : 3 : 7
3
Imran then gives of his share of the money to Bhavin.

DO NOT WRITE IN THIS AREA

5
What percentage of the 6000 rupees does Bhavin now have?
Give your answer correct to the nearest whole number.

DO NOT WRITE IN THIS AREA

....................................................... %

(Total for Question 9 is 5 marks)

10
*P45841A01024*
10 The diagram shows a circle inside a rectangle.

Diagram NOT
DO NOT WRITE IN THIS AREA

accurately drawn

2.5 cm
7.6 cm

13.8 cm

Work out the area of the shaded region.

Give your answer correct to 3 significant figures.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . cm2

(Total for Question 10 is 3 marks)

11
*P45841A01124* Turn over
11 The frequency table shows information about the weights of 80 adults.

DO NOT WRITE IN THIS AREA

Weight (w kg) Frequency
40 < w - 50 4
50 < w - 60 7
60 < w - 70 21
70 < w - 80 21
80 < w - 90 18
90 < w - 100 7
100 < w - 110 2

(a) Complete the cumulative frequency table.

Weight (w kg) Cumulative frequency

40 < w - 50 4

DO NOT WRITE IN THIS AREA

40 < w - 60
40 < w - 70
40 < w - 80
40 < w - 90
40 < w - 100
40 < w - 110
(1)

DO NOT WRITE IN THIS AREA

12
*P45841A01224*
(b) On the grid, draw a cumulative frequency graph for your table.
(2)
DO NOT WRITE IN THIS AREA

60
Cumulative
frequency 50

10
DO NOT WRITE IN THIS AREA

0
40 50 60 70 80 90 100 110
Weight (w kg)

.......................................................

(2)
(d) Use your graph to find an estimate for the interquartile range of the weights of the
adults.
DO NOT WRITE IN THIS AREA

....................................................... kg
(2)

(Total for Question 11 is 7 marks)

13
*P45841A01324* Turn over
12 Solve the simultaneous equations 4x + 5y = 13
3x – 2y = 27

DO NOT WRITE IN THIS AREA

Show clear algebraic working.

DO NOT WRITE IN THIS AREA

x = .......................................................

y = ....................................................... DO NOT WRITE IN THIS AREA

(Total for Question 12 is 4 marks)

14
*P45841A01424*
13 The straight line L SDVVHVWKURXJKWKHSRLQWV í DQG
Find an equation of the line that is parallel to LDQGSDVVHVWKURXJKWKHSRLQW í
DO NOT WRITE IN THIS AREA

Give your answer in the form ax + by = c where a, b and c are integers.

DO NOT WRITE IN THIS AREA

.......................................................
DO NOT WRITE IN THIS AREA

(Total for Question 13 is 5 marks)

15
*P45841A01524* Turn over
14 A particle is moving along a straight line.
The fixed point O lies on this line.
The displacement of the particle from O at time t seconds is s metres where

DO NOT WRITE IN THIS AREA

s = 2t3 – 12t2 + 7t
(a) Find an expression for the velocity, v m/s, of the particle at time t seconds.

v = .......................................................
(2)

DO NOT WRITE IN THIS AREA

(b) Find the time at which the acceleration of the particle is instantaneously zero.

....................................................... seconds
(2)
DO NOT WRITE IN THIS AREA

(Total for Question 14 is 4 marks)

16
*P45841A01624*
15 The diagram shows two mathematically similar vases, A and B.
Diagram NOT
DO NOT WRITE IN THIS AREA

accurately drawn

A B

Vase A has a surface area of 120 cm2

Vase B has a surface area of 750 cm2 and a volume of 1600 cm3
Work out the volume of vase A.
DO NOT WRITE IN THIS AREA

cm3
DO NOT WRITE IN THIS AREA

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . .

(Total for Question 15 is 3 marks)

17
*P45841A01724* Turn over
16 ABCDEFGH is a cuboid.

D A

DO NOT WRITE IN THIS AREA

Diagram NOT
C accurately drawn
B
8 cm

E F
5 cm
H 17 cm G

The cuboid has

length 17 cm
width 5 cm
height 8 cm
Work out the size of the angle that AH makes with the plane EFGH.
Give your answer correct to 1 decimal place.

DO NOT WRITE IN THIS AREA

°
.......................................................

(Total for Question 16 is 4 marks)

18
*P45841A01824*
17 The diagram shows a trapezium.

x+6
DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn

x–1

3x – 4

All measurements on the diagram are in centimetres.

The area of the trapezium is 119 cm2
(i) Show that 2x2 – x – 120 = 0
DO NOT WRITE IN THIS AREA

(ii) Find the value of x.

Show your working clearly.
DO NOT WRITE IN THIS AREA

x = .......................................................

(Total for Question 17 is 6 marks)

19
*P45841A01924* Turn over
t +1
18 Make t the subject of the formula m=
t−3

DO NOT WRITE IN THIS AREA

DO NOT WRITE IN THIS AREA
.......................................................

(Total for Question 18 is 4 marks)

DO NOT WRITE IN THIS AREA

20
*P45841A02024*
19 Diagram NOT
A
accurately drawn
DO NOT WRITE IN THIS AREA

D 75°

C
27°

A, B, C and D are points on a circle, centre O.

Angle DAB = 75°
Angle DBC = 27°
Work out the size of angle ODC.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

°
.......................................................

(Total for Question 19 is 4 marks)

21
*P45841A02124* Turn over
20 A metal cube has sides of length 4.5 cm, correct to the nearest 0.5cm.
The cube is melted down and the metal is used to make small spheres.

DO NOT WRITE IN THIS AREA

Each sphere has a radius of 3 mm, correct to the nearest millimetre.
Work out the greatest number of spheres that could be made from the metal.
Show your working clearly.

DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 20 is 5 marks)

22
*P45841A02224*
21 There are 9 counters in a bag.
There is a number on each counter.
DO NOT WRITE IN THIS AREA

1 1 2 2 2 3 3 3 3

Kal takes at random 3 counters from the bag.

He adds together the numbers on the 3 counters to get his Total.
Work out the probability that his Total is 6
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 21 is 5 marks)

23
*P45841A02324* Turn over
22 The diagram shows a pentagon.
Diagram NOT

DO NOT WRITE IN THIS AREA

12 cm 12 cm accurately drawn

105° 105°

8 cm 8 cm

13 cm

Work out the area of the pentagon.

Give your answer correct to 3 significant figures.

DO NOT WRITE IN THIS AREA

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . cm2

(Total for Question 22 is 6 marks)

TOTAL FOR PAPER IS 100 MARKS

24
*P45841A02424*
Mark Scheme (Results)

June 2016

Pearson Edexcel International GCSE

Mathematics A (4MA0)
Paper 3H

Pearson Edexcel Level 1/Level Certificate

Mathematics A (KMA0)
Paper 3H
Edexcel and BTEC Qualifications

Edexcel and BTEC qualifications come from Pearson, the world’s

leading learning company. We provide a wide range of qualifications
including academic, vocational, occupational and specific
programmes for employers. For further information, please visit our
website at www.edexcel.com.

Our website subject pages hold useful resources, support material

and live feeds from our subject advisors giving you access to a
portal of information. If you have any subject specific questions
about this specification that require the help of a subject specialist,
you may find our Ask The Expert email service helpful.

www.edexcel.com/contactus

Pearson: helping people progress, everywhere

Our aim is to help everyone progress in their lives through education. We
believe in every kind of learning, for all kinds of people, wherever they are
in the world. We’ve been involved in education for over 150 years, and by
working across 70 countries, in 100 languages, we have built an
international reputation for our commitment to high standards and raising
achievement through innovation in education. Find out more about how
we can help you and your students at: www.pearson.com/uk

Summer 2016
Publications Code 4MA0_3H_1606_MS
All the material in this publication is copyright
© Pearson Education Ltd 2016
General Marking Guidance
 All candidates must receive the same treatment. Examiners
must mark the first candidate in exactly the same way as they
mark the last.
 Mark schemes should be applied positively. Candidates must
be rewarded for what they have shown they can do rather
than penalised for omissions.
 Examiners should mark according to the mark scheme not
according to their perception of where the grade boundaries
may lie.
 There is no ceiling on achievement. All marks on the mark
scheme should be used appropriately.
 All the marks on the mark scheme are designed to be
awarded. Examiners should always award full marks if
deserved, i.e. if the answer matches the mark scheme.
Examiners should also be prepared to award zero marks if the
candidate’s response is not worthy of credit according to the
mark scheme.
 Where some judgement is required, mark schemes will
provide the principles by which marks will be awarded and
exemplification may be limited.
 When examiners are in doubt regarding the application of the
mark scheme to a candidate’s response, the team leader must
be consulted.
 Crossed out work should be marked UNLESS the candidate
has replaced it with an alternative response.
 Types of mark
o M marks: method marks
o A marks: accuracy marks
o B marks: unconditional accuracy marks (independent of
M marks)
 Abbreviations
o cao – correct answer only
o ft – follow through
o isw – ignore subsequent working
o SC - special case
o oe – or equivalent (and appropriate)
o dep – dependent
o indep – independent
o eeoo – each error or omission
 No working
If no working is shown then correct answers normally score
full marks
If no working is shown then incorrect (even though nearly
correct) answers score no marks.
 With working
If there is a wrong answer indicated on the answer line always
check the working in the body of the script (and on any
diagrams), and award any marks appropriate from the mark
scheme.
If it is clear from the working that the “correct” answer has
been obtained from incorrect working, award 0 marks.
Any case of suspected misread loses A (and B) marks on that
part, but can gain the M marks.
If working is crossed out and still legible, then it should be
given any appropriate marks, as long as it has not been
replaced by alternative work.
If there is a choice of methods shown, then no marks should
be awarded, unless the answer on the answer line makes
clear the method that has been used.
If there is no answer on the answer line then check the
working for an obvious answer.
 Ignoring subsequent work
It is appropriate to ignore subsequent work when the
additional work does not change the answer in a way that is
inappropriate for the question: eg. Incorrect cancelling of a
fraction that would otherwise be correct.
It is not appropriate to ignore subsequent work when the
additional work essentially makes the answer incorrect eg
algebra.
Transcription errors occur when candidates present a correct
answer in working, and write it incorrectly on the answer line;
mark the correct answer.
 Parts of questions
Unless allowed by the mark scheme, the marks allocated to
one part of the question CANNOT be awarded in another.
International GCSE Maths
Apart from questions 6, 12, 17, 20 (where the mark scheme states otherwise) the correct answer, unless obtained from an incorrect method,
should be taken to imply a correct method.
Q Working Answer Mark Notes
1 a 60 ÷ 12 × 150 or 60 ÷ 12 (=5) or 150 ÷ 12 (=12.5) M1 allow x ÷ 12 × 60 oe where
x is 300 or 250 or 100 or 2
750 2 A1
b 625 ÷ 250 × 12 oe M1 complete method
30 2 A1
Total 4 marks

2 a 2×(−5)2 + 6×−2 or M1
2(−5)2 + 6(−2) or
50 and −12
38 2 A1
b T = 4x + 10y oe 3 B3 for a correct final answer
(award B2 if T = 4x + 10y is incorrectly simplified)

If not B3 then
B2 for T = 4x + ky or T = kx + 10y (k may be 0)) or 4x + 10y

B1 for 4x or 10y or T = (linear expression in x and y)

Total 5 marks
3 0×4 + 1×3 + 2×12 + 3×5 + 4×8 + 5×5 + 6×2 + 7×1 or M1 condone one error
(0) + 3 + 24 + 15 + 32 + 25 + 12 + 7 (=118)
“118” ÷ “40” M1 dep
NB. Allow a value other than 40 provided it has
clearly come from the sum of the frequency
column
2.95 3 A1 Accept 3 from 118÷40
SC: B2 for 3.05
Total 3 marks

4 ai 6, 12 1 B1 cao
aii 2,3,4,6,8,9,10,12,14 1 B1 cao
b no members in common 1 B1 accept , e.g. members of A are even and
members of B are odd; no numbers the same
Total 3 marks
5 y = 3x – 5 4 B4 For a correct line between x = −2 and x = 3
x −2 −1 0 1 2 3 drawn
y −11 −8 −5 −2 1 4 from
x = −2 to
x=3
B3 For a correct straight line segment through at least 3 of
(−2, −11) (−1, −8) (0, −5) (1, −2) (2, 1) (3, 4)
OR
for all of (−2, −11) (−1, −8) (0, −5) (1, −2) (2, 1) (3, 4) plotted
but not joined

B2 For at least 2 correct points plotted (ignore incorrect points)

OR
for a line drawn with a positive gradient through (0, −5) and
clear intention to use a gradient of 3
(eg. a line through (0, −5) and (0.5, −2)

B1 For at least 2 correct points stated (may be in a table) or may

be shown in working eg. 3 × 2 – 5 = 1
OR
for a line drawn with a positive gradient through (0, −5) but
not a line joining (0, −5) and (3, 0)
OR
a line with gradient 3
Total 4 marks
6 a 9 4 2 M1 9 4
+ for or or
30 30 30 30
both fractions expressed as equivalent fractions with
denominators that are a common multiple of 10 and 15 eg.
45 20
and
150 150
shown A1 conclusion to given answer coming from correct working
b 21 7 3 M1 63 28
÷ or Both fractions expressed as improper fractions eg. ,
8 6 24 24
21 7
and
8 6
21 6 126 M1 or for both fractions expressed as equivalent fractions with
× or denominators that are a common multiple of 8 and 6 eg.
8 7 56
126 56 63 28
÷ or
48 48 24 24

shown A1 1 9
conclusion to 2 or from correct working – either
4 4
126
sight of the result of the multiplication e.g. must be
56
9
seen or correct cancelling prior to the multiplication with
4
Total 5 marks
7 a y(3y + 2) 1 B1
b M1 for 3 correct terms
or
4 correct terms ignoring signs or
x2 − 7x + a for any non-zero value of a or
... − 7x − 18
x2 − 7x − 18 2 A1
ci 6k < 20 − 5 M1 for a correct first step to solve the inequality (accept an
equation in place of an inequality) or
2.5 oe given as answer
k < 2.5 oe A1 final answer must be an inequality
cii 2 3 B1 for 2
or ft from an incorrect inequality of the form k < a in (i)
d 7x4y 2 B2 accept 7x4y1
B1 for ax n y m with 2 of a = 7, n = 4, m = 1 (n≠ 0, m≠ 0)
or
7x 4 y 3
correct expression with two of 7, x4, y e.g.
y2
Total 8 marks
8 AB sin 53 sin 90 M1 Alternative methods
sin 53o = or  or
M1 for AC or angle B evaluated correctly
13.4 AB 13.4
AB 13.4 AND then used in a correct method to
 or find AB
sin 53 sin 90
AB
cos 37 = AB
13.4 eg. AB2 + 8.06..2 = 13.42 , tan 53 =
8.06...
13.4 M1 M1 for a fully correct method
13.4 × sin 53o or  sin 53
sin 90 eg.; 13.42  8.06..2 , 8.06…× tan 53
or 13.4 × cos37
10.7 3 A1 awrt 10.7
Total 3 marks

9 6000 ÷ (2 + 3 + 7 ) × 7 (=3500) or M1
6000 ÷ (2 + 3 + 7 ) × 2 (=1000)
3 M1
× “3500” (=2100)
5
3 M1
(6000 ÷ (2 + 3 + 7 ) × 2) + × “3500” (=3100)
5
or
1000 + 2100

"3100" M1 dep on previous M1

100
6000
52 5 A1 Accept 51.6 - 52
Total 5 marks
10 π × 2.52 (=19.6...) or 13.8 × 7.6 (=104.88) M1
13.8 × 7.6 − π × 2.52 M1 correct method
85.2 3 A1 for answer in range 85 – 85.3
Total 3 marks

11 a 4 ,11 ,32 ,53 ,71 ,78 ,80 1 B1

b 2 M1 ft from table for at least 5 points plotted
correctly at end of interval
or
ft from sensible table for all 7 points plotted
consistently within each interval in the freq
table at the correct height

correct cf graph A1 accept curve or line segments

accept curve that is not joined to (40,0)

c Reading from graph at w = 85 M1 ft from a cumulative frequency graph

eg. reading of 60 – 64 provided method is shown
16 − 20 2 A1 ft from a cumulative frequency graph
provided method is shown
d Use of 20 and 60 (or 20.25 and 60.75) M1 ft from a cumulative frequency graph
eg. readings of 61− 65 and 83−87 provided method is shown
eg. 85 − 63
18 − 22 2 A1 ft from a cumulative frequency graph
provided method is shown
Total 7 marks
12 e.g. 12x + 15y = 39 4 M1 for multiplication to give coefficients of x or y the
− 12x − 8y = 108 same and correct operation selected to eliminate
one variable
e.g. (condone any one error in multiplication)
27  2 y or
4( )  5 y  13 for correct rearrangement of one equation followed
3
by correct substitution in the other
23y = −69; y = −3 A1 cao depends on M1
12x + 15×−3 = 39 M1 (dep on 1st M1) for substituting the found variable
or starting again to find second variable as M1
above
x = 7; y = −3 A1 Award 4 marks for correct values if at least M1
scored
Total 4 marks

13 93  3  5 M1 for method to find gradient of L

e.g.  
6  2  4 
y = "0.75"x + c M1 use of their gradient in an equation M2 for
c may be numerical 3
M1 method to find c
y  1  " "( x  5) oe
19 4
−1 = "0.75"× 5 + c (c =  )
4
3 19 A1 correct equation
y  x oe
(equation in any form)
4 4
4y − 3x = −19 A1 oe with integer coefficients
e.g. 3x – 4y = 19; 4y = 3x − 19
Total 5 marks
14 a 2 × 3t2 ; −12 × 2t ; 7 2 M1 evidence of differentiation; at least
two terms correct
6t2 − 24t + 7 A1
b 6×2t − 24 = 0 2 M1 ft from a quadratic in (a) for
correct differentiation and
equating to zero
2 A1 ft
Total 4 marks

15 120  2  750  5  3 M1 Correct linear scale factor

   oe or    oe or (accept ratios)
750  5  120  2 
0.43 ( = 0.064) oe or 2.53 ( =15.625) oe M1 or for 1600 ÷ 6.253 oe or
1600 × 0.163 oe
102.4 A1
Total 3 marks

16 angle AHF identified 4 M1 may be implied by a correct calculation

(FH=) 172  52 or 314 (=17.7...) M1 or (AH = ) 172  52  82 (=19.4..) or
378 or 3 42
8 M1 dep on previous M1
tan AHF =
"17.7..." "17.7..."
or cos AHF = or
"19.4..."
8
sin AHF = ( × sin90) or
"19.4..."
"19.4.."2  "17.7.."2  82
cosAHF =
2  "19.4.." "17.7.."
24.3 A1 answer in range 24.2 − 24.4
Total 4 marks
17 i 1 6 M1 correct algebraic expression for any relevant
e.g.  ( x  6  3x  4)  ( x  1) or (x + 6)(x − 1)
2 area
or (x − 1)(3x − 4)
1
or  ( x  1)(3x  4  ( x  6))
2
1 M1 for correct equation with at least one pair of
eg.  (4 x 2  2 x  2)  119
2 brackets expanded correctly

shown A1 for completion to given equation

ii (2x ±15)(x ± 8) (=0) or M1 Start to solve quadratic condone one sign

  1  (1)  4  2  120
2 error in substitution if quadratic formula
or used; allow −12 or 12 or 1 in place of (−1)2
2 2
2 2
 1 1 ft from an incorrect 3 term quadratic
 x       60  0
 4 4 equation
1  1  960 M1 dep
(2x +15)(x − 8) (=0) or or ft method from an incorrect 3 term quadratic
4
2
equation
1 1
x      60 or
4 4

−7.5 and 8 given as solutions

8 A1 Award all 3 marks if first M1 awarded and

8 alone given as final answer
Total 6 marks
18 m(t – 3) = t + 1 or 4 M1 clearing fraction
mt – 3m = t + 1
e.g. M1 for expanding bracket
mt − t = 1 + 3m or AND
t – mt = −1 − 3m rearranging so that all terms in t are isolated on one
side of a correct equation
t(m − 1) or M1 take t out as a common factor (in an equation)
t(1 – m)
3m  1 A1 3m  1
t or t  oe
m 1 1 m
Total 4 marks

19 Angle DCB = 180 − 75 (=105) 4 M1 Use of opposite angles in a cyclic

quadrilateral sum to 180o
Angle DOB = 2 × 75 (=150) M1 Use of angle at centre is twice
angle at circumference
E.g. (180 – 105 – 27) + (180 – 150)÷2 or M1 Complete method
360 – (150 + 105 + 27 + (180 – 150)÷2)
63 A1
Total 4 marks
20 4.75 or 4.25 or 47.5 or 42.5 5 B1 
Allow 4.749
3.5 or 2.5 or 35 or 25 B1
4 M1 
   0.253 (=0.0654498…) or Allow 4.749
3
4
   2.53 (=65.4498…) or
3
4.75 × 4.75 × 4.75 (= 107.171875) or
47.5 × 47.5 × 47.5 (=107171.875)
4  M1 indep – accept use of 4.5 and 0.3
“4.75”3 ÷     "0.25"3  (=1637.465...) or candidate’s bounds
3 
units must be consistent
1637 A1 1637 must come from correct
working with correct figures
Total 5 marks
21 3 2 1 6 1  5 M1 (probabilities from selecting 2, 2, 2)
eg.     
9 8 7  504 84  3 2 1 6  3 3 3  27 
allow      or     
9 9 9  729  9 9 9  729 

2 3 4  24 1 M1 (probabilities from selecting 1, 2, 3)

eg.     
9 8 7  504 21  2 3 4  24 
allow     
9 9 9  729 
24  144 6 2  M1 (probabilities for all combinations of 1, 2, 3)
6 " "    
504  504 21 7  24  144 
allow 6  " "  
729  729 
2 3 4 3 2 1  6 1  M1 complete correct method
6        
9 8 7 9 8 7  21 84 
150 A1 25
oe eg. , 0.298, 0.297619…
504 84
150  50  171  19 
(NB. An answer of   or  
729  243  729  81 
scores M1M1M1M0A0)
Total 5 marks
22 122 + 82 − 2×12×8×cos(105) (=257...) M1
257(....) or 257( 16.05..) A1 for 257 or awrt 258 or 16 - 16.1
If M1 has been awarded then allow the use of
the candidate’s value for AD in all subsequent
working
A
eg. M1 (dep on first M1)
complete method to find height of pentagon or
E B any angle within triangle ADC
E.g.
angle ADC = angle ACD = 66.08…
angle DAC = 47.8…
D C
H angle DAH = angle CAH = 23.9…
(AH = ) "16.05.."2  6.52 (=14.6...) or (accept all these angles rounded or truncated
to 3 or more sig figs)
 "16.05"2  132  "16.05"2 
( ADC ) cos 1   (=66.08..)
 2  "16.05"13 
eg. M1 any one relevant area
0.5×12×8×sin(105) (=46.3...) or (any calculated values used must come from a
12×8×sin(105) (=92.7…) or correct method)
0.5×13×"14.6" (=95.4...) or
0.5 × 13 × "16.05" × sin ("66.1")
eg. M1 (dep on first M1)
2 ×0.5×12×8×sin(105) + 0.5×13×"14.6" or complete correct method
2×0.5×12×8×sin(105) + 0.5 × 13 × "16.05" × sin
("66.1")
188 6 A1 accept answer in range 188 – 188.5
Total 6 marks
Pearson Education Limited. Registered company number 872828
with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
Write your name here
Surname Other names

Centre Number Candidate Number

Pearson Edexcel
International GCSE

Mathematics A
Paper 3HR

Higher Tier
Thursday 26 May 2016 – Morning Paper Reference

Time: 2 hours 4MA0/3HR

You must have: Total Marks
Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser, calculator. Tracing paper may be used.

Advice
• Check
Read each question carefully before you start to answer it.
• your answers if you have time at the end.
Turn over

P45864A
©2016 Pearson Education Ltd.
*P45864A0120*
1/1/1/1/
International GCSE MATHEMATICS
FORMULAE SHEET – HIGHER TIER

DO NOT WRITE IN THIS AREA

Pythagoras’ Volume of cone = 1
r 2h Volume of sphere = 4
r3
3 3
Theorem
c Curved surface area of cone = rl Surface area of sphere = 4 r 2
b
r
a l
h
a + b2 = c2
2
r

adj = hyp cos

hyp opp = hyp sin
opp opp = adj tan In any triangle ABC
C
adj opp
or sin b a
hyp

DO NOT WRITE IN THIS AREA

adj A B
cos c
hyp

opp a b c
tan Sine rule:
adj sin A sin B sin C

Cosine rule: a2 b2 + c 2 2bc cos A

1
Area of triangle 2 ab sin C
cross
section
h
lengt
Volume of prism = area of cross section length

Area of a trapezium = 12 (a + b)h

r Circumference of circle = 2 r a
DO NOT WRITE IN THIS AREA

Area of circle = r 2 h

r
The Quadratic Equation
Volume of cylinder = r h 2 The solutions of ax2 + bx + c 0,
h where a 0, are given by
Curved surface area
of cylinder = 2 rh b + b2 4ac
x
2a

2
*P45864A0220*
Answer ALL TWENTY TWO questions.

Write your answers in the spaces provided.

DO NOT WRITE IN THIS AREA

You must write down all the stages in your working.

1 Rafael and Roger played tennis against each other 30 times.

Each of the times they played, either Rafael won or Roger won.
The ratio of the number of times Rafael won to the number of times Roger won is 7 : 3
(a) Work out the number of times Rafael won.

.......................................................

(2)
DO NOT WRITE IN THIS AREA

In a school, there are 75 girls in the tennis squad.

The ratio of the number of boys in the tennis squad to the number of girls in the tennis
squad is 4 : 3
(b) Work out the number of boys in the tennis squad.

.......................................................
DO NOT WRITE IN THIS AREA

(2)

(Total for Question 1 is 4 marks)

3
*P45864A0320* Turn over
2 (a) Factorise fully 2x2 – 4x

DO NOT WRITE IN THIS AREA

.......................................................

(2)
A = 2p + 3q
(b) Work out the value of p when A = 32 and q = 7

p = .......................................................
(3)

DO NOT WRITE IN THIS AREA

(Total for Question 2 is 5 marks)

3 There are 50 marbles in a bag.

35 of the marbles are brown.
Otti takes at random a marble from the bag.
He records the colour of the marble and puts the marble back in the bag.
He does this 300 times.
Work out an estimate for the number of brown marbles he takes.

DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 3 is 2 marks)

4
*P45864A0420*
4 Work out the size of an exterior angle of a regular polygon with 8 sides.
DO NOT WRITE IN THIS AREA

°
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .

(Total for Question 4 is 2 marks)

5 In a sale, normal prices are reduced by 8%

(a) The normal price of a jacket is £28
DO NOT WRITE IN THIS AREA

Work out the price of the jacket in the sale.

£ .......................................................
(3)
(b) In the sale, the price of a shirt decreases by £3
Work out the normal price of the shirt.
DO NOT WRITE IN THIS AREA

£ .......................................................
(3)

(Total for Question 5 is 6 marks)

5
*P45864A0520* Turn over
6 (a) Solve the inequalities –4 < 3x + 5 - 11

DO NOT WRITE IN THIS AREA

.......................................................

(3)
(b) Write down the integer values of x which satisfy –4 < 3x + 5 - 11

DO NOT WRITE IN THIS AREA

.......................................................

(2)

(Total for Question 6 is 5 marks)

7 Write 792 as a product of its prime factors.

Show your working clearly.

DO NOT WRITE IN THIS AREA

.........................................................................................

(Total for Question 7 is 3 marks)

6
*P45864A0620*
8
y
DO NOT WRITE IN THIS AREA

3
P
2

–5 –4 –3 –2 –1 O 1 2 3 4 5 x
–1
Q
–2

–3
DO NOT WRITE IN THIS AREA

–4

–5

(a) Describe fully the single transformation that maps shape P onto shape Q.

(2)
(b) Rotate shape Q 90° clockwise about (1,0)
Label the new shape R.
(2)

(Total for Question 8 is 4 marks)

DO NOT WRITE IN THIS AREA

7
*P45864A0720* Turn over
9 Li throws a 6-sided biased dice once.
The table shows the probability that the dice will land on 1, 2, 3, 5 or 6

DO NOT WRITE IN THIS AREA

Number 1 2 3 4 5 6
Probability 0.15 0.1 0.05 0.2 0.15

(a) Work out the probability that the dice will land on 4

.......................................................

(2)
(b) Work out the probability that the dice will land on an odd number.

DO NOT WRITE IN THIS AREA

.......................................................

(2)

(Total for Question 9 is 4 marks)

DO NOT WRITE IN THIS AREA

8
*P45864A0820*
10 Julie asked 50 children how many exercise sessions they each took part in last month.
The table shows information about her results.
DO NOT WRITE IN THIS AREA

Number of exercise sessions Frequency

0 to 6 13
7 to 13 10
14 to 20 16
21 to 27 7
28 to 34 4

Calculate an estimate for the total number of exercise sessions the children took part in
last month.
DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 10 is 3 marks)

7
11 The line L passes through the point (3, 1) and is parallel to the line with equation y = – 2x.
2
Find an equation for the line L.
DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 11 is 3 marks)

9
*P45864A0920* Turn over
a11
12 (a) Simplify fully
a 2 × a5

DO NOT WRITE IN THIS AREA

.......................................................

(2)
(b) Make p the subject of p + 4q = 3p + 5

.......................................................

(2)
(c) Expand and simplify (2y + 3)(4y – 1)

DO NOT WRITE IN THIS AREA

....................................................................

(2)
1
(d) Simplify (8a b )
6 3 3

.......................................................

(2)
DO NOT WRITE IN THIS AREA

(Total for Question 12 is 8 marks)

10
*P45864A01020*
13 Here is the quadrilateral ABCD.
DO NOT WRITE IN THIS AREA

9.8 cm Diagram NOT

A B
accurately drawn

3.6 cm

8.4cm
D

Angle BAD = 90° and angle BCD = 90°

AB = 9.8 cm
AD = 3.6 cm
BC = 8.4 cm
Calculate the length of DC.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

....................................................... cm

(Total for Question 13 is 4 marks)

11
*P45864A01120* Turn over
14 Linford and Alan race against each other in a competition.
If one of them wins a race, he wins the competition.

DO NOT WRITE IN THIS AREA

If the race is a draw, they run another race.
They run a maximum of three races.
Each time they race, the probability that Linford wins is 0.35
Each time they race, the probability that there is a draw is 0.05
(a) Complete the probability tree diagram.

race 1 race 2 race 3

Linford Linford Linford
0.35 ................. .................
wins wins wins

0.05 ................. .................

draw draw draw
................ . ................. .................

DO NOT WRITE IN THIS AREA

Alan Alan Alan
wins wins wins

(2)
(b) Calculate the probability that Linford wins the competition.

DO NOT WRITE IN THIS AREA

......................................................

(3)

(Total for Question 14 is 5 marks)

12
*P45864A01220*
9 2
15 y = x3 – x – 54x + 10
2
DO NOT WRITE IN THIS AREA

dy
(a) Find
dx

.......................................................

(2)
9 2
The curve with equation y = x3 – x – 54x + 10 has two turning points.
2
(b) Find the x coordinate of each of these two points.
DO NOT WRITE IN THIS AREA

..................................................................................

(3)
DO NOT WRITE IN THIS AREA

(Total for Question 15 is 5 marks)

13
*P45864A01320* Turn over
16 The incomplete histogram shows information about the heights of a group of children.

DO NOT WRITE IN THIS AREA

Frequency
density

DO NOT WRITE IN THIS AREA

110 120 130 140 150

Height of children (cm)

There were 10 children with heights between 130cm and 135cm.

(a) How many children had heights between 110cm and 130cm?

DO NOT WRITE IN THIS AREA

.......................................................

(3)
There were 6 children with heights between 135cm and 145cm.
(b) Show this information on the histogram.

(1)

(Total for Question 16 is 4 marks)

14
*P45864A01420*
17 D Diagram NOT
accurately drawn
DO NOT WRITE IN THIS AREA

9cm E

4cm 5cm

C 4.5cm B A

Triangle ABE is similar to triangle ACD.

AED and ABC are straight lines.
EB and DC are parallel.
AE = 5 cm, BC = 4.5 cm, BE = 4 cm, CD = 9cm
(a) Calculate the length of AD.
DO NOT WRITE IN THIS AREA

....................................................... cm
(2)
(b) Calculate the length of AB.

....................................................... cm
(2)
The area of quadrilateral BCDE is x cm2
The area of triangle ABE is ycm2
DO NOT WRITE IN THIS AREA

(c) Find an expression for y in terms of x.

Give your answer as simply as possible.

y = .......................................................
(3)

(Total for Question 17 is 7 marks)

15
*P45864A01520* Turn over
18 f is the function such that
x
f(x) =

DO NOT WRITE IN THIS AREA

3x + 1
(a) Find f (0.5)

.......................................................

(1)
(b) Find ff(–1)

DO NOT WRITE IN THIS AREA

.......................................................

(2)
(c) Find the value of x that cannot be included in any domain of f

.......................................................

(1)
(d) Express the inverse function f –1 in the form f –1(x) = ...
Show clear algebraic working.

DO NOT WRITE IN THIS AREA

f –1(x) = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)

(Total for Question 18 is 7 marks)

16
*P45864A01620*
19
C Diagram NOT
accurately drawn
DO NOT WRITE IN THIS AREA

O
100°
B
P

A, B and C are points on a circle, centre O.

PA and PC are tangents to the circle.
Angle ABC = 100°
Calculate the size of angle APC.
DO NOT WRITE IN THIS AREA

°
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .

(Total for Question 19 is 3 marks)

DO NOT WRITE IN THIS AREA

17
*P45864A01720* Turn over
50 x 2 − 8
20 (a) Simplify fully
10 x − 4
Show clear algebraic working.

DO NOT WRITE IN THIS AREA

DO NOT WRITE IN THIS AREA
.......................................................

(3)
(b) Given that a is a positive integer, show that

3a ( 12a + a 3a )
is always a multiple of 3

DO NOT WRITE IN THIS AREA

(3)

(Total for Question 20 is 6 marks)

18
*P45864A01820*
21 Solve 3 × 42k+8 = 24
Show your working clearly.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

k = .......................................................

(Total for Question 21 is 4 marks)

DO NOT WRITE IN THIS AREA

19
*P45864A01920* Turn over
22 P Q
Diagram NOT
R accurately drawn

DO NOT WRITE IN THIS AREA

30°

The diagram shows a circle, centre C.

PR is a chord of the circle.
The area of the shaded region is 100 cm2
Angle PCR = 30°
Calculate the length of the arc PQR.
Give your answer correct to 3 significant figures.

DO NOT WRITE IN THIS AREA

....................................................... cm

(Total for Question 22 is 6 marks)

TOTAL FOR PAPER IS 100 MARKS

20
*P45864A02020*
Mark Scheme (Results)

June 2016

Pearson Edexcel International GCSE

Mathematics A (4MA0)
Paper 3HR
Edexcel and BTEC Qualifications

Edexcel and BTEC qualifications come from Pearson, the world’s

Our website subject pages hold useful resources, support material

www.edexcel.com/contactus

Pearson: helping people progress, everywhere

Summer 2016
Publications Code 4MA0_3HR_1606_MS
All the material in this publication is copyright
© Pearson Education Ltd 2016
General Marking Guidance
 All candidates must receive the same treatment. Examiners
must mark the first candidate in exactly the same way as they
mark the last.
 Mark schemes should be applied positively. Candidates must
be rewarded for what they have shown they can do rather
than penalised for omissions.
 Examiners should mark according to the mark scheme not
according to their perception of where the grade boundaries
may lie.
 There is no ceiling on achievement. All marks on the mark
scheme should be used appropriately.
 All the marks on the mark scheme are designed to be
awarded. Examiners should always award full marks if
deserved, i.e. if the answer matches the mark scheme.
Examiners should also be prepared to award zero marks if the
candidate’s response is not worthy of credit according to the
mark scheme.
 Where some judgement is required, mark schemes will
provide the principles by which marks will be awarded and
exemplification may be limited.
 When examiners are in doubt regarding the application of the
mark scheme to a candidate’s response, the team leader must
be consulted.
 Crossed out work should be marked UNLESS the candidate
has replaced it with an alternative response.
 Types of mark
o M marks: method marks
o A marks: accuracy marks
o B marks: unconditional accuracy marks (independent of
M marks)
 Abbreviations
o cao – correct answer only
o ft – follow through
o isw – ignore subsequent working
o SC - special case
o oe – or equivalent (and appropriate)
o dep – dependent
o indep – independent
o eeoo – each error or omission
o awrt –answer which rounds to
 No working
If no working is shown then correct answers normally score
full marks
If no working is shown then incorrect (even though nearly
correct) answers score no marks.
 With working
If there is a wrong answer indicated on the answer line always
check the working in the body of the script (and on any
diagrams), and award any marks appropriate from the mark
scheme.
If it is clear from the working that the “correct” answer has
been obtained from incorrect working, award 0 marks.
Any case of suspected misread loses A (and B) marks on that
part, but can gain the M marks.
If working is crossed out and still legible, then it should be
given any appropriate marks, as long as it has not been
replaced by alternative work.
If there is a choice of methods shown, then no marks should
be awarded, unless the answer on the answer line makes
clear the method that has been used.
If there is no answer on the answer line then check the
working for an obvious answer.
 Ignoring subsequent work
It is appropriate to ignore subsequent work when the
additional work does not change the answer in a way that is
inappropriate for the question: eg. Incorrect cancelling of a
fraction that would otherwise be correct.
It is not appropriate to ignore subsequent work when the
additional work essentially makes the answer incorrect eg
algebra.
Transcription errors occur when candidates present a correct
answer in working, and write it incorrectly on the answer line;
mark the correct answer.
 Parts of questions
Unless allowed by the mark scheme, the marks allocated to
one part of the question CANNOT be awarded in another.
Apart from Questions 7, 18d and 20a, 20b & 21 where the mark scheme states otherwise, the correct answer, unless clearly obtained by an
incorrect method, should be taken to imply a correct method.

Q Working Answer Mark Notes

1. (a) 7 2 M1 A Complete method to find either
 30 oe (eg 30 ÷ (7 + 3) = 3, 7 × ‘3’) or share
10
3
 30 (= 9)
10
21 A1
(b) 75 2 M1 Complete method
 4 oe
3
100 A1
Total 4 marks
Q Working Answer Mark Notes
2. (a) 2x(x – 2) 2 B2 Also award B2 for (2x + 0)(x – 2)
B1 for incomplete factorisation
2( x² − 2x) or x(2x – 4) or 2x taken
out as a common factor.

(b) 32 = 2p + 3 × 7 3 M1 Correct substitution

2p = 32 – 3 × 7 or 2p = 32 – 21 or 2p = 11 or M1 Rearranging to make 2p or p the

32  21 subject (or −2p or –p)
p
2
11
2 A1oe
Total 5 marks

Q Working Answer Mark Notes

3. 35 2 M1 A fully correct method
× 300 oe, eg 35 × 6, 0.7 × 300, etc
50
210
A1 cao (award M1 only)
210 300
Total 2 marks
Q Working Answer Mark Notes
4. 360 (8  2) 180 2 M1 For complete correct method for
or 180  exterior angle
8 8

45 A1 Answer of 135 scores M0A0

Total 2 marks

Q Working Answer Mark Notes

5. (a) 8 3 M1 92
 28 or 2.24 M2 for  28
100 100
28 – "2.24" M1 dep

25.76 A1
(b) 3 3 3 3
or 100 oe M2 M1 for or 0.375 or 3 = 8%
0.08 8 8

37.50 A1 Accept 37.5

Total 6 marks
Q Working Answer Mark Notes
6. (a) 9  3x  6 or 3x > –9 and 3x ≤ 6 or 3 M2 For both ends correct for 3x or
4 5 11 5 4 5 11 5
  x  or x    and x   x  or one end correct for x
3 3 3 3 3 3 3 3
or x > −3 or x ≤ 2 M1 for one end correct for 3x or
5
x  , eg 3x > –9 or
3
3x ≤ 6 or
answers of x = −3 & x = 2

–3<x≤2 A1 Accept x > –3, x ≤ 2

(b) – 2, – 1, 0, 1, 2 2 B2ft B1 for five correct values and one

incorrect value or four correct
values with no incorrect value
Only ft from an inequality in the
form a  x  b
Total 5 marks
Q Working Answer Mark Notes
7. 792 = 2 × 396 = 2× 2 × 198 3 M1 For at least 2 correct steps in
= 2 × 2 × 2 × 99 = 2 × 2 × 2 × 3 × 33 repeated factorisation (may be seen
in a tree diagram or ‘ladder’)
2, 2, 2, 3, 3, 11 A1 Condone inclusion of 1 (maybe a
fully correct tree or factor ladder)
2 × 2 × 2 × 3 × 3 × 11 A1 Or 23  32 11
NB: Candidates showing no
working score 0 marks
Total 3 marks

Q Working Answer Mark Notes

8. (a) Translation 2 B2 B1 for translation
5 to the right and 4 down B1 for 5 to the right and 4 down
or (–54)
These marks are independent but
award no marks if the answer is not a
single transformation.
(b) R correct 2 B2 (– 2, – 1 ), ( 0, – 1 ), (0, – 2 ),
(– 1, – 2 ),
Condone omission of label
B1 for 90° anticlockwise rotation
about (1,0) or for
Correct orientation but incorrect
position.
Total 4 marks
Q Working Answer Mark Notes
9. (a) 1 – (0.15 + 0.1 + 0.05 + 0.2 + 0.15) 2 M1
0.35 A1 oe
(b) 0.15 + 0.05 + 0.2 2 M1
0.4 A1 oe
Total 4 marks

Q Working Answer Mark Notes

10. 3 × 13 + 10 × 10 + 17 × 16 + 24 × 7 + 31 × 4 3 M1 For at least 2 products f × x
Or 39 + 100 + 272 + 168 + 124 consistently within intervals
(including end points)
M1 For completely correct method
(condone 1 error)
NB: Products do not need to be
evaluated
703 A1 cao Do not ISW to find mean
SC award 2 marks for 14.06 if no
other marks gained
Total 3 marks
Q Working Answer Mark Notes
11. gradient = −2 3 M1 for m = – 2 stated or y = k – 2x
where k ≠ 7/2

1 = 3 × ‘(–2)’ + c or y – 1 = ‘−2’(x – 3) oe M1ft Correct substitution to find c for

their gradient
y = –2x + 7 A1oe (M2 for −2x + 7 or L = −2x + 7)
Total 3 marks
Q Working Answer Mark Notes
12. (a) a11
a6
a9
a 11
e.g. or or 5 oe 2 M1 For or any index law used
a7 a 2
a a7
correctly
a4 A1
(b) 4q – 5 = 3p – p oe eg −2p = 5 – 4q 2 M1 For correctly collecting terms in p
one side and other terms on the
other side
4q  5
p oe, eg p = 2q – 2.5
2 A1
(c) 8y² – 2y + 12y – 3 2 M1 For any three correct terms
or for 4 correct terms ignoring signs
or for 8y² + 10y + k for any non-zero
value of k or for ....+10y – 3

8y² + 10y – 3 A1
(d) 2a b2 2 B2 B1 for two of 2 or a 2 or b as part of a
product
Total 8 marks

Q Working Answer Mark Notes

13. 3.6² + 9.8² or 109 4 M1 A correct first step to find DB
√"3.6² + 9.8² " or 109 (=10.4…) M1 Accept 10.4(403065...) rounded or
truncated to at least 3 SF
√"109" – 8.4² M1
6.2 A1 oe
Total 4 marks
Q Working Answer Mark Notes
14. (a) 2 B1 For 0.6 on LHS branch
Correct probabilities B1ft For all other probabilities correct
(b) 0.35 + 0.05 × 0.35 + 0.05 × 0.05 × 0.35 oe 3 M2 ft from tree diagram
(=0.35 + 0.0175 + 0.000875) M1 for 0.05 × 0.35 or 0.05² × 0.35
oe
2947
0.368375 A1 oe eg
8000
Accept 0.36(8375) rounded or
truncated to at least 2 SF
Total 5 marks

Q Working Answer Mark Notes

15. (a) 9
2 M1 For any two of 3x², – 2  x, or –54
2
A1
3x² – 9x – 54
(b) 3x² – 9x – 54 = 0 3 M1ft For letting (a) = 0

Eg 3(x – 6)(x + 3) ( = 0 ) or M1ft For correct factors or correct

substitution into the quadratic
(9)  (9) 2  4  3  54 formula
(x =)
23 Only ft for a 3 term quadratic & if
M1 scored in (a)

x = – 3 and x = 6 A1
Total 5 marks
Q Working Answer Mark Notes
16. (a) 1 Square = 0.5 or 2 squares = 1 oe 3 M1 1 Square = 0.5 or 2 squares = 1
 
Or fd 10  2 calculated or marked at correct place
5  
Or correct fd 10  2 calculated
5
on vertical axis with no contradictions or marked on the vertical axis with
no contradictions
1 × 10 + 2 × 5 + 3 × 5 (=10 + 10 + 15) oe M1 Complete method to find total
number of children, eg 10, 10, and
15 frequencies assigned to correct
blocks
35 A1
(b) Correct block 1 B1
Total 4 marks
Q Working Answer Mark Notes
17. (a) 9 4 2 M1 For the correct SF seen or used
or oe
4 9
11.25 A1oe
(b) 5 x 4 x 2 M1 A fully correct equation in x or a
Eg  or  or correct calculation for x
"11.25" x  4.5 9 x  4.5
5 4.5 "11.25" 5
 or 4.5  or 2.25x = x + 4.5
4 x 5
oe
3.6 A1oe
(c) 16 81 3 M1
2.25² or 5.0625 or or or 81 : 16 or
81 16
16 65
16 : 81 or or or 65 : 16 or 16 : 65
65 16
65 x M1 For a fully correct expression in x
5.0625y – y = x or  oe and y that can be rearranged to
16 y
give y in terms of x
16 x x
A1oe eg
65 4.0625
Accept 0.246(1538....)x rounded or
truncated to at least 3SF
Total 7 marks
Q Working Answer Mark Notes
18. (a) 1 1
5 B1oe
(b) 2 M1 f( – 1 ) = 1 or substitution of
2

x = −1 into
 x
(3x  1) 

1
3x (3x  1)  1
5 A1oe
(c) 1 1
 B1
3
(d) y x 3 M1 For writing function in the
x y
3y 1 3x  1 form x 
y
or
x(3y + 1) = y or 3xy + x = y y(3x + 1) = x or 3xy + y = x 3y 1
x
y and multiplying
3x  1
both sides by the
denominator

3xy – y = − x or 3xy – x = − y or M1 For gathering terms in x or y

y(3x – 1) = – x x(3y – 1) = −y (whichever is applicable)
oe oe correctly

x x A1 Dep on M1
or must be in terms of x
1  3x 3x  1
Total 7 marks
Q Working Answer Mark Notes
19. 100 × 2 3 M1 Complete method to find obtuse
360 – "100 × 2" (=160) angle AOC – could be seen in
correct place on diagram

360 – (90 + 90 + "160") M1 dep for correct method to find APC

20 A1
Total 3 marks
Q Working Answer Mark Notes
20. (a) 2(5 x  2)(5 x  2) (5 x  2)(5 x  2) 3 M2 Factorising numerator and
or or
2(5 x  2) 5x  2 denominator in a correct quotient
(5 x  2)(10 x  4) (10 x  4)(5 x  2) M1 for 2(25x² – 4) or a correctly
or oe factorised numerator or
2(5 x  2) 2(5 x  2)
25 x 2  4
denominator or
5x  2

5x + 2 A1 dep on at least M1
(b) 12a  3a  a 3a  3a or better 3 M1 For correct expansion or
√12𝑎 = 2√3√𝑎 or 12a  2 3a
or 6a or 3a² from correct working
6a + 3a² A1

6a  3a 2 Show B1ft dep on at least M1

eg 3(2a + a²) or 3a(2 + a) or  2a  a 2
3
or explanation that 6a and 3a² are multiples of 3
so overall expression is a multiple of 3
Total 6 marks
Q Working Answer Mark Notes
21. 3 3
(22 )2 k 8  23 or 4  8 or
2
24k 16  23 4 M2 M1 for 42 k 8 = 8 or 3  4 2  24
3
or 4  42 k 8
2

4k + 16 = 3 or 2k + 8 = 1.5 oe M1 A correct equation in k or a fully

correct method to find k
13 A1oe Dep on at least M2

4
Total 4 marks
Q Working Answer Mark Notes
22. 30 6 M2 For a correct equation involving r²
  r 2  0.5r 2 sin 30  100 oe
360 30  r2
M1 for  r 2
(or ) or
360 12
 30  0.5r 2 sin 30 (or 0.25r²)
r2   0.5sin 30   100
 360 
   3 
r2    100
 12 

1200 M1 For a correct equation with r² the

r² = 𝜋 – 3
subject

1200 M1 For correctly isolating r. Accept

r=√ 92.(05984992...) rounded or
𝜋–3
truncated to at least 2SF
1200 30 1 M1 A correct expression for the length
2𝜋 × √𝜋 – 3 × 360 oe eg 2𝜋×92….× of are PQR
12

48.2 A1 Accept answers which round to

48.2
Total 6 marks
Pearson Education Limited. Registered company number 872828
with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
Write your name here
Surname Other names

Centre Number Candidate Number

Pearson Edexcel Certificate
Pearson Edexcel
International GCSE

Mathematics A
Paper 4H

Higher Tier
Thursday 9 June 2016 – Morning Paper Reference
4MA0/4H
Time: 2 hours KMA0/4H

You must have: Total Marks

Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser, calculator. Tracing paper may be used.

Advice
• Check
Read each question carefully before you start to answer it.
• your answers if you have time at the end.
Turn over

P45863A
©2016 Pearson Education Ltd.
*P45863A0124*
1/1/1/1/
International GCSE MATHEMATICS
FORMULAE SHEET – HIGHER TIER

DO NOT WRITE IN THIS AREA

Pythagoras’ Volume of cone = 1
r 2h Volume of sphere = 4
r3
3 3
Theorem
c Curved surface area of cone = rl Surface area of sphere = 4 r 2
b
r
a l
h
a + b2 = c2
2
r

adj = hyp cos

hyp opp = hyp sin
opp opp = adj tan In any triangle ABC
C
adj opp
or sin b a
hyp

DO NOT WRITE IN THIS AREA

adj A B
cos c
hyp

opp a b c
tan Sine rule:
adj sin A sin B sin C

Cosine rule: a2 b2 + c 2 2bc cos A

1
Area of triangle 2 ab sin C
cross
section
h
lengt
Volume of prism = area of cross section length

Area of a trapezium = 12 (a + b)h

r Circumference of circle = 2 r a
DO NOT WRITE IN THIS AREA

Area of circle = r 2 h

r
The Quadratic Equation
Volume of cylinder = r h 2 The solutions of ax2 + bx + c 0,
h where a 0, are given by
Curved surface area
of cylinder = 2 rh b + b2 4ac
x
2a

2
*P45863A0224*
Answer ALL TWENTY TWO questions.

Write your answers in the spaces provided.

DO NOT WRITE IN THIS AREA

You must write down all the stages in your working.

1 Here are the first five terms of an arithmetic sequence.

7 10 13 16 19

Find an expression for the nth term of the sequence.

DO NOT WRITE IN THIS AREA

........................................................

(Total for Question 1 is 2 marks)

2 Solve 8y – 18 = 3( y + 3)
Show clear algebraic working.
DO NOT WRITE IN THIS AREA

y = ........................................................

(Total for Question 2 is 3 marks)

3
*P45863A0324* Turn over
3 In a sale, all normal prices are reduced by 20%
(a) The normal price of a television set is 485 euros.

DO NOT WRITE IN THIS AREA

Work out the sale price of the television set.

........................................................ euros
(3)

DO NOT WRITE IN THIS AREA

(b) In the sale, the normal price of a tablet computer is reduced by 79 euros.
Work out the normal price of the tablet computer.

DO NOT WRITE IN THIS AREA

........................................................ euros
(3)

(Total for Question 3 is 6 marks)

4
*P45863A0424*
4
E Diagram NOT
DO NOT WRITE IN THIS AREA

accurately drawn
A 50q B
pq

C 63q
D
qq

F G

EFG is a triangle.
AB is parallel to CD.
(a) Write down the value of p
p = ........................................................
(1)
(b) Write down the value of q
DO NOT WRITE IN THIS AREA

q = ........................................................
(1)
Here is a hexagon.

3xq 139q Diagram NOT

accurately drawn
164q xq

97q 156q

(c) Work out the value of x

DO NOT WRITE IN THIS AREA

x = ........................................................
(3)

(Total for Question 4 is 5 marks)

5
*P45863A0524* Turn over
5 (a) Simplify m5 × m2
........................................................

DO NOT WRITE IN THIS AREA

(1)
(b) Simplify c11 ÷ c3
........................................................

(1)
(c) Simplify (a5)3
........................................................

(1)
(d) Expand and simplify 4(2x + 3) + 2(x + 5)

........................................................

(2)

DO NOT WRITE IN THIS AREA

(Total for Question 5 is 5 marks)

6 Students in class 9Y took part in a sponsored swim.

The table gives information about the amount of money, in £, raised by each student.

Money raised (£x) Frequency

0-x6 4
6 - x 12 6
12 - x 18 8
18 - x 24 9
24 - x 30 3

Work out an estimate for the total amount of money raised by the students in class 9Y. DO NOT WRITE IN THIS AREA

£. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 6 is 3 marks)

6
*P45863A0624*
7 (a) Complete the table of values for y = x 2 – 4x + 2
DO NOT WRITE IN THIS AREA

x –1 0 1 2 3 4 5

y 2 –2 –1

(2)
(b) On the grid, draw the graph of y = x 2 – 4x + 2 for all values of x from –1 to 5

y
8

7
DO NOT WRITE IN THIS AREA

–2 –1 O 1 2 3 4 5 6 x
–1

–2
DO NOT WRITE IN THIS AREA

–3
(2)

(Total for Question 7 is 4 marks)

7
*P45863A0724* Turn over
8
y

DO NOT WRITE IN THIS AREA

7
6
5
B
4
3
A
2
1

–4 –3 –2 –1 O 1 2 3 4 5 6 7 8 9 10 11 12 x
–1
–2
–3

DO NOT WRITE IN THIS AREA

(a) Describe fully the single transformation that maps triangle A onto triangle B.

(3)

⎛ 5⎞
(b) On the grid, translate triangle A by the vector ⎜ ⎟
⎝ −4⎠
Label the new shape C.
(1)

DO NOT WRITE IN THIS AREA

8
*P45863A0824*
y
6
DO NOT WRITE IN THIS AREA

5
4
3
D
2
1

–4 –3 –2 –1 O 1 2 3 4 5 6 7 x
–1
–2
–3
–4
–5
DO NOT WRITE IN THIS AREA

(Total for Question 8 is 6 marks)

DO NOT WRITE IN THIS AREA

9
*P45863A0924* Turn over
9
C

DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn

60 cm

A 13.5 cm B

Work out the perimeter of the triangle.

DO NOT WRITE IN THIS AREA

........................................................ cm

(Total for Question 9 is 4 marks)

10
*P45863A01024*
10 The highest common factor (HCF) of 140 and x is 20
The lowest common multiple (LCM) of 140 and x is 420
DO NOT WRITE IN THIS AREA

Find the value of x.

DO NOT WRITE IN THIS AREA

x = ........................................................

(Total for Question 10 is 2 marks)

DO NOT WRITE IN THIS AREA

11
*P45863A01124* Turn over
11 The table gives the populations of each of five countries in 2014

DO NOT WRITE IN THIS AREA

Country Population
China 1.4 × 109
India 1.3 × 109
USA 3.2 × 108
Ethiopia 9.7 × 107
Mexico 1.2 × 108

(a) Write 9.7 × 107 as an ordinary number.

....................................................................................

(1)
The population of Russia in 2014 was 140000000

DO NOT WRITE IN THIS AREA

(b) Write 140 000000 in standard form.

........................................................

(1)
In 2014, there were more people living in China than were living in the USA.
(c) How many more?
Give your answer in standard form.

........................................................

(2)
DO NOT WRITE IN THIS AREA

In 2014, the population of India was k times the population of Mexico.

(d) Work out the value of k.
Give your answer to the nearest whole number.

k = ........................................................
(2)

(Total for Question 11 is 6 marks)

12
*P45863A01224*
12
A
Diagram NOT
DO NOT WRITE IN THIS AREA

accurately drawn
4 cm

11.7 cm B 6 cm
E

C 13.5 cm D

The diagram shows triangle ACD.

B is a point on AC and E is a point on AD so that BE is parallel to CD.
AE = 4 cm
AC = 11.7 cm
DO NOT WRITE IN THIS AREA

BE = 6 cm
CD = 13.5 cm
(a) Calculate the length of AB.

........................................................ cm
(2)
(b) Calculate the length of ED.
DO NOT WRITE IN THIS AREA

........................................................ cm
(2)

(Total for Question 12 is 4 marks)

13
*P45863A01324* Turn over
13 M is directly proportional to p3
M = 128 when p = 8

DO NOT WRITE IN THIS AREA

(a) Find a formula for M in terms of p.

........................................................

(3)
(b) Find the value of M when p = 5

DO NOT WRITE IN THIS AREA

........................................................

(1)

(Total for Question 13 is 4 marks)

x 2 − 25
14 Simplify
2x2 − 9x − 5

DO NOT WRITE IN THIS AREA

........................................................

(Total for Question 14 is 3 marks)

14
*P45863A01424*
x+3 x−2
15 (a) Write + as a single fraction in its simplest form.
5 3
DO NOT WRITE IN THIS AREA

........................................................

(3)
1
(b) Simplify (8a9e6) 3
DO NOT WRITE IN THIS AREA

........................................................

(2)
2 3
(c) Solve y+ y=5
3 8

Show clear algebraic working.

DO NOT WRITE IN THIS AREA

y = ........................................................
(3)

(Total for Question 15 is 8 marks)

15
*P45863A01524* Turn over
16 In a bag there is a total of 20 coins.

10 coins are 20 cent coins

DO NOT WRITE IN THIS AREA

6 coins are 10 cent coins
4 coins are 5 cent coins

Emma takes at random two of the coins from the bag.

(a) Complete the probability tree diagram.
(2)

First coin Second coin

.............. 20 cent coin

..............
20 cent coin 10 cent coin

..............

DO NOT WRITE IN THIS AREA

10 5 cent coin
20

..............
20 cent coin

.............. ..............
10 cent coin 10 cent coin

..............

5 cent coin
..............

.............. 20 cent coin

DO NOT WRITE IN THIS AREA
..............

5 cent coin 10 cent coin

..............

5 cent coin

16
*P45863A01624*
(b) Work out the probability that Emma takes two 5 cent coins.
DO NOT WRITE IN THIS AREA

........................................................

(2)
(c) Work out the probability that the total value of the two coins is 20 cents or less.
DO NOT WRITE IN THIS AREA

........................................................

(3)

(Total for Question 16 is 7 marks)

DO NOT WRITE IN THIS AREA

17
*P45863A01724* Turn over
17 f is the function such that f(x) = 2x – 5
g is the function such that g (x) = x 2 – 10

DO NOT WRITE IN THIS AREA

(a) Find f (4)

........................................................

(1)
(b) Find fg (–4)

........................................................

(2)
(c) Express the inverse function f –1 in the form f –1(x) = ...

DO NOT WRITE IN THIS AREA

f –1(x) = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(d) Solve gf (x) = –1

DO NOT WRITE IN THIS AREA

........................................................

(4)
(Total for Question 17 is 9 marks)

18
*P45863A01824*
18 Miss Cook asked each student in her class how long it took them, in minutes, to travel to
school that morning.
The incomplete histogram shows information about the times it took the students who
DO NOT WRITE IN THIS AREA

took no more than 30 minutes to travel to school.

Frequency
density
DO NOT WRITE IN THIS AREA

0
0 10 20 30 40 50 60
Time (minutes)

9 students took between 15 minutes and 30 minutes to travel to school.

(a) How many students took no more than 30 minutes to travel to school?
DO NOT WRITE IN THIS AREA

........................................................

(2)
12 students took between 30 and 55 minutes to travel to school.
(b) Use this information to complete the histogram.

(2)

(Total for Question 18 is 4 marks)

19
*P45863A01924* Turn over
19 Simplify (7 + 2 50 í 2 )

DO NOT WRITE IN THIS AREA

Give your answer in the form a + b 18 where a and b are integers.
Show your working clearly.

DO NOT WRITE IN THIS AREA

........................................................

(Total for Question 19 is 3 marks)

DO NOT WRITE IN THIS AREA

20
*P45863A02024*
20
Diagram NOT
DO NOT WRITE IN THIS AREA

10 cm accurately drawn

10 cm

The diagram shows a solid shape made from a cone on top of a cylinder.
The cone has a radius of 10 cm and a height of 10 cm.
The cylinder has a radius of 10 cm and a height of 10 cm.
The centre of the base of the cone coincides with the centre of the top face of the cylinder.
DO NOT WRITE IN THIS AREA

The total surface area of the solid is A cm2

Show that A = (300 + 100 2 )ʌ
DO NOT WRITE IN THIS AREA

(Total for Question 20 is 4 marks)

21
*P45863A02124* Turn over
21 Each student in a group of 32 students was asked the following question.

“Do you have a desktop computer (D), a laptop (L) or a tablet (T )?”

DO NOT WRITE IN THIS AREA

Their answers showed that

19 students have a desktop computer

17 students have a laptop
16 students have a tablet
9 students have both a desktop computer and a laptop
11 students have both a desktop computer and a tablet
7 students have both a laptop and a tablet
5 students have all three.

(a) Using this information, complete the Venn diagram to show the number of students in
each appropriate subset.

D L

DO NOT WRITE IN THIS AREA

............................ ............................ ............................

............................

.................. . . . . . . . . . . ............................

............................

T
............................
DO NOT WRITE IN THIS AREA

(3)
One of the students with both a desktop computer and a laptop is chosen at random.
(b) Find the probability that this student also has a tablet.

........................................................

(1)

(Total for Question 21 is 4 marks)

22
*P45863A02224*
22
M
DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn
P
R
O

Q N
OMN is a triangle.
1
P is the point on OM such that OP = OM
4
Q is the midpoint of ON
R is the midpoint of PN
→ →
OP = p OQ = q
DO NOT WRITE IN THIS AREA

(a) Find, in terms of p and q,

→
(i) MN

........................................................

→
(ii) PR

........................................................

(2)
(b) Use a vector method to prove that QR is parallel to OP
DO NOT WRITE IN THIS AREA

(2)

(Total for Question 22 is 4 marks)

TOTAL FOR PAPER IS 100 MARKS

23
*P45863A02324*
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

*P45863A02424*
Do NOT write on this page
BLANK PAGE

24
Mark Scheme (Results)

June 2016

Pearson Edexcel International GCSE

Mathematics A (4MA0)
Paper 4H

Pearson Edexcel Level 1/Level 2 Certificate

Mathematics A (KMA0)
Paper 4H
Edexcel and BTEC Qualifications

Edexcel and BTEC qualifications come from Pearson, the world’s

Our website subject pages hold useful resources, support material

www.edexcel.com/contactus

Pearson: helping people progress, everywhere

Summer 2016
Publications Code 4MA0_4H_1606_MS
All the material in this publication is copyright
© Pearson Education Ltd 2016
General Marking Guidance
 All candidates must receive the same treatment. Examiners
must mark the first candidate in exactly the same way as they
mark the last.
 Mark schemes should be applied positively. Candidates must
be rewarded for what they have shown they can do rather
than penalised for omissions.
 Examiners should mark according to the mark scheme not
according to their perception of where the grade boundaries
may lie.
 There is no ceiling on achievement. All marks on the mark
scheme should be used appropriately.
 All the marks on the mark scheme are designed to be
awarded. Examiners should always award full marks if
deserved, i.e. if the answer matches the mark scheme.
Examiners should also be prepared to award zero marks if the
candidate’s response is not worthy of credit according to the
mark scheme.
 Where some judgement is required, mark schemes will
provide the principles by which marks will be awarded and
exemplification may be limited.
 When examiners are in doubt regarding the application of the
mark scheme to a candidate’s response, the team leader must
be consulted.
 Crossed out work should be marked UNLESS the candidate
has replaced it with an alternative response.
 Types of mark
o M marks: method marks
o A marks: accuracy marks
o B marks: unconditional accuracy marks (independent of
M marks)
 Abbreviations
o cao – correct answer only
o ft – follow through
o isw – ignore subsequent working
o SC - special case
o oe – or equivalent (and appropriate)
o dep – dependent
o indep – independent
o eeoo – each error or omission
 No working
If no working is shown then correct answers normally score
full marks
If no working is shown then incorrect (even though nearly
correct) answers score no marks.
 With working
If there is a wrong answer indicated on the answer line always
check the working in the body of the script (and on any
diagrams), and award any marks appropriate from the mark
scheme.
If it is clear from the working that the “correct” answer has
been obtained from incorrect working, award 0 marks.
Any case of suspected misread loses A (and B) marks on that
part, but can gain the M marks.
If working is crossed out and still legible, then it should be
given any appropriate marks, as long as it has not been
replaced by alternative work.
If there is a choice of methods shown, then no marks should
be awarded, unless the answer on the answer line makes
clear the method that has been used.
If there is no answer on the answer line then check the
working for an obvious answer.
 Ignoring subsequent work
It is appropriate to ignore subsequent work when the
additional work does not change the answer in a way that is
inappropriate for the question: eg. Incorrect cancelling of a
fraction that would otherwise be correct.
It is not appropriate to ignore subsequent work when the
additional work essentially makes the answer incorrect eg
algebra.
Transcription errors occur when candidates present a correct
answer in working, and write it incorrectly on the answer line;
mark the correct answer.
 Parts of questions
Unless allowed by the mark scheme, the marks allocated to
one part of the question CANNOT be awarded in another.
International GCSE Maths June 2016 – Paper 4H Mark scheme
Apart from Questions 2, 15(c), 19, 20 and 22(b) (where the mark scheme states otherwise), the correct answer, unless clearly obtained by
an incorrect method, should be taken to imply a correct method.
Q Working Answer Mark Notes
1 M1 For an + 4 where a is an integer
and a≠ 0 or for 3n + b where b is
an integer
3n + 4 A1 Fully correct expression
ScB1 for n = 3n + 4
2 ScB1 for 3t + 4, etc.
Total 2 marks
2 (8y – 18 =) 3y + 9 M1 For correct expansion of bracket
8y – 3y = 9 + 18 or 5y = 27 oe M1 For collecting terms in y on one
side and constant terms on the
other (as part of a correct equation)

5.4 oe A1 27 2
Eg 5 or 5 5
Dep on at least M1
ScB1 for
8y – 18 = 3y + 3 AND 8y – 3y = 3 + 18 or
3 8y – 18 = 3y + 3 AND 5y = 21
Alternative Method
8𝑦 – 18 8𝑦 18 M1 For dividing both sides of the
= y + 3 or – = y + 3 oe
3 3 3 equation by 3 as part of a correct
8𝑦 18
equation
–y=3+ or 5y = 27 oe M1 For collecting terms in y on one
3 3
side and constant terms on the
other (as part of a correct equation)
5.4 oe A1 27 2
Eg 5 or 5 5
3
Dep on at least M1
Total 3 marks
3 (a) 0.8 × 485 or 485 – 0.2 × 485 or 485 – “97” oe M2 For a complete method
If not M2 then:
M1 for 0.2 × 485 or 97 oe

388 A1 cao
3
(b) 79 79 M2 For a complete method
or × 100 or 3.95 × 100 or 79 × 5 oe
0.2 20 If not M2 then:

M1 For 20% = 79 or
0.2x = 79 or
79
or 3.95 or
20
𝑥 100
= oe
79 20

395 A1 cao
3 ScB2 for 316
Total 6 marks
4 (a) 63 1 B1
(b) 50 1 B1
(c) Eg (6 – 2) × 180 or 4 × 180 or 720 oe M1 For complete method to find the
total of interior angles or 720
Eg 3x + x +164 + 139 + 97 + 156 = 720 or 4x +556 = 720 oe or M1 Dep
For a correct equation using their
“720” – (164 + 139 + 97 + 156) “720” – 556 164 720 or
or or oe
4 4 4 For a complete numerical method

41 A1
3
Alternative Method
Eg 180 – 156 + 180 – 139 + 180 – 164 + 180 – 97 + 180 – x + M2 For an equation coming from the
180 – 3x = 360 or correct method relating to the sum
24 + 41 + 16 + 83 + 180 – x + 180 – 3x = 360 or of exterior angles.
1080 – 556 – 4x = 360
41 3 A1
Total 5 marks

5 (a) m7 1 B1
(b) c8 1 B1
(c) a15 1 B1
(d) 8x + 12 + 2x + 10 M1 Any three terms correct out of
four.
10x + 22 A1 Allow 2(5x + 11)
2 Do not ISW
Total 5 marks
6 Eg (3×4) + (9×6) + (15×8) + (21×9) + (27×3) or M1 f × x for 4 products with x used
12 + 54 + 120 + 189 + 81 consistently within interval
(including end points ) & intention
to add.
M1 (dep) for use of all correct half-
way values
456 A1 Do not ISW
3 ScB2 for 15.2
Total 3 marks

7 (a) 7, (2), −1, (−2), (−1), 2, 7 B2 B1 for at least 2 correct

2
(b) (−1, 7), (0, 2), (1, −1), (2, −2), (3, −1), (4, 2), Correct curve B2 For the correct smooth curve
(5, 7) 1
through all 7 points (± 2 sq)

B1 ft for at least 6 points from

1
their table plotted correctly (± 2
sq) provided at least B1 scored
in (a)
2
Total 4 marks
8 (a) Enlargement B1 For Enlargement
Scale factor 2 B1 For (Scale factor =) 2
Centre (1, 0) B1 For (Centre) (1, 0)
NB if more than one
transformation mentioned then no
3 marks.
(b) Correct triangle at
(10, −2), (7, −2), (7,−1) B1 Correct triangle in correct place
1
(c) M1 Triangle congruent to D and with
correct orientation
Correct triangle at A1
(1, 0),(2, 0),(2, 3) ScB1 for triangle with vertices at
2 (4, 2), (5, 2) and (4, −1)
Total 6 marks
9 13.52 + 60² or 182.25 + 3600 or 3782.25 M1 For squaring and adding
√"3782.25" or awrt 61.5 M1 (Dep) for square root
13.5 + 60 + √"3782.25" or 13.5 + 60 + 61.5 M1 Dep
135 A1 cao
NB: A0 if 61.5 is rounded from an
4 inexact value (eg 61.505…)
Alternative method – using Trigonometry
60 M1 For finding a correct angle AND a
Eg A = 77.3(196…) and sin”77.3” = 𝐴𝐶
60 correct trig statement
(AC =) sin"77.3" or awrt 61.5 M1 (Dep) For an expression for AC

60
13.5 + 60 + sin"77.3" or 13.5 + 60 + 61.5 M1 Dep
135 A1 cao
NB: A0 if 61.5 is rounded from an
inexact value (eg 61.505…)
4
Total 4 marks
10 20 = 2, 2, 5 M1 For identifying the prime factors
140 = 2, 2, 5, 7 for 2 of the 3 numbers 20,140,420
420 = 2, 2, 3, 5, 7 (can be implied by a factor tree,
repeated division or Venn
diagram) or

For a complete Venn diagram for x

and 140 with 20 in the intersection
or
x = 20 × 3 or
420
20 ×7 × y = 420 or 20 × 7 or
At least the 1st 3 multiples of 20 or
140x = 420 × 20 oe
60 2 A1 Allow 2×2×3×5
Total 2 marks

11 (a) 97 000 000 1 B1

(b) 1.4 × 108 1 B1 Accept, for example, 1.40 × 108
(c) 1.4 × 10 – 3.2 × 10 or
9 8
M1 For 1.4 × 109 – 3.2 × 108 or
1 400 000 000 – 320 000 000 or 1 080 000 000 digits 108
1.08 × 109 2 A1 Accept 1.1 × 109
(d) (1.3 × 109) ÷ (1.2 × 108) or M1 Condone missing brackets
1 300 000 000 ÷ 120 000 000 or 10.8(333…)
11 2 A1 Accept 1.1 × 101
Total 6 marks
12 (a) 13.5 9 6 4 M1 For correct scale factor or correct
Eg or 4 or 2.25 or 13.5 or 9 or 0.444(444…) or
6
9 4 11.7 equation involving AB or correct
(AB =) 11.7 ÷ 4 or (AB =) 11.7 × 9 or (AB =) 6 × 13.5 oe expression for AB
𝐴𝐵 4 𝐴𝐵 11.7
= 9 or = 13.5 oe Accept 0.444(444…) rounded to at
11.7 6
least 3SF
5.2 2 A1
(b) 9 4 M1 For a correct expression for ED or
Eg (AD =) 4 × 4 or (AD =) "5.2" × 11.7 or
9 4 AD or
(ED) = [4 × 4] – 4 or (ED) = "5.2" × (11.7 – “5.2”) or
𝐴𝐷 9 𝐴𝐷 4
= 4 or 11.7 = "5.2" or For a correct equation involving
4
9 𝐸𝐷 4 ED or AD
ED + 4 = 4 × 4 or 11.7 –"5.2" = "5.2" or
AD = 9
5 2 A1
Total 4 marks
13 (a) M = k×p³ M1 𝑀
For M = kp³ or p³ = 𝑘 oe
Do not allow M = p³ oe
128 = k × 8³
M1 For a correct substitution into a
correct equation.
Implies first M1.
Award M2 if k = 0.25 stated
unambiguously in (a) or (b).
M = 0.25p³ A1 Award 3 marks if answer is
M = kp³ but k is evaluated in part
3 (b)
(b) 31.25 B1ft for their value of k only for
equations of the form M = kp³ oe
1 and if k ≠ 1
Total 4 marks

14 (x – 5)(x + 5) M1 For (x + 5)(x – 5)

(2x + 1)(x − 5) M1(indep) For (2x + 1)(x – 5) or
2(x + 0.5)(x – 5) or
2(2x + 1)(0.5x – 2.5)

x+5 A1 cao
2x + 1 3 No ISW
Total 3 marks
15 (a) 3(𝑥+3) 5(𝑥 −2) 3(𝑥+3)+5(𝑥−2) M1 For a common denominator as part
Eg + or 3×5
oe
of 1 or 2 fractions (must be a
3×5 3×5
correct expression)
3𝑥 + 9 + 5𝑥 – 10 3𝑥 + 9 5𝑥 – 10 M1 For a correct expansion of brackets
Eg or + oe
3×5 3×5 3×5
as part of 1 or 2 fractions (must be
a correct expression)
8𝑥 − 1 A1 cao
15 3 Do not ISW
(b) M1 For two of 2, a³, e² in a product
with three terms
2a³e² 2 A1 Do not ISW
(c) 16+9 16 9 25 M1 For simplifying the LHS or
Eg y (= 5) or 24y + 24y (= 5) or 24y (= 5) or
24
2 3 multiplying both sides by 24
y( + ) (= 5) or y(0.6̇ + 0.375) (= 5) or 1.0416̇y (= 5) or
3 8
2 3
24 ×3y + 24 × 8y = 24 × 5

1
Eg 25y = 5 × 24 or 25y = 120 or y = 5 ÷ 1 or M1 Dep on 1st M1 gained
24
5 5
y = 1.0416̇ or y = 2 3
For the removal of the
+
3 8 denominator(s) as part of a correct
equation or for correctly isolating y

4.8 A1oe Dep on 1st M1 gained.

ScM2 for 16y + 9y = 120
M0A0 for trial and improvement
NB: Decimals must be exact to
gain any credit:
3 Eg Award M0 for y(0.667 + 0.375)
Total 8 marks
16 (a) 6 4 B1 6 4
For 20 , 20 correct on LH branches
,
20 20

9 6 4 10 5 4 10 6 3
B1 For all other branches correct
19 19 19 19 19 19 19 19 19
2
(b) 4 3 M1ft From their Tree diagram
×
20 19
12
380
oe A1ft From their Tree diagram
3
oe. Eg 95
Accept 0.031(57…) rounded or
truncated to at least 3 decimal
places.
12
380
oe 2
(c) 6 5 6 4 M1ft For one correct product from
× or 0.078(947 … ) or × or
20 19 20 19 their Tree diagram
4 3
0.063(157 … ) or 20 × 19 or 0.031(578…)

6 5 6 4 4 6 4 3
× + × + × + × M1ft For sum of all correct products
20 19 20 19 20 19 20 19 from their Tree diagram
90 9
380
oe A1 For 38 oe or 0.236(842…)
NB: Accept use of decimals if
rounded or truncated to at least 3
decimal places.
3
With Replacement
6 6 4 6 4 4 M1
× or 0.09 or × or 0.06 or × or 0.04
20 20 20 20 20 20

6 6 6 4 4 6 4 4 100
× 20 + 20 × 20 + 20 × 20 + 20 × 20 or 400 or 0.25 oe M1
20
Alternative method
10 9 10 6 10 4 6 10 4 10
Eg 1 – (20 × 19 + 20 × 19 + 20 × 19 + 20 × 19 + 20
× 19) M2 For a complete method.
10 9 Ft from their Tree diagram
or × oe
20 19
90 9
oe A1 For 38 oe or 0.236(842…)
380
NB: Accept use of decimals if
rounded or truncated to at least 3
decimal places.
3
Total 7 marks
17 (a) 3 1 B1
(b) M1 For 2((−4)² − 10) – 5 oe or
(−4)² − 10 or 6
7 2 A1
(c) 1 M1
2x = y + 5 or 2y = x + 5 or 2(y + 5)
1 oe
(x + 5) A1
2
2
(d) (2x – 5)² − 10 (= −1) or M1 For a correct expression for gf(x)
4x² − 10x − 10x + 25 − 10 (= −1)

4x² − 20x + 16 (= 0) or M1 For a correct 3 part quadratic or

2x² − 10x +8 (= 0) or For (2x – 5)² = 9
x² − 5x +4 (= 0) or
(2x – 5)² = 9

(4x − 4)(x − 4) (= 0) or M1 For factorising a correct equation

(2x – 2)(x – 4) (= 0) or or for use of quadratic formula
(x – 4)(x – 1) (= 0) or with a correct equation or
2x – 5 = ± 3 For 2x – 5 = ± 3
2
––5±√(–5) –4(1)(4)
(may be partially evaluated;
2(1)
condone lack of brackets around negative numbers)
x = 1, x = 4 4 A1
Alternative method
Eg a² – 10 = – 1 oe M1 For a correct equation relating to
g(a) = – 1
a² = 9 M1 For a² = 9

2x – 5 = ± 3 M1 For 2x – 5 = ± 3
x = 1, x = 4 4 A1
Total 9 marks

18 (a) 2+4+9 M1 9
For 15 or 0.6 or
0.2 × 10 + 0.8 × 5 or 2 + 4 or 6
For at least 1 correct frequency
density on scale without incorrect
values (1cm = 0.1 fd) or
For 1 cm square = 0.5 person oe
stated
15 2 A1
(b) M1 12 24
or 0.48 or 5 or 4.8 or
25
a bar drawn with the correct height
Correct bar drawn 2 A1 4.8 cm high
Total 4 marks
19 Eg 7 × 5 – 7 ×2 × √2 + 5 × 2× √50 – 2 × 2 × √50 × √2 or M1 For brackets expanded correctly
35 − 14√2 + 10√50 − 4√100 or (need not be simplified)
35 − 14√2 +10√50 – 40 or 35 − 14√2 + 50√2 – 20 × 2
M1 a = −5 or b = 12
Dep on scoring the first M1

−5 + 12√18 3 A1 Dep on M1
Total 3 marks

20 𝜋 × 20 × 10 or 200π or 628.(318…) oe M1 For the curved surface area of the

cylinder
√102 + 10² or 10√2 or 14.1(421…) oe M1 For the slant height of the cone

𝜋 × 10 × 10√2 or 100𝜋√2 or 444.(288…) or M1dep For the curved surface area of the
141.(421…)π oe cone

Eg 100𝜋 + 200𝜋 + 𝜋 × 10 × 10√2 Correct solution A1 cso

For a correct exact expression for
the total surface area that will lead
to (300 + 100√2)𝜋
4
Dep on M3
Total 4 marks
21 (a) M1 For 5 in the middle and 1 from
D 4(D∩L∩T′) or 2(L∩T∩D') or
4 4 6 L
6(D∩T∩L')
6 5 M1 For any 4 correct entries
2
A1 For all correct including 2 outside
T 3 2 the circles inside the rectangle
3
(b) 5 B1 ft from incorrect diagram
9 1
Total 4 marks
22 (a) (i) 2q – 4p oe 1 B1 Eg 2( q – 2p )
1
(ii) q− p oe B1 Eg 0.5( –p + 2q )
2
1
1 1 1
(b) ⃗⃗⃗⃗⃗ =) −q + p + q − p or p oe
Eg (𝑄𝑅 M1 For (𝑄𝑅⃗⃗⃗⃗⃗ ) = p or
2 2 2
For (𝑄𝑅⃗⃗⃗⃗⃗ ) = –q + p + “their a(ii)”
⃗⃗⃗⃗⃗ ) = q – “their a(ii)”
or (𝑄𝑅

Eg (𝑄𝑅⃗⃗⃗⃗⃗ =) 1p and 𝑄𝑅
⃗⃗⃗⃗⃗ = 0.5𝑂𝑃
⃗⃗⃗⃗⃗ or Shown 1
⃗⃗⃗⃗⃗ ) = p and a valid
2 A1 For (𝑄𝑅 2
⃗⃗⃗⃗⃗ =) 1p and ⃗⃗⃗⃗⃗
(𝑄𝑅 𝑂𝑃 = 2𝑄𝑅 ⃗⃗⃗⃗⃗ conclusion such as:
2
⃗⃗⃗⃗⃗ = 0.5𝑂𝑃
𝑄𝑅 ⃗⃗⃗⃗⃗ or 𝑂𝑃
⃗⃗⃗⃗⃗ = 2𝑄𝑅
⃗⃗⃗⃗⃗ or
1
p is a multiple of 2p or
They have the same direction but
OP is twice as long or
They have the same vector
2 component.
Total 4 marks
Pearson Education Limited. Registered company number 872828
with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
Write your name here
Surname Other names

Centre Number Candidate Number

Pearson Edexcel
International GCSE

Mathematics A
Paper 4HR

Higher Tier
Thursday 9 June 2016 – Morning Paper Reference

Time: 2 hours 4MA0/4HR

You must have: Total Marks
Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser, calculator. Tracing paper may be used.

Advice
• Check
Read each question carefully before you start to answer it.
• your answers if you have time at the end.
Turn over

P46228A
©2016 Pearson Education Ltd.
*P46228A0124*
1/1/1/1/
International GCSE MATHEMATICS
FORMULAE SHEET – HIGHER TIER

DO NOT WRITE IN THIS AREA

Pythagoras’ Volume of cone = 1
r 2h Volume of sphere = 4
r3
3 3
Theorem
c Curved surface area of cone = rl Surface area of sphere = 4 r 2
b
r
a l
h
a2 + b2 = c2
r

adj = hyp cos

hyp opp = hyp sin
opp opp = adj tan In any triangle ABC
C
adj opp
or sin b a
hyp

DO NOT WRITE IN THIS AREA

adj A B
cos c
hyp

opp a b c
tan Sine rule:
adj sin A sin B sin C

Cosine rule: a2 b2 + c 2 2bc cos A

1
Area of triangle 2 ab sin C
cross
section
h
lengt
Volume of prism = area of cross section length

Area of a trapezium = 12 (a + b)h

r Circumference of circle = 2 r a
DO NOT WRITE IN THIS AREA

Area of circle = r 2 h

r
The Quadratic Equation
Volume of cylinder = r h 2 The solutions of ax2 + bx + c 0,
h where a 0, are given by
Curved surface area
of cylinder = 2 rh b + b2 4ac
x
2a

2
*P46228A0224*
Answer ALL TWENTY ONE questions.

Write your answers in the spaces provided.

DO NOT WRITE IN THIS AREA

You must write down all the stages in your working.

1
y
11

6
DO NOT WRITE IN THIS AREA

4
S
3

–2 –1 O 1 2 3 4 5 6 7 8 9 10 11 x
–1

–2

(a) Enlarge shape S, by scale factor 2, centre (1,1).

DO NOT WRITE IN THIS AREA

Label the new shape T.

(2)
(b) Describe fully the single transformation that maps shape T onto shape S.

. . . . . . . . . . . .............................. ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(Total for Question 1 is 3 marks)

3
*P46228A0324* Turn over
2 (a) Solve 6tí t + 9
Show clear algebraic working.

DO NOT WRITE IN THIS AREA

t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(b) Expand and simplify 3(2y + 2) + 2(y í

DO NOT WRITE IN THIS AREA

......................................................

(2)
(c) Simplify fully 4wxy ÷ (8xy)

DO NOT WRITE IN THIS AREA

......................................................

(2)

(Total for Question 2 is 7 marks)

4
*P46228A0424*
3 There were 2.1 million people living in Dubai in 2013
1.75 million of these people were not born in Dubai.
DO NOT WRITE IN THIS AREA

(a) Work out 1.75 as a percentage of 2.1

Give your answer correct to 1 decimal place.

...................................................... %
(2)
The unit of currency in Dubai is the dirham.
7KHH[FKDQJHUDWHLV GLUKDP
The cost of a pair of running shoes in Dubai is 343 dirham.
The cost of an identical pair of running shoes in the UK is £54.99
The pair of running shoes is more expensive in Dubai than in the UK.
DO NOT WRITE IN THIS AREA

(b) How much more expensive?

Give your answer to the nearest dirham.

...................................................... dirham
(3)
A plane flies a distance of 5522 km from London to Abu Dhabi in 7 hours 24 minutes.
(c) Work out the average speed of the plane.
Give your answer in kilometres per hour, correct to 3 significant figures.
DO NOT WRITE IN THIS AREA

...................................................... kilometres per hour

(3)

(Total for Question 3 is 8 marks)

5
*P46228A0524* Turn over
4 Here is a kite ABCD.

A Diagram NOT

DO NOT WRITE IN THIS AREA

accurately drawn
111°

D B

Angle DAB

Angle ADC

(a) Work out the size of angle ABC.

DO NOT WRITE IN THIS AREA

°
......................................................

(2)

DO NOT WRITE IN THIS AREA

6
*P46228A0624*
Two of these kites are arranged so that a shorter side of one of the kites is placed on top
of a shorter side of the other kite, as shown in the diagram below.
DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn

(b) Work out the size of angle x.

DO NOT WRITE IN THIS AREA

°
......................................................

(2)
(c) Work out the size of angle y.
DO NOT WRITE IN THIS AREA

°
......................................................

(3)

(Total for Question 4 is 7 marks)

7
*P46228A0724* Turn over
5 (a) Complete the table of values for y x2 – 4x + 2

DO NOT WRITE IN THIS AREA

x í í 0 1 2 3 4 5

y 14 2 í 2

(2)
(b) On the grid, draw the graph of y x2 – 4x + 2 for values of xIURPíWR

y
16

DO NOT WRITE IN THIS AREA

–3 –2 –1 O 1 2 3 4 5 6 x
–2

–4
DO NOT WRITE IN THIS AREA

(2)
The point P (k, 4) where k > 0 lies on the graph of y x2 – 4x + 2
(c) Use your graph to find an estimate for the value of k.

......................................................

(1)

(Total for Question 5 is 5 marks)

8
*P46228A0824*
6 Here is a list of numbers written in order of size.

3 6 x y
DO NOT WRITE IN THIS AREA

The numbers
have a median of 8
have a mean of 11
Find the value of x and the value of y.
DO NOT WRITE IN THIS AREA

x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 6 is 3 marks)

DO NOT WRITE IN THIS AREA

9
*P46228A0924* Turn over
7 Here are two circles.
Diagram NOT
accurately drawn

DO NOT WRITE IN THIS AREA

O
3cm 2cm

The circles have the same centre O.

The radius of the inner circle is 3 cm.
The width of the shaded region between the inner circle and outer circle is 2cm.

DO NOT WRITE IN THIS AREA

Work out the area of the shaded region.
Give your answer correct to 3 significant figures.

DO NOT WRITE IN THIS AREA

...................................................... cm2

(Total for Question 7 is 3 marks)

10
*P46228A01024*
8 Louis makes a model of a plane.
The wingspan of the model is 50 centimetres.
DO NOT WRITE IN THIS AREA

The wingspan of the real plane is 80 metres.

(a) Work out the scale of the model.
Give your answer in the form 1: n

1:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
DO NOT WRITE IN THIS AREA

The length of the real plane is 72 metres.

(b) Work out the length of the model.
Give your answer in centimetres.
DO NOT WRITE IN THIS AREA

...................................................... centimetres
(2)

(Total for Question 8 is 4 marks)

11
*P46228A01124* Turn over
9 There are 30 apples in a box.
The mean weight of these 30 apples is 120 grams.

DO NOT WRITE IN THIS AREA

There are 10 apples in a bag.
The mean weight of these 10 apples is 95 grams.
Work out the mean weight of the 40 apples.

...................................................... grams

DO NOT WRITE IN THIS AREA

(Total for Question 9 is 3 marks)

10 Solve 4x + 3y
3x + 5y í
Show clear algebraic working.

DO NOT WRITE IN THIS AREA

x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 10 is 4 marks)

12
*P46228A01224*
11 Here is a triangle QRS.
Diagram NOT
S
DO NOT WRITE IN THIS AREA

accurately drawn
15cm

R Q
SQ FP
Angle RSQ
Area of triangle QRS FP2
Work out the size of angle SQR.
Give your answer correct to 1 decimal place.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

°
......................................................

(Total for Question 11 is 4 marks)

13
*P46228A01324* Turn over
12 The table gives some information about the incomes, £I, of 100 people in the UK.

DO NOT WRITE IN THIS AREA

Income (£I) Frequency

0 < I - 10000 12

10000 < I - 20000 41

20000 < I - 30000 25

30000 < I - 40000 12

40000 < I - 50000 6

50000 < I - 60000 4

(a) Complete the cumulative frequency table.

DO NOT WRITE IN THIS AREA

Cumulative
Income (£I)
frequency

0 < I - 10000 12

0 < I - 20000

0 < I - 30000

0 < I - 40000

0 < I - 50000

0 < I - 60000
(1)

DO NOT WRITE IN THIS AREA

14
*P46228A01424*
(b) On the grid, draw a cumulative frequency graph for your table.
DO NOT WRITE IN THIS AREA

100

60
Cumulative
frequency
40

20
DO NOT WRITE IN THIS AREA

0
0 10000 20000 30000 40000 50000 60000
Income (£)

(2)
(c) Use your graph to find an estimate for
(i) the median,

£. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) the interquartile range.
DO NOT WRITE IN THIS AREA

£. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)

(Total for Question 12 is 6 marks)

15
*P46228A01524* Turn over
13 (a) Write 250 000 in standard form.

DO NOT WRITE IN THIS AREA

......................................................

(1)
The radius of the planet Jupiter is 6.99 × 107 metres.
The radius of the Earth is 6.37 × 106 metres.
The volume of Jupiter is k times the volume of the Earth.
(b) Assuming that both planets are spheres, calculate the value of k.
Give your answer correct to 3 significant figures.

DO NOT WRITE IN THIS AREA

......................................................

(3)

(Total for Question 13 is 4 marks)

DO NOT WRITE IN THIS AREA

16
*P46228A01624*
2 − 3y 1
14 (a) Solve 2 y + =
4 4
DO NOT WRITE IN THIS AREA

Show clear algebraic working.

DO NOT WRITE IN THIS AREA

y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(b) Factorise 3x2 – 8x – 3

......................................................

(2)
(c) Expand and simplify 4x(x + 3) – (2x – 3)2
DO NOT WRITE IN THIS AREA

......................................................

(3)

(Total for Question 14 is 8 marks)

17
*P46228A01724* Turn over
15 Naveed has two bags of tiles, bag A and bag B.
There are 10 tiles in bag A.

DO NOT WRITE IN THIS AREA

7 of these tiles are red.
The other 3 tiles are white.
There are 8 tiles in bag B.
5 of these tiles are red.
The other 3 tiles are white.
Naveed takes at random one tile from each bag.
(a) Work out the probability that the tiles are the same colour.

DO NOT WRITE IN THIS AREA

......................................................

(3)
All 18 tiles are put in a box.
Naveed takes at random one tile from the box.
He does not replace the tile.
Naveed then takes at random a second tile from the box.
(b) Work out the probability that both tiles are red.
DO NOT WRITE IN THIS AREA

......................................................

(2)

(Total for Question 15 is 5 marks)

18
*P46228A01824*
16 Solve 2x2 – 6x
Give your solutions correct to 3 significant figures.
DO NOT WRITE IN THIS AREA

Show your working clearly.

DO NOT WRITE IN THIS AREA

............................................................................................................

(Total for Question 16 is 3 marks)

DO NOT WRITE IN THIS AREA

19
*P46228A01924* Turn over
17 The diagram shows a prism.
M Diagram NOT
12cm

DO NOT WRITE IN THIS AREA

accurately drawn
P

L 20cm

Q
N 30°

R
Triangle PQR is a cross section of the prism.
PR FP
MP = 12 cm
Angle PRQ
Angle PQR

DO NOT WRITE IN THIS AREA

Calculate the size of the angle that the line MR makes with the plane RQLN.
Give your answer correct to 1 decimal place.

DO NOT WRITE IN THIS AREA

°
......................................................

(Total for Question 17 is 5 marks)

20
*P46228A02024*
18 The Venn diagram shows a universal setE and three sets X, Y and Z.
DO NOT WRITE IN THIS AREA

X Y
4
7 3

0
3

Z
2

The numbers shown represent numbers of elements.

n(X´
DO NOT WRITE IN THIS AREA

n(Z
(a) Complete the Venn diagram.

(2)
(b) Find the value of
(i) n( X Z)

......................................................

(ii) n(X Y´ )
DO NOT WRITE IN THIS AREA

......................................................

(2)

(Total for Question 18 is 4 marks)

21
*P46228A02124* Turn over
19
A B Diagram NOT

DO NOT WRITE IN THIS AREA

accurately drawn

D
C N
AB is parallel to DC
DC AB
M is the midpoint of BC
o
AD 2b
o
AB a
o
(a) Find BM in terms of a and b.
Give your answer in its simplest form.

DO NOT WRITE IN THIS AREA

......................................................

(2)
N is the point such that DCN is a straight line and DC : CN
(b) Show that AMN is a straight line.

DO NOT WRITE IN THIS AREA

(2)

(Total for Question 19 is 4 marks)

22
*P46228A02224*
20 The sketch shows the curve with equation y x2 + 4 and the line with equation y x + 10
DO NOT WRITE IN THIS AREA

y x2 + 4

M B

y x + 10 A

O x

The line cuts the curve at the points A and B.

DO NOT WRITE IN THIS AREA

M is the midpoint of AB.

Find the coordinates of M.
Show clear algebraic working.
DO NOT WRITE IN THIS AREA

......................................................

(Total for Question 20 is 6 marks)

23
*P46228A02324* Turn over
21 y at2 – 2at
x a t

DO NOT WRITE IN THIS AREA

Express y in terms of x and a.
Give your answer in the form
xp xq
y= −
ma 3 na
where p, q, m and n are integers.

DO NOT WRITE IN THIS AREA

......................................................

(Total for Question 21 is 4 marks)

TOTAL FOR PAPER IS 100 MARKS

24
*P46228A02424*
Mark Scheme (Results)

June 2016

Pearson Edexcel International GCSE

Mathematics A (4MA0)
Paper 4HR
Edexcel and BTEC Qualifications

Edexcel and BTEC qualifications come from Pearson, the world’s

Our website subject pages hold useful resources, support material

www.edexcel.com/contactus

Pearson: helping people progress, everywhere

Summer 2016
Publications Code 4MA0_4HR_1606_MS
All the material in this publication is copyright
© Pearson Education Ltd 2016
General Marking Guidance
 All candidates must receive the same treatment. Examiners
must mark the first candidate in exactly the same way as they
mark the last.
 Mark schemes should be applied positively. Candidates must
be rewarded for what they have shown they can do rather
than penalised for omissions.
 Examiners should mark according to the mark scheme not
according to their perception of where the grade boundaries
may lie.
 There is no ceiling on achievement. All marks on the mark
scheme should be used appropriately.
 All the marks on the mark scheme are designed to be
awarded. Examiners should always award full marks if
deserved, i.e. if the answer matches the mark scheme.
Examiners should also be prepared to award zero marks if the
candidate’s response is not worthy of credit according to the
mark scheme.
 Where some judgement is required, mark schemes will
provide the principles by which marks will be awarded and
exemplification may be limited.
 When examiners are in doubt regarding the application of the
mark scheme to a candidate’s response, the team leader must
be consulted.
 Crossed out work should be marked UNLESS the candidate
has replaced it with an alternative response.
 Types of mark
o M marks: method marks
o A marks: accuracy marks
o B marks: unconditional accuracy marks (independent of
M marks)
 Abbreviations
o cao – correct answer only
o ft – follow through
o isw – ignore subsequent working
o SC - special case
o oe – or equivalent (and appropriate)
o dep – dependent
o indep – independent
o eeoo – each error or omission
 No working
If no working is shown then correct answers normally score
full marks
If no working is shown then incorrect (even though nearly
correct) answers score no marks.
 With working
If there is a wrong answer indicated on the answer line always
check the working in the body of the script (and on any
diagrams), and award any marks appropriate from the mark
scheme.
If it is clear from the working that the “correct” answer has
been obtained from incorrect working, award 0 marks.
Any case of suspected misread loses A (and B) marks on that
part, but can gain the M marks.
If working is crossed out and still legible, then it should be
given any appropriate marks, as long as it has not been
replaced by alternative work.
If there is a choice of methods shown, then no marks should
be awarded, unless the answer on the answer line makes
clear the method that has been used.
If there is no answer on the answer line then check the
working for an obvious answer.
 Ignoring subsequent work
It is appropriate to ignore subsequent work when the
additional work does not change the answer in a way that is
inappropriate for the question: eg. Incorrect cancelling of a
fraction that would otherwise be correct.
It is not appropriate to ignore subsequent work when the
additional work essentially makes the answer incorrect eg
algebra.
Transcription errors occur when candidates present a correct
answer in working, and write it incorrectly on the answer line;
mark the correct answer.
 Parts of questions
Unless allowed by the mark scheme, the marks allocated to
one part of the question CANNOT be awarded in another.
International GCSE Maths June 4HR 2016

Apart from questions 2a, 10, 14a 16, 20 (where the mark scheme states otherwise) the correct answer, unless clearly obtained by an
incorrect method, should be taken to imply a correct method
Ques Spec Grade Working Answer Mark Notes
1 a Vertices at 2 B2 If not B2 then B1 for correct size shape in wrong
(3,5)(7,5)(7,7)(5,7) position but correct orientation or 3 correct
coordinates, or for enlargement SF3 centre (1,1)
b Enlargement SF 1 B1 Single transformations only
0.5, centre (1,1)
Total 3 marks

2 a Eg 6t − 2t = 5 + 9 3 M2 For all t terms on one side and all numbers on the

or 4t = 14 or −4t = −14 oe other side of a correct equation or M1 for all t terms
on one side or all numbers on one side of a correct
equation eg 4t – 5 = 9 or 6t = 2t + 14 or
6t – 2t – 5 = 9 or 6t = 2t + 9 + 5 etc
3.5 A1 oe dep on M1
b 6y  6  2y  8 2 M1 For 3 correct terms
8y  2 A1 oe eg 2(4y – 1)
c w 2 B2 oe eg 0.5w
2 B1 for partial, but correct, simplification with at least
4 w wx 2 w wy
2 correct cancellations, eg , , ,
8 2x 4 2y

w(4÷8) etc or kw where k is a number and k ≠ ½

Total 7 marks
3 a 1.75 2 M1 Fully correct method to find %
 100 oe
2.1
83.3 A1 83.3 or better
b 54.99 × 5.52 (= 303.(54...)) or 3 M1
343 ÷ 5.52 (=62.(137...))
343 − (54.99 × 5.52 )(=39.(45..)) or M1
(343 ÷ 5.52) – 54.99 (=7.(14...))
39 A1 (also accept answers in range 39.45 to 39.5)
c  24  3 B1
7h 24 min = 7.4 h  or 7  oe or
 60 
444 (mins) or 26640 (secs)

5522 5522 5522

or × 60 or M1 use of d/t, allow
7 .4 444 7.24
5522
 3600
26640
746 A1 746 - 746.22
Total 8 marks
4 a 360 − 2 × 111 − 90 2 M1 A complete method to find angle ABC
48 A1
b 111 − 90 2 M1
21 A1
c 540 − 90 − 90 − 111 – 111 3 M2 For a fully correct method to find angle y or M1 if
using pentagon for (5−2)×180 (=540) or for an
or 180 – 2 × ‘21’ isosceles triangle drawn with y at apex or for
showing use of parallel lines on diagram
or 2 × (180 – 111)

or 360 − 111 = 249

180 − (360 – ‘21’ −249 − 48)
oe 138 A1
Total 7 marks

5 a 7,−1,−2, 7 2 B2 all correct

B1 for 2 or 3 correct
b Correct curve 2 M1 for plotting at least 6 points correctly from their
table (dep on B1 earned in (a))
A1 fully correct curve
c 4.4 – 4.5 1 B1 ft any parabola with 2 intersections with y = 4,
1 value for x only. Condone eg (4.4, 4)
Total 5 marks
6 x = 10 3 B1
3 + 6 + x + y = 4 × 11 oe M1 Showing that the total of the 4 numbers is 4 × 11
oe, eg x + y = 35 (ft incorrect x for M1) or values
of x and y that total 35 (where x  10, y  25)
y= 25 A1
Total 3 marks

7   3 2 (= 9𝜋 = 28.27..) or 3 M1 A correct calculation for the area of one of the

  (3  2)2 (=25𝜋 =78.53..) circles
  52    32 oe eg 16𝜋 M1 A correct calculation for the shaded area

50.3 A1 50.2 – 50.3

Total 3 marks

8 a 8000 2 M1
8000:50 or 50:8000 or oe
50

160 A1
b 72 72 × 100 ÷ ‘160’ 2 M1 A correct method to find the length of the model,
 50 oe
80 ft their answer to (a)
45 A1 cao (If ans 1.6 in (a) then do not award marks for
72 ÷ 1.6 = 45)
Total 4 marks
9 30 × 120 (= 3600) or 10 × 95 (= 950) 3 M1 30 × 120 or 10 × 95

(“3600” + “950”) ÷ (30 + 10) M1 a fully correct method to find the mean weight of
(= “4550” ÷ “40”) the 40 apples
113.75 A1 accept 113.8, 114 providing M2 scored
Total 3 marks

10 12x + 9y = 18 20x + 15y = 30 4 M1 for coefficients of x or y the same with the correct
12x + 20y =−4 9x + 15y = −3 operation to eliminate one variable (allow one
(11y = −22) (11x = 33) error) or for correct rearrangement of one
equation followed by substitution in the other.
y = −2 x=3 A1 ( dep on M1)
4x + 3×−2 = 6 4 × 3 + 3y = 6 M1 (dep on M1) for substituting for the other variable
or starting again to eliminate the other variable
x = 3, y = −2 A1 (dep on M1, M1)
Total 4 marks
11 SR  (60  15)  2 (=8) 4 M1
'8' '8' 15
tan SQR  M1ft (or M1 for sin SQR  or cos SQR 
15 '17 ' '17 '
where ‘17’ comes from a fully correct method)
 '8'  M1ft  '8'  1  15 
SQR  tan 1   (or sin 1   or cos  )
 15   '17 '   '17 ' 
28.1 A1 28.07 – 28.1
Total 4 marks

12 a 12, 53, 78, 90, 96, 100 Correct table 1 B1

b Correct 2 B2 fully correct cf graph – points at ends of intervals
cumulative and joined with curve or line segments
frequency graph If not B2 then B1(ft from a table with only one
arithmetic error) for 4 or 5 of their points from
table plotted consistently within each interval at
their correct heights and joined with smooth curve
or line segments
ci 18000-20000 3 B1 ft from their cumulative frequency graph
M1ft For use of 25 and 75, or 25.25 and 75.75, or
28000(27000-29000) and 13000 (12000 – 14000)
stated or indicated on graph. Ft from a cf graph
provided method is shown.
ii 13000 – 17000 A1ft from their cf graph
Total 6 marks
13 a 2.5 ×105 1 B1 cao
b 4 3 4 (6.99  10 7 ) 3
 (6.99  10 7 )3 ÷ M1 for  (6.99  10 7 )3 or M2 oe
3 3 (6.37  10 6 ) 3
 4  (6.37  10 6 )3   4  (6.37  10 6 )3 
 3  or  3 
(1.43... 1024 )  (1.08... 1021 ) M1 for a complete method
1320 A1 accept answers which round to 1320 or 1.32 × 103
Total 4 marks

14 a 2  3y 1 3 M1 For multiplying each term by 4 or writing all

4  2y  4   4  or terms with 4 as a denominator or isolating terms
4 4
8y 2  3y 1 with denominator 4 on one side of equation and 2y
  or or −2y the other side
4 4 4
1 2  3y
2y   oe
4 4
8 y  (2  3 y)  1 or 8y = −1 + 3y M1 A correct equation with no fractions
Or 5 y  1 oe
−0.2 A1 dep on at least M1 earned
b 2 M1 for (3x ± 1)(x ± 3)
(3x  1)( x  3) A1
c 4 x  12 x or 4 x  12 x  9 or
2 2 3 M1 For expansion of 4x(x + 3) or (2x – 3)² or
4 x2  12 x  9 oe −(2x – 3)²
4 x 2  12 x  4 x 2  12 x  9 M1 Fully correct expansions with correct removal of
bracket (ie all signs correct)
24x − 9 or 3(8x - 3) A1
Total 8 marks
15 a 7 5 3 3 3 M1 for one correct product
 + 
10 8 10 8
M1 for both correct products (and no others) added
44
80 A1oe (55% or 0.55)
b 12 11 2 M1 Correct product

18 17
132 A1oe Accept 0.43(137...) rounded or truncated to at
306 least 2SF
Total 5 marks

16   6  (6)2  4  2  3 3 M1 condone one sign error, brackets not necessary.

( x ) Some simplification may already be done – if so
2 2 this must be correct. (accept 6² for (−6)²)

6  12 M1
( x )
4
A1 answers rounding to 2.37 & 0.634
0.634 & 2.37 dep on M1
Total 3 marks
17 5 B1 Recognition of angle LRM as required angle either
drawn on diagram or from working
PQ(ML)  20sin 30o (=10) or M2 For a correct method to calculate
PQ(ML) & MR or
MR  122  202 = 544 = 4 34 MR & LR or
=23.32..)
PQ(ML) & LR (NB: LR requires use of RQ =
LR = 12  ( RQ)
2 2
= 202  102 or 20cos30  300  10 3  17.32.. )
122  (10 3)2  444  2 111  21.07..
Or M1 for a correct method to calculate one of the
sides PQ or MR or LR
10  ML  M1 (Dep on M2) Use of a correct trig ratio to find
sin MRL    or angle MRL
4 34  MR 
2 111  LR 
cos MRL    or
4 34  MR 
10  ML 
tan MRL   
2 111  LR 
25.4 A1 25.38 - 25.5
Total 5 marks
18 a 5 and 6 in the 2 B2 Both correct, B1 for one correct
correct regions of
the Venn diagram
bi 25 2 B1 Correct or ft from their Venn Diagram dep on both
ii values entered
12 B1 Correct or ft dep on a value for “5” in Venn diagram
Total 4 marks

19 a  
BC  −4a +2b + 8a (=4a + 2b) 2 M1 A correct method to find BC in terms of a and b
2a + b A1
b  2 M1ft
AM  4a + ‘2a + b’ (=6a + b) and Correct vectors for AM and AN or for
 AM and MN or for AN and MN (need not be
AN  2b + 8a + 4a (=12a + 2b)
simplified) ft their BM from (a)
or

AM  4a + ‘2a + b’ (=6a + b) and

MN  ’b + 2a’ + 4a (=6a + b)
or

AN  2b + 8a + 4a (=12a + 2b) and

MN  ’b + 2a’ + 4a (=6a + b)
oe
Show For AN  2 AM or AM  MN or AN  2MN oe
A1 and there is a common point. oe
Total 4 marks
20 x 2  4  x  10 6 M1 Equations equal to each other
x2  x  6( 0) M1 for reduction to 3 term quadratic
( x  3)( x  2)( 0) M1 Factorisation or correct use of quadratic formula
x = 3, x = −2 A1 Correct values for x dep on M2
x  3, y  13, x  2, y  8 M1 (y=)10 + 3 and (y=)10 − 2 or (y mid=) 10 + 0.5
dep on previous A1 awarded
(0.5, 10.5) A1 dep on previous A1 awarded
or or
x 2  4  x  10 6 M1 Equations equal to each other
x2  x  6( 0) M1 for reduction to 3 term quadratic
Sum of roots = 1 so midpoint has M1 for Sum of roots = 1 and midpoint has x -
x coordinate 0.5 coordinate = sum of roots ÷2
A1 0.5 dep on M2
M1 0.5 + 10 dep on previous A1 awarded
(0.5, 10.5) A1 10.5 dep on previous A1 awarded
or
y  ( y  10)2  4 6 M1 Correct substitution of y – 10 for x
y 2  21y  104( 0) M1 for reduction to 3 term quadratic
( y  8)( y  13)( 0) M1 Factorisation or correct use of quadratic formula
y  8, y  13 A1 Correct values for y dep on M2
x  3, y  13, x  2, y  8 M1 (x=)13 – 10 and (x=)8 – 10 or (x mid)=10.5 – 10
dep on previous A1 awarded
(0.5, 10.5) A1 dep on previous A1 awarded
Total 6 marks
21 x 4 M1 Correct rearrangement for t or correct
t or x 2  (2a t )2 or
2a expression for x 2 or x 4
x 4  (2a t )4 oe
 x 
2
x4 M1 Correct expressions for t or t² or for at² or 2at in
t    oe or t 2  oe terms of x and a
 2a  16a 4
2
 x  2  2 M1 For correct substitution of t and t² into
 x 
y  a     2a  oe expression for y
 2a    2a 
x4 x2 A1 Fully correct answer in required form
y 
16a 3 2a
Total 4 marks
Pearson Education Limited. Registered company number 872828
with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
Write your name here
Surname Other names

Centre Number Candidate Number

Pearson Edexcel
International GCSE

Mathematics A
Paper 3H

Higher Tier
Monday 9 January 2017 – Morning Paper Reference

Time: 2 hours 4MA0/3H

You must have: Total Marks
Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser, calculator. Tracing paper may be used.

Advice
• Check
Read each question carefully before you start to answer it.
• your answers if you have time at the end.
Turn over
Turn over

P48406A
©2017 Pearson Education Ltd.
*P48406A0124*
2/1/1/1/
International GCSE MATHEMATICS
FORMULAE SHEET – HIGHER TIER

DO NOT WRITE IN THIS AREA

Pythagoras’ Volume of cone = 1
r 2h Volume of sphere = 4
r3
3 3
Theorem
c Curved surface area of cone = rl Surface area of sphere = 4 r 2
b
r
a l
h
a + b2 = c2
2
r

adj = hyp cos

hyp opp = hyp sin
opp opp = adj tan In any triangle ABC
C
adj opp
or sin b a
hyp

DO NOT WRITE IN THIS AREA

adj A B
cos c
hyp

opp a b c
tan Sine rule:
adj sin A sin B sin C

Cosine rule: a2 b2 + c 2 2bc cos A

1
Area of triangle 2 ab sin C
cross
section
h
lengt
Volume of prism = area of cross section length

Area of a trapezium = 12 (a + b)h

r Circumference of circle = 2 r a
DO NOT WRITE IN THIS AREA

Area of circle = r 2 h

r
The Quadratic Equation
Volume of cylinder = r h 2 The solutions of ax2 + bx + c 0,
h where a 0, are given by
Curved surface area
of cylinder = 2 rh b + b2 4ac
x
2a

2
*P48406A0224*
Answer ALL TWENTY FOUR questions.

Write your answers in the spaces provided.

DO NOT WRITE IN THIS AREA

You must write down all the stages in your working.

1 The average speed for an aeroplane flight from Dubai to London is 750 km / h.
The flight time from Dubai to London is 7 hours 18 minutes.
(a) Work out the flight distance from Dubai to London.
DO NOT WRITE IN THIS AREA

....................................................... km
(3)
(b) Change 750 kilometres per hour to a speed in metres per second.
Give your answer correct to the nearest whole number.
DO NOT WRITE IN THIS AREA

....................................................... m/s
(3)

(Total for Question 1 is 6 marks)

3
*P48406A0324* Turn over
2 Three integers have a mean of 7, a median of 5 and a range of 14
Find the three integers.

DO NOT WRITE IN THIS AREA

.......................................... .......................................... ..........................................

(Total for Question 2 is 2 marks)

DO NOT WRITE IN THIS AREA

2 4 13
3 Show that 5 í = 1
3 5 15

DO NOT WRITE IN THIS AREA

(Total for Question 3 is 3 marks)

4
*P48406A0424*
4

15 cm
DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn

15 cm 15 cm
70 cm

15 cm
DO NOT WRITE IN THIS AREA

The diagram shows a design made from wire.

The design is made from
a square with side 70 cm,
a circle with diameter 40 cm,
4 straight pieces each of length 15 cm.
Find the total length of wire needed for the design.
Give your answer correct to the nearest centimetre.
DO NOT WRITE IN THIS AREA

....................................................... cm

(Total for Question 4 is 4 marks)

5
*P48406A0524* Turn over
5 (a) Factorise 7h + h2

DO NOT WRITE IN THIS AREA

.......................................................

(1)
(b) Expand and simplify 4(p + 5) + 7(p – 2)

.......................................................

(2)
D = 7c2 + f
(c) Work out the value of D when c íDQGf = 5

DO NOT WRITE IN THIS AREA

D = .......................................................
(2)
(d) Solve 5(q± ±q
Show clear algebraic working.

q = .......................................................
DO NOT WRITE IN THIS AREA

(3)
H 6ROYHWKHLQHTXDOLW\±t .

.......................................................

(2)

(Total for Question 5 is 10 marks)

6
*P48406A0624*
6 The table gives information about the distances, in kilometres, Darren travelled to deliver
100 parcels.
DO NOT WRITE IN THIS AREA

Distance travelled (d km) Frequency

0d-5 28
5 d - 10
10 d - 15 20
15 d - 20 14
20 d - 25 6

Work out an estimate for the mean distance Darren travelled to deliver these parcels.
DO NOT WRITE IN THIS AREA

....................................................... km

(Total for Question 6 is 4 marks)

7 5DFKHO0DULRDQG6DQMLWVKDUHVRPHPRQH\LQWKHUDWLRV
0DULRUHFHLYHV
Work out the difference between the amount received by Rachel and the amount received by Sanjit.
DO NOT WRITE IN THIS AREA

£. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 7 is 3 marks)

7
*P48406A0724* Turn over
8 (a) On the grid, draw the graph of y íx + 4 for values of xIURPíWR

DO NOT WRITE IN THIS AREA

–2 –1 O 1 2 4 5 6 x
–1

–2

–4

–5

–6

–7
(4)
DO NOT WRITE IN THIS AREA

(b) Show by shading on the grid, the region defined by all three of the inequalities

y -íx + 4
y .í
x. 1
Label your region R.

(3)

(Total for Question 8 is 7 marks)

8
*P48406A0824*
9 Simplify (2x 2í x x – 5)
Give your answer in the form ax2 + bx + c
DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 9 is 3 marks)

DO NOT WRITE IN THIS AREA

10 In a sale, normal prices are reduced by 18%

7KHVDOHSULFHRIDQXPEUHOODLV
Work out the normal price of the umbrella.
DO NOT WRITE IN THIS AREA

£. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 10 is 3 marks)

9
*P48406A0924* Turn over
11 The frequency table gives information about the lengths of time 100 people spent in a
coffee shop.

DO NOT WRITE IN THIS AREA

Time (t minutes) Frequency
0 t - 20 4
20 t - 40 12
40 t - 60 26
60 t - 80 42
80 t - 100 12
100 t - 120 4

(a) Complete the cumulative frequency table.

Time (t minutes) Cumulative frequency

0 t - 20

DO NOT WRITE IN THIS AREA

0 t - 40
0 t - 60
0 t - 80
0 t - 100
0 t - 120
(1)

DO NOT WRITE IN THIS AREA

10
*P48406A01024*
(b) On the grid, draw a cumulative frequency graph for your table.
DO NOT WRITE IN THIS AREA

100

60
Cumulative
frequency

20
DO NOT WRITE IN THIS AREA

0
0 20 40 60 80 100 120

Time (minutes)
(2)
(c) Use your graph to find an estimate for the lower quartile.

....................................................... minutes
(1)
DO NOT WRITE IN THIS AREA

(d) Use your graph to find an estimate for the number of these people who spent longer
than 70 minutes in the coffee shop.

.......................................................

(2)

(Total for Question 11 is 6 marks)

11
*P48406A01124* Turn over
12

DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn
48°

A O
x

A, B, C and D are points on a circle with centre O.

Angle ABC = 48°
(a) (i) Calculate the size of angle x.

DO NOT WRITE IN THIS AREA

°
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .

(ii) Give a reason for your answer.

. . . . . . . . . . . ........................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)
(b) (i) Calculate the size of angle ADC.

°
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .

(ii) Give a reason for your answer.

DO NOT WRITE IN THIS AREA

. . . . . . . . . . . ........................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(Total for Question 12 is 4 marks)

12
*P48406A01224*
13 0LFDKLQYHVWVIRU\HDUVDWSHU\HDUFRPSRXQGLQWHUHVW
:RUNRXWWKHYDOXHRIWKHLQYHVWPHQWDWWKHHQGRI\HDUV
DO NOT WRITE IN THIS AREA

$. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 13 is 3 marks)

DO NOT WRITE IN THIS AREA

14 T is directly proportional to x
T = 400 when x = 625
(a) Find a formula for T in terms of x.
DO NOT WRITE IN THIS AREA

.......................................................

(3)
(b) Calculate the value of T when x = 56.25

.......................................................

(1)

(Total for Question 14 is 4 marks)

13
*P48406A01324* Turn over
15
Diagram NOT
accurately drawn

DO NOT WRITE IN THIS AREA

14 cm

17 cm

Calculate the perimeter of the triangle.

Give your answer correct to 1 decimal place.

DO NOT WRITE IN THIS AREA

....................................................... cm

(Total for Question 15 is 4 marks)

14
*P48406A01424*
16 The diagram shows two mathematically similar pots, A and B.

Diagram NOT
DO NOT WRITE IN THIS AREA

accurately drawn
8 cm

A B

A has a volume of 264 cm

BKDVDYROXPHRIFP
A has a height of 8 cm
(a) Work out the height of pot B.
DO NOT WRITE IN THIS AREA

....................................................... cm
(2)
B KDVDVXUIDFHDUHDRIFP2
(b) Work out the surface area of pot A.
DO NOT WRITE IN THIS AREA

....................................................... cm2
(2)

(Total for Question 16 is 4 marks)

15
*P48406A01524* Turn over
17 Solve the equation 5x2 + 8x±
Show your working clearly.
*LYH\RXUVROXWLRQVFRUUHFWWRVLJQLILFDQWILJXUHV

DO NOT WRITE IN THIS AREA

..............................................................................................

(Total for Question 17 is 3 marks)

DO NOT WRITE IN THIS AREA

18 The curve with equation y = 10x2x + 5 has a minimum at point A.
Find the coordinates of A.
Show your working clearly.

DO NOT WRITE IN THIS AREA

(. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . )

(Total for Question 18 is 4 marks)

16
*P48406A01624*
5m + 2e
19 Make e the subject of k =
3e
DO NOT WRITE IN THIS AREA

.......................................................
DO NOT WRITE IN THIS AREA

(Total for Question 19 is 4 marks)

20 x FRUUHFWWRVLJQLILFDQWILJXUH
y FRUUHFWWRVLJQLILFDQWILJXUHV
z FRUUHFWWRGHFLPDOSODFH
Calculate the upper bound of x(y – z)
Show your working clearly.
DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 20 is 3 marks)

17
*P48406A01724* Turn over
21 The Venn diagram shows a universal set E and sets A, B and CZKHUHDQG
represent numbers of elements.

DO NOT WRITE IN THIS AREA

A B

6 7

2
5

4
8

(a) Find n(A B) a

DO NOT WRITE IN THIS AREA

.......................................................

(1)
(b) Find n((A C) a B)

.......................................................

(1)
(c) On the Venn diagram, shade the region that represents the set (A B) C

DO NOT WRITE IN THIS AREA

(1)

(Total for Question 21 is 3 marks)

18
*P48406A01824*
22
A Diagram NOT
accurately drawn
DO NOT WRITE IN THIS AREA

7.2 cm

75°
O B

The diagram shows a sector OAB of a circle, centre O.

Angle AOB = 75°
Length of arc AB = 7.2 cm
Calculate the area of the sector.
*LYH\RXUDQVZHUFRUUHFWWRVLJQLILFDQWILJXUHV
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

....................................................... cm2

(Total for Question 22 is 4 marks)

19
*P48406A01924* Turn over
23 Solve the simultaneous equations
x2 + y2 = 52
2x + y = 8

DO NOT WRITE IN THIS AREA

Show clear algebraic working.

DO NOT WRITE IN THIS AREA

..........................................................................................................................

(Total for Question 23 is 6 marks)

20
*P48406A02024*
24 The diagram shows three boxes containing beads.
DO NOT WRITE IN THIS AREA

Box A Box B Box C

(DFKER[FRQWDLQVEODFNEHDGVDQGZKLWHEHDGV
Tim takes at random a bead from box A and puts it into box B.
He then takes at random a bead from box B and puts it into box C.
Finally, he takes at random a bead from box C and puts it into box A.
&DOFXODWHWKHSUREDELOLW\WKDWWKHUHDUHVWLOOEODFNEHDGVDQGZKLWHEHDGVLQHDFKRI
the three boxes.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

..................................................................................

(Total for Question 24 is 3 marks)

TOTAL FOR PAPER IS 100 MARKS

21
*P48406A02124*
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

*P48406A02224*
Do NOT write on this page.
BLANK PAGE

22
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

BLANK PAGE

Do NOT write on this page.

*P48406A02324*
23
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

*P48406A02424*
Do NOT write on this page.
BLANK PAGE

24
Mark Scheme (Results)

January 2017

International GCSE Mathematics A 4MA0/3H

Edexcel and BTEC Qualifications

Edexcel and BTEC qualifications come from Pearson, the world’s

Our website subject pages hold useful resources, support material

www.edexcel.com/contactus

Pearson: helping people progress, everywhere

Janaury 2017
Publications Code 4MA0_3H_1701_MS
All the material in this publication is copyright
© Pearson Education Ltd 2017
General Marking Guidance
• All candidates must receive the same treatment. Examiners
must mark the first candidate in exactly the same way as they
mark the last.
• Mark schemes should be applied positively. Candidates must
be rewarded for what they have shown they can do rather
than penalised for omissions.
• Examiners should mark according to the mark scheme not
according to their perception of where the grade boundaries
may lie.
• There is no ceiling on achievement. All marks on the mark
scheme should be used appropriately.
• All the marks on the mark scheme are designed to be
awarded. Examiners should always award full marks if
deserved, i.e. if the answer matches the mark scheme.
Examiners should also be prepared to award zero marks if the
candidate’s response is not worthy of credit according to the
mark scheme.
• Where some judgement is required, mark schemes will
provide the principles by which marks will be awarded and
exemplification may be limited.
• When examiners are in doubt regarding the application of the
mark scheme to a candidate’s response, the team leader must
be consulted.
• Crossed out work should be marked UNLESS the candidate
has replaced it with an alternative response.
• Types of mark
o M marks: method marks
o A marks: accuracy marks
o B marks: unconditional accuracy marks (independent of
M marks)
• Abbreviations
o cao – correct answer only
o ft – follow through
o isw – ignore subsequent working
o SC - special case
o oe – or equivalent (and appropriate)
o dep – dependent
o indep – independent
o eeoo – each error or omission
• No working
If no working is shown then correct answers normally score
full marks
If no working is shown then incorrect (even though nearly
correct) answers score no marks.
• With working
If there is a wrong answer indicated on the answer line always
check the working in the body of the script (and on any
diagrams), and award any marks appropriate from the mark
scheme.
If it is clear from the working that the “correct” answer has
been obtained from incorrect working, award 0 marks.
Any case of suspected misread loses A (and B) marks on that
part, but can gain the M marks.
If working is crossed out and still legible, then it should be
given any appropriate marks, as long as it has not been
replaced by alternative work.
If there is a choice of methods shown, then no marks should
be awarded, unless the answer on the answer line makes
clear the method that has been used.
If there is no answer on the answer line then check the
working for an obvious answer.
• Ignoring subsequent work
It is appropriate to ignore subsequent work when the
additional work does not change the answer in a way that is
inappropriate for the question: eg. Incorrect cancelling of a
fraction that would otherwise be correct.
It is not appropriate to ignore subsequent work when the
additional work essentially makes the answer incorrect eg
algebra.
Transcription errors occur when candidates present a correct
answer in working, and write it incorrectly on the answer line;
mark the correct answer.
• Parts of questions
Unless allowed by the mark scheme, the marks allocated to
one part of the question CANNOT be awarded in another.
International GCSE Maths
Apart from questions 3, 5d, 17, 18, 20 & 23 (where the mark scheme states otherwise) the correct answer, unless clearly obtained from an incorrect
method, should be taken to imply a correct method.
Q Working Answer Mark Notes
1 (a) 18 ÷ 60 oe or 3 M1 for changing time to a decimal (7.3)
18 3
7.3 or 7 or 7 or 7 × 60 + 18 (=438)
60 10
"438" M1 for speed × time
750 × “7.3” oe or 750 × oe (allow 750 × 7.18 or answer of 5385)
60
5475 A1
(b) for at least one correct operation 3 M1 for one or two of ×1000, ÷60, ÷60
eg. 750 × 1000, 750 ÷ 60 or (can be implied by 750 000 or 12.5 or12500
1000 5 or 0.2083)
(= 0.27....) or
60 × 60 18
750 ×1000 M1 complete correct method
oe
60 × 60
208 A1 •
accept answers in range 208 – 208.3

Alternative mark scheme ft from (a)

“5475” × 1000 (=5475000) OR 3 M1
7 × 60 + 18 = 438 and 438 × 60 (=26280 (sec))
“5475000” ÷ 26280 M1 dep
complete correct method
208 A1 •
accept answers in range 208 – 208.3
Total 6 marks
2 3 × 7 (=21) 2 M1 or for 3 numbers with a total of 21
or 3 numbers with a median of 5
or 3 numbers with a range of 14
or (a + c =) 3 × 7 – 5 (=16)

1, 5, 15 A1 numbers can be in any order

Total 2 marks
3 17 19 3 M1 for correct improper fractions (subtraction sign not necessary)
−
3 5 OR two improper fractions with a common denominator with at least one
of the fractions correct
85 57 M1 for correct fractions with a common denominator a multiple of 15
E.g. − or 85𝑎 57𝑎
15 15 i.e. in form 15𝑎 −
17 × 5 − 3 ×19 15𝑎
oe
15
shown A1 13
dep on M2 for correct conclusion to 1 from correct working with sight of
15
28
the result of the subtraction e.g.
15
Alternative method
10 12 3 M1 for two correct fractions with a common denominator a multiple of 15
(5) – (3)
15 15
2
− M1
15
shown A1 13
dep on M2 for correct conclusion to 1 from correct working with sight of
15
2
or 2 −
28
the result of the subtraction e.g.
15 15
Alternative method
10 12 3 M1 for two correct fractions with a common denominator a multiple of 15
E.g. 5 –3
15 15
25 12 M1 for a complete correct method
E.g. 4 –3
15 15
shown A1 13
dep on M2 for correct conclusion to 1 from correct working
15
Total 3 marks
4 π × ( 70 – 2 × 15) or π × 40 (=125(.6…)) 4 M1 oe

4 × 15 (=60) and 4 × 70 (=280) or 340 M1 independent

“125.6...” + “60” + “280” M1 dep on M2

466 A1 for answer in range 465.6 – 466

Total 4 marks
5 (a) h (7 + h) 1 B1
(b) 4p + 20 + 7p −14 2 M1 Any 3 terms correct

11p + 6 A1 cao
NB 11p + 6 followed by, for
example, 17p scores M1 A0
(c) 7 × (−2)² + 5 or 7 × 4 + 5 or 2 M1 for correct substitution
7 (−2)² + 5 or 7 × 4 or 28

33 A1
(d) 5q – 15 (= 12 – q) 3 M1
12 q
or q − 3 = −
5 5
E.g. 5q + q = 12 + 15 or 6q = 27 M1 For a correct equation with the q
terms collected on one side of the
equation and the non q terms on
the other side.

ft from 5q – 3 = 12 – q for this

mark only

4.5 A1 9
for 4.5 or oe dep on at least M1
2
(e) −7t ≥ 31 – 3 or 7t ≤ 3 – 31 oe 2 M1 −7t ≥ 31 – 3 or 7t ≤ 3 – 31 or − 4
or t ≥ −4
accept an equation or the wrong
inequality sign in the working
t ≤ −4 A1 or for −4 ≥ t
Total 10 marks
6 2.5 × 28 + 7.5 × 32 + 12.5 × 20 + 17.5 × 14 + 4 M2 f × d for at least 4 products with correct mid-
22.5 × 6 or interval values and intention to add.
70 + 240 + 250 + 245 + 135 or
940 If not M2 then award M1 for
d used consistently for at least 4 products within
interval (including end points) and intention to
add
or
for at least 4 correct products with correct mid-
interval values with no intention to add

(2.5 × 28 + 7.5 × 32 + 12.5 × 20 + 17.5 × 14 + M1 dep on M1

22.5 × 6) ÷ 100 or NB: accept their 100 if addition shown
(70 + 240 + 250 + 245 + 135) ÷ 100 or
“940” ÷ 100

9.4 A1 SC: B2 for answer of 9.44

(B1 for 944 in working)
Total 4 marks

7 96 ÷ 3 (= 32) 3 M1 5
M2 for × 96
3
9 × ‘32’(=288) or 4 × ‘32’(=128) M1 dep
or (9 − 4) × ‘32’

160 A1
Total 3 marks
8 (a) (−1, 6) (0, 4) (1, 2) Correct line between 4 B4 For a correct line between x = −1 and x = 5
(2, 0) (3, −2) (4, −4) x = −1 and x = 5
(5, −6)
B3 For a correct line through at least 3 of (−1, 6) (0, 4) (1, 2)
(2, 0) (3, −2) (4, −4) (5, −6)
OR
for all of (−1, 6) (0, 4) (1, 2) (2, 0) (3, −2) (4, −4) (5, −6)
plotted but not joined.

B2 For at least 2 correct points plotted

B1 For at least 2 correct points stated (may be in a table) or

seen in working
OR
for a line drawn with a negative gradient through (0, 4)
OR
for a line with the correct gradient.
(b) 3 M1 for y = −4 drawn; accept full or dashed line
NB A shaded rectangle implies a choice of lines so M0
M1 for x = 1 drawn; accept full or dashed line
NB A shaded rectangle implies a choice of lines so M0
For correct region A1ft for correct region identified.
identified Condone no label if region clear.
ft from an incorrect straight line in part (a)
Total 7 marks
9 4x² + 6x + 6x + 9 or 4x² + 12x + 9 3 M1 for at least 3 terms correct in expansion
of first pair of brackets

2x² − 10x + 3x – 15 or 2x2 – 7x – 15 M1 for at least 3 terms correct in expansion

of second pair of brackets or
all 4 terms correct ignoring signs

allow –2x2 – 7x – 15
2x² + 19x + 24 A1

Alternative method
(2x + 3)[(2x + 3) – (x – 5)] M1

(2x + 3)(x + 8) M1

2x² + 19x + 24 A1
Total 3 marks

10 0.82x = 25.83 or 82% = 25.83 3 M1 or for use of 0.82 in a calculation

25.83 25.83 M1
or × 100
0.82 82

31.5(0) A1
Total 3 marks
11 (a) 4, 16, 42, 84, 96, 100 4, 16, 42, 84, 96, 100 1 B1 cao
(b) (20, 4) (40, 16) (60, 42) (80, 84) 2 M1 (ft from sensible table i.e. clear attempt at addition)
(100, 96) (120, 100)
for at least 4 points plotted correctly at end of
interval
or
for all 6 points plotted consistently within each
interval in the freq table at the correct height

correct cf graph A1 accept curve or line segments

accept curve that is not joined to (0,0)

(c) 46 - 48 1 B1 ft from a cumulative frequency graph

(d) E.g. reading from graph at t = 70 2 M1 for evidence of using graph at t = 70

ft from a cumulative frequency graph provided

method is shown
36 – 38 A1 100 – ‘63’ ft from a cf graph

ft from a cumulative frequency graph provided

method is shown
Total 6 marks
12 (a)(i) 2 × 48 96 1 B1
(ii) The angle at the 1 B1 NB : accept twice, double, origin
centre is double the (O)
angle at the accept ‘angle at circumference is
circumference half the angle at the centre’ oe
180 − 48 132 1 B1
(b) (i)
(ii) The opposite angles 1 B1 accept supplementary angles
in a cyclic accept
quadrilateral total The angle at the centre is double
180° the angle at the circumference
with
angles at a point sum to 360o
Total 4 marks

13 0.0275 × 4000 (=110) 3 M1 for interest for first year M2 for 1.02753 × 4000 oe
or
330 or
answer of 4330
E.g. M1 for a complete method
0.0275 × (4000 + “110”) (=113.025)
and
0.0275 × (4000 + “110” + “113.025”)

4339.16 A1 Accept answer in range 4339 – 4340

NB: Answer in range 339 – 340 gets M2A0
Total 3 marks
14 (a) T = k√𝑥 3 M1 or for T = mx
k may be numeric (but not 1)
400 = k√625 or k = 16 or M1 implies the first M1
400 = m625 or m = 256
T =16√𝑥 A1 accept T = 256 x
Award 3 marks if T = k√𝑥 but k is evaluated
correctly in part (a) or (b).
SC: B2 for correct formula for x in terms of T
(b) 120 1 B1 ft for a correct answer from a substitution into
an equation (or expression) in the form (T =)
k√𝑥 except
for k = 1
Total 4 marks
15 (x² =) 17² + 14² − 2 × 17 × 14 × cos(123°) 4 M1

E.g. (x² =) 744(.248......) or M1 for correct order of operations

(x² =) 17² + 14² − −259(.2… )

(x =)27.28..... A1 for missing side in range

27.2 – 27.3

58.3 B1ft dep on M1 ft for “27.28” + 31

Alternative scheme
(height =) 14 × sin(180 – 123) (=11.7…) M1

14 × cos(180 – 123) (=7.6…) M1

"11.7"2 + "(17 + 7.6)"2 (=27.28) A1

58.3 B1ft dep on M1 ft for “27.28” + 31

Total 4 marks
16 (a) 264 891 2 3 2 M1 correct linear scale factor
3 or 3 or or or oe or 2 : 3 or correct ratio
891 264 3 2
(numbers may be in either order)
or
3
264 : 3 891 (= 6.415 : 9.622)

12 A1 cao
(b) 2 3 2 M1 correct method to find the surface
459 × � �² oe or 459 ÷ �2�² oe or
3 area of A
459 × 41(.153…) ÷ 92(.594…)
204 A1 cao
Total 4 marks
17 −8 ± √524 3 M2 If not M2 then M1 for
or
10
−8 ± √82 − −460 −8 ± √82 − 4 × 5 × −23
oe or 2×5
2×5

−8 ± 2√131 condone one sign error in substitution;

allow partial correct evaluation
10
NB: denominator must be 2×5 or 10 and
there must be evidence for correct order of
operations in the numerator
1.49, −3.09 A1 for answers in range
1.489 to 1.489105 and −3.089 to −3.0891045

Award M2 A1 for answers in range

1.489 to 1.489105 and −3.089 to −3.0891045
with sufficient correct working that would gain at
least M1

Alternative scheme

4 16 3 M1 for completing the square

5[(x + 5)² − ] oe
25

4 23 16 M1
− ± + oe
5 5 25
1.49, −3.09 A1 for answers in range
1.489 to 1.489105 and −3.089 to −3.0891045
Total 3 marks
18  dy  M1 for differentiating 10x2 or 9x correctly −9
=  20 x + 9 M2 for
2 ×10
 dx 
−b
(from )
20x + 9 = 0 M1 dy 2a
equating their (of the form ax + b)
dx
to zero, dep on previous M1
x = −0.45 oe A1 dep on at least M1
for x = −0.45 oe
(−0.45, 2.975) oe 4 A1ft dep on M2
accept fractions
 9 39   9 119 
 − , 2  or  − , 
 20 40   20 40 
Alternative scheme
(completing the square)
9 M1
( x + ) 2 + …..
20
9  9 
2
5 M1
( x + )2 −   + = 0
20  20  10
x = −0.45 oe A1 dep on at least M1
for x = −0.45 oe
(−0.45, 2.975) oe 4 A1ft dep on M2
accept fractions
 9 39   9 119 
 − , 2  or  − , 
 20 40   20 40 
19 5m + 2e 4 M1 Squaring both sides or clearing
k2 = or k =
3e 5m + 2e fraction
3e

3ek² = 5m + 2e M1 Clearing fraction and squaring

both sides

3ek² − 2e = 5m or −5m = 2e – 3ek² M1 Isolating terms in e in a correct

e(3k² − 2) = 5m or −5m = e(2 – 3k²) equation

5𝑚 A1 5m −5m
e= for e = or e = oe
3𝑘 2 −2 3k − 2
2
2 − 3k 2

Total 4 marks

20 3.5 or 2.5 or 5.25 or 5.35 3 M1 accept 3.49̇ or 3.499… or 5.349̇ or 5.3499... or 8.3749̇ or
or 8.365 or 8.375 8.37499..
3.5(8.375 – 5.25) or M1 or for UB1 ×(UB2 – LB) oe where
3.5 × 8.375 – 3.5 × 5.25
3 < UB1 ≤ 3.5 and 8.37 < UB2 ≤ 8.375 and 5.25 ≤ LB < 5.3

175 A1 dep on M2 – correct working must be seen

or 10.9375
16
Total 3 marks
21 (a) 12 1 B1
(b) 7 1 B1
(c) 1 B1 Must be unambiguous
Correct region shaded

Total 3 marks

22 75 4 M1 for a correct equation linking the angle and arc length

× 𝜋 ×d (2r) = 7.2
360

75
NB: 0.208(3… ) may be used in place of
360
360
or 4.8 in place of
75
7.2 × 360 7.2 × 360 M1 for a complete method to find the radius or diameter.
oe or oe or
75 × π 75 × 2 × π

d = 11(.0…) or r = 5.5(0…)
75  "11" 
2
75 M1 dep on previous M1
×π ×   or × π × "5.5"2 or
360  2  360
75
× 95(.04...)
360
19.8 A1 for answer in range 19.8 – 19.82
Total 4 marks
23 x² + (8−2x)² = 52 6 M1 for elimination of one variable
8 −𝑦
� 2
� ² + y² = 52
x² + 4x² − 16x – 16x + 64 =52 M1 (indep) for a correct expansion of
8 −𝑦
(8 – 2x)² or � �²
2
64−8𝑦−8𝑦+𝑦²
� 4
� + y² = 52

5x² − 32x + 12 (= 0) A1 for correct simplified 3 term quadratic equation in any form
(may not be equated to zero)
5y² − 16y – 144 (= 0)

(5x – 2)(x – 6) (=0) M1 (5y – 36)(y + 4) (=0)

−−32 ±�(−32)² −4×5×12
or −−16 ±�(−16)²−4×5×−144
2×5
(may be partially evaluated, condone lack or
2×5
of brackets around negative numbers) (may be partially evaluated, condone lack of brackets
around negative numbers)

NB: can ft for this mark only provided M1 awarded and a 3

term quadratic

2 A1 for both x values (or both y values)

x = 5 or x = 6
36
y = 5 or y = −4
2 36 A1 for both solutions with x and y values correctly paired
x = 5 oe, y = 5 oe
x = 6 , y = −4

Total 6 marks
24 6 7 7  49  3 4 4  4  3 M1
9
× 10
× 10  =  oe or 9
× ×
10 10  =  oe OR
 150   75 
6 7 3 4
9
× 10
× a and 9
× 10
×b
a and b must both be a single fraction where
7 4
0 < a, b < 1 and a ≠ , b ≠
10 10
6 7 7 3 4 4 M1 Both products correct
× 10 × 10 oe and 9 × 10 × 10 oe
9
(addition not needed)

19 A1 342
oe E.g.
50 900

Total 3 marks
Pearson Education Limited. Registered company number 872828
with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
Write your name here
Surname Other names

Centre Number Candidate Number

Pearson Edexcel
International GCSE

Mathematics A
Paper 3HR

Higher Tier
Monday 9 January 2017 – Morning Paper Reference

Time: 2 hours 4MA0/3HR

You must have: Total Marks
Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser, calculator. Tracing paper may be used.

Advice
• Check
Read each question carefully before you start to answer it.
• your answers if you have time at the end.
Turn over
Turn over

P48108A
©2017 Pearson Education Ltd.
*P48108A0124*
1/1/1/
International GCSE MATHEMATICS
FORMULAE SHEET – HIGHER TIER

DO NOT WRITE IN THIS AREA

Pythagoras’ Volume of cone = 1
r 2h Volume of sphere = 4
r3
3 3
Theorem
c Curved surface area of cone = rl Surface area of sphere = 4 r 2
b
r
a l
h
a + b2 = c2
2
r

adj = hyp cos

hyp opp = hyp sin
opp opp = adj tan In any triangle ABC
C
adj opp
or sin b a
hyp

DO NOT WRITE IN THIS AREA

adj A B
cos c
hyp

opp a b c
tan Sine rule:
adj sin A sin B sin C

Cosine rule: a2 b2 + c 2 2bc cos A

1
Area of triangle 2 ab sin C
cross
section
h
lengt
Volume of prism = area of cross section length

Area of a trapezium = 12 (a + b)h

r Circumference of circle = 2 r a
DO NOT WRITE IN THIS AREA

Area of circle = r 2 h

r
The Quadratic Equation
Volume of cylinder = r h 2 The solutions of ax2 + bx + c 0,
h where a 0, are given by
Curved surface area
of cylinder = 2 rh b + b2 4ac
x
2a

2
*P48108A0224*
Answer ALL TWENTY THREE questions.

Write your answers in the spaces provided.

DO NOT WRITE IN THIS AREA

You must write down all the stages in your working.

1 The area of the floor of a room is 12 m2
Change 12 m2 into cm2

....................................................... cm2

(Total for Question 1 is 2 marks)

2 Each exterior angle of a regular polygon is 18q

DO NOT WRITE IN THIS AREA

Work out the number of sides of this regular polygon.

.......................................................

(Total for Question 2 is 2 marks)

3 A is the point with coordinates (4, 11)

B is the point with coordinates (8, 3)
Work out the coordinates of the midpoint of AB.
DO NOT WRITE IN THIS AREA

(............................ , ......... . . . . . . . . . . . . . . . . . . . )

(Total for Question 3 is 2 marks)

3
*P48108A0324* Turn over
4 A plane flew 8740 km from Nairobi to Hong Kong.
The flight time was 13 hours 15 minutes.

DO NOT WRITE IN THIS AREA

Work out the average speed of the plane.
Give your answer, in kilometres per hour, correct to the nearest whole number.

DO NOT WRITE IN THIS AREA

....................................................... kilometres per hour

(Total for Question 4 is 3 marks)

DO NOT WRITE IN THIS AREA

4
*P48108A0424*
5 There are 80 counters in a bag.
The counters are either red or blue.
DO NOT WRITE IN THIS AREA

The ratio of the number of red counters to the number of blue counters is 3: 1
Michael takes 15% of the red counters out of the bag.
1
Alison takes of the blue counters out of the bag.
5
How many counters are now in the bag?
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 5 is 5 marks)

5
*P48108A0524* Turn over
6
y

DO NOT WRITE IN THIS AREA

4
A
3

–8 –7 –6 –5 –4 –3 –2 –1 O 1 2 3 4 5 6 7 8 x

DO NOT WRITE IN THIS AREA

–1

–2

–3

–4

–5
B
–6

–7

–8

(a) Describe fully the single transformation that maps shape A onto shape B.
DO NOT WRITE IN THIS AREA

. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)
(b) On the grid, rotate shape A 90q anticlockwise about (0, 0)
Label the new shape C.
(2)

(Total for Question 6 is 4 marks)

6
*P48108A0624*
7 On the grid, draw the graph of y + 2x = 6 for values of x from –2 to 4
DO NOT WRITE IN THIS AREA

y
12

9
DO NOT WRITE IN THIS AREA

1
DO NOT WRITE IN THIS AREA

–3 –2 –1 O 1 2 3 4 5 x
–1

–2

–3

–4

(Total for Question 7 is 4 marks)

7
*P48108A0724* Turn over
8 A lion is 224 cm long.
Simon makes a scale model of the lion.

DO NOT WRITE IN THIS AREA

He uses a scale of 1 : 8
(a) Work out the length of the scale model.

....................................................... cm
(2)
In 2010, there were 411 Asiatic lions in India.
In 2015, there were 523 Asiatic lions in India.
(b) Work out the percentage increase in the number of Asiatic lions in India from
2010 to 2015

DO NOT WRITE IN THIS AREA

Give your answer correct to 1 decimal place.

....................................................... %
DO NOT WRITE IN THIS AREA

(3)

(Total for Question 8 is 5 marks)

8
*P48108A0824*
9 The table gives information about the weights of 20 rugby players.
DO NOT WRITE IN THIS AREA

Weight (w kg) Frequency

80 w - 90 3

90 w - 100 5

100 w - 110 7

110 w - 120 4

120 w - 130 1

(a) Write down the modal class.

.......................................................

(1)
DO NOT WRITE IN THIS AREA

(b) Work out an estimate for the total weight of these 20 rugby players.
DO NOT WRITE IN THIS AREA

....................................................... kg
(3)

(Total for Question 9 is 4 marks)

9
*P48108A0924* Turn over
10 Here is an isosceles triangle.

DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn

18 cm 18 cm

14 cm

Work out the area of the triangle.

Give your answer correct to 3 significant figures.

DO NOT WRITE IN THIS AREA

....................................................... cm2

(Total for Question 10 is 4 marks)

10
*P48108A01024*
11 (a) Solve 7x + 2y = 16
5x – 2y = 20
DO NOT WRITE IN THIS AREA

Show clear algebraic working.

DO NOT WRITE IN THIS AREA

x = .......................................................

y = .......................................................
(3)
(b) Expand and simplify (k + 9)(k – 5)

.......................................................

(2)
DO NOT WRITE IN THIS AREA

1
5 −
⎛ y ⎞ 3
(c) Simplify ⎜ 6 8 ⎟
⎝ 8x y ⎠

.......................................................

(3)
(Total for Question 11 is 8 marks)

11
*P48108A01124* Turn over
12 The cumulative frequency table shows information about the times, in minutes, 80 people
waited at an airport.

DO NOT WRITE IN THIS AREA

Time (t minutes) Cumulative frequency

0 t - 20 5

0 t - 40 18

0 t - 60 42

0 t - 80 66

0 t - 100 78

0 t - 120 80

(a) On the grid opposite, draw a cumulative frequency graph for the table.
(2)

DO NOT WRITE IN THIS AREA

(b) Use your graph to find an estimate for the median time.

....................................................... minutes
(2)

DO NOT WRITE IN THIS AREA

.......................................................

(2)

12
*P48108A01224*
80
DO NOT WRITE IN THIS AREA

50
Cumulative
frequency
40
DO NOT WRITE IN THIS AREA

0
0 20 40 60 80 100 120

Time (minutes)
DO NOT WRITE IN THIS AREA

(Total for Question 12 is 6 marks)

13
*P48108A01324* Turn over
13 (a) Write 7.9 × 10 – 4 as an ordinary number.

DO NOT WRITE IN THIS AREA

.......................................................

(1)
(b) Work out (6.5 × 10 5) × (3.1 × 10 4)
Give your answer in standard form.

.......................................................

DO NOT WRITE IN THIS AREA

(2)

(Total for Question 13 is 3 marks)

14 Amil invests £9000 for 3 years in a savings account.

He gets 1.8% per year compound interest.
How much money will Amil have in his savings account at the end of 3 years?

DO NOT WRITE IN THIS AREA

£. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 14 is 3 marks)

14
*P48108A01424*
15 Line A has equation 3x – 4y = 5
Line B goes through the points (4, 7) and (–1, 3)
DO NOT WRITE IN THIS AREA

Are lines A and B parallel?

Show your working clearly.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

(Total for Question 15 is 4 marks)

15
*P48108A01524* Turn over
3x + 1 x − 4
16 (a) Solve − =2
5 3

DO NOT WRITE IN THIS AREA

Show clear algebraic working.

DO NOT WRITE IN THIS AREA

x = .......................................................
(3)
7 − 2p
(b) Make p the subject of the formula t =
3p + 1

DO NOT WRITE IN THIS AREA

.......................................................

(4)

(Total for Question 16 is 7 marks)

16
*P48108A01624*
17 P, R, Q and S are four points on a circle.

Q
DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn
R 12 cm

X
3 cm

4 cm S

RXS is a diameter of the circle.

PXQ is a chord of the circle.
DO NOT WRITE IN THIS AREA

PX = 4 cm, XQ = 12 cm, SX = 3 cm.

Work out the radius of the circle.
DO NOT WRITE IN THIS AREA

....................................................... cm

(Total for Question 17 is 3 marks)

17
*P48108A01724* Turn over
7 p − p2
18 Given that p is a prime number, rationalise the denominator of
p3

DO NOT WRITE IN THIS AREA

Simplify your answer.

DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 18 is 3 marks)

DO NOT WRITE IN THIS AREA

18
*P48108A01824*
3
19 The function f is defined as f(x) =
2−x
DO NOT WRITE IN THIS AREA

(a) State the value of x which cannot be included in any domain of f.

.......................................................

(1)
(b) Find f(–4)

.......................................................

(1)
(c) Express the inverse function f –1 in the form f –1(x) = ...
DO NOT WRITE IN THIS AREA

f –1(x) = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
2x + 1
The function g is defined as g(x) =
3
(d) Express the function fg in the form fg(x) = ...
Simplify your answer.
DO NOT WRITE IN THIS AREA

fg(x) = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)

(Total for Question 19 is 6 marks)

19
*P48108A01924* Turn over
20 A curve has equation y = x3 – 4x2 + 5x + 4
dy
(a) Find

DO NOT WRITE IN THIS AREA

.......................................................

(2)
(b) Find the x coordinates of the points where the curve with equation y = x 3 – 4x 2 + 5x + 4
has a gradient of 1
Show clear algebraic working.

DO NOT WRITE IN THIS AREA

.......................................................

(4)

(Total for Question 20 is 6 marks)

20
*P48108A02024*
21 The shape OABC is made from a triangle and a sector of a circle.

16 cm B
A
DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn
60q

12 cm

38q
O C

OAB is a triangle.
OBC is a sector of a circle, centre O.
OA = 12 cm
AB = 16 cm
Angle OAB = 60q
Angle BOC = 38q
DO NOT WRITE IN THIS AREA

Work out the area of OABC.

Give your answer correct to 3 significant figures.
DO NOT WRITE IN THIS AREA

....................................................... cm2

(Total for Question 21 is 5 marks)

21
*P48108A02124* Turn over
22 There are 12 sweets in a bag.
4 of the sweets are lemon flavour.

DO NOT WRITE IN THIS AREA

4 of the sweets are strawberry flavour.
4 of the sweets are orange flavour.
Luke takes at random 3 of the sweets.
Work out the probability that exactly 2 of the sweets that Luke takes are the same flavour.

DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 22 is 5 marks)

22
*P48108A02224*
23 The diagram shows trapezium ABCD.

B c C
DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn
b

A D

BC is parallel to AD
AD = 3BC
→ →
AB = b, BC = c
→
(a) Find, in terms of b and c, the vector CD
Give your answer in its simplest form.
DO NOT WRITE IN THIS AREA

.......................................................

(2)
The point P lies on the line AC such that AP:PC = 2: 1
(b) Is BPD a straight line?
Show your working clearly.
DO NOT WRITE IN THIS AREA

(4)

(Total for Question 23 is 6 marks)

TOTAL FOR PAPER IS 100 MARKS

23
*P48108A02324*
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

*P48108A02424*
Do NOT write on this page
BLANK PAGE

24
Mark Scheme (Results)

January 2017

International GCSE Mathematics A

4MA0/3HR
Edexcel and BTEC Qualifications

Edexcel and BTEC qualifications come from Pearson, the world’s

Our website subject pages hold useful resources, support material

www.edexcel.com/contactus

Pearson: helping people progress, everywhere

January 2017
Publications Code 4MA0_3HR_1701_MS
All the material in this publication is copyright
© Pearson Education Ltd 2017
General Marking Guidance
• All candidates must receive the same treatment. Examiners
must mark the first candidate in exactly the same way as they
mark the last.
• Mark schemes should be applied positively. Candidates must
be rewarded for what they have shown they can do rather
than penalised for omissions.
• Examiners should mark according to the mark scheme not
according to their perception of where the grade boundaries
may lie.
• There is no ceiling on achievement. All marks on the mark
scheme should be used appropriately.
• All the marks on the mark scheme are designed to be
awarded. Examiners should always award full marks if
deserved, i.e. if the answer matches the mark scheme.
Examiners should also be prepared to award zero marks if the
candidate’s response is not worthy of credit according to the
mark scheme.
• Where some judgement is required, mark schemes will
provide the principles by which marks will be awarded and
exemplification may be limited.
• When examiners are in doubt regarding the application of the
mark scheme to a candidate’s response, the team leader must
be consulted.
• Crossed out work should be marked UNLESS the candidate
has replaced it with an alternative response.
• Types of mark
o M marks: method marks
o A marks: accuracy marks
o B marks: unconditional accuracy marks (independent of
M marks)
• Abbreviations
o cao – correct answer only
o ft – follow through
o isw – ignore subsequent working
o SC - special case
o oe – or equivalent (and appropriate)
o dep – dependent
o indep – independent
o eeoo – each error or omission
• No working
If no working is shown then correct answers normally score
full marks
If no working is shown then incorrect (even though nearly
correct) answers score no marks.
• With working
If there is a wrong answer indicated on the answer line always
check the working in the body of the script (and on any
diagrams), and award any marks appropriate from the mark
scheme.
If it is clear from the working that the “correct” answer has
been obtained from incorrect working, award 0 marks.
Any case of suspected misread loses A (and B) marks on that
part, but can gain the M marks.
If working is crossed out and still legible, then it should be
given any appropriate marks, as long as it has not been
replaced by alternative work.
If there is a choice of methods shown, then no marks should
be awarded, unless the answer on the answer line makes
clear the method that has been used.
If there is no answer on the answer line then check the
working for an obvious answer.
• Ignoring subsequent work
It is appropriate to ignore subsequent work when the
additional work does not change the answer in a way that is
inappropriate for the question: eg. Incorrect cancelling of a
fraction that would otherwise be correct.
It is not appropriate to ignore subsequent work when the
additional work essentially makes the answer incorrect eg
algebra.
Transcription errors occur when candidates present a correct
answer in working, and write it incorrectly on the answer line;
mark the correct answer.
• Parts of questions
Unless allowed by the mark scheme, the marks allocated to
one part of the question CANNOT be awarded in another.
International GCSE Maths January 2017 – Paper 3HR Mark scheme
Apart from Questions 11a, 15, 16a where the mark scheme states otherwise, the correct answer, unless clearly obtained by an incorrect method,
should be taken to imply a correct method.

Q Working Answer Mark Notes

2
1 100 or 10 000 M1 e.g. 12 × 100²
120 000 2 A1
Total 2 marks

2 (2n − 4)90 M1
360 ÷ 18 or = 162 or
n
(n − 2)180
= 162
n
20 2 A1
Total 2 marks

3  4 + 8 11 + 3  M1 4 + 8 11 + 3
 ,  for or oe or (6, y) or
 2 2  2 2
(x, 7) or (7, 6)
(6 , 7) 2 A1
Total 2 marks
4 15 ÷ 60 (=0.25) or 13.25 or 13 × 60 + 15 (=795) or M1
13 × 3600 + 15 × 60 (=47700)
8740 ÷ “13.25” or 8740 ÷ “795” × 60 or M1 accept 8740 ÷ 13.15 or an answer of
8740 ÷ “47700” × 3600 664 - 665
660 3 A1 accept 659.6 – 660
Total 3 marks

5 80 ÷ (3 + 1) (=20) or 20 or 60 5 M1
0.15 × (3 × “20”) (=9) M1 M1 for 0.85 × (3×”20”) = 51
“20” ÷ 5 (=4) M1 4
M1 for × “20” (=16)
5
80 – “9” – “4” M1 M1 for “16” + “51”
67 A1
or
5 3 15 9 5 M1 3 85 51
× (= or 0.1125) M1 × (= or 0.6375)
4 100 80 4 100 80
1 1 1 M1 1 4 1
× (= or 0.05) M1 × (=or 0.2)
4 5 20 4 5 5
9 1  13  M1 51 1
" "+ " "  =  or “0.1125” + “0.05”(=0.1625) M1 +
80 20  80  80 5
13 67 M1 51 1 67
(1 − " ") × 80 or (1−“0.1625”)×80 or M1 ( + ) × 80 oe or
80 80 80 5 80
67 A1
Total 5 marks
6 a B1 for reflection
Reflection in y = −1 2 B1 for y = −1
NB. If more than one transformation then
award no marks
b Vertices at (−2, 1) (−2, 6) (−5, 1) (−5, 3) 2 B2 If not B2 then award B1 for a correct
transformation 90o clockwise about (0, 0) or 3
vertices correct or correct shape in correct
orientation but in wrong position
Total 4 marks
7 y = 6 – 2x drawn from 4 B4 For a correct line between x = −2 and x = 4
x −2 −1 0 1 2 3 4 x = −2 to
y 10 8 6 4 2 0 −2 x=4

B3 For a correct straight line segment through at

least 3 of
(−2, 10) (−1, 8) (0, 6) (1, 4) (2, 2) (3, 0) (4,−2)

OR for all of (−2, 10) (−1, 8) (0, 6) (1, 4) (2, 2)

(3, 0) (4, −2)
plotted but not joined

B2 For at least 2 correct points plotted

B1 For at least 2 correct points stated (may be in a

table) OR

for a line drawn with a negative gradient

through (0, 6) OR
a line with gradient −2
Total 4 marks
8 a 224 ÷ 8 oe 2 M1
28 A1
b 523 – 411 (=112) or 3 M1
523 523
(= 1.273...) or ×100 (=127.3...)
411 411
"112" M1 dep
×100 or 100×“1.273” – 100
411
or “127.3” – 100
27.3 A1 27.25 – 27.3
Total 5 marks

9 a 100 < w ≤ 110 1 B1

b 85 × 3 + 95 × 5 + 105 × 7 + 115 × 4 + 125 3 M2 for frequency × mid-interval for at least 4
products multiplied consistently and
255 + 475 + 735 + 460 + 125 summing

If not M2 then award M1 for multiplying

consistently by value within intervals for at
least 4 products (eg. end of interval) and
summing products or mid-intervals used
but not summed.
2050 A1 SC : B2 for an answer of 102.5
Total 4 marks
10 182 – (14÷2)2 (=275) 4 M1 7 7
or M1 for cosx = or siny =
18 18
18 + 18 − 14
2 2 2
or cos z =
2 ×18 ×18
182 − (14 ÷ 2) 2 or 275 or 5 11 or 16.5… or M1 7
or M1 for x = cos -1   or x = 67.1…
16.6  18 
7
or y = sin −1   or y = 22.8…
 18 
 182 + 182 − 142 
or z = cos −1   or z = 45.77...
 2 ×18 ×18 
0.5 × 14 × “16.5…” or 35 11 M1 or M1 for 0.5×14×18×sin(“67.1…”) or
0.5×18×18×sin(2×”22.8…”) or
0.5×18×18×sin(“45.77...”)
116 A1 116 – 116.1
NB Allow use of Hero’s formula
Total 4 marks
Alternative scheme
25(25 – 18)(25 – 18)(25 – 14)(= 13475) oe 4 M2

√13475 oe M1
116 A1
Total 4 marks
11 a e.g.12x = 36 or 24y = −60 3 M1 for addition of given equations or a complete method to
eliminate y or x (condone one arithmetic error)

e.g. 7 ´ ”3”+ 2y = 16 or M1 (dep) for method to find second variable

7x + 2 ×−2.5 = 16
x = 3 oe, y = A1 dep on M1 for both values correct.
−2.5 NB. Candidates showing no working score zero
b k2 + 9k – 5k − 45 2 M1 for 3 terms correct or all 4 terms correct ignoring signs or
y2 + 4k +….. or… + 4k − 45
k2 + 4k − 45 A1
c −
1 1 3 NB: do not accept decimal powers unless recurring dot is
 1  3  8x 6 y 8 
3
shown
eg  6 3  or  5  or
 8x y   y 
 −5
 M1oe any one of
 y 3  correct simplification of y term or
 −8 
oe reciprocal or
 0.5 x −2 y 3 
  cube root of at least all variables
  M1oe any two of
 
1

( )
6 3 3
eg 8x y or  −1
1
 or
correct simplification of y term or
reciprocal or
 8 3 x −2 y −1 
  cube root of at least all variables
 2 3 8

 2x y  oe
 5 
 y3 
 
A1oe  y   1  n m
2x2y e.g.  −2 
SCB2 for  2  or ax y with 2 of
 0.5 x   2x y 
a = 2, n = 2, m = 1
Total 8 marks
12 a correct graph 2 B2 Points at end of intervals and joined with curve or line
segments

If not B2 then B1 for 5 or 6 of their points from table

plotted consistently within each interval at their correct
heights and joined with smooth curve or line segments
b 2 M1 ft for a cf graph horizontal line or mark drawn at 40 or
40.5 or vertical line at correct place, ft their cf graph

57 – 59 A1 ft from their cf graph

c 2 M1ft for reading from cf axis ft their graph from 90 on time
axis or 72 ft
8 A1ft
Total 6 marks

13 a 0.00079 1 B1 cao
b 2 M1 for 20.15 × 109 or 20 150 000 000
or 2.015 × 10n where n ≠ 10
2.015 × 1010 A1 For 2 × 1010 or better
Total 3 marks
14 9000 × 0.018 (= 162) or 3 M1 3 ×1.8 M2 for 9000 × 1.0183
9000 × 1.018 (=9162) or for × 9000
100
(=486) or 9486
(9000 + “162)×0.018 (=164.916) M1 for complete method
(“9162” + “164.916”)×0.018 (= 167.88…)
“9162” + “164.916” + “167.88”
9494.8(0) A1 accept 9494.8 - 9495
Total 3 marks

15 −4y = 5 – 3x 4 M1 isolates term in y

y = 0.75x (+ c) or gradient of A = 0.75 oe M1
3−7  4  M1 or y = 0.8x (+ c) oe
gradient of B =  =  oe
−1 − 4  5 
No with correct figures A1 eg. No gradient of A = 0.75 but
gradient of B = 0.8 oe
Total 4 marks
16 a e.g. 3(3x + 1) – 5(x – 4) = 2×15 or 3 M1 deals with fractions eg. finds common
3(3 x + 1) 5( x − 4) denominator (15 or a multiple of 15) or
− =2 or multiplies by common multiple in a correct
15 15 equation.
3(3 x + 1) − 5( x − 4)
=2
15
e.g. 9x + 3 – 5x + 20 = 30 M1 Expands brackets and multiplies by common
denominator in a correct equation
1.75 oe A1 dep on M1
b t(3p + 1) = 7 – 2p 4 M1 multiplies by 3p + 1 must have brackets
3pt + 2p = 7 – t M1 isolates terms in p
p(3t + 2) = 7 – t M1 takes p out as a common factor
7−t A1 t −7
p= or p = oe with p as the subject
3t + 2 −3t − 2
Total 7 marks

17 12 RX 3 M1 or (2r – 3) × 3 = 12 × 4
e.g. = or 12 × 4 = XR × 3 or 3x = 48
3 4
(XR = ) 12 × 4 ÷ 3 (=16) M1 or 2r – 3 = 12 × 4 ÷ 3 or XR = 16
or an answer of 19
19
9.5 A1oe e.g.
2
Total 3 marks
18 7 p − p2 7 p − p2 p3 3 M1 1

or × oe 7 p 2 − p2
e.g.
p p p3 p3 3
2
p
7 p−p 7 p−p p p M1
2 7
p
× or 7 p2 − p 2
p p p p p e.g. oe
p3
7 p p3 − p 2 p3
oe
p3
7− p p A1 7− p p 7
for or − p oe or
p p p
3
7 − p2
oe
p
Total 3 marks
19 a 2 1 B1
b 0.5 oe 1 B1
c y(2 – x) = 3 or x(2 – y) = 3 oe 2 M1
2x − 3 A1 3 − 2x 3
or 2 −
x −x x
must be in terms of x
d 3 2 M1
oe
2x +1
2−
3
9 A1
5 − 2x
Total 6 marks

20 a 2 M1 for any 2 of 3x2 or – 8x or + 5 differentiated

correctly
3x2 – 8x + 5 A1
b 3x2 – 8x + 5 = 1 4 M1 ft from (a)
3x2 – 8x + 4 = 0 M1 ft rearrange ready to solve, ft as long as
ax2 – bx + c
eg (3x – 2)(x − 2) = 0 M1 ft correct method to solve quadratic – if
using formula, every term to be substituted
correctly as long as ax2 – bx + c
2 A1 cao dep on M2
,2 Ignore any attempts to find y values
3
Total 6 marks
21 (OB2 = ) 122 + 162 – 2 × 12 × 16 × cos(60o) 5 M1 M2 for
(OB =) 208 or 4 13 or 14.4…. or (OB ) = 208 2 M1 √(122 + 162 – 2 × 12 × 16 × cos(60o))
0.5 × 12 × 16 × sin(60o) (= 83.1…or 48 3 ) or M1 ft their 14.4 provided first M1
38 awarded.
× π × "14.4"× "14.4" (=68.9…) or
360
38
× π × "208" (=68.9…)
360
38 M1 ft their 14.4 provided first M1
0.5 × 12 × 16 × sin(60o) + × π × "14.4"× "14.4" awarded.
360
(68.9....+ 83.1...)
152 A1 awrt 152
Total 5 marks
22 4 3 4 48 2 5 M1 4 3 8 96 4
× × =( = ) oe M2 for × × =( = ) oe
12 11 10 1320 55 12 11 10 1320 55
4 3 4 4 3 4 M1
3× × × or 2 × × ×
12 11 10 12 11 10
4 3 4 4 3 4 M1 4 3 8
3×2× × × oe or 3 × 3 × × × M1 for 3 × × × oe
12 11 10 12 11 10 12 11 10
4 3 4 M1 4 3 8
3×3×2× × × oe M1 for 3 × 3 × × × oe
12 11 10 12 11 10
36 A1 864
oe eg. (0.65(45454...))
55 1320
Alternative using 1 – (all different + all the same)
4 4 4 4 3 2 5 M1
× × or × ×
12 11 10 12 11 10
4 4 4 4 3 2 M1
× × × 6 or × × ×3
12 11 10 12 11 10
4 4 4 4 3 2 M1
× × × 6 and × × × 3
12 11 10 12 11 10
4 4 4 4 3 2 M1
1 – [( × × × 6) + ( × × × 3)]
12 11 10 12 11 10
36 A1 864
oe eg. (0.65(45454...))
55 1320
Total 5 marks
SC: With replacement (maximum marks M3) Total 5 marks
22 4 4 4 192 1 4 4 4 128 2 3 M1 4 4 8
3× × × =( = ) or 2 × × × =( = ) or × ×
12 12 12 1728 9 12 12 12 1728 27 12 12 12
4 4 4 4 4 4 M1 4 4 8
3×2× × × oe or 3×3× × × oe or 3 × × ×
12 12 12 12 12 12 12 12 12
4 4 4 M1 4 4 8
3 × 3 × 2 × × × oe M1 for 3 × 3 × × ×
12 12 12 12 12 12
   
23 a CD = CB + BA + AD or −c – b + 3c 2 M1
2c – b A1
  2   1   
b 4 M1ft Ft their CD
= BA + AC or=
BP PD AC + CD
3 3
 2 2 1 M1ft
BP = −b + (b + c) (= c − b) or
3 3 3
 1 7 2
PD = (b + c) + 2c – b (= c − b)
3 3 3
 2 2 1 M1  1
BP = −b + (b + c) (= c − b) AND or BP = (2c – b) and
3 3 3 
3
 1 7 2 CD = 2c – b
PD = (b + c) + 2c – b (= c − b)
3 3 3
OR
 2 2 1
BP = −b + (b + c) (= c − b) AND
 3 3 3
BD = −b + 3c
OR
 1 7 2
PD = (b + c) + 2c – b (= c − b) AND
 3 3 3
BD = −b + 3c
No with correct A1  1
appropriate E.g. BP = (2c – b) and

3
vectors and reason
CD = 2c – b are parallel and
therefore not in a straight line
OR
Correct simplified vectors for two
of BP, BD, PD with explanation
that vectors are not a multiple of
each other
Total 6 marks
Pearson Education Limited. Registered company number 872828
with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
Write your name here
Surname Other names

Centre Number Candidate Number

Pearson Edexcel
International GCSE

Mathematics A
Paper 4H

Higher Tier
Tuesday 17 January 2017 – Morning Paper Reference

Time: 2 hours 4MA0/4H

You must have: Total Marks
Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser, calculator. Tracing paper may be used.

Advice
• Check
Read each question carefully before you start to answer it.
• your answers if you have time at the end.
Turn over
Turn over

P48109A
©2017 Pearson Education Ltd.
*P48109A0128*
1/1/1/1/
International GCSE MATHEMATICS
FORMULAE SHEET – HIGHER TIER

DO NOT WRITE IN THIS AREA

Pythagoras’ Volume of cone = 1
r 2h Volume of sphere = 4
r3
3 3
Theorem
c Curved surface area of cone = rl Surface area of sphere = 4 r 2
b
r
a l
h
a2 + b2 = c2
r

adj = hyp cos

hyp opp = hyp sin
opp opp = adj tan In any triangle ABC
C
adj opp
or sin b a
hyp

DO NOT WRITE IN THIS AREA

adj A B
cos c
hyp

opp a b c
tan Sine rule:
adj sin A sin B sin C

Cosine rule: a2 b2 + c 2 2bc cos A

1
Area of triangle 2 ab sin C
cross
section
h
lengt
Volume of prism = area of cross section length

Area of a trapezium = 12 (a + b)h

Circumference of circle = 2 r a
r
DO NOT WRITE IN THIS AREA

Area of circle = r 2 h

r
The Quadratic Equation
Volume of cylinder = r h 2 The solutions of ax2 + bx + c 0,
h where a 0, are given by
Curved surface area
of cylinder = 2 rh b + b2 4ac
x
2a

2
*P48109A0228*
Answer ALL TWENTY ONE questions.

Write your answers in the spaces provided.

DO NOT WRITE IN THIS AREA

You must write down all the stages in your working.

1 The table below shows information about the number of goals scored by a football club
in each of its last 45 games.

Number of goals Number of games

0 7
1 14
2 8
3 10
4 5
5 0
DO NOT WRITE IN THIS AREA

6 1

Find the median number of goals.

Show your working clearly.

.......................................................
DO NOT WRITE IN THIS AREA

(Total for Question 1 is 2 marks)

3
*P48109A0328* Turn over
2 Here is a biased five-sided spinner.

DO NOT WRITE IN THIS AREA

red

blue
orange

green
yellow

When the spinner is spun, it can land on red, orange, yellow, green or blue.
The probabilities that it lands on red, orange and yellow are given in the table.

Colour red orange yellow green blue

DO NOT WRITE IN THIS AREA

Probability 0.4 0.2 0.1

The probability that the spinner lands on green is the same as the probability that the
spinner lands on blue.
Michael spins the spinner once.
(a) Work out the probability that the spinner lands on green.

.......................................................

(3)
Jenny spins the spinner 200 times.
DO NOT WRITE IN THIS AREA

(b) Work out an estimate for the number of times the spinner lands on red.

.......................................................

(2)

(Total for Question 2 is 5 marks)

4
*P48109A0428*
3 The weekly rent for a holiday apartment is £530, which is the same as 715.5 euros.
The weekly rent for a holiday cottage is £750
DO NOT WRITE IN THIS AREA

Using the same rate of currency exchange, work out the weekly rent for the cottage in euros.

....................................................... euros

(Total for Question 3 is 3 marks)

4 (a) (i) Use your calculator to work out the value of

DO NOT WRITE IN THIS AREA

16௘
îíʌ

Write down all the figures on your calculator display.

..................................................................................

(ii) Write your answer to (a)(i) correct to 3 significant figures.

.......................................................

(3)
DO NOT WRITE IN THIS AREA

4.2 × 10 ௘
(b) Work out
700 000

Give your answer in standard form.

.......................................................

(2)

(Total for Question 4 is 5 marks)

5
*P48109A0528* Turn over
5 Abri walks along a path from her home to a local village.
Here is the distance-time graph for her journey from her home to the village.

DO NOT WRITE IN THIS AREA

Village

Distance
from
Abri’s 2
home
(km)

DO NOT WRITE IN THIS AREA

Home 0
12 00 12 30 13 00 13 30
Time

Benito leaves the village at 12 30 and walks at a constant speed along the same path to
Abri’s home.
He arrives at Abri’s home at 13 15
(a) Show the information about Benito’s journey on the grid.
(2)

(b) How far from the village were Abri and Benito when they passed each other?

DO NOT WRITE IN THIS AREA

....................................................... km
(1)

(Total for Question 5 is 3 marks)

6
*P48109A0628*
6 A has coordinates (11, 3e)
B has coordinates (1, 7e)
The midpoint of AB has coordinates (x, y)
DO NOT WRITE IN THIS AREA

(a) Find the value of x.

x= .......................................................

(1)
(b) Find an expression for y in terms of e.
Simplify your answer.
DO NOT WRITE IN THIS AREA

y= .......................................................

(2)

(Total for Question 6 is 3 marks)

7 P ∪ Q = {a , b,c,d ,e,f }
P ∩ Q = {e}
a ∈ P, c ∈ Q, f ∉ P, {b,d} ∩ Q = ∅
(a) List the members of the set P.
DO NOT WRITE IN THIS AREA

.......................................................

(2)
(b) List the members of the set Q.

.......................................................

(1)

(Total for Question 7 is 3 marks)

7
*P48109A0728* Turn over
8 North

DO NOT WRITE IN THIS AREA

A North

DO NOT WRITE IN THIS AREA

The diagram shows point A and point B on a map.
The point C is due south of A
The bearing of C from B is 235°
(a) Mark the point C on the map.
(2)
The bearing of a point D from B is 168°
(b) Find the bearing of B from D

°
.......................................................
DO NOT WRITE IN THIS AREA

(2)
Gordon measures a length on the map as 6.3 cm correct to 1 decimal place.
(c) Write down the lower bound for this length.

....................................................... cm
(1)

(Total for Question 8 is 5 marks)

8
*P48109A0828*
9 The diagram shows a ladder, EF, leaning against a vertical wall.
The foot, E, of the ladder is on horizontal ground.
DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn

3.5 m

E 2.1 m G
EG = 2.1 m FG = 3.5 m angle EGF = 90°
(a) Work out the length of the ladder.
Give your answer correct to 1 decimal place.
DO NOT WRITE IN THIS AREA

....................................................... m
(3)
(b) Work out the size of angle EFG.
Give your answer correct to the nearest degree.
DO NOT WRITE IN THIS AREA

°
.......................................................

(3)

(Total for Question 9 is 6 marks)

9
*P48109A0928* Turn over
10 Solve the simultaneous equations
௘xí௘y = 33

DO NOT WRITE IN THIS AREA

௘x௘y = 18
Show clear algebraic working.

DO NOT WRITE IN THIS AREA

x = .......................................................

y = .......................................................

(Total for Question 10 is 3 marks)

DO NOT WRITE IN THIS AREA

10
*P48109A01028*
11 y
5
DO NOT WRITE IN THIS AREA

–4 –3 –2 –1 O 1 2 3 4 5 6 x
–1
Q
–2

–3

–4
DO NOT WRITE IN THIS AREA

(a) On the grid, reflect triangle Q in the line x = 1

Label the new triangle R.
(2)
Triangle R is mapped onto triangle S by a reflection in the line y = 0
(b) Describe fully the single transformation that maps triangle Q onto triangle S.

. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)

(Total for Question 11 is 5 marks)

DO NOT WRITE IN THIS AREA

11
*P48109A01128* Turn over
12 The straight line LKDVHTXDWLRQ ௘xí௘y = 15
(a) Find the gradient of L.

DO NOT WRITE IN THIS AREA

.......................................................

(3)
(b) Find the coordinates of the point where L crosses the y-axis.

DO NOT WRITE IN THIS AREA

( ............................ , ............................ )
(1)
(c) Find an equation of the line that is parallel to L and crosses the xD[LVDW í

DO NOT WRITE IN THIS AREA

.......................................................

(2)

(Total for Question 12 is 6 marks)

12
*P48109A01228*
13 D
Diagram NOT
accurately drawn
DO NOT WRITE IN THIS AREA

79° 41°
A C
B
B, D and E are points on a circle, centre O.
ABC is a tangent to the circle.
DEC is a straight line.
Angle ABD = 79° and angle ECB = 41°
(a) Write down the size of angle BED.
DO NOT WRITE IN THIS AREA

°
.......................................................

(1)
(b) Work out the size of angle BOE.

°
.......................................................
DO NOT WRITE IN THIS AREA

(2)

(Total for Question 13 is 3 marks)

13
*P48109A01328* Turn over
14 There are 52 cards in a pack.
12 cards are picture cards.
40 cards are number cards.

DO NOT WRITE IN THIS AREA

Melina takes at random a card from the pack.
She keeps the card and then takes at random a second card from the remainder of the pack.
(a) Complete the probability tree diagram.
First card Second card
picture
...........................
card

picture
card
...........................

number
...........................
card

DO NOT WRITE IN THIS AREA

picture
...........................
card

...........................
number
card

number
...........................
card
(3)
(b) Work out the probability that the two cards Melina takes are both picture cards or
both number cards.

DO NOT WRITE IN THIS AREA

.......................................................

(3)

(Total for Question 14 is 6 marks)

14
*P48109A01428*
15 y
B
Diagram NOT
DO NOT WRITE IN THIS AREA

E accurately drawn

A
C
D

O x

→ ⎛ 3⎞ → ⎛ 4⎞
AB = ⎜ ⎟ and AC = ⎜ ⎟
⎝ 2⎠ ⎝−1 ⎠
→
(a) Find, as a column vector, BC
DO NOT WRITE IN THIS AREA

.......................................................

(2)
BCDE is a parallelogram.
→ →
CD =௘AC
(b) Find the length of CE.
Give your answer correct to 2 decimal places.
DO NOT WRITE IN THIS AREA

.......................................................

(3)

(Total for Question 15 is 5 marks)

15
*P48109A01528* Turn over
16 g = 23 × 3 × 7 2 h = 2 × 3 × 73
(a) Express gh as a product of powers of its prime factors.

DO NOT WRITE IN THIS AREA

Simplify your answer.

.......................................................

(2)
g
= 2a × 3b × 7c
h
(b) Find the value of a, the value of b and the value of c.

DO NOT WRITE IN THIS AREA

a = .......................................................

b = .......................................................

c = .......................................................
(2)
(c) Show that (7 − 2 5 ) (7 + 2 5 ) = 29
Show your working clearly. DO NOT WRITE IN THIS AREA

(2)
16
*P48109A01628*
1
= 3n
3 4
9
DO NOT WRITE IN THIS AREA

(d) Work out the exact value of n.

.......................................................

(3)

(Total for Question 16 is 9 marks)

17 A particle moves along a straight line.

The fixed point O lies on this line.
DO NOT WRITE IN THIS AREA

The displacement of the particle from O at time t seconds is s metres where

9
s = 4t 2 −
t

Find the velocity of the particle at time 5 seconds.

DO NOT WRITE IN THIS AREA

....................................................... m/s

(Total for Question 17 is 3 marks)

17
*P48109A01728* Turn over
2x
18 The function f is such that f (x) =
3x + 5

DO NOT WRITE IN THIS AREA

D )LQG I í

.......................................................

(1)
3
The function g is such that g (x) =
x+4
(b) Find gí (6)

DO NOT WRITE IN THIS AREA

.......................................................

(2)
F )LQG IJ í

.......................................................

(2)
DO NOT WRITE IN THIS AREA

18
*P48109A01828*
(d) Solve the equation f (x) = g (x)
Show clear algebraic working.
DO NOT WRITE IN THIS AREA

.......................................................

(4)

(Total for Question 18 is 9 marks)

DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

19
*P48109A01928* Turn over
19 Here is the graph of y = h (x)

DO NOT WRITE IN THIS AREA

y
10 –

9–

8–

7–

6–

5–

4–

3–

2–

DO NOT WRITE IN THIS AREA

1–
–

–
í í í O 1 2 3 4 x
í –

í –

DO NOT WRITE IN THIS AREA

20
*P48109A02028*
(a) Use the graph to find an estimate for the gradient of the curve y = h (x DW í
DO NOT WRITE IN THIS AREA

.......................................................

(3)
(b) By drawing a suitable straight line on the grid, find an estimate for the solution of the
equation h (x) =íx
Give your answer correct to 1 decimal place.
DO NOT WRITE IN THIS AREA

.......................................................

(2)
The equation h (x) = k has 3 different solutions for a < k < b
(c) Use the graph to find an estimate for the value of a and the value of b.

a = .......................................................

b = .......................................................
(2)
DO NOT WRITE IN THIS AREA

(Total for Question 19 is 7 marks)

21
*P48109A02128* Turn over
20 The histogram shows information about the times taken by 160 cyclists to complete the
Tour de France cycle race.

DO NOT WRITE IN THIS AREA

Frequency
30
density

DO NOT WRITE IN THIS AREA

0
84 85 86 87 88 89 90
Time (hours)
6 cyclists took less than 85 hours.
(a) Work out an estimate for the number of the 160 cyclists who took less than 86 hours.

DO NOT WRITE IN THIS AREA

.......................................................

(2)

22
*P48109A02228*
(b) For these 160 cyclists, work out an estimate for the time taken by the cyclist who
finished in 50th position.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

....................................................... hours
(2)

(Total for Question 20 is 4 marks)

DO NOT WRITE IN THIS AREA

23
*P48109A02328* Turn over
21 The diagram shows a cuboid ABCDEFGH.

E K H

DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn

9 cm
F
G

D
C

A 21 cm B

AB = 21 cm and CH = 9 cm.
K is the point on EH such that angle AKB = 68° and BK = 16.5 cm.
(a) Calculate the size of angle BAK.
Give your answer correct to 1 decimal place.

DO NOT WRITE IN THIS AREA

°
.......................................................

(3)

24
*P48109A02428*
(b) Calculate the size of the angle between the line BK and the plane ABCD.
Give your answer correct to 1 decimal place.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

°
.......................................................

(2)

(Total for Question 21 is 5 marks)

TOTAL FOR PAPER IS 100 MARKS

DO NOT WRITE IN THIS AREA

25
*P48109A02528*
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

*P48109A02628*
Do NOT write on this page.
BLANK PAGE

26
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

BLANK PAGE

Do NOT write on this page.

*P48109A02728*
27
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

*P48109A02828*
Do NOT write on this page.
BLANK PAGE

28
Mark Scheme (Results)

January 2017

International GCSE Mathematics A

4MA0/4H
Edexcel and BTEC Qualifications

Edexcel and BTEC qualifications come from Pearson, the world’s

Our website subject pages hold useful resources, support material

www.edexcel.com/contactus

Pearson: helping people progress, everywhere

January 2017
Publications Code 4MA0_4H_1701_MS
All the material in this publication is copyright
© Pearson Education Ltd 2017
General Marking Guidance
• All candidates must receive the same treatment. Examiners
must mark the first candidate in exactly the same way as they
mark the last.
• Mark schemes should be applied positively. Candidates must
be rewarded for what they have shown they can do rather
than penalised for omissions.
• Examiners should mark according to the mark scheme not
according to their perception of where the grade boundaries
may lie.
• There is no ceiling on achievement. All marks on the mark
scheme should be used appropriately.
• All the marks on the mark scheme are designed to be
awarded. Examiners should always award full marks if
deserved, i.e. if the answer matches the mark scheme.
Examiners should also be prepared to award zero marks if the
candidate’s response is not worthy of credit according to the
mark scheme.
• Where some judgement is required, mark schemes will
provide the principles by which marks will be awarded and
exemplification may be limited.
• When examiners are in doubt regarding the application of the
mark scheme to a candidate’s response, the team leader must
be consulted.
• Crossed out work should be marked UNLESS the candidate
has replaced it with an alternative response.
• Types of mark
o M marks: method marks
o A marks: accuracy marks
o B marks: unconditional accuracy marks (independent of
M marks)
• Abbreviations
o cao – correct answer only
o ft – follow through
o isw – ignore subsequent working
o SC - special case
o oe – or equivalent (and appropriate)
o dep – dependent
o indep – independent
o awrt – answer which rounds to
o eeoo – each error or omission
• No working
If no working is shown then correct answers normally score
full marks
If no working is shown then incorrect (even though nearly
correct) answers score no marks.
• With working
If there is a wrong answer indicated on the answer line always
check the working in the body of the script (and on any
diagrams), and award any marks appropriate from the mark
scheme.
If it is clear from the working that the “correct” answer has
been obtained from incorrect working, award 0 marks.
Any case of suspected misread loses A (and B) marks on that
part, but can gain the M marks.
If working is crossed out and still legible, then it should be
given any appropriate marks, as long as it has not been
replaced by alternative work.
If there is a choice of methods shown, then no marks should
be awarded, unless the answer on the answer line makes
clear the method that has been used.
If there is no answer on the answer line then check the
working for an obvious answer.
• Ignoring subsequent work
It is appropriate to ignore subsequent work when the
additional work does not change the answer in a way that is
inappropriate for the question: eg. Incorrect cancelling of a
fraction that would otherwise be correct.
It is not appropriate to ignore subsequent work when the
additional work essentially makes the answer incorrect eg
algebra.
Transcription errors occur when candidates present a correct
answer in working, and write it incorrectly on the answer line;
mark the correct answer.
• Parts of questions
Unless allowed by the mark scheme, the marks allocated to
one part of the question CANNOT be awarded in another.
International GCSE Maths January 2017 – Paper 4H Mark scheme
Apart from Questions 10, 16, 18 and 19 where the mark scheme states otherwise, the correct answer, unless clearly obtained by an incorrect method,
should be taken to imply a correct method.
Q Working Answer Mark Notes
1 45 + 1 45 2 M1 For an ordered list at least as far as the
or 23 or or 22.5
2 2 first 2
2 A1
Total 2 marks

2 (a) 1 − 0.4 − 0.2 − 0.1 or 0.3 3 M1

1 − 0.4 − 0.2 − 0.1 "0.3" M1 dep
or
2 2
0.15 A1
(b) 200 × 0.4 2 M1
80 A1 Note:
Award M1A1 for 80 out of 200
Award M1A0 for 80/200
Total 5 marks
3 715.5 3 M2 For a complete method
Eg × 750 or 1.35 × 750 oe
530
750 If not M2 then M1 for
Or × 715.5 or 1.41(509...) × 715.5 oe 715.5
530 or 1.35 oe or
530 530 530
Or 750 ÷ or 715.5÷
715.5 750
oe 530
or 0.740(740…) oe or
715.5
750
or 1.41(509...) oe
530
530
750
or 0.706(666…) oe
=
530 x 750 × 715.5
1012.50 A1 Accept 1012.5
Total 3 marks

4 (a) (i) 256 256 3 M1 For 32.8(58...) rounded or truncated to

or
36 − π 32.8(584...) at least 3SF seen
7.791004515 A1 Allow 7.791(0045...) rounded or
truncated to at least 4SF
(ii) 7.79 B1 ft if at least 4SF given in (i)
(b) 2 M1 for 0.06 oe or 6 × 10n where n is a
negative integer other than −2
6 × 10−2 A1
Total 5 marks

5 (a) straight line from 2 B2 B1 for a single straight line with

(12 30, 3.5) to negative gradient that starts at
(1315, 0) (12 30, 3.5) or ends at (1315, 0)
Ignore lines before 12:30
(b) 1 1 B1 Ft if B1 scored in (a)
Total 3 marks
6 (a) 6 1 B1
(b) 3e + 7e 10e 2 M1 For an unsimplified expression
( y =) or ( y =) oe or
equivalent to 5e
2 2
7e − 3e
(=y )3e + or (=
y )3e + 2e oe or
2
7e − 3e
(=y )7e − or (=y )7e − 2e oe
2
5e A1 cao
Total 3 marks

7 (a) a, b, d, e a, b, d, e 2 B2
B1 for
a, e or
a, b, d or b, d, e or
a, b, e or a, d, e or
a, b, c, d, e or a, b, d, e, f
or a Venn diagram with a, c, e, f
correctly shown
(b) c, e, f 1 B1
Total 3 marks

8 (a) 2 M1 For a point marked due south of A or

on a correct bearing (within overlay)
from B.
Correct point A1 within overlay
(b) 168 + 180 or 360 − 12 2 M1 For a complete method or
for clearly identifying the reflex angle
on the diagram.
348 A1 cao
(c) 6.25 1 B1 cao
Total 5 marks
9 (a)
( EF 2 =)2.12 + 3.52 (= 4.41 + 12.25 =16.66) 3 M1

M1 dep
=
( EF ) 2.12 + 3.52 or 16.66
4.1 A1 allow 4.08(166…) rounded or
truncated to at least 2DP
(b) 2.1 3 M1 ft 4.1 from (a)
tan F = or tan F = 0.6
3.5
2.1
sin F = or sin F = 0.512(195...)
4.1
3.5
cos F = or cos F = 0.853(658...)
4.1
 2.1  −1
M1 ft 4.1 from (a)
tan −1   or tan 0.6 or
 3.5 
 2.1  −1
sin −1   or sin 0.512(195) or
 4.1 
 3.5  or cos −1 0.853(658)
cos −1  
 4.1 
31 A1 ft 4.1 from (a)
Accept 30.8 – 31.4
Total 6 marks
10 Eg 8 y − −2 y= 18 − 33 or 10 y = −15 or 3 M1 For a correct method to find an
−2 y − 8 y = 33 − 18 or −10 y = 15 or equation in x or y. Allow one
arithmetical error.
25 x = 150 or 5 x + 4(5 x − 33) = 18 or
33 + 2 y + 8 y =18 or 18 − 8 y − 2 y =33
Eg 5× 6 – 2y = 33 or 5× 6 + 8y = 18 or M1 For a correct substitution
5x – 2× –1.5 = 33 or 5x + 8× –1.5 = 18 Dep on first M1awarded
x = 6 , y = −1.5 A1 oe
dep on M1

Total 3 marks
11 (a) 2 M1 For clearly identifying the line x = 1
or
For a reflection in any vertical line
triangle drawn A1 SCB1 for a correct reflection in y = 1
( −3, 0) ( −1, −3) ,
( −3, −2)
(b) S (−3, 0), (−3, 2), (−1, 3) 3 M1 Ft for S
o
rotation of 180 with A1 rotation 180o oe or
centre (1, 0) Enlargement sf = −1
A1 (1, 0)

SCB2 for a fully correct description of

their transformation if S is in the
incorrect position

Note: Award M1A1A1 for a correct

description even if S not drawn

Award no Answer marks if more than

one transformation is given.

Total 5 marks
12 (a) 2=
y 3 x − 15 or −2 y = 15 − 3 x or 1.5 x − y =7.5 3 M1 Or for finding the coordinates of two
correct points that lie on the line
3 x − 15
or y = 15 − 3 x oe
M1 difference of y values
=y 1.5 x − 7.5 or y = or for any
2 −2 difference of x values
two correct points on the line
1.5 A1 oe
Do not penalise a mistake in the
constant term if the correct answer is
given.
SCB2 for 1.5x
SCB1 ft from their y = ax + b
(b) (0, −7.5) 1 B1 oe
(c) =
0 1.5 × −2 + c or 3 × −2 = k or y=
− 0 1.5( x − −2) 2 M1 ft 1.5 from (a) or c = 3
=y 1.5 x + 3 A1 ft 1.5 from (a)
or 3 x − 2 y = =
−6 or y 1.5( x + 2)
oe
Total 6 marks

13 (a) 79o 1 B1
(b) ∠BDE = 79 − 41 or 180 − 101 − 41(= 38) or 2 M1 may be marked on diagram
∠OBE =90 − 38 or 90 − (180 − 101 − 41) (=52)
76 A1
Total 3 marks
14 (a) 12 40 11 40 12 39 3 B3 B1 for each pair.
, , , , , Accept equivalent fractions
52 52 51 51 51 51 Eg
12 3 40 10 12 4 39 13
= = , =, =,
52 13 52 13 51 17 51 17
Accept equivalent decimals correct to
at least 2dp (0.23, 0.77, 0.22, 0.78,
0.24, 0.76)
(b) 12 11 132 11 3 M1 ft their M2 for
× or or or 0.049(773...) or tree 12 40 40 12
52 51 2652 221 1−� × + × �
diagram 52 51 52 51
40 39 1560 130 10 (= 1-0.361(99…))
× or or or or 0.588(235...)
52 51 2652 221 17

12 11 40 39 132 1560 11 10 M1
× + × or + or + oe
52 51 52 51 2652 2652 221 17
141 A1 0.638(009…) rounded or truncated to
221 at least 3 DP or oe
Total 6 marks
Alternative Method - With Replacement
12 12 144 9 M1 M2 for
× or or or 0.053(254...) or 12 40 40 12
52 52 2704 169 1 − �52 × 52 + 52 × 52
�
40 40 1600 100 (=1-0.355(029…))
× or or or 0.591(715...)
52 52 2704 169

12 12 40 40 144 1600 9 100 M1

× + × or + or +
52 52 52 52 2704 2704 169 169
1744 109
or or or 0.644(970....) oe
2704 169
15 (a)  4   3 2 M1
  −   oe
 −1  2 
1 A1
 
 −3 

(b)  4   1  7 3 M1 Ft their BC in (a)
2   −   (=  ) For a correct expression for ��⃗
𝐶𝐸 or ��⃗
𝐸𝐶
 −1  −3   1 
in terms of column vectors
M1 Dep on 
first M1 awarded
7 2 + 12 ft their CE


7.07 A1 7.07106… rounded or truncated to at

least 2DP
Accept 50 or 5 2
Total 5 marks
16 (a) 23+1 × 31+1 × 7 2+3 2 M1 or for a product of powers of 2, 3 and
7 with two powers correct,
or for an attempt to find prime factors
of 2420208 (allow one arithmetical
error) or
for 24 , 32 , 75
24 × 32 × 75 A1
3−1 1−1 2 −3
(b) 2 ×3 ×7 2 M1 or for any two correct.
2, 0, −1 A1 Accept 22 × 30 × 7−1
(c)
Eg 7 2 − (2 5) 2 or 7 2 − 14 5 + 14 5 − (2 5)2 2 M1 For a correct unsimplified exact
expansion
7 2 may be simplified to 49 and
(2 5)2 as far as 20
Show that A1 Correct solution (simplified correctly)
dep on M1
(d) 1 − 43 1 1 3 M1 Or for 94 = 38
4 or 9 or or
3
oe
9 3 3
(32 ) 4 38
−4 −8 1 M1
(32 ) 3 or 3 3 or 8
33
8 A1 oe
−
2
3 Eg −2 or −2.6 but not a decimal
3
approximation.
Total 9 marks
17 9 3 M2
(=
v )8t + v )8t + 9t −2
or (=
t2 9
M1 for 8t or 9t −2 or
t2
40.36 A1 oe
Total 3 marks
18 (a) 4 1 B1
3 − 4x
or ( g −1 ( x= ) 3x − 4 or
(b) 3 3 3−4 ×6 2 M1
6= or (x =) − 4 or oe )
6 6
x+4 x
−3 12 A1 oe

(c) 3 2 M1 3
2× Or for (g(−5) =
) or −3
2 × −3 −5 + 4 −5 + 4
f (−3) or or
3 × −3 + 5 3
3× +5
−5 + 4
1 A1 6 3
1 or or or 1.5
2 4 2
(d) 2 x( x + 4)= 3(3 x + 5) or 2 x 2 + 8 x = 9 x + 15 oe or 4 M1
2 x( x + 4) 3(3x + 5)
= or
(3x + 5)( x + 4) (3x + 5)( x + 4)
2 x( x + 4) 3(3x + 5)
− (= 0)
(3x + 5)( x + 4) (3x + 5)( x + 4)
2 x 2 − x − 15 A1
2 x − x − 15(=
2
0) or (= 0)
(3x + 5)( x + 4)
(2 x + 5)( x − 3) M1 or correct substitution into quadratic
(2 x + 5)( x − 3)(= 0) or (= 0) formula
(3x + 5)( x + 4) or correctly completing the square
−2 12 , 3 A1 dep on previous M1

Total 9 marks
19 (a) tangent at (−1, 6) 3 M1 For a drawing a tangent
difference in y values M1 Dep on first M1 awarded
difference in x values difference in y values
For for any
difference in x values
two points on a tangent (ignore
negative gradient) or
For gradient in the range 4 to 6
inclusive
−5 A1 Accept answer in the range -6 to -4
inclusive
dep on M1
(b) graph y =−2 x + 7 2 M1 For the correct line drawn
2.2 A1 dep on M1
Accept 2.15 – 2.25
(c) M1 For a = −4 or 8.2b 8.3
−4,8.2 A1 allow 8.2b 8.3
Total 7 marks

20 (a) 6 + 10 + 8 or 2 M1 Or for 1 (small) square = 0.1 or

1 1 1 1 (big) square = 2.5 or
12 × + 20 × + 16 × or 48 × 0.5 or For 6, 10 and 8 marked correctly on
2 2 2
60 × 0.1 + 100 × 0.1 + 80 × 0.1 or 240 × 0.1 or
the diagram
2.4 × 2.5 + 4 × 2.5 + 3.2 × 2.5 or 9.6 × 2.5
24 A1
1 1
(b) 50 − 6 − 10 − 16 or 50 − 32 or 36 × or × 54 or 18 or
2 3
2 M1 For a vertical line at Time = 87
180 (small) squares or 180 × 0.1 or
7.2 (big) squares or 7.2 × 2.5
87 A1 cao
Total 4 marks
21 (a) 16.5 21 sin BAK sin 68 3 M1 For a correct equation using the Sine
Eg = or = Rule
sin BAK sin 68 16.5 21
16.5 × sin 68 M1
(sin BAK =) or 0.728(5016…) oe or
21
 16.5 × sin 68  or
( BAK =) sin −1  
 21 
−1
( BAK =) sin (0.728(5016...)) oe
46.8 A1 Accept 46.7(609...) rounded or
truncated to at least 1dp
or (α =) sin −1 
(b) 9 9  2 M1 Or for a correct equation using the
sin α =  Sine Rule
16.5  16.5 
33.1 A1 Accept 33.0(557...) rounded or
truncated to at least 1dp
Total 5 marks
Pearson Education Limited. Registered company number 872828
with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
Write your name here
Surname Other names

Centre Number Candidate Number

Pearson Edexcel
International GCSE

Mathematics A
Paper 4HR

Higher Tier
Tuesday 17 January 2017 – Morning Paper Reference

Time: 2 hours 4MA0/4HR

You must have: Total Marks
Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser, calculator. Tracing paper may be used.

Instructions
• Use black ink or ball-point pen.
• Fill in the boxes at the top of this page with your name,
centre number and candidate number.
• Withoutallsufficient
Answer questions.
• Answer the questions working, correct answers may be awarded no marks.
• – there may be more spacein the spaces provided
than you need.
• You must NOT write anything on the formulae page.
Calculators may be used.
• Anything you write on the formulae page will gain NO credit.
Information
• The total mark for this paper is 100.
• –Theusemarks for each question are shown in brackets
this as a guide as to how much time to spend on each question.

Advice
• Check
Read each question carefully before you start to answer it.
• your answers if you have time at the end.
Turn over
Turn over

P48405RA
©2017 Pearson Education Ltd.

2/1/1/1/
*P48405rA0124*
International GCSE MATHEMATICS
FORMULAE SHEET – HIGHER TIER

DO NOT WRITE IN THIS AREA

Pythagoras’ Volume of cone = 1
r 2h Volume of sphere = 4
r3
3 3
Theorem
c Curved surface area of cone = rl Surface area of sphere = 4 r 2
b
r
a l
h
a2 + b2 = c2
r

adj = hyp cos

hyp opp = hyp sin
opp opp = adj tan In any triangle ABC
C
adj opp
or sin b a
hyp

DO NOT WRITE IN THIS AREA

adj A B
cos c
hyp

opp a b c
tan Sine rule:
adj sin A sin B sin C

Cosine rule: a2 b2 + c 2 2bc cos A

1
Area of triangle 2 ab sin C
cross
section
h
lengt
Volume of prism = area of cross section length

Area of a trapezium = 12 (a + b)h

r Circumference of circle = 2 r a
DO NOT WRITE IN THIS AREA

Area of circle = r 2 h

r
The Quadratic Equation
Volume of cylinder = r h 2 The solutions of ax2 + bx + c 0,
h where a 0, are given by
Curved surface area
of cylinder = 2 rh b + b2 4ac
x
2a

2
*P48405rA0224*
Answer ALL TWENTY ONE questions.

Write your answers in the spaces provided.

DO NOT WRITE IN THIS AREA

You must write down all the stages in your working.

1 Here is a list of ingredients for making 24 Rocky Road Crunchy Bars.

Rocky Road Crunchy Bars

Ingredients for 24 bars

125 grams butter
300 grams chocolate
3 tablespoons syrup
200 grams biscuits
100 grams marshmallows
2 teaspoons icing sugar

Silvester wants to make 30 Rocky Road Crunchy Bars.

DO NOT WRITE IN THIS AREA

(a) Work out the amount of marshmallows he needs.

....................................................... grams
(2)
Nigella makes some Rocky Road Crunchy Bars.
She uses 850 grams of chocolate.
(b) Work out the number of Rocky Road Crunchy Bars she makes.
DO NOT WRITE IN THIS AREA

.......................................................

(2)

(Total for Question 1 is 4 marks)

3
*P48405rA0324* Turn over
2 Here is a biased 4-sided spinner.

DO NOT WRITE IN THIS AREA

2 4
3

The spinner is spun.

The table shows the probability that the spinner lands on 1 and the probability that it
lands on 2

Number 1 2 3 4
Probability 0.15 0.4

(a) Work out the probability that the spinner will land on 1 or on 2

DO NOT WRITE IN THIS AREA

.......................................................

(1)
The probability that the spinner will land on 3 is twice the probability that the spinner
will land on 4
(b) Work out the probability that the spinner will land on 3

.......................................................

(2)
Daljit is going to spin the spinner 160 times. DO NOT WRITE IN THIS AREA

.......................................................

(2)

(Total for Question 2 is 5 marks)

4
*P48405rA0424*
3 In a sale, normal prices are reduced by 35%
The normal price of a bed is $1200
DO NOT WRITE IN THIS AREA

Work out the sale price of the bed.

$ .......................................................

(Total for Question 3 is 3 marks)

4 The diagram shows a rectangle and a circle.

Diagram NOT
accurately drawn
DO NOT WRITE IN THIS AREA

8 cm
20 cm

30 cm
The rectangle has length 30 cm and width 20 cm.
The circle has radius 8 cm.
Work out the area of the shaded region.
Give your answer correct to 3 significant figures.
DO NOT WRITE IN THIS AREA

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . cm2

(Total for Question 4 is 4 marks)

5
*P48405rA0524* Turn over
5 E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {2, 3, 5, 7}
B = {1, 3, 5, 7, 9}

DO NOT WRITE IN THIS AREA

(a) List the members of the set
(i) A B

.......................................................

(ii) A B

.......................................................

(2)
(b) Find n(A‫މ‬

.......................................................

(1)

DO NOT WRITE IN THIS AREA

(Total for Question 5 is 3 marks)

Diagram NOT
12.8 cm accurately drawn
x cm

9.7 cm
Work out the value of x.
Give your answer correct to 3 significant figures.

DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 6 is 3 marks)

6
*P48405rA0624*
7 (a) Expand 3(4p + 5)
DO NOT WRITE IN THIS AREA

.......................................................

(1)
(b) Factorise 6r + 14

.......................................................

(1)
(c) Work out the value of y2íy when y í
DO NOT WRITE IN THIS AREA

.......................................................

(2)
w5 × w8
(d) Simplify
w4

.......................................................

(2)
(e) Write down the inequality shown on the number line.
DO NOT WRITE IN THIS AREA

x
2 3 4 5 6 7 8 9 10

.......................................................

(2)

(Total for Question 7 is 8 marks)

7
*P48405rA0724* Turn over
8 The diagram shows a parallelogram ABCD.

B C

DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn

(7xí íx

A D

Angle BAD = (7xí

Angle ADC íx
Work out the value of x.
Show clear algebraic working.

DO NOT WRITE IN THIS AREA

x = .......................................................

(Total for Question 8 is 3 marks) DO NOT WRITE IN THIS AREA

8
*P48405rA0824*
9 The diagram shows the positions of two towns, A and B.
North
DO NOT WRITE IN THIS AREA

Diagram NOT
B accurately drawn

110 km
North

x
A 60 km
The distance from A to B is 110 km.
B is 60 km east of A.
(a) Work out the size of angle x.
Give your answer correct to 1 decimal place.
DO NOT WRITE IN THIS AREA

....................................................

(3)
(b) Work out the bearing of B from A.
Give your answer correct to the nearest degree.

....................................................

(2)
DO NOT WRITE IN THIS AREA

The distance from A to B is 110 km correct to 2 significant figures.

....................................................... km
(ii) Write down the upper bound for the distance from A to B.

....................................................... km
(2)

(Total for Question 9 is 7 marks)

9
*P48405rA0924* Turn over
10 m = 34 × 53
n = 33 × 52 × 11

DO NOT WRITE IN THIS AREA

(a) Find the Lowest Common Multiple (LCM) of m and n.

.......................................................

(2)
(b) Find the Highest Common Factor (HCF) of 5m and 3n.

DO NOT WRITE IN THIS AREA

.......................................................

(2)

(Total for Question 10 is 4 marks)

DO NOT WRITE IN THIS AREA

10
*P48405rA01024*
11 Here is the straight line L drawn on a grid.
y
DO NOT WRITE IN THIS AREA

5
L
4

í í í O 1 2 3 4 x

í
DO NOT WRITE IN THIS AREA

Find an equation for L.

.......................................................

(Total for Question 11 is 2 marks)

DO NOT WRITE IN THIS AREA

11
*P48405rA01124* Turn over
12 Joaquim takes part in two cycle races.
The probability that he wins the first race is 0.6

DO NOT WRITE IN THIS AREA

The probability that he wins the second race is 0.7
(a) Complete the probability tree diagram.

First race Second race

Joaquim
0.7 wins

Joaquim
wins
0.6

..............
Joaquim does
not win

Joaquim

DO NOT WRITE IN THIS AREA

..............
wins
..............

Joaquim does
not win

..............
Joaquim does
not win
(2)
(b) Work out the probability that Joaquim wins both races.

DO NOT WRITE IN THIS AREA

.......................................................

(2)

12
*P48405rA01224*
Joaquim takes part in a third cycle race.
The probability that Joaquim wins the third race is 0.2
DO NOT WRITE IN THIS AREA

.......................................................

(3)
DO NOT WRITE IN THIS AREA

(Total for Question 12 is 7 marks)

DO NOT WRITE IN THIS AREA

13
*P48405rA01324* Turn over
13 P is inversely proportional to the square of q.
When q = 2, P = 12.8

DO NOT WRITE IN THIS AREA

(a) Find a formula for P in terms of q.

.......................................................

(3)
(b) Find the value of P when q = 8

DO NOT WRITE IN THIS AREA

.......................................................

(1)

(Total for Question 13 is 4 marks)

DO NOT WRITE IN THIS AREA

14
*P48405rA01424*
14 ABCDE and AWXYZ are two mathematically similar pentagons.
X
DO NOT WRITE IN THIS AREA

Diagram NOT
6 cm accurately drawn
C Y
W D
B
8 cm
5 cm

A 4 cm E Z

AE = 4 cm WX = 6 cm DE = 5 cm YZ = 8 cm
(a) Calculate the length of AZ.
DO NOT WRITE IN THIS AREA

....................................................... cm
(2)
(b) Calculate the length of BC.

....................................................... cm
(2)
The area of pentagon AWXYZ is 52.48 cm2
(c) Calculate the area of the shaded region.
DO NOT WRITE IN THIS AREA

............................................. . . . . . . . . . . cm2
(3)

(Total for Question 14 is 7 marks)

15
*P48405rA01524* Turn over
15 (a) Factorise y2íyí

DO NOT WRITE IN THIS AREA

.......................................................

(2)
4
(b) Solve =5
e−3

e = .......................................................
(2)

3 2

DO NOT WRITE IN THIS AREA

.......................................................

(3)

(Total for Question 15 is 7 marks)

16
*P48405rA01624*
16 The table shows information about the heights, in metres, of 45 of the world’s tallest men.

Height (h metres) Number of men

DO NOT WRITE IN THIS AREA

2.31 h - 2.35 10

2.35 h - 2.40 12

2.40 h - 2.47 13

2.47 h - 2.72 10

(a) Use the information in the table to complete the histogram.

275

250

225
DO NOT WRITE IN THIS AREA

200

175

Frequency 150
density
125

100

0
DO NOT WRITE IN THIS AREA

2.3 2.4 2.5 2.6 2.7

Height (metres)
(2)
(b) Find an estimate for the number of these men with height between 2.32 metres and 2.34 metres.

.......................................................

(1)

(Total for Question 16 is 3 marks)

17
*P48405rA01724* Turn over
17 D
Diagram NOT

DO NOT WRITE IN THIS AREA

accurately drawn

O
C

B
A, B, and C are points on the circumference of a circle, centre O.
DAE is a tangent to the circle.

DO NOT WRITE IN THIS AREA

(a) Work out the size of angle ACB.

.......................................................

(2)
(b) Work out the size of angle CAD.

DO NOT WRITE IN THIS AREA

.......................................................

(2)

(Total for Question 17 is 4 marks)

18
*P48405rA01824*
18 Here is the graph of y = x3 í 0.2x2 í 9x + IRUí - x - 3
DO NOT WRITE IN THIS AREA

y
20

í í í í O 1 2 3 x
í

í
DO NOT WRITE IN THIS AREA

(a) Use the graph to find an estimate for the solution of the
equation x3 í 0.2x2 í 9x + 7 = í

.......................................................

(2)
(b) By drawing a suitable straight line on the grid, find an estimate for the solution of the
equation x3 í 0.2x2 í 4x + 7 = 0
DO NOT WRITE IN THIS AREA

.......................................................

(3)

(Total for Question 18 is 5 marks)

19
*P48405rA01924* Turn over
19 The diagram shows a solid cone.

Diagram NOT

DO NOT WRITE IN THIS AREA

accurately drawn

5 cm

The radius of the base of the cone is 5 cm.

The total surface area of the cone is 90ʌcm2
Work out the volume of the cone.
Give your answer as a multiple of ʌ.

DO NOT WRITE IN THIS AREA

....................................................... cm3

(Total for Question 19 is 5 marks)

20
*P48405rA02024*
20 (3 + c )(2 c − 3) = 1 + k c
where c and k are prime numbers.
DO NOT WRITE IN THIS AREA

(a) Find the value of c and the value of k.

c = ......................................... k = .........................................
(3)
1
DO NOT WRITE IN THIS AREA

pm =
p× 3
p2

(b) Find the value of m.

DO NOT WRITE IN THIS AREA

m = .......................................................
(3)

(Total for Question 20 is 6 marks)

21
*P48405rA02124* Turn over
21 A rectangular piece of card has length (3x í 13) cm and width (x í 2) cm.
A square, with sides of length 25 cm, is removed from each corner of the card.

DO NOT WRITE IN THIS AREA

25 cm
Diagram NOT
25 cm accurately drawn

(xí FP

(3xí FP

The card is then folded along the dashed lines to make an open box with height 25 cm as
shown below.
Diagram NOT
accurately drawn

DO NOT WRITE IN THIS AREA

25 cm

(a) Show that the length of the open box is (3x í 63) cm.

(1)

DO NOT WRITE IN THIS AREA

22
*P48405rA02224*
The volume of the open box is 81 900 cm3
(b) Find the value of x.
DO NOT WRITE IN THIS AREA

Show clear algebraic working.

DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

x = .......................................................
(5)

(Total for Question 21 is 6 marks)

TOTAL FOR PAPER IS 100 MARKS

23
*P48405rA02324*
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

*P48405rA02424*
Do NOT write on this page.
BLANK PAGE

24
Mark Scheme (Results)

January 2017

International GCSE Mathematics A

4MA0/4HR
Edexcel and BTEC Qualifications

Edexcel and BTEC qualifications come from Pearson, the world’s

Our website subject pages hold useful resources, support material

www.edexcel.com/contactus

Pearson: helping people progress, everywhere

January 2017
Publications Code 4MA0_4HR_1701_MS
All the material in this publication is copyright
© Pearson Education Ltd 2017
General Marking Guidance
• All candidates must receive the same treatment. Examiners
must mark the first candidate in exactly the same way as they
mark the last.
• Mark schemes should be applied positively. Candidates must
be rewarded for what they have shown they can do rather
than penalised for omissions.
• Examiners should mark according to the mark scheme not
according to their perception of where the grade boundaries
may lie.
• There is no ceiling on achievement. All marks on the mark
scheme should be used appropriately.
• All the marks on the mark scheme are designed to be
awarded. Examiners should always award full marks if
deserved, i.e. if the answer matches the mark scheme.
Examiners should also be prepared to award zero marks if the
candidate’s response is not worthy of credit according to the
mark scheme.
• Where some judgement is required, mark schemes will
provide the principles by which marks will be awarded and
exemplification may be limited.
• When examiners are in doubt regarding the application of the
mark scheme to a candidate’s response, the team leader must
be consulted.
• Crossed out work should be marked UNLESS the candidate
has replaced it with an alternative response.
• Types of mark
o M marks: method marks
o A marks: accuracy marks
o B marks: unconditional accuracy marks (independent of
M marks)
• Abbreviations
o cao – correct answer only
o ft – follow through
o isw – ignore subsequent working
o SC - special case
o oe – or equivalent (and appropriate)
o dep – dependent
o indep – independent
o eeoo – each error or omission
• No working
If no working is shown then correct answers normally score
full marks
If no working is shown then incorrect (even though nearly
correct) answers score no marks.
• With working
If there is a wrong answer indicated on the answer line always
check the working in the body of the script (and on any
diagrams), and award any marks appropriate from the mark
scheme.
If it is clear from the working that the “correct” answer has
been obtained from incorrect working, award 0 marks.
Any case of suspected misread loses A (and B) marks on that
part, but can gain the M marks.
If working is crossed out and still legible, then it should be
given any appropriate marks, as long as it has not been
replaced by alternative work.
If there is a choice of methods shown, then no marks should
be awarded, unless the answer on the answer line makes
clear the method that has been used.
If there is no answer on the answer line then check the
working for an obvious answer.
• Ignoring subsequent work
It is appropriate to ignore subsequent work when the
additional work does not change the answer in a way that is
inappropriate for the question: eg. Incorrect cancelling of a
fraction that would otherwise be correct.
It is not appropriate to ignore subsequent work when the
additional work essentially makes the answer incorrect eg
algebra.
Transcription errors occur when candidates present a correct
answer in working, and write it incorrectly on the answer line;
mark the correct answer.
• Parts of questions
Unless allowed by the mark scheme, the marks allocated to
one part of the question CANNOT be awarded in another.
International GCSE Maths: Apart from Questions 8, 18 and 21, where the mark scheme states otherwise, the correct answer, unless clearly
obtained by an incorrect method, should be taken to imply a correct method.

Q Working Answer Mark Notes

1 (a) 100 2 M1 100 30
e.g. × 30 For (=4.16(66..)) or or
24 24 24
24 30
1.25 or = oe
100 x
125 A1
(b) 850 300 M1 Complete method to find number
e.g. × 24 or 850 ÷ oe made
300 24
2
68 A1 cao
Total 4 marks

2 (a) 0.15 + 0.4 0.55 1 B1

(b) 1 − (0.15 + 0.4) 0.45 2 M1
or (= 0.15)
3 3

0.3 A1
(c) 160 × 0.4 2 M1

64 A1
Total 5 marks
3 35 3 M1
×1200 oe or 420 [Award M2 for
100
1200 × (1 – 0.35)]
1200 – "420" M1 dep
780 A1 SC M1 for 1620
Total 3 marks

4 30 × 20 or 600 4 M1 For area of rectangle

𝜋 × 82 or 201.(0619298...) or 64π M1 Indep for area of circle

eg 𝜋 × 82 or 201.(0619298..) or
64π
30 × 20 – 𝜋 × 82 M1
399 A1 Accept 398 -399.1
Total 4 marks

5 (a)(i) {3, 5, 7} 2 B1
(a)(ii) {1, 2, 3, 5, 7, 9} B1
(b) 6 1 B1
Total 3 marks
6 12.8² – 9.7² or 163.84 – 94.09 or 69.75 3 M1 For squaring and subtracting
−1  9.7 
= =
[ a cos   ( 40.7...) and
 12.8 
x x
= sin 40.7.. = or tan 40.7.. ]
12.8 9.7
12.82 − 9.7 2 M1dep For square root
= =
[ x 12.8sin 40.7..or x 9.7 tan 40.7.. ]
8.35 A1 Allow 8.35 - 8.352
Total 3 marks

7 (a) 12p + 15 1 B1

(b) 2(3r + 7) 1 B1
(c) (−5)² − 3 × −5 oe M1 or +25 or +15
40 2 A1
(d) w 13 2 w13
or w × w8 or w5 × w4 M1 For or w × w8 or w5 × w4
w4 w4
w9 A1
(e) 2 M1 For x ≥ 3 or x < 9 or 3 < x ≤ 9

3≤x<9 A1 Accept [3, 9) or 9 > x ≥ 3

Total 8 marks
8 160 – 3x + 7x – 20 = 180 or 3 M1 For a correct equation
2(160 – 3x) + 2(7x – 20) = 360 oe

e.g. 4x = 180 – 140 or – 3x + 7x = 180 + 20 – 160 M1 For isolating the terms in x in a

or 4x =40 or 14x – 6x = 360 – 320 + 40 oe correct equation
10 A1 Dep on at least M1
Total 3 marks

9 (a) 60 3 M1
cos x = or cos x = 0.545(4545...)
110

 60  M1
(x = ) cos −1  
 110 
56.9 A1 56.9 – 57
(b) 90 – 56.9(4426885...) oe 2 M1ft for complete method, ft from (a) if
033 "(a)" < 90, 90 – their x
A1ft accept (0)33 – (0)33.1 or ft
(c)(i) 105 2 B1

(c)(ii) 115 B1 •
Accept 114.9
Total 7 marks
10 (a) 2
M1 For 3a × 5b ×11 with a = 4 or b = 3
111375
A1 Accept 34 × 53 ×11 oe
(b) 2 M1 For 34 × 5q or 3 p × 52 (and no 11)
or n × 33 × 5² where n ≠ 11

2025 A1 Accept 34 × 52 oe
Total 4 marks

11 2 M1 For y = –2x + c (c ≠ 1) or
y = mx + 1
or for a correct method to find the
gradient
or m = −2 and c = 1 stated
or −2x + 1 or L = –2x + 1
y = –2x + 1 A1
oe

Total 2 marks
12 (a) 2 B1 For 0.4 on LH branch
Correct probabilities B1 For 0.3, 0.7 and 0.3 on RH branches
(b) 2 M1 For 0.6 × 0.7
0.42 A1 oe
(c) 0.6 × "0.3" × "0.8" + "0.4" × 0.7 × "0.8" + "0.4" × 3 M2ft For a complete method
"0.3" × 0.2 (= 0.144 + 0.224 + 0.024) oe M1ft for 0.6 × "0.3" × "0.8" or 0.144
 18 
  or "0.4" × 0.7 × "0.8" or 0.224
 125 
 28 
  or "0.4" × "0.3" × 0.2 or 0.024
 125 
 3 
 
 125 

0.392 49
A1cao oe
125
Alternative method
1 – [(0.6 × 0.7 × 0.2) + (0.4 × 0.3 × 0.8) + M2ft For complete method
(0.6 × 0.7 × 0.8) + (0.6 × 0.3 × 0.2) + M1ft for 1 – (at least 2 correct
(0.4 × 0.7 × 0.2)] products).
0.392 A1cao 49
125
Total 7 marks
13 (a) k 3 M1 k
P= Allow Pq² = k or q 2 =
q2 p
1
Do not allow P =
q2
k M1 For correct substitution in a correct
12.8 = oe or k = 12.8 × 2² or k = 51.2 equation. Implies first M1
22
Award M2 if k = 51.2 stated
unambiguously

51.2 A1 Award 3 marks if answer is

p=
q2 k
P = 2 but k is evaluated in (a) or (b)
q
51.2
SCB2 for Pq² = 51.2 or q 2 =
p
(b) 51.2
0.8 1 k
8² B1ft ft equation in the form P = 2 oe
q
Total 4 marks
14 (a) 8 5 2 M1 For correct scale factor or
e.g. or 1.6 or or 0.625 or correct expression for AZ or
5 8
8 5 for a correct equation involving AZ
e.g. 4 × or 4 ÷ oe or oe
5 8
AZ 8 AZ 4
e.g. = or = oe
4 5 8 5
6.4 A1 32
oe e.g.
5
(b) 8 5 6× 4 2 M1 Correct expression for BC
Eg 6 ÷ or 6 × or oe 3.75
5 8 "6.4" A1 oe
(c) 52.48 3 M2 For a fully correct method or
52.48 −
1.62 52.48
M1 for or 20.5
1.62
31.98 A1 Accept 32.0 or 32
Total 7 marks
15 (a) M1 For (y ± 8)(y ± 6)
(y – 8)(y + 6) 2 A1 cao
(b) 4 M1
4 = 5(e – 3) or 4 = 5e – 15 or =e–3
5
A1
19 2 4
35 or 3.8
5
(c) 3( x − 1) − 2( x + 1) 3( x − 1) 2( x + 1) 3 M1 3( x − 1) − 2( x + 1)
or − oe e.g.
( x + 1)( x − 1) ( x + 1)( x − 1) ( x + 1)( x − 1) x2 −1

3x − 3 − 2 x − 2 M1
oe
( x + 1)( x − 1)
x −5 A1 x −5
oe e.g.
( x + 1)( x − 1) x2 −1
Total 7 marks

16 (a) 10 2 M1 Or bar of height 40 wrong width

or 40
2.72 − 2.47
Correct bar A1
(b) 5 1 B1
Total 3 marks
17 (a) 0.5 × (360 – 260) or 0.5 × 100 M1 For a complete method
50 2 A1
(b) e.g. 360 – (“50” + 260 + 30) (= 20), 90 – "20" 2 M1ft For a complete method.
180 − 100
or + 30
2
70 A1
Total 4 marks

18 (a) M1 Line y = –5 drawn or clear attempt

–3.4 2 to take reading at y = –5
A1
Accept –3.35 to –3.45 inclusive
(b) 3 M2 y = – 5x drawn.

M1 for x³ – 0.2x² – 9x + 7 = –5x or

y = –5x oe

–2.5 A1 dep on at least M1 (−2.45 - −2.55)

Total 5 marks
19 (𝜋 × 5²) + 𝜋 × 5 × l 5 M1 For a correct expression for total
(25𝜋) + 5𝜋l surface area

(l =) 13 A1 For the correct slant height

(h = ) 132 − 52 or 144 or 12 M1 For the correct method to find h

ft if first M1 scored
1 M1 For the correct method to find V
(V = ) × π × 52 ×12 (= 314 - 314.3) ft if first M1 scored
3
100𝜋 A1
Total 5 marks

20 (a) 6√𝑐 – 9 +2c – 3√𝑐 or 3√𝑐 – 9 +2c 3 M1 Accept √𝑐 √𝑐 or (√𝑐 )2 instead of c

c=5 A1
k=3 B1
(b) 1 m +1+
2 3 M1
2
or p 3
=1
p× p3
−5 M1
1 2
5
or p 3
or m + 1 + =0
3
3
p
5 A1 −5
− 3
p gains M2 only
3
Total 6 marks
21 (a) 3x – 13 – 50 1 B1 or 3x – 13 – 25 − 25
(b) x – 52 5 B1 or x – 2 – 25 × 2

25(3x – 63)(x – 52) (= 81900) M1 For a correct expression for

volume of box

eg 3x² – 156x – 63x + 3276 (= 3276) M1 For brackets correctly expanded

or 75x² – 3900x – 1575x +81900 (= 81900)

eg 3x² – 219x = 0 or 3x(x – 73) = 0 M1 For correctly reducing to 2 term
or 75x² – 5475x = 0 quadratic equation

(x = 0) or x = 73 73 A1 For x = 73
NB: A1 dependent on at least 2
method marks
Total 6 marks
Pearson Education Limited. Registered company number 872828
with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
Write your name here
Surname Other names

Centre Number Candidate Number

Pearson Edexcel Certificate
Pearson Edexcel
International GCSE

Mathematics A
Paper 3H

Higher Tier
Thursday 25 May 2017 – Morning Paper Reference
4MA0/3H
Time: 2 hours KMA0/3H

You must have: Total Marks

Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser, calculator. Tracing paper may be used.

Advice
• Check
Read each question carefully before you start to answer it.
• your answers if you have time at the end.

Turn over

P48487A
©2017 Pearson Education Ltd.

1/1/1/1/1/
*P48487A0124*
International GCSE MATHEMATICS
FORMULAE SHEET – HIGHER TIER

DO NOT WRITE IN THIS AREA

Pythagoras’ Volume of cone = 1
r 2h Volume of sphere = 4
r3
3 3
Theorem
c Curved surface area of cone = rl Surface area of sphere = 4 r 2
b
r
a l
h
a + b2 = c2
2
r

adj = hyp cos

hyp opp = hyp sin
opp opp = adj tan In any triangle ABC
C
adj opp
or sin b a
hyp

DO NOT WRITE IN THIS AREA

adj A B
cos c
hyp

opp a b c
tan Sine rule:
adj sin A sin B sin C

Cosine rule: a2 b2 + c 2 2bc cos A

1
Area of triangle 2 ab sin C
cross
section
h
lengt
Volume of prism = area of cross section length

Area of a trapezium = 12 (a + b)h

r Circumference of circle = 2 r a
DO NOT WRITE IN THIS AREA

Area of circle = r 2 h

r
The Quadratic Equation
Volume of cylinder = r h 2 The solutions of ax2 + bx + c 0,
h where a 0, are given by
Curved surface area
of cylinder = 2 rh b + b2 4ac
x
2a

2
*P48487A0224*
Answer ALL TWENTY TWO questions.

Write your answers in the spaces provided.

DO NOT WRITE IN THIS AREA

You must write down all the stages in your working.

1 D )DFWRULVH ௘a + 25

.........................................

(1)
(b) Factorise 7w௘2í௘w

.........................................

(1)
(c) Expand p௘2( pí
DO NOT WRITE IN THIS AREA

.........................................

(2)
(d) Expand and simplify (xí x + 7)

.........................................

(2)
G = f í௘f
DO NOT WRITE IN THIS AREA

(e) Work out the value of G when f = 2

G = .........................................
(2)

(Total for Question 1 is 8 marks)

3
*P48487A0324* Turn over
2

DO NOT WRITE IN THIS AREA

5
P

DO NOT WRITE IN THIS AREA

–6 –5 ± ± –2 –1 O 1 2 5 6 7 8 9 10 x
–1

–2

(a) On the grid, enlarge shape PZLWKVFDOHIDFWRUDQGFHQWUH

Label the new shape Q.
(2)
(b) On the grid, rotate shape PWKURXJKDQWLFORFNZLVHDERXWWKHSRLQW
DO NOT WRITE IN THIS AREA

Label the new shape R.

(2)

(Total for Question 2 is 4 marks)

4
*P48487A0424*
3 +HUHLVDOLVWRILQJUHGLHQWVQHHGHGWRPDNHDSSOHDQGEODFNEHUU\FUXPEOHIRUSHRSOH
DO NOT WRITE IN THIS AREA

Apple and Blackberry Crumble

,QJUHGLHQWVIRUSHRSOH

120 grams flour

80 grams sugar
90 grams butter
JUDPV DSSOHV
115 grams blackberries

Rufus wants to make apple and blackberry crumble for 10 people.

(a) Work out the amount of apples he needs.
DO NOT WRITE IN THIS AREA

......................................... grams
(2)
Roland makes apple and blackberry crumble for a group of people.
He uses 920 grams of blackberries.
(b) Work out the number of people in the group.
DO NOT WRITE IN THIS AREA

.........................................

(2)

(Total for Question 3 is 4 marks)

5
*P48487A0524* Turn over
4 7KHWDEOHVKRZVLQIRUPDWLRQDERXWWKHOHQJWKVLQFPRIOHDYHV

DO NOT WRITE IN THIS AREA

Length (L cm) Frequency

0L-1

1L-2 5

2 L - 11

L -

L - 5 6

(a) Write down the modal class.

.........................................

(1)
E :RUNRXWDQHVWLPDWHIRUWKHPHDQOHQJWKRIWKHOHDYHV

DO NOT WRITE IN THIS AREA

Give your answer correct to 1 decimal place.

......................................... cm
(4)
DO NOT WRITE IN THIS AREA

(Total for Question 4 is 5 marks)

6
*P48487A0624*
5 (a) Use your calculator to work out the value of

7.3 + 2.1
DO NOT WRITE IN THIS AREA

+ 2.22
6.4

Give your answer as a decimal.

Write down all the figures on your calculator display.

.......................................................

(2)
E *LYH\RXUDQVZHUWRSDUW D FRUUHFWWRVLJQLILFDQWILJXUHV
DO NOT WRITE IN THIS AREA

.......................................................

(1)

(Total for Question 5 is 3 marks)

DO NOT WRITE IN THIS AREA

7
*P48487A0724* Turn over
6 On the grid, draw the graph of y ௘x IRUYDOXHVRIxIURPíWR

DO NOT WRITE IN THIS AREA

y
12

DO NOT WRITE IN THIS AREA

± –2 –1 O 1 2 x DO NOT WRITE IN THIS AREA

–2

(Total for Question 6 is 3 marks)

8
*P48487A0824*
7

A FP B Diagram NOT

DO NOT WRITE IN THIS AREA

22° accurately drawn

C
Calculate the length of AC.
*LYH\RXUDQVZHUFRUUHFWWRVLJQLILFDQWILJXUHV
DO NOT WRITE IN THIS AREA

......................................... cm

(Total for Question 7 is 3 marks)

DO NOT WRITE IN THIS AREA

9
*P48487A0924* Turn over
8 ,Q'RQDOG¶VZHHNO\SD\ZDV
,Q'RQDOG¶VZHHNO\SD\ZDV

DO NOT WRITE IN THIS AREA

D :RUNRXWWKHSHUFHQWDJHLQFUHDVHLQ'RQDOG¶VSD\EHWZHHQDQG

......................................... %
(3)
,Q'RQDOG¶VZHHNO\SD\ZDVRIKLVZHHNO\SD\LQ

DO NOT WRITE IN THIS AREA

E :RUNRXW'RQDOG¶VZHHNO\SD\LQ

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3) DO NOT WRITE IN THIS AREA

(Total for Question 8 is 6 marks)

10
*P48487A01024*
9 Use ruler and compasses to construct the bisector of angle PQR.
You must show all your construction lines.
DO NOT WRITE IN THIS AREA

R
DO NOT WRITE IN THIS AREA

(Total for Question 9 is 2 marks)

10 Solve the simultaneous equations

௘x௘y
௘xí௘y = 16
Show clear algebraic working.
DO NOT WRITE IN THIS AREA

x = .........................................

y = .........................................

(Total for Question 10 is 4 marks)

11
*P48487A01124* Turn over
11 The table gives information about the ages of all the 90 adults in a supermarket.

DO NOT WRITE IN THIS AREA

Age (t years) Frequency
20 t -
t - 28
t - 50
50 t - 60 16
60 t - 70 8
70 t - 80

One of these 90 adults is picked at random.

(a) Find the probability that this adult's age is more than 50 years.

DO NOT WRITE IN THIS AREA

.........................................

(2)
(b) Complete the cumulative frequency table for these 90 adults.

Cumulative
Age (t years)
frequency

20 t -

20 t - 50

20 t - 60
DO NOT WRITE IN THIS AREA

20 t - 70

20 t - 80
(1)

12
*P48487A01224*
(c) On the grid, draw a cumulative frequency graph for your table.
DO NOT WRITE IN THIS AREA

Cumulative 50
frequency

20
DO NOT WRITE IN THIS AREA

0
20 50 60 70 80
Age (t years)
(2)
All of these adults with an age greater than 65 years receive a discount on their shopping bill.
(d) Use your graph to find an estimate for the number of these adults who receive a discount.
DO NOT WRITE IN THIS AREA

.........................................

(2)

(Total for Question 11 is 7 marks)

13
*P48487A01324* Turn over
12 D :ULWH LQVWDQGDUGIRUP

DO NOT WRITE IN THIS AREA

.........................................

(1)
7.8 × 10 5
(b) Work out
2.4 × 10 −4

Give your answer in standard form.

.........................................

(2)

DO NOT WRITE IN THIS AREA

(Total for Question 12 is 3 marks)

DO NOT WRITE IN THIS AREA

14
*P48487A01424*
13 Here are two mathematically similar cups, A and B.

Diagram NOT
DO NOT WRITE IN THIS AREA

accurately drawn

A B
8 cm
12 cm

9 cm d cm

A has height 12 cm and base diameter 9 cm.

B has height 8 cm and base diameter d cm.
(a) Work out the value of d.

.........................................
DO NOT WRITE IN THIS AREA

(2)
The volume of B is 160 millilitres.
(b) Work out the volume of A.

millilitres
.........................................

(2)
Two solid plates, P and Q, are mathematically similar and made of the same material.
The surface area of P is p cm2
The surface area of Q is q cm2
The weight of P is w grams.
DO NOT WRITE IN THIS AREA

(c) Find an expression for the weight of Q.

Give your answer in terms of p, q and w.

......................................... grams
(2)

(Total for Question 13 is 6 marks)

15
*P48487A01524* Turn over
( x)
8
14 (a) Simplify

DO NOT WRITE IN THIS AREA

.........................................

(1)
6 + 4y
(b) Solve í௘y
3

Show clear algebraic working.

DO NOT WRITE IN THIS AREA

y = .........................................
(4)
(c) Make g the subject of gí ghh

DO NOT WRITE IN THIS AREA

.........................................

(3)

(Total for Question 14 is 8 marks)

16
*P48487A01624*
15 P is directly proportional to U࣠
P ZKHQr
DO NOT WRITE IN THIS AREA

Find a formula for P in terms of r.

DO NOT WRITE IN THIS AREA

.........................................

(Total for Question 15 is 3 marks)

( )( )
16 5 2 − e 3 2 + e = f 2 − 6

Given that e and f are positive integers,

find the value of e and the value of f.
DO NOT WRITE IN THIS AREA

e = .........................................

f = .........................................

(Total for Question 16 is 3 marks)

17
*P48487A01724* Turn over
17 y
V

DO NOT WRITE IN THIS AREA

Q
Diagram NOT
accurately drawn
X
R

P S
Y
O x
PQS is a triangle.
X is the midpoint of QS and Y is the midpoint of PS.
R is the point of intersection of PX and QY.
V is a point so that VQXS is a straight line.
l l
PQ = a PS = b

DO NOT WRITE IN THIS AREA

(a) Find, in terms of a and b,
(i) l
QS

.........................................

l
(ii) QY

.........................................

l
(iii) PX

.........................................

(3)
l = 2 PX
PKDVFRRUGLQDWHV DQGPR l
3
l = ⎛ 4⎞ l ⎛ −5⎞
PR ⎜⎝ 2⎟⎠ and XV = ⎜⎝ 4 ⎟⎠
DO NOT WRITE IN THIS AREA

(b) Work out the coordinates of V.

(. . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . )
(3)

(Total for Question 17 is 6 marks)

18
*P48487A01824*
18 A and B are two sets.
n(E ) = 50
DO NOT WRITE IN THIS AREA

n(A B
n(A) = 5
n(B) = 9
(a) Complete the Venn diagram to show the numbers of elements.

E
A B

.................... .................... ....................

DO NOT WRITE IN THIS AREA

....................

(2)
(b) Find
(i) n(A Bƍ

.........................................

(ii) n(A Bƍ

.........................................

(2)

(Total for Question 18 is 4 marks)

DO NOT WRITE IN THIS AREA

19
*P48487A01924* Turn over
4
19 I௘ x) =
x−3

DO NOT WRITE IN THIS AREA

x−2
J௘ x) =
x

(a) Express the inverse function f í in the form f í(x) = ...

DO NOT WRITE IN THIS AREA

f í(x) = .........................................

(3)
(b) Solve fg(a) = 1
Show clear algebraic working.

DO NOT WRITE IN THIS AREA

a= .........................................

(3)

(Total for Question 19 is 6 marks)

20
*P48487A02024*
20 A bag contains 12 marbles.
RIWKHPDUEOHVDUHUHGRIWKHPDUEOHVDUHEOXHDQGRIWKHPDUEOHVDUHJUHHQ
DO NOT WRITE IN THIS AREA

5DMWDNHVDWUDQGRPPDUEOHVIURPWKHEDJ
Find the probability that exactly 2 of these marbles are blue.
DO NOT WRITE IN THIS AREA

.........................................

(Total for Question 20 is 3 marks)

DO NOT WRITE IN THIS AREA

21
*P48487A02124* Turn over
21 The diagram shows a triangular prism with a horizontal base ABCD.

DO NOT WRITE IN THIS AREA

Diagram NOT
B accurately drawn

V
10 cm
7 cm C
A
18 cm
M

M is the midpoint of AD.

The vertex V is vertically above M.
DC = 18 cm, BC = 10 cm, MV = 7 cm.

DO NOT WRITE IN THIS AREA

Calculate the size of the angle between VC and the plane ABCD.
*LYH\RXUDQVZHUFRUUHFWWRVLJQLILFDQWILJXUHV

DO NOT WRITE IN THIS AREA

°
.........................................

(Total for Question 21 is 4 marks)

22
*P48487A02224*
3 x − 15
22 Simplify fully − 2
2 x + 12 x − 2 x − 48
DO NOT WRITE IN THIS AREA

Show clear algebraic working.

DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

.........................................

(Total for Question 22 is 5 marks)

TOTAL FOR PAPER IS 100 MARKS

23
*P48487A02324*
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

*P48487A02424*
Do NOT write on this page.
BLANK PAGE

24
Mark Scheme (Results)

Summer 2017

Pearson Edexcel International GCSE

In Mathematics A (4MA0) Paper 3H
Edexcel and BTEC Qualifications

Edexcel and BTEC qualifications are awarded by Pearson, the UK’s largest
awarding body. We provide a wide range of qualifications including academic,
vocational, occupational and specific programmes for employers. For further
information visit our qualifications websites at www.edexcel.com or
www.btec.co.uk. Alternatively, you can get in touch with us using the details
on our contact us page at www.edexcel.com/contactus.

Pearson: helping people progress, everywhere

Pearson aspires to be the world’s leading learning company. Our aim is to help
everyone progress in their lives through education. We believe in every kind of
learning, for all kinds of people, wherever they are in the world. We’ve been involved
in education for over 150 years, and by working across 70 countries, in 100 languages,
we have built an international reputation for our commitment to high standards and
raising achievement through innovation in education. Find out more about how we
can help you and your students at: www.pearson.com/uk

Summer 2017
Publications Code 4MA0_3H_1706_MS
All the material in this publication is copyright
© Pearson Education Ltd 2017
General Marking Guidance
 All candidates must receive the same treatment. Examiners
must mark the first candidate in exactly the same way as they
mark the last.
 Mark schemes should be applied positively. Candidates must
be rewarded for what they have shown they can do rather
than penalised for omissions.
 Examiners should mark according to the mark scheme not
according to their perception of where the grade boundaries
may lie.
 There is no ceiling on achievement. All marks on the mark
scheme should be used appropriately.
 All the marks on the mark scheme are designed to be
awarded. Examiners should always award full marks if
deserved, i.e. if the answer matches the mark scheme.
Examiners should also be prepared to award zero marks if the
candidate’s response is not worthy of credit according to the
mark scheme.
 Where some judgement is required, mark schemes will
provide the principles by which marks will be awarded and
exemplification may be limited.
 When examiners are in doubt regarding the application of the
mark scheme to a candidate’s response, the team leader must
be consulted.
 Crossed out work should be marked UNLESS the candidate
has replaced it with an alternative response.
 Types of mark
o M marks: method marks
o A marks: accuracy marks
o B marks: unconditional accuracy marks (independent of
M marks)
 Abbreviations
o cao – correct answer only
o ft – follow through
o isw – ignore subsequent working
o SC - special case
o oe – or equivalent (and appropriate)
o dep – dependent
o indep – independent
o eeoo – each error or omission
 No working
If no working is shown then correct answers normally score
full marks
If no working is shown then incorrect (even though nearly
correct) answers score no marks.
 With working
If there is a wrong answer indicated on the answer line always
check the working in the body of the script (and on any
diagrams), and award any marks appropriate from the mark
scheme.
If it is clear from the working that the “correct” answer has
been obtained from incorrect working, award 0 marks.
Any case of suspected misread loses A (and B) marks on that
part, but can gain the M marks.
If working is crossed out and still legible, then it should be
given any appropriate marks, as long as it has not been
replaced by alternative work.
If there is a choice of methods shown, then no marks should
be awarded, unless the answer on the answer line makes
clear the method that has been used.
If there is no answer on the answer line then check the
working for an obvious answer.
 Ignoring subsequent work
It is appropriate to ignore subsequent work when the
additional work does not change the answer in a way that is
inappropriate for the question: eg. Incorrect cancelling of a
fraction that would otherwise be correct.
It is not appropriate to ignore subsequent work when the
additional work essentially makes the answer incorrect eg
algebra.
Transcription errors occur when candidates present a correct
answer in working, and write it incorrectly on the answer line;
mark the correct answer.
 Parts of questions
Unless allowed by the mark scheme, the marks allocated to
one part of the question CANNOT be awarded in another.
International GCSE Maths: Apart from Question 9, 10, 14b, 19b and 22, where the mark scheme states otherwise, the correct answer, unless
clearly obtained by an incorrect method, should be taken to imply a correct method.

Q Working Answer Mark Notes

1 (a) 5(2a + 5) 1 B1
(b) w(7w  4) 1 B1
(c) M1 for p³ or (−)5p²
p³  5p² 2 A1
(d) x² + 7x − 3x − 21 M1 for 3 correct terms or
4 correct terms ignoring signs or
x² + 4x + c or
.... + 4x  21

x² + 4x  21 2 A1
(e) 2³ – 7 × 2 or 8 – 14 or 8 – 7 × 2 or 2³ – 14 M1
6 2 A1
Total 8 marks
2 (a) Vertices at (5, 3) (5, 9) B2 If not B2 then award

(3, 9) (3, 5) (1, 5) (1, 3) B1 for shape of correct size and

orientation in incorrect position or
2 4 out of 6 vertices correct

(b) Vertices at (7, 1) (7, 3) B2 If not B2 then award

(4, 3) (4,2) (6, 2) (6,1 ) B1 for correct orientation but
incorrect position or
B1 for rotation 90°clockwise
2 about (7, 3)

Total 4 marks

3 (a) 300 M1 for a correct scale factor or a correct first step

E.g. 10
4 300 10
E.g. or 75 or or 2.5 or 300 ÷ 4 (=75)
4 4
750 2 A1

(b) 920 M1 for a correct scale factor or a correct first step

E.g. 4
115 920 115
E.g. or 8 or or 28.75
115 4
32 2 A1
Total 4 marks
4 (a) 3<L≤ 1 B1 Accept 3  4
4
(b) Eg 0.5×4 + 1.5×5 + 2.5×11 + 3.5×14 + 4.5×6 M2 f × d for at least 4 products with correct mid-
interval values and intention to add.
or 2 + 7.5 + 27.5 + 49 + 27
If not M2 then award M1 for
or 113 d used consistently for at least 4 products
within interval (including end points) and
intention to add
or
for at least 4 correct products with correct
mid-interval values with no intention to add

(0.5 × 4 + 1.5 × 5 + 2.5 × 11 + 3.5 × 14 + 4.5 × 6) ÷ M1 dep on M1 (ft their products)

40 NB: accept their 40 if addition of frequencies
or 113 ÷ 40 is shown
2.8 4 A1 Allow 2.82, 2.83 or 2.825
Total 5 marks

5 (a) M1 47 121 5047

for or 1.46875 or or 4.84 or or
32 25 800
6.30875 truncated or rounded to at least 1 dp
6.30875 2 A1
(b) 6.31 1 B1 ft from (a) provided answer to (a) has more than 3
sig figs
Total 3 marks
6 (3, 2) (2, 0) (1, 2) Correct line between 3 B3 for a correct line between x = 3 and x = 3 (inclusive)
(0, 4) (1, 6) (2, 8) (3, 10) x = 3 and x = 3
If not B3 then award B2 for
a correct line through at least 3 of
(3, 2) (2, 0) (1, 2) (0, 4) (1, 6) (2, 8) (3, 10) or
for all above points plotted correctly but not joined

If not B2 then award B1 for

any 2 correct points stated (could be in a table) or plotted or
may be seen in working e.g. 2 × 1 + 4 = 6 or
for a line with a positive gradient through (0, 4) or
for a line with gradient 2
Total 3 marks
7 14.9 M1 M1 for
cos22 = or
AC BC = 14.9 × tan22 oe (= 6.019 – 6.02)
14.9
sin(90  22)  or AND
AC
(AC2 = ) 14.92 + 6.019…2
AC 14.9
 oe
sin 90 sin(90  22)

14.9 M1
(AC = ) or M1 for (AC ) = 14.92  6.019...2
cos 22
14.9
 AC   ( × sin 90)
sin 68
16.1 3 A1 Accept 16.07 − 16.1
Total 3 marks
8 (a) 668.8  640 or 28.8 M1
668.8
M2 for (100) or
640
"28.8" ÷ 640 (×100) or 0.045 M1 dep 1.045 or 104.5

4.5 3 A1
(b) 668.8 M2 for a complete method
100 oe or
95
668.8 If not M2 then award M1 for
oe 668.8
0.95 (=7.04) or
95
0.95x = 668.8 oe
704 3 A1
Total 6 marks

9 Arc centre Q cutting QP and QR at A and B M1 for a relevant pair of intersecting

with AQ = BQ and arcs with same radius arcs within guidelines
centre A and B intersecting in guidelines
Correct angle bisector 2 A1 dep on M1

SC: B1 for line within guidelines

Total 2 marks
10 Eg M1 for coefficient of x or y the same and correct
10x + 35y = 155 6x + 21y = 93 operation to eliminate selected variable (condone
 10x  6y = 32 + 35x  21y = 112 any one arithmetic error in multiplication) or
for correct rearrangement of one equation
followed by correct substitution in the other.

A1 cao (dep on M1)

M1 (dep on 1st M1) for substituting their found value

into one of the equations
or
correct method of elimination to find the second
variable (as for first M1)

x = 5, y = 3 4 A1 cao
Award 4 marks for correct values if at least first
M1 scored
Total 4 marks
11 (a) 16  8  4 M1
90
28 2 A1 28 14
oe for oe E.g. , 0.31(1…), 31(.1…)%
90 90 45
(b) 4, 32, 62, 78, 86, 90 1 B1 cao

(c) (30, 4) (40, 32) (50, 62) (60, 78) M1 (ft from sensible table i.e. clear attempt at addition)
(70, 86) (80, 90)
for at least 4 points plotted correctly at end of
interval
or
for all 6 points plotted consistently within each
interval in the freq table at the correct height
(e.g. used values of 25, 35, 45 etc on age axis)

correct cf graph 2 A1 accept curve or line segments

accept curve that is not joined to (20,0)

(d) E.g. reading from graph at t = 65 M1 for evidence of using graph at t = 65

or reading of 82 – 84
or mark on cf axis from using t = 65 ft from a cumulative frequency graph provided
method is shown

6–8 2 A1 dep on a cf graph in part (c)

ft from a cumulative frequency graph provided
method is shown
Total 7 marks
12 (a) 4.51104 1 B1 cao
(b) 780000 M1 for 3250000000 oe (e.g. 325 ×
0.00024 107) or
3.25 × 105 - -4 oe or
3.25 10n where n is an integer

3.25 109 2 A1
Total 3 marks
13 (a) 8 12 d 8 M1 for a correct scale factor or
E.g. ( 0.66...) or (=1.5) or  oe a correct equation (may be in ratio
12 8 9 12
or form e.g. 12 : 8 = 9 : d)
9 12 accept 0.66… or 1.33… rounded
( 0.75) or ( 1.33...) or truncated to 2 or more decimal
12 9
places
6 2 A1
(b) 3 M1 for a correct scale factor
 12  V 12
160    oe or 3  3
8 160 8  12 
  ( 3.375) or
8
3
8
  ( 0.296...)
 12 
540 2 A1
(c) 3
M1 q p  p
for or or   or

p q  q
3
 q
 
 p  oe
 
3 2 3 3
 q A1  q  q 2
w    oe for w    oe e.g. w   
 p   p
 p
Total 6 marks
14 (a) x4 1 B1
(b) 6 + 4y = 3(5  2y) M1 for removing fraction

6 + 4y = 15  6y M1 for correct expansion of bracket in a

correct equation

4y + 6y = 15  6 or 10y = 9 M1 for a correct equation with y terms

isolated on one side

ft their equation if first M1 awarded

9 4 A1 dep on at least M2
oe
10
SC: B2 for an answer of
y = 1.5 oe with working shown or
y = −0.1oe with working shown
Alternative scheme
6 4y M1 for dividing both terms on LHS by 3
  5 2y
3 3 allow 1.3(3…)
4y 6 M1 for a correct equation with y terms
 2y  5  isolated on one side
3 3
allow 1.3(3…)
10 y M1 for y terms collated
3 allow 3.3(3…)
3
9 4 A1 dep on at least M2
oe
10
14 (c) g  gh = 3h + 1 or −1 – 3h = gh − g M1 for a correct equation with terms in g
isolated on one side of the equation

g(1  h) = 3h + 1 or −1 – 3h = g(h – 1) M1 for taking g out as a common factor

(must be two terms in g but terms may
not be correct (terms in g may not be
isolated))

3h  1 3 A1 3h  1 1  3h
g oe for g  oe e.g. g 
(1  h) (1  h) (h  1)
Total 8 marks

15 P  kr 3 M1 Allow mP = r³
Do not allow P = r³

343  k  3.53 oe or k = 8 or M1 for correct substitution into a correct

m × 343 = 3.53 oe or m = 0.125 oe equation.
Implies first M1

P = 8r³ 3 A1 for P = 8r³ oe (P must be the subject)

(Award M2A0 for correct equation with r as

subject given as final answer)

Award M2A1 if P = kr³ on the answer line

and k evaluated as 8
Award M2A0 if P  8r3 is given as final
answer
Total 3 marks
16 E.g. M1 for rational terms correct ( 5 2  3 2  e² )
5 2  3 2 + 5e 2  3e 2  e² or or
30 + 2e 2  e² irrational terms correct (5e 2  3e 2 )

NB: 5 2  3 2 may be fully or partially

simplified

5 2  3 2  e² = −6 oe or M1 dep on M1
rational terms correct and e = 6 or

5 2 e3 2e= 2 f oe or
5e  3e = f oe
e=6 3 A1
f = 12
Total 3 marks
17 (a)(i) a + b oe B1
1
(a)(ii) a + 0.5b 1 B1 for a + 0.5b oe
ft from (i)
(a)(iii) 0.5a + 0.5b 1 B1 for 0.5a + 0.5b oe
(may not be simplified)
ft from (i)
(b)  4  6 M1
PX  1.5        or (7, 3) seen as coordinates for R
 2  3

⃗⃗⃗⃗⃗  4   5   6   5  1
𝑃𝑉 = 1.5   +   or   +   or   or
 2  4   3  4  7
(X) = (3 + 1.5 × 4, 1 + 1.5 × 2) or (3 + 6, 1 + 3) or (9,
 9
4) or OX   
 4

⃗⃗⃗⃗⃗ =   +   or  4
3 1 M1 dep
𝑂𝑉   or V ("9"5 , "4" + 4)
1  7  8
(4, 8) 3 A1 SC: If M0 then award
B1 for (4, y) or (x, 8)
Total 6 marks

18 (a) 1, 4, 5, 40 2 B2 for all four correct

(B1 for 2 or 3 correct)
(b)(i) 1 1 B1 ft from their Venn diagram
(b)(ii) 45 1 B1 ft from their Venn diagram
Total 4 marks
19 (a) 4 4 M1 for x(y  3) = 4 or y(x  3) = 4
x y
y 3 x 3
x(y  3) = 4 y(x  3) = 4

xy = 4 + 3x or xy = 4 + 3y or M1 (implies the first M1)

4 4
y 3  x 3 
x y
4  3x 3 A1 4  3x 4
oe for oe e.g.  3
x x x
19 (b) 4 a2 M1 for a correct expression for fg(a)
E.g.  fg(a)   a  2 or 4 =  3 or
3 a
a
4a
( 1)
a  2  3a
E.g. 4a = a 23a or M1 for a correct equation where the
fraction has been removed.
7a = a  2
1 3 A1 dep on M1
a oe Accept −0.333(333...) rounded or
3
truncated to at least 3SF

Condone the use of x rather than a

(b) Alternative scheme
4  3 1 M1 for use of f-1fg(a) = f-1(1)
E.g. g(a) = f-1(1) or g(a) = oe or
1
4  3 1 a  2 a2 NB. ft for “f-1”
= or 7 =
1 a a
E.g. 7a = a  2 M1 for a correct equation where the
fraction has been removed.
NB. ft for “f-1”
1 3 A1 dep on M1
a oe Accept −0.333(333...) rounded or
3
truncated to at least 3SF
Total 6 marks
20 4 3 8  96  4 M1
  =  oe or or
12 11 10  1320  55
4 3 6  72  4 3 2  24 
  =  and     oe
12 11 10  1320  12 11 10  1320 
4 3 6  216 
or 3       oe or
12 11 10  1320 
4 3 2  72 
3      or
12 11 10  1320 

4 3 8 M1 for a complete method

3   oe or
12 11 10

4 3 6 4 3 2
3    +   
 12 11 10 12 11 10 
288 3 A1 288 12
for oe e.g.
1320 1320 55
accept 0.218(1818...) or 21.8(18…)%
rounded or truncated to at least 3SF
SC : with replacement (maximum 2 marks)
4 4 8 128 2
M1 for   oe or oe e.g. or
12 12 12 1728 27
4 4 6 4 4 2
  and   oe or
12 12 12 12 12 12
4 4 6 4 4 2
3   or 3   
12 12 12 12 12 12
384 2
A1 for oe e.g.
1728 9
Total 3 marks
21 B1 for identifying the correct angle on the diagram
(may be implied by a correct trig statement)
(MC=) 52  182 or 349 or 18.6(8154....) M1 for a correct method to find MC or VC
Accept 18.6(8154....) rounded or truncated to at
least 3sf.
(VC=) 5 2  7 2  18 2 or 398 or
Accept 19.9(4993..) rounded or truncated to at
19.9(499..)
least 3 sf

 7  M1 dep M1
VCM   tan 1   or for a complete method to find angle VCM (could
 349 
be use of sine or cosine rule)
 7 
VCM   sin 1   or
 398   349 
e.g. 90 − tan 1  
 349   7 
VCM   cos1  
 398 
20.5 4 A1 accept 20.5 − 20.62
Total 4 marks
22 E.g. M1 x² 2x 48 correctly factorised
3 x  15 3 x  15 NB : May be seen at a later stage
 or 
2( x  6) ( x  8)( x  6) 2 x  12 ( x  8)( x  6)

3( x  8)  2( x  15) M1 for a correct common denominator with

E.g. or
2( x  8)( x  6) numerators correct
3( x  8) 2( x  15)
 This may be a single fraction or two fractions;
2( x  8)( x  6) 2( x  8)( x  6) denominators may be expanded – if so, must
be correct.

3x  24  2 x  30 M1 for a correct single fraction with brackets in

2( x  8)( x  6) numerator removed correctly; denominators
may be expanded – if so, must be correct.

x6 M1 for a correct single fraction with the numerator

2( x  8)( x  6) simplified; denominators may expanded – if
so, must be correct.

1 5 A1 dep on at least M2
2( x  8) 1 1 1 1
for or or or
2( x  8) 2 x  16 16  2x 2(8  x)
Total 5 marks
Alternative scheme
22 E.g. M1 x² 2x 48 correctly factorised
3 x  15 3 x  15 NB : May be seen at a later stage
 or 
2( x  6) ( x  8)( x  6) 2 x  12 ( x  8)( x  6)

3( x 2  2 x  48)  (2 x  12)( x  15) M1 for a correct common denominator with

(2 x  12)( x 2  2 x  48) numerators correct

This may be a single fraction or two fractions;

denominators may be expanded – if so, must
be correct.

3x 2  6 x  144  2 x 2  30 x  12 x  180 M1 for a correct single fraction with brackets in

E.g. or numerator removed correctly; denominators
(2 x  12)( x 2  2 x  48)
may be expanded – if so, must be correct (2x3
x 2  12 x  36 + 8x2 – 120x – 576 )
(2 x  12)( x 2  2 x  48)
( x  6) 2 x6 M1 for a correct single fraction with the numerator
E.g. or factorised; denominators may expanded – if so,
(2 x  12)( x  2 x  48)
2
2( x  8)( x  6)
must be correct.

1 5 A1 dep on at least M2
2( x  8) 1 1 1 1
for or or or
2( x  8) 2 x  16 16  2x 2(8  x)
Total 5 marks
Pearson Education Limited. Registered company number 872828
with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
Write your name here
Surname Other names

Centre Number Candidate Number

Pearson Edexcel
International GCSE

Mathematics A
Paper 3HR

Higher Tier
Thursday 25 May 2017 – Morning Paper Reference

Time: 2 hours 4MA0/3HR

You must have: Total Marks
Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser, calculator. Tracing paper may be used.

Instructions
• Use black ink or ball-point pen.
• centre
Fill in the boxes at the top of this page with your name,
number and candidate number.
• Answer all questions.
• Without sufficient working, correct answers may be awarded no marks.
• Answer the questions in the spaces provided
– there may be more space than you need.
• Calculators may be used.
• You must NOT write anything on the formulae page.
Anything you write on the formulae page will gain NO credit.

Information
• The total mark for this paper is 100.
• The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.

Advice
• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end.

Turn over

1/1/1/
*P48488A0124*
International GCSE MATHEMATICS
FORMULAE SHEET – HIGHER TIER

DO NOT WRITE IN THIS AREA

Pythagoras’ Volume of cone = 1
r 2h Volume of sphere = 4
r3
3 3
Theorem
c Curved surface area of cone = rl Surface area of sphere = 4 r 2
b
r
a l
h
a + b2 = c2
2
r

adj = hyp cos

hyp opp = hyp sin
opp opp = adj tan In any triangle ABC
C
adj opp
or sin b a
hyp

DO NOT WRITE IN THIS AREA

adj A B
cos c
hyp

opp a b c
tan Sine rule:
adj sin A sin B sin C

Cosine rule: a2 b2 + c 2 2bc cos A

1
Area of triangle 2 ab sin C
cross
section
h
lengt
Volume of prism = area of cross section length

Area of a trapezium = 12 (a + b)h

r Circumference of circle = 2 r a
DO NOT WRITE IN THIS AREA

Area of circle = r 2 h

r
The Quadratic Equation
Volume of cylinder = r h 2 The solutions of ax2 + bx + c 0,
h where a 0, are given by
Curved surface area
of cylinder = 2 rh b + b2 4ac
x
2a

2
*P48488A0224*
Answer ALL TWENTY ONE questions.

Write your answers in the spaces provided.

DO NOT WRITE IN THIS AREA

You must write down all the stages in your working.

1 a=6 b = 2.84 c= 5
a−b
Work out the value of
c2
DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 1 is 2 marks)

2 Solve 5x – 8 = x – 10
Show clear algebraic working.
DO NOT WRITE IN THIS AREA

x = .......................................................

(Total for Question 2 is 3 marks)

3
*P48488A0324* Turn over
3 A B
Diagram NOT
accurately drawn

DO NOT WRITE IN THIS AREA

142°
62°

D C E
x°

ABCD is a parallelogram.
BEFC is a rhombus.
Angle DAB = 142°
Angle CBE = 62°
Calculate the value of x.

DO NOT WRITE IN THIS AREA

x = .......................................................
DO NOT WRITE IN THIS AREA

(Total for Question 3 is 3 marks)

4
*P48488A0424*
4 The currency in Bangladesh is the taka.
1 pound (£) = 119 taka
DO NOT WRITE IN THIS AREA

(a) Change 3500 taka to pounds.

Give your answer correct to 2 decimal places.

£. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
The currency in Thailand is the baht.
1 pound (£) = 52 baht
(b) Change 8500 baht to taka.
DO NOT WRITE IN THIS AREA

Give your answer correct to the nearest whole number.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . taka
(3)
An aeroplane takes 2 hours and 24 minutes to fly from Bangkok to Dhaka.
The aeroplane flies a distance of 1534 km.
(c) Work out the average speed of the aeroplane.
Give your answer in kilometres per hour correct to 3 significant figures.
DO NOT WRITE IN THIS AREA

....................................................... kilometres per hour

(3)

(Total for Question 4 is 8 marks)

5
*P48488A0524* Turn over
5 There is a World Peace Bell in South Korea.
At its widest, the bell has a circular cross section with a diameter of 2.5 m.

DO NOT WRITE IN THIS AREA

(a) Work out the circumference of a circle with diameter 2.5 m.
Give your answer correct to 3 significant figures.

....................................................... m
(2)
The World Peace Bell in South Korea has a height of 4.7 m.
At its widest, the bell has a circular cross section with a diameter of 2.5 m.
A scale model is made of the bell.
At its widest, the scale model has a circular cross section with a diameter 10 cm.

DO NOT WRITE IN THIS AREA

(b) Work out the height of the scale model.
Give your answer in centimetres.

....................................................... cm
(2)
DO NOT WRITE IN THIS AREA

(Total for Question 5 is 4 marks)

6
*P48488A0624*
6 Ahmed, Beth and Cleo are three friends.
The mean age, in years, of Ahmed, Beth and Cleo is 21
DO NOT WRITE IN THIS AREA

The mean age, in years, of Ahmed and Beth is 19

(a) Work out Cleo’s age.

....................................................... years
(3)
DO NOT WRITE IN THIS AREA

Ahmed is the youngest of the three friends.

The median age, in years, of the three friends is 20
(b) Find the range of their ages.
DO NOT WRITE IN THIS AREA

....................................................... years
(3)

(Total for Question 6 is 6 marks)

7
*P48488A0724* Turn over
7 Write 336 as a product of its prime factors.
Show your working clearly.

DO NOT WRITE IN THIS AREA

.......................................................

DO NOT WRITE IN THIS AREA

(Total for Question 7 is 3 marks)

8
y
6
5
4
3
2 T
1

–5 –4 –3 –2 –1 O 1 2 3 4 5 x
–1
–2
DO NOT WRITE IN THIS AREA

–3
–4
–5
–6

(a) On the grid above, rotate triangle T 90° clockwise about (0, 2).
(2)

8
*P48488A0824*
y
5
DO NOT WRITE IN THIS AREA

4
3
2 S
1

–5 –4 –3 –2 –1 O 1 2 3 4 5 x
–1
–2
–3
–4
–5
DO NOT WRITE IN THIS AREA

⎛ −1⎞
(b) On the grid, translate shape S by the vector ⎜ ⎟ .
⎝ −3⎠ (1)

(Total for Question 8 is 3 marks)

9 (a) Simplify 2e2 f × 5e3 f

.......................................................

(2)
(b) Factorise x2 – 5x – 6
DO NOT WRITE IN THIS AREA

.......................................................

(2)

(Total for Question 9 is 4 marks)

9
*P48488A0924* Turn over
10 The price of 1 kg of silver on 1st January 2010 was $607
By 1st January 2015, the price of 1 kg of silver had decreased by 9.4%

DO NOT WRITE IN THIS AREA

(a) Work out the price of 1 kg of silver on 1st January 2015.
Give your answer correct to the nearest dollar ($).

DO NOT WRITE IN THIS AREA

$. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
Between 1st January 2010 and 1st January 2015, the price of 1 tonne of copper decreased
by 20%
This was a decrease of $1320
(b) Work out the price of 1 tonne of copper on 1st January 2010.

DO NOT WRITE IN THIS AREA

$. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)

(Total for Question 10 is 6 marks)

10
*P48488A01024*
11 There are 9 red counters and 11 blue counters in a bag.
There are no other counters in the bag.
DO NOT WRITE IN THIS AREA

Emeka takes at random a counter from the bag and writes down the colour of the counter.
He puts the counter back in the bag.
Natasha takes at random a counter from the bag and writes down the colour of the counter.
(a) Complete the probability tree diagram.

Emeka Natasha

red
9
20
DO NOT WRITE IN THIS AREA

..............

blue

(2)
(b) Work out the probability that Emeka takes a red counter from the bag and Natasha
takes a blue counter from the bag.

.......................................................

(2)
DO NOT WRITE IN THIS AREA

.......................................................

(3)

(Total for Question 11 is 7 marks)

11
*P48488A01124* Turn over
12 The table gives information about the number of males in each age group in a survey of
100 males working in Singapore in 2014.

DO NOT WRITE IN THIS AREA

Age (A years) Frequency
15 -A 20 2
20 -A 25 7
25 -A 30 9
30 -A 35 10
35 -A 40 11
40 -A 45 12
45 -A 50 12
50 -A 55 12
55 -A 60 11
60 -A 65 14

DO NOT WRITE IN THIS AREA

(a) Complete the cumulative frequency table.

Age (A years) Cumulative frequency

15 -A 20
15 -A 25
15 -A 30
15 -A 35
15 -A 40
15 -A 45
15 -A 50
15 -A 55
15 -A 60
DO NOT WRITE IN THIS AREA

15 -A 65
(1)
(b) On the grid, draw a cumulative frequency graph for your table.
(2)
(c) Use your graph to find an estimate for the lower quartile.

....................................................... years
(2)

12
*P48488A01224*
DO NOT WRITE IN THIS AREA

100

60
Cumulative
frequency 50

20
DO NOT WRITE IN THIS AREA

0
15 20 25 30 35 40 45 50 55 60 65 70
Age (years)

The total number of males aged under 65 working in Singapore in 2014 was 1 200 000

Using this information and your graph,

(d) work out an estimate for the number of males working in Singapore in 2014 who
were less than 52 years old.
DO NOT WRITE IN THIS AREA

.......................................................

(3)

(Total for Question 12 is 8 marks)

13
*P48488A01324* Turn over
13 On the grid, show by shading the region defined by the inequalities
y5 and y 2x + 1 and x + y

DO NOT WRITE IN THIS AREA

Label your region R.

y
12

DO NOT WRITE IN THIS AREA

O 1 2 3 4 5 6 7 8 9 10 11 12 x

(Total for Question 13 is 3 marks) DO NOT WRITE IN THIS AREA

14
*P48488A01424*
14 ABCDE is a regular pentagon with sides of length 10 cm.

A Diagram NOT
DO NOT WRITE IN THIS AREA

accurately drawn

E B

D 10 cm C

Calculate the area of triangle ACD.

Give your answer correct to 3 significant figures.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

....................................................... cm2

(Total for Question 14 is 6 marks)

15
*P48488A01524* Turn over
15 For the curve C with equation
y = 2x3 – 3x2 – 12x + 9

DO NOT WRITE IN THIS AREA

dy
(a) find
dx

.......................................................

(2)
(b) Find the gradient of CDWWKHSRLQWZLWKFRRUGLQDWHV í

DO NOT WRITE IN THIS AREA

.......................................................

(2)
The curve C has a gradient of –12 at the point where x = k and at the point where x = m.
Given that k m
(c) find the value of k and the value of m.

DO NOT WRITE IN THIS AREA

k = .......................................................

m = .......................................................
(3)

(Total for Question 15 is 7 marks)

16
*P48488A01624*
ax + b
16 Make x the subject of the formula y=
cx + d
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 16 is 4 marks)

DO NOT WRITE IN THIS AREA

17
*P48488A01724* Turn over
17
Y Diagram NOT
6 cm accurately drawn

DO NOT WRITE IN THIS AREA

X
12 cm

C A
B 9 cm

The points B, C, Y and X lie on a circle.

AXY and ABC are straight lines.
AX = 12 cm XY = 6 cm AB = 9 cm
Calculate the length of BC.

DO NOT WRITE IN THIS AREA

....................................................... cm
DO NOT WRITE IN THIS AREA

(Total for Question 17 is 3 marks)

18
*P48488A01824*
18 Solve the simultaneous equations
y2 + 4x = 12
DO NOT WRITE IN THIS AREA

2x + 3y = 10
Show clear algebraic working.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 18 is 6 marks)

19
*P48488A01924* Turn over
19 The diagram shows two solid shapes, shape A and shape B.
Shape A is made of a hemisphere and a cone.
Shape B is a cylinder.

DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn

36 cm

r cm

2r cm
53 cm

A B

DO NOT WRITE IN THIS AREA

For shape A
radius of the hemisphere is 36 cm
radius of the base of the cone is 36 cm
height of the cone is 53 cm
For shape B
radius of the cylinder is r cm
height of the cylinder is 2r cm
The volume of shape A = the volume of shape B
Calculate the height of shape B.

DO NOT WRITE IN THIS AREA

20
*P48488A02024*
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

....................................................... cm

(Total for Question 19 is 6 marks)

DO NOT WRITE IN THIS AREA

21
*P48488A02124* Turn over
20 k = 2p – 1 where p is an integer 1
N = k2 – 1

DO NOT WRITE IN THIS AREA

Show that 2p + 1 is a factor of N

DO NOT WRITE IN THIS AREA

(Total for Question 20 is 3 marks)

DO NOT WRITE IN THIS AREA

22
*P48488A02224*
21 Here is a shape ABCDE.
B
DO NOT WRITE IN THIS AREA

A
(x – 3) cm

120° C Diagram NOT

accurately drawn
(x – 2) cm

E D

ABDE is a rectangle in which AB = 2BD

BCD is a triangle in which angle BCD = 120°
BC = (xí FP CD = (xí FP
The area of the rectangle ABDE is S cm2
Show that S can be expressed in the form S = ax2 + bx + c
where a, b and c are integers to be found.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

S = .......................................................

(Total for Question 21 is 5 marks)

TOTAL FOR PAPER IS 100 MARKS

23
*P48488A02324*
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

*P48488A02424*
Do NOT write on this page
BLANK PAGE

24
Mark Scheme (Results)

Summer 2017

Pearson Edexcel International GCSE

In Mathematics A (4MA0) Paper 3HR
Edexcel and BTEC Qualifications

Pearson: helping people progress, everywhere

Summer 2017
Publications Code 4MA0_3HR_1706_MS
All the material in this publication is copyright
© Pearson Education Ltd 2017
General Marking Guidance
 All candidates must receive the same treatment. Examiners
must mark the first candidate in exactly the same way as they
mark the last.
 Mark schemes should be applied positively. Candidates must
be rewarded for what they have shown they can do rather
than penalised for omissions.
 Examiners should mark according to the mark scheme not
according to their perception of where the grade boundaries
may lie.
 There is no ceiling on achievement. All marks on the mark
scheme should be used appropriately.
 All the marks on the mark scheme are designed to be
awarded. Examiners should always award full marks if
deserved, i.e. if the answer matches the mark scheme.
Examiners should also be prepared to award zero marks if the
candidate’s response is not worthy of credit according to the
mark scheme.
 Where some judgement is required, mark schemes will
provide the principles by which marks will be awarded and
exemplification may be limited.
 When examiners are in doubt regarding the application of the
mark scheme to a candidate’s response, the team leader must
be consulted.
 Crossed out work should be marked UNLESS the candidate
has replaced it with an alternative response.
 Types of mark
o M marks: method marks
o A marks: accuracy marks
o B marks: unconditional accuracy marks (independent of
M marks)
 Abbreviations
o cao – correct answer only
o ft – follow through
o isw – ignore subsequent working
o SC - special case
o oe – or equivalent (and appropriate)
o dep – dependent
o indep – independent
o eeoo – each error or omission
 No working
If no working is shown then correct answers normally score
full marks
If no working is shown then incorrect (even though nearly
correct) answers score no marks.
 With working
If there is a wrong answer indicated on the answer line always
check the working in the body of the script (and on any
diagrams), and award any marks appropriate from the mark
scheme.
If it is clear from the working that the “correct” answer has
been obtained from incorrect working, award 0 marks.
Any case of suspected misread loses A (and B) marks on that
part, but can gain the M marks.
If working is crossed out and still legible, then it should be
given any appropriate marks, as long as it has not been
replaced by alternative work.
If there is a choice of methods shown, then no marks should
be awarded, unless the answer on the answer line makes
clear the method that has been used.
If there is no answer on the answer line then check the
working for an obvious answer.
 Ignoring subsequent work
It is appropriate to ignore subsequent work when the
additional work does not change the answer in a way that is
inappropriate for the question: eg. Incorrect cancelling of a
fraction that would otherwise be correct.
It is not appropriate to ignore subsequent work when the
additional work essentially makes the answer incorrect eg
algebra.
Transcription errors occur when candidates present a correct
answer in working, and write it incorrectly on the answer line;
mark the correct answer.
 Parts of questions
Unless allowed by the mark scheme, the marks allocated to
one part of the question CANNOT be awarded in another.
Apart from questions 2, 7 and 18 (where the mark scheme states otherwise) the correct answer, unless clearly obtained by an
incorrect method, should be taken to imply a correct method

Ques Working Answer Mark Notes

1 6  2.84 6  2.84 M1 or for 0.63
or oe
( 5) 2
5 NB: Accept 2.23(6…) in place of 5
0.632 2 A1 79
for 0.632 or
125
SC : B1 for an answer of 1.41(31…)
Total 2 marks

2 5x – x = 8 – 10 M1 for correct rearrangement with x terms on one side and

numbers on the other in a correct equation or
the correct simplification of either x terms or numbers on
one side in a correct equation
eg. 4x − 8 = −10 ; 5x = x – 2

4x = −2 M1 or –4x = 2 or 4x + 2 = 0 or −4x – 2 = 0
NB: This mark implies the previous M1
−0.5 3 A1 2
oe e.g.  dep on M1
4
Total 3 marks

3 Angle BCD = 142o or M1 for angle BCD = 142o or

Angle BCF = 180 − 62 (=118o) or angle BCF = (180 − 62) o
Angle ABC = 180 – 142 (=38)
360 – 142 – “118” or “38” + 62 M1 for a complete method to find x
100 3 A1
Total 3 marks
4a 3500 ÷ 119 M1
29.41 2 A1 for 29.41 – 29.412

b 8500 ÷ 52 or 163(.461..) M1 M1 for 8500 × 119 =1011500 M1 for 119 ÷ 52 (=2.28…)

“163.461.”.× 119 M1 dep M1 for “1011500” ÷ 52 M1 for 8500 × “2.28…”

19452 3 A1 for 19380 − 19520

c 24 M1
24 ÷ 60 (=0.4) or 2.4 or 2 oe or
60
2 × 60 + 24 (=144)

1534 ÷ 2.4 oe or M1 (allow 1534 ÷ 2.24 or answer of 684(.82…) or 685)

(1534 ÷ 144) × 60 oe
639 3 A1 for 639 – 639.17
Total 8 marks

5a  2.5  M1
π × 2.5 oe or 2 × π ×  
 2 
7.85 2 A1 7.85 – 7.86

b 4.7 470 M1 or for digits 188

10  oe or 10  oe
2.5 250
18.8 2 A1 accept 19 if 18.8 seen
Total 4 marks
6a abc ab M1
 21 or  19 or
3 2
3 × 21(=63) or 2 × 19(=38)
3 × 21 − 2 × 19 M1 for a complete method
25 3 A1
b 2 ×19 − 20 (=18) or M1 ft from (a) for a complete method to find age of 3rd person
21×3 – 20 – “25” (=18)

“25” – “18” M1 dep

or for 18 – 25
7 3 A1 ft from answer in (a)
Total 6 marks

7 e.g. 2 × 2 × 7 × 12 or M1 for the start of a correct method

at least 3 divisions in a factor tree e.g. may be a factor tree or consecutive divisions
condone 1 error
All 6 correct prime factors, no extras M1 e.g. from a factor tree, ignore 1s
(2,2,2,2,3,7,(1))
2×2×2×2×3×7 3 A1 oe dep on M1, M1
Total 3 marks

8a Correct triangle 2 B2
(−1, −2) (−1, 0) (2, −2) (B1 for a rotation of 90o clockwise about a different centre
i.e. a triangle in the same orientation as the correct triangle
or
rotation by 90o anticlockwise about (0, 2))
b Correct trapezium 1 B1
(1, −1) (1, −2) (3, 1) (3, −2)
Total 3 marks
9a 10e5 f 2 2 B2 If not B2 then award B1 for
ke5 f 2 , k  10 or 10e5 f a or 10eb f 2 a, b ≠ 0

b (x − 6)(x + 1) 2 B2 If not B2 then award B1 for

(x – 1)(x + 6) or
(x – 3)(x – 2) or (x + 3)(x – 2) or (x – 3)(x + 2)
Total 4 marks

10a 100 − 9.4 (= 90.6) 9.4 M1

 607 oe ( 57.058)
100
"90.6" 607 – “57.058” M1 (dep)
 607 oe
100
550 3 A1 for 549.942 or 549.94 or 549.9

b 100 M2 for a complete method

 1320 oe
20
If not M2 then award M1 for a correct first step

1320 ÷ 20 (=66) or 0.2x = 1320 or

1320 ÷ 2 (=660)

6600 3 A1
Total 6 marks
11a Complete correct binary M1
structure for selection of two
counters
OR
At least one additional red
9
branch labelled and at least
20
two blue branches labelled
11
20
Correct 2 A1
probability tree
diagram
b 9 11 M1 9 11
 for ' '' '
20 20 20 20
99 2 A1 99
(ft diagram) for or 0.2475 or 24.75%
400 400

c 9 9 11 11 M1 for one correct product 9 11

' '' ' or ' '' ' ft from diagram M1 for 2 × ' '' ' oe
20 20 20 20 20 20
(ft from (a))

9 9 11 11 M1 for the complete method 9 11

' '' ' + ' '' ' ft from diagram M1 for 1 − 2 × ' '' '
20 20 20 20 20 20

202 3 A1 202
oe or 0.505 or 50.5%
400 400
Total 7 marks
12a 2, 9, 18, 28, 39, 51, 63, 75, 86, 100 Correct table 1 B1
b M1 (ft from sensible table i.e. clear attempt at addition)

for at least 8 points plotted correctly at end of interval

or
for all 10 points plotted consistently within each interval in the
freq table at the correct height

Correct cf graph 2 A1 accept curve or line segments

accept graph that is not joined to (0,15)

c E.g. for a mark drawn at 25 on their M1 for intention to use 25 on cf axis

cumulative frequency diagram
ft from a cumulative frequency graph provided method is shown
33 – 35 2 A1 33 - 35
ft from a cumulative frequency graph provided method is shown

d E.g. reading of 66 – 68 (%) M1 for a reading taken from 52 on age axis

or reading from graph at A = 52 ft from a cumulative frequency graph provided method is shown
or mark on cf axis from using A = 52

"68" M1 (dep)
1200(000)
100
792000 – 816000 3 A1 for answer in the range 792000 – 816000
Total 8marks

13 M1 for either y = 2x + 1 or x + y = 10 drawn correctly

M1 for all lines drawn correctly
Correct region 3 A1 for all 3 lines correct and the region identified
Lines may be full lines or broken lines
Total 3 marks
14 Scheme 1 (interior angle and angle ADC and an angle in triangle ADC) Let X be midpoint of DC

(5 - 2) × 180 M1 or for 108 seen as an interior angle

(Angle DEA =) = 108
5
Angle EDA or EAD = (180 – 108)÷2 = 36 M1

Angle ADC or ACD = 108 – 36 = 72 or M1 Angles may be seen on diagram

Angle DAC = 108 – 2 × 36 (=36) or
 "16.18"2  "16.18"2  102 
Angle DAC = cos 1  
 2  "16.18" "16.18" 
Angle DAX or CAX = (108 – 2 × 36) ÷ 2 (=18)

E.g. M1 10
AX = 5×tan72 (=15.38…) or AX = 5 ÷ tan18 (=15.38…) or or for AD   sin108 (=16.18…) or
sin 36
AX = 5×tanADC or AX = 5 ÷ tanDAX or 10
AD2 = 102 + 102 − 2×10×10cos108 (=261.8) or AD   sin 72
sin 36
AD = 102  102  2 10 10  cos108 (=16.18) or
10  sin 72 Allow 16 or 16.2 for AD throughout
AD = (=16.18)
sin 36
NB: Allow the value on the diagram for angle ADC
or DAX if used in an otherwise correct trig statement
1 M1 dep on previous M1
E.g. Area = × 10 × “15.38…” oe or
2
0.5 × 10 × “16.18” × sin72 or 0.5 × “16.18”×”16.18”×sin36 or NB: Allow the value on the diagram for angle ADC
0.5 × 10 × “16.18” × sinADC or 0.5 × “16.18”×”16.18”×sinDAX or DAX if used in an otherwise correct area statement
76.9 6 A1 for answer in the range 76.5 – 77

SC: B4 for an answer in the range 53 – 53.5

Total 6 marks
14 Scheme 2 (only interior angle needed) Let X be midpoint of DC

(5 - 2) × 180 M1 or for 108 seen as an interior angle

(Angle DEA =) = 108
5

AD2 =102 + 102 − 2×10×10cos108 (=261.8) or M1 Allow 16 or 16.2 for AD throughout

AD = 10  10  2 10 10  cos108 (=16.18)
2 2

AX2 = “261.8” − 52 (= 236.8) or M1

AX2 = “16.18”2 − 52 (= 236.8)

"236.8" (=15.38..) M1

0.5 × 10 × “15.38” M1
76.9 6 A1 for answer in the range 76.5 – 77

SC: B4 for an answer in the range 53 – 53.5

Total 6 marks

15a 3×2×x2 − 3×2x − 12 M1 for one of 3×2×x2 (=6x2) or −3×2x (=6x) or −12
6 x 2  6 x  12 2 A1
b 6 × 2 − 6 × 2 − 12
2
M1 substitute x = 2 in (a)
ft from answer to (a) (must be a quadratic expression)
0 2 A1
c 6 x  6 x  12  12
2 M1 ft from answer to (a) (must be a quadratic expression)

x=1 ,0 A1 for both correct solutions

1, 0 3 A1 for k = 1 and m = 0
Total 7 marks
16 cxy  dy  ax  b M1 both terms in original denominator multiplied by y

e.g. cxy  ax  b  dy or M1 for isolating terms in x and non x terms correctly

dy – b = ax – cxy ft from cxy + d = ax + b or cx + dy = ax + b

x(cy  a)  b  dy M1 for taking out a factor of x correctly provided there are

two terms in x
b  dy 4 A1 b  dy dy  b
x for x  oe e.g. x 
cy  a cy  a a  cy
Total 4 marks

17 12 × (12+ 6) = 9 × (9 + BC) oe or M1

12 × (12+ 6) = 9 × AC oe or

AC = 24

12  (12  6) M1 for a complete method

( BC )  9 oe or
9
24 – 9

15 3 A1
Total 3 marks
18 y 2  4 x  12 M1 for eliminating one variable
4 x  6 y  20 with subtraction or
multiplication of equation(s) to get same multiple of y
 10  2 x 
2
with subtraction (condone one arithmetic error) or
   4 x  12 or
 3 
either rearrangement of one equation and then correct
 12  y 2 
2   3 y  10 oe substitution into second equation (condone algebraic
 4  error in rearrangement)

E.g. y 2  6 y  8 or A1 reduction to a correct 3 term quadratic;

4x2 – 4x – 8 = 0 terms may not all be ‘on the same side’

E.g. (y − 2)(y − 4) (= 0) or M1 ft if first M1 awarded and equation is quadratic

4(x − 2)(x + 1) (=0) for correct factorisation or
correct substitution into formula

A1 for y = 2, y = 4 or x = 2, x = −1
correct x or y values implies previous M1

10  3  2 10  3  4 M1 (dep on the previous M1)

( x ) or for correct substitution to find both values
2 2
10  2  2 10  2  (1)
( y ) or
3 3
x = 2, y = 2 or 6 A1 values for x and y must be correctly paired
x = −1, y = 4 dep on M1 awarded
Total 6 marks
19  M1 for volume of cone
(Vc )  362  53 (=22896π = 71930)
3
2 M1 for volume of hemi-sphere
(VH )  363 (=31104π = 97716)
3
NB : 54000π or 169646 implies first two method marks

2  M1 (dep on at least M1)

  r 2  2r  "  363 " + "  362  53" oe for forming an equation with correct volume expression for
3 3
cylinder
"54000 " M1
r 3 = 30
2
2 × “30” M1 (dep previous M1)
60 6 A1
Total 6 marks

20 (2 p )2  2 p  2 p  1 or M2 for correct expansion

22 p  2 p  2 p  1 or If not M2 then award M1 for
4 p  2 p  2 p 1
3 terms correct from (2 p )2  2 p  2 p  1
N  2 p 1 (2 p 1  1) Shown A1 for correct factorised expression from correct working
(dep on M2)
Total 3 marks
Alternative method
N  (k  1)(k  1) M1 for correct factorisation

N  (2 p  1  1)(2 p  1  1) M1 for correct factorisation and substitution (implies B1)

N  2 p 1 (2 p 1  1) Shown 3 A1 for correct factorised expression (dep on M2)

21 (( BD)2 ) ( x  2)2  ( x  3)2  2( x  2)( x  3) cos(120) M1

( x  2)2  x2  2 x  2 x  4 oe M1 (independent)
correct expansion of (x – 2)2 or (x – 3)2
( x  3)2  x2  3x  3x  9 oe

x2  4 x  4  x2  6 x  9  x2  5x  6 (= 3x 2  15x  19 ) A1 correct quadratic for BD2 with all terms

expanded
may not be simplified
Area = 2BD2 oe or M1 (independent)
Area = 2 × (“ 3x 2  15x  19 ”)
6 x2  30 x  38 5 A1
Total 5 marks
8a 8b
y y
5 5

4 4

3 3

2 T 2 S

1 1

-5 -4 -3 -2 -1 0 1 2 3 4 5 x -5 -4 -3 -2 -1 0 1 2 3 4 5 x
-1 -1

-2 -2

-3 -3

-4 -4

-5 -5
12

Cumulative
percentage 100

15 20 25 30 35 40 45 50 55 60 65 70
Age (years)
13

y
12

6
R

0 2 4 6 8 10 12 x
Pearson Education Limited. Registered company number 872828
with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
Write your name here
Surname Other names

Centre Number Candidate Number

Pearson Edexcel Certificate
Pearson Edexcel
International GCSE

Mathematics A
Paper 4H

Higher Tier
Thursday 8 June 2017 – Morning Paper Reference
4MA0/4H
Time: 2 hours KMA0/4H

You must have: Total Marks

Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser, calculator. Tracing paper may be used.

Advice
• Check
Read each question carefully before you start to answer it.
• your answers if you have time at the end.
Turn over

1/1/1/
*P48490A0124*
International GCSE MATHEMATICS
FORMULAE SHEET – HIGHER TIER

DO NOT WRITE IN THIS AREA

Pythagoras’ Volume of cone = 1
r 2h Volume of sphere = 4
r3
3 3
Theorem
c Curved surface area of cone = rl Surface area of sphere = 4 r 2
b
r
a l
h
a + b2 = c2
2
r

adj = hyp cos

hyp opp = hyp sin
opp opp = adj tan In any triangle ABC
C
adj opp
or sin b a
hyp

DO NOT WRITE IN THIS AREA

adj A B
cos c
hyp

opp a b c
tan Sine rule:
adj sin A sin B sin C

Cosine rule: a2 b2 + c 2 2bc cos A

1
Area of triangle 2 ab sin C
cross
section
h
lengt
Volume of prism = area of cross section length

Area of a trapezium = 12 (a + b)h

r Circumference of circle = 2 r a
DO NOT WRITE IN THIS AREA

Area of circle = r 2 h

r
The Quadratic Equation
Volume of cylinder = r h 2 The solutions of ax2 + bx + c 0,
h where a 0, are given by
Curved surface area
of cylinder = 2 rh b + b2 4ac
x
2a

2
*P48490A0224*
Answer ALL TWENTY THREE questions.

Write your answers in the spaces provided.

DO NOT WRITE IN THIS AREA

You must write down all the stages in your working.

1 P = {p, o, r, t, u, g, a, l}
I = {i, t, a, l, y}
(a) List the members of the set
(i) P I

..................................................................................

(ii) P I

..................................................................................

(2)
F = {f, r, a, n, c, e}
DO NOT WRITE IN THIS AREA

(b) Is it true that I F = ?

Tick (9) the appropriate box.
Yes No

Explain your answer.

. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(Total for Question 1 is 3 marks)

DO NOT WRITE IN THIS AREA

3
*P48490A0324* Turn over
2 M = 2W࣠2 – 7t
(a) Work out the value of M when t í

DO NOT WRITE IN THIS AREA

M =. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(b) Solve 4(x x – 10
Show clear algebraic working.

DO NOT WRITE IN THIS AREA

x =. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
y is an integer.
í y -
(c) Write down all the possible values of y. DO NOT WRITE IN THIS AREA

..................................................................................

(2)

(Total for Question 2 is 7 marks)

4
*P48490A0424*
3 Lyn went on holiday to India.
She changed £250 into rupees.
DO NOT WRITE IN THIS AREA

7KHH[FKDQJHUDWHZDV UXSHHV
(a) How many rupees did Lyn get?

............................ rupees
(2)
When she returns from holiday, Lyn has four 500 rupee notes.
She changes this money into pounds.
7KHH[FKDQJHUDWHLVQRZ UXSHHV
(b) Work out how many pounds Lyn gets.
Give your answer to the nearest pound.
DO NOT WRITE IN THIS AREA

£ ............................
(3)

(Total for Question 3 is 5 marks)

4 Point AKDVFRRUGLQDWHV í

Point B has coordinates (1, 5)
DO NOT WRITE IN THIS AREA

Find the coordinates of the midpoint of AB.

( ............................ , ............................ )

(Total for Question 4 is 2 marks)

5
*P48490A0524* Turn over
5 Each time Astrid plays a game of chess against her computer, she will win or draw or lose.
For each game of chess

DO NOT WRITE IN THIS AREA

WKHSUREDELOLW\WKDWVKHZLOOZLQLV
the probability that she will lose is three times the probability that she will draw.
On Monday, Astrid is going to play 20 games of chess against her computer.
(a) Work out an estimate for the number of games of chess Astrid wins on Monday.

.........................................

(2)
On Tuesday, Astrid plays a game of chess against her computer.
(b) Work out the probability that she will lose.

DO NOT WRITE IN THIS AREA

.........................................

(3)

(Total for Question 5 is 5 marks)

6 There are 6 batteries in a small packet of batteries.

7KHUHDUHEDWWHULHVLQDODUJHSDFNHWRIEDWWHULHV DO NOT WRITE IN THIS AREA

Chow buys m small packets of batteries and g large packets of batteries.

The total number of batteries Chow buys is T.
Write down a formula, in terms of m and g, for T.

..................................................................................

(Total for Question 6 is 3 marks)

6
*P48490A0624*
7 3 23
7 (a) Show that + =
12 8 24
DO NOT WRITE IN THIS AREA

(2)
2 1 4
(b) Show that 1 × 2
3 15 9
DO NOT WRITE IN THIS AREA

(3)
DO NOT WRITE IN THIS AREA

(Total for Question 7 is 5 marks)

7
*P48490A0724* Turn over
8 Each interior angle of a regular polygon is 156°
Work out the number of sides of the polygon.

DO NOT WRITE IN THIS AREA

......................................................

(Total for Question 8 is 3 marks)

9 0DQX/LDPDQG1HGVKDUH LQWKHUDWLRV
Liam then gives Ned £75

DO NOT WRITE IN THIS AREA

Express the amount of money that Ned now has as a percentage of the £420
Give your answer correct to the nearest whole number.

DO NOT WRITE IN THIS AREA

......................................... %

(Total for Question 9 is 4 marks)

8
*P48490A0824*
10 (a) Simplify H࣠8 × H࣠7
DO NOT WRITE IN THIS AREA

.........................................

(1)
12 g 10
(b) Simplify fully
3g 2

.........................................

(2)
(c) Write down the value of P࣠0
DO NOT WRITE IN THIS AREA

.........................................

(1)
2
(d) Simplify fully ( 27 x )
6 3

.........................................

(2)

(Total for Question 10 is 6 marks)

DO NOT WRITE IN THIS AREA

9
*P48490A0924* Turn over
11
A

DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn

7 cm

D B

C
A, B, C and D are points on a circle.
ABCD is a square of side 7 cm.

DO NOT WRITE IN THIS AREA

Work out the total area of the shaded regions.
Give your answer correct to the nearest whole number.

DO NOT WRITE IN THIS AREA

......................................... cm2

(Total for Question 11 is 5 marks)

10
*P48490A01024*
12 Here are the heights, in millimetres, of 11 seedlings.
DO NOT WRITE IN THIS AREA

Work out the interquartile range of these heights.

DO NOT WRITE IN THIS AREA

......................................... mm

(Total for Question 12 is 3 marks)

DO NOT WRITE IN THIS AREA

11
*P48490A01124* Turn over
13 Here are the equations of four straight lines.
Line A y ௘x

DO NOT WRITE IN THIS AREA

Line B ௘y íx
Line C ௘xí௘y
Line D y í௘x
Two of these lines are parallel.
(a) Which two lines?

DO NOT WRITE IN THIS AREA

....................................................................

(2)
5
Line LKDVDJUDGLHQWRIí DQGSDVVHVWKURXJKWKHSRLQWZLWKFRRUGLQDWHV
2
(b) Find an equation of L.
Give your answer in the form D࣠[ + E࣠\ = c where a, b and c are integers.

DO NOT WRITE IN THIS AREA

.......................................................

(3)

(Total for Question 13 is 5 marks)

12
*P48490A01224*
14
C
DO NOT WRITE IN THIS AREA

Diagram NOT
B
accurately drawn

52°

A, B, C and D are points on a circle, centre O.

Angle ABD = 52°
(a) (i) Write down the size of angle ACD.
DO NOT WRITE IN THIS AREA

°
.........................................

(ii) Give a reason for your answer.

. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)
(b) (i) Write down the size of angle AOD.

°
.........................................

(ii) Give a reason for your answer.

. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA

. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(Total for Question 14 is 4 marks)

13
*P48490A01324* Turn over
15 Here is a trapezium.

(2xí

DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn
(x

(x + 5)
All measurements are in centimetres.
The area of the trapezium is 60 cm2
D 6KRZWKDW x௘2௘xí

DO NOT WRITE IN THIS AREA

(3)
(b) Work out the value of x
Show your working clearly.
*LYH\RXUDQVZHUFRUUHFWWRVLJQLILFDQWILJXUHV

DO NOT WRITE IN THIS AREA

.......................................................

(3)

(Total for Question 15 is 6 marks)

14
*P48490A01424*
16 The probability that it will rain on Saturday is 0.8
If it rains on Saturday, the probability that it will rain on Sunday is 0.65
DO NOT WRITE IN THIS AREA

If it does not rain on Saturday, the probability that it will rain on Sunday is 0.4
(a) Use this information to complete the probability tree diagram.

Saturday Sunday

rain
....................

rain
0.8
....................

does not rain

DO NOT WRITE IN THIS AREA

rain
....................

....................

does not rain

....................

does not rain

(2)
(b) Work out the probability that it will rain on just one of these two days.
DO NOT WRITE IN THIS AREA

.......................................................

(3)

(Total for Question 16 is 5 marks)

15
*P48490A01524* Turn over
17 Curve C has equation y ௘x௘±௘x௘2 – 25x

dy
(a) Find

DO NOT WRITE IN THIS AREA

....................................................................

(2)
(b) Find the x coordinates of the points on C where the gradient is 5
Show clear algebraic working.

DO NOT WRITE IN THIS AREA

....................................................................

(4)

(Total for Question 17 is 6 marks)

16
*P48490A01624*
18 The table gives information about the times, in minutes, some people waited in the
accident and emergency department at a hospital.
DO NOT WRITE IN THIS AREA

Time (t minutes) Frequency

0 t - 60
t - 270
t - 120 150
120 t - 240 156
240 t - 24

On the grid, draw a histogram for this information.

DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

0
0 60 120 180 240
Time (minutes)

(Total for Question 18 is 3 marks)

17
*P48490A01724* Turn over
19 ABCD is a kite.
A

DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn
6.4 cm

D 110° B

C
Work out the area of the kite.

DO NOT WRITE IN THIS AREA

*LYH\RXUDQVZHUFRUUHFWWRVLJQLILFDQWILJXUHV

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . cm2

(Total for Question 19 is 3 marks) DO NOT WRITE IN THIS AREA

18
*P48490A01824*
20 $FDUWUDYHOVDGLVWDQFHRINPFRUUHFWWRWKHQHDUHVWNP
The car takes 45.8 minutes correct to 1 decimal place.
DO NOT WRITE IN THIS AREA

Work out the lower bound for the average speed of the car.
Show your working clearly.
Give your answer in km/h correct to 1 decimal place.
DO NOT WRITE IN THIS AREA

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . km/h

(Total for Question 20 is 4 marks)

DO NOT WRITE IN THIS AREA

19
*P48490A01924* Turn over
21 LMNP is a quadrilateral.

DO NOT WRITE IN THIS AREA

M FP
N Diagram NOT
58° accurately drawn
FP
72°
P

15.6 cm

L
Work out the size of angle MLP.
*LYH\RXUDQVZHUFRUUHFWWRVLJQLILFDQWILJXUHV

DO NOT WRITE IN THIS AREA

°
.......................................................

(Total for Question 21 is 6 marks)

20
*P48490A02024*
22 m = 8 × 10n where n is an integer.
1
−
Express m 3 in standard form.
DO NOT WRITE IN THIS AREA

Give your answer, in terms of n, as simply as possible.

.......................................................
DO NOT WRITE IN THIS AREA

(Total for Question 22 is 3 marks)

DO NOT WRITE IN THIS AREA

21
*P48490A02124* Turn over
23 The diagram shows a solid hemisphere.

Diagram NOT

DO NOT WRITE IN THIS AREA

accurately drawn

16
The hemisphere has a total surface area of ʌ cm2
3
The hemisphere has a volume of N࣠ʌ cm
Find the value of k.

DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 23 is 4 marks)

TOTAL FOR PAPER IS 100 MARKS

22
*P48490A02224*
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

BLANK PAGE

Do NOT write on this page

*P48490A02324*
23
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

*P48490A02424*
Do NOT write on this page
BLANK PAGE

24
Mark Scheme (Results)

Summer 2017

Pearson Edexcel International GCSE

In Mathematics (4MA0) Paper 4H
Edexcel and BTEC Qualifications

Pearson: helping people progress, everywhere

Summer 2017
Publications Code 4MA0_4H_1706_MS
All the material in this publication is copyright
© Pearson Education Ltd 2017
General Marking Guidance
 All candidates must receive the same treatment. Examiners
must mark the first candidate in exactly the same way as they
mark the last.
 Mark schemes should be applied positively. Candidates must
be rewarded for what they have shown they can do rather
than penalised for omissions.
 Examiners should mark according to the mark scheme not
according to their perception of where the grade boundaries
may lie.
 There is no ceiling on achievement. All marks on the mark
scheme should be used appropriately.
 All the marks on the mark scheme are designed to be
awarded. Examiners should always award full marks if
deserved, i.e. if the answer matches the mark scheme.
Examiners should also be prepared to award zero marks if the
candidate’s response is not worthy of credit according to the
mark scheme.
 Where some judgement is required, mark schemes will
provide the principles by which marks will be awarded and
exemplification may be limited.
 When examiners are in doubt regarding the application of the
mark scheme to a candidate’s response, the team leader must
be consulted.
 Crossed out work should be marked UNLESS the candidate
has replaced it with an alternative response.
 Types of mark
o M marks: method marks
o A marks: accuracy marks
o B marks: unconditional accuracy marks (independent of
M marks)
 Abbreviations
o cao – correct answer only
o ft – follow through
o isw – ignore subsequent working
o SC - special case
o oe – or equivalent (and appropriate)
o dep – dependent
o indep – independent
o eeoo – each error or omission
 No working
If no working is shown then correct answers normally score
full marks
If no working is shown then incorrect (even though nearly
correct) answers score no marks.
 With working
If there is a wrong answer indicated on the answer line always
check the working in the body of the script (and on any
diagrams), and award any marks appropriate from the mark
scheme.
If it is clear from the working that the “correct” answer has
been obtained from incorrect working, award 0 marks.
Any case of suspected misread loses A (and B) marks on that
part, but can gain the M marks.
If working is crossed out and still legible, then it should be
given any appropriate marks, as long as it has not been
replaced by alternative work.
If there is a choice of methods shown, then no marks should
be awarded, unless the answer on the answer line makes
clear the method that has been used.
If there is no answer on the answer line then check the
working for an obvious answer.
 Ignoring subsequent work
It is appropriate to ignore subsequent work when the
additional work does not change the answer in a way that is
inappropriate for the question: eg. Incorrect cancelling of a
fraction that would otherwise be correct.
It is not appropriate to ignore subsequent work when the
additional work essentially makes the answer incorrect eg
algebra.
Transcription errors occur when candidates present a correct
answer in working, and write it incorrectly on the answer line;
mark the correct answer.
 Parts of questions
Unless allowed by the mark scheme, the marks allocated to
one part of the question CANNOT be awarded in another.
International GCSE Maths
Apart from questions 2b, 7, 15a, 15b, 20 (where the mark scheme states otherwise) the correct answer, unless clearly obtained by an
incorrect method, should be taken to imply a correct method

Q Working Answer Mark Notes

1 (a) (i) t, a, l 1 B1
(a)(ii) p, o, r, t, u, g, a, l, i, y 1 B1 No repeats
(b) No with reason 1 B1 eg. ‘a is in both sets’ or ‘they
share a member’ oe (but not
members/letters)
Total 3 marks

2 (a) 2 × (−3)2 – 7×(−3) oe e.g. 2(9) –(−21) M1 Brackets must be round (−3)²
or 2×9 + 21 or 18 + 21
39 2 A1
(b) 9 x 10 M1 for 4x + 12 (may not be in an equation) or for
4x + 12 = 9x – 10 or x  3   oe dividing RHS by 4
4 4
12 + 10 = 9x – 4x or −9x + 4x = −12 M1 (ft from 4x + b = 9x – 10, b≠0)
−10 for all terms in x isolated on one side and
or 22 = 5x or −5x = −22 numbers on other side
or 3 + 2.5 = 2.25x – x or 1.25x = 5.5
4.4 3 A1 22 2
for 4.4 oe eg. , 4 dep on at least M1
5 5
(c) −1, 0, 1, 2, 3 2 B2 B1 for −2, −1, 0, 1, 2 or list with one error or
omission: e.g. −2, −1, 0, 1, 2, 3 ; −1, 0, 1, 2 ;
−1, 1, 2, 3
Total 7 marks
3 (a) 250 × 97 M1 Completely correct method or
figures 2425(0) e.g. 242.5
24 250 2 A1
(b) 4 × 500 (=2000) or 500 ÷ 93.5 (=5.34759…) M1
(4 × 500 ) ÷ 93.5 or “5.34..” × 4 M1
21 3 A1 21 – 21.4
Total 5 marks

4 4  1 95 M1 or for (−1.5 , y) or (x, 7) or (7, −1.5)

or
2 2
(−1.5 , 7) 2 A1 oe
Total 2 marks
5 (a) 20 × 0.3 M1 6
Or for an answer of
20
6 2 A1 condone ‘6 out of 20’
(b) 0.3 + x + 3x = 1 M1 oe, e.g. 4x = 0.7 M1 for (20 – “6”) ÷ 4 (=3.5)
(1 – 0.3) ÷ 4 or 0.175 M1 complete method to find x 3  "3.5"
or 3x M1 for
or 20
(1 – 0.3) × 0.75
0.525 3 A1 21 A1 for 0.525 oe
oe, e.g. , 52.5%
40
(accept 0.53 from correct
working)
Total 5 marks

6 T = 6m + 9g 3 B3 Or T = 3(2m + 3g) [award B2 if T = 6m + 9g is

incorrectly simplified](condone T = 6×m + 9×g)
if not B3 then
B2 for T = 6m + kg or T =km + 9g (k may be
zero) or 6m + 9g
if not B2 then
B1 for 6m or 9g or T = am + bg (where a ≠ 0 or
6 and b ≠ 0 or 9)
Total 3 marks
7 (a) 14 9 56 36 M1 correct fractions with common
eg.  or  oe
denominators and intention to add
24 24 96 96
14 9 23 56 36 92 23 shown 2 A1 dep on M1
  or    oe
24 24 24 96 96 96 24
(b) 5 31 M1 fractions written as correct
 oe
improper fractions and intention to
3 15
multiply
1 31 155 M1 correct cancelling or multiplication
 or oe
of numerators and denominators
3 3 45
without cancelling
1 31 31 155 31 20 shown 3 A1 31 20
  or  or 3 oe or 3 dep on M2
3 3 9 45 9 45 9 45
Total 5 marks

8 180 – 156 (=24) or 180(n – 2) = 156n oe M1

or 90(2n – 4) = 156n oe
360 ÷ “24” or (180 × 2) ÷ (180 – 156) or M1 complete method
90  4
2  90  156
15 3 A1
Total 3 marks
9 420 ÷ (4 + 5 + 3) (=35) M1 M2 for
[or Manu = 140 or Liam = 175]
“35” × 3 (=105) M1 or Ned = 105 3
 420 oe
12
"105" 75 M1
100 oe
420
43 4 A1 42.85 – 43
Total 4 marks

10 (a) e15 1 B1
(b) M1 4g 9
for ng8 or 4gm or
g
4g8 2 A1 4 8
(condone g)
1
(c) 1 1 B1
(d)
2 2
1
12 3
1
12 3
M1 or kx4 or 9xn (not just 9 or xn)
(3x ) or 9(x²)² or (729 x ) or 9( x ) or
3
729x12 or 9 3 x12
9x4 2 A1
Total 6 marks
11 7 M1 Start of method to find radius or diameter of
eg (d2 = ) 72 + 72 or r2 + r2 = 7² or cos 45 = or circle
d
7 r r
sin 45 = or cos 45 = or sin 45 =
d 7 7
49 M1 complete method to find radius or diameter
eg (d=) 98 (9.899..) or (r=) (=4.9...) or or r2
2
(if method to find radius or diameter shown
7 7
d= or d = or r2 = 24.5 then allow use of radius = 5 for method
cos 45 sin 45 marks only)
or r = 7cos 45 or r = 7sin 45
eg. π × “4.9..”2 (=76.969...) M1 For method to find area of circle or semi-
circle or quarter circle – use of radius from
correct working
eg. π × “4.9..”2 – 72 M1 for complete method
28 5 A1 27.9 – 28
Total 5 marks

12 10 12 15 16 17 19 19 23 24 27 27 or M1 Ordered list – allow one error or omission

15 and 24 identified M1
9 3 A1
Total 3 marks
13 (a) y = 3 – 1.5x or 2x – 1.5 = y or M1 If using gradients, must state m =
m = 2 (A) or m = −1.5 (B) or m = 2 (C) or m = −2 (D) or gradient =
A and C 2 A1 (allow correct equations listed)
(b) 5 5 M1 c can be any value,
y=  x + c or y – y1 =  ( x  x1 )
2 2 5
e.g. y   x  3
2
5 11 5 11 M1
3=  × 1 + c or c = oe or y =  x + or
2 2 2 2
5
y – 3 =  ( x  1) or 2(y – 3) = −5(x – 1)
2
5x + 2y = 11 3 A1 oe eg. 10x + 4y = 22 or in a
different but correct form but must
have integer values,
e.g. 2y = −5x + 11
Total 5 marks

14 (a) (i) 52 B1
(a) (ii) angles in same segment or angles subtended 2 B1 Dep on B1 in (ai)
by the same arc
(b) (i) 104 B1 accept 256
(b) (ii) angle at centre is twice angle at circumference 2 B1oe Dep on B1 in (bi) or correct working
Total 4 marks
15 (a) 1 M1 correct expression for area
 ( x  5  2 x  4)  ( x  3) or (trapezium)
2
(3x + 1)(x + 3) = 120 or
(2x – 4)(x + 3) + ½(9 – x)(x + 3) or (rectangle + triangle)
(x + 5)(x + 3) − ½(9 – x)(x + 3) (rectangle – triangle)
1 M1 correct expansion of (all pairs) brackets in
 (3x 2  9 x  x  3)  60 oe a correct equation
2

3x² + 10x + 3 = 120 or shown 3 A1 dep on fully correct working to get to

1.5x² + 5x + 1.5 = 60 3x2 + 10x – 117 = 0
(b) 10  1504 M2 If not M2 then M1 for
or
6
10  102  4  3  117
10  102  1404
oe or 23
23
(may have just + rather than ±)
10  4 94 Condone one sign error in substitution;
6 allow partial evaluation
NB: denominator must be 2 × 3 or 6 and there
must be evidence for correct order of
operations in the numerator
4.80 3 A1 Award M2A1 for answers in range
4.796 – 4.8 (and no other answer) with
sufficient correct working that would gain
at least M1
[Award M2A0 for working sufficient for
M1 with both the –ve and +ve answers
(−8.13 & 4.80)]
Total 6 marks
16 (a) 0.2, 0.65, 0.35, 0.4, 2 B2oe B1 for any 2 correct probabilities (in
0.6 correct position)
(b) 0.8 × “0.35”(=0.28) or “0.2” × “0.4”(=0.08) M1 ft from M2 ft from (a) for
(a) 1−(0.8×‘0.6’+‘0.2’×‘0.6’)
M1 for 1 – (0.8×‘0.65’)
or 1− (‘0.2’×‘0.6’)
0.8 × “0.35” + “0.2” × “0.4” M1 ft from
(a)
0.36 oe 3 A1 9
eg , 36%
25
Total 5 marks
17 (a) 2 M1 for 2 correct from 3 × 8x² , −3×2x
24x2 – 6x – 25 A1 ,−25
fully correct
(b) 24x2 – 6x – 25 = 5 M1 ft from (a)
24x2 – 6x – 30 (= 0) or 4x2 – x – 5 (= 0) M1 ft from (a) for a 3 term quadratic
or 12x² − 3x – 15 (= 0) with no coefficients of zero
(4x – 5)(6x + 6) (=0) or (4x – 5)(x + 1) (= 0) M1 ft from (a) for a 3 term quadratic
(4x – 5)(3x + 3) (= 0) or with no coefficients of zero.
  1  (1)2  4  4  5 If using quadratic formula some
simplification may be seen.
2 4
1.25 oe, −1 4 A1 cao dep on M1
[ignore attempts to work out y
values]
Total 6 marks

18 60 ÷ 30 (=2) or 270 ÷ 60 (=4.5) or 150 ÷ 30 M1 for use of area

(=5) or 156 ÷ 120 (=1.3) or 24 ÷ 60 (=0.4) eg. any one correct fd or any 2
correct bars of different widths
fd : 2, 4.5, 5, 1.3, 0.4 M1 for any 4 correct fd or bars
histogram 3 A1 for a correct histogram, including
frequency density (FD) label and
scale/correct key
Total 3 marks
19 0.5 × 6.4 × 9.7 × sin 110 (= 29.16…) M1 M2 for
2 × “29.16…” M1 6.4 × 9.7 × sin 110
58.3 3 A1 for 58.3 – 58.4
alternative
AC = 6.42  9.72  2  9.7  6.4  cos110 (=13.323...) M1 For method to find AC and angle
DAC or angle ACD
sin110
DAC = sin 1 (  9.7)( 43.167...) or
'13.323'
sin110
ACD = sin 1 (  6.4)( 26.83...)
'13.323'
Area = (sin ‘43.167..’ × 6.4 × 2 × ‘13.323..’) ÷ 2 M1 find DB and then area using half
Or area = (sin ’26.83..’ × 9.7 × 2 × ’13.323...’) ÷ 2 product of diagonals
58.3 A1 for 58.3 – 58.4
Total 3 marks

20 45.75 or 45.85 or 63.25 or 63.75 B1 Accept 45.849 or 45.8499... or

63.749 or 63.7499...
63.25 45.85 M1 LB1 UB2
(= 1.379)... or (=0.764)... Or for or where
45.85 60 UB2 60
63.25  LB1  63.5 ,
45.8  UB2  45.85
63.25 63.25 M1 LB1 LB1
× 60 oe e.g. × 60 oe, e.g.
45.85 0.764... UB2 '0.764...'
82.8 4 A1 Or better (82.76990185)
Total 4 marks
21 15.62 + 4.32 – 2×15.6×4.3×cos72o (=220.39…) M1 substitution into Cosine rule
LN = 14.8(4561…) A1 14.8(4561…)
sin 58 sin MLN M1 ft LN dep on 1st M1
 or
or correct start to alternative method to
"14.8.." 13.7
sin NLP sin 72 find angle MLN or angle NLP or angle
 or LNP
4.3 "14.8"
sin LNP sin 72
 [4.3²=14.8..²+15.6²−2×14.8×15.6cosNLP]
15.6 "14.8.."
 sin 58  M1 ft LN dep on 1st M1
MLN  sin 1  13.7  (=51.49..) or or complete alternative method to find
 "14.8.." 
angle MLN or angle NLP or angle LNP
 sin 72 
NLP  sin 1   4.3  (=15.99..) or
 "14.8"  NB: LNP = 180 −87.99 = 92.009...
 sin 72 
LNP  sin 1  15.6  (=87.99 or 92.00..)
 "14.8"   14.8..2  15.62  4.32 
NLP  cos 1  
 2 14.8.. 15.6 
 sin 58  M1 ft LN dep on 1st M1
MLN  sin 1  13.7  (=51.49..) and or complete method to find angle MLN
 "14.8.." 
and angle NLP (or LNP acute or obtuse)
 sin 72 
NLP  sin 1   4.3  (=15.99..) or
 "14.8" 
 sin 72 
LNP  sin 1  15.6  (=87.99 or 92.00..)
 "14.8" 
67.5 6 A1 for 67.46 – 67.8
Total 6 marks
22 1 M1 Correct first stage.
 1 3
or  2 103n  or
1 1
e.g.  9n 
or
 8 10  3
8 109 n

 
1 1 9 n
3
8 109 n or (8 3 10 3
) or

 
1 1 
 1 and 1 
or  21 and (103n )1  oe
 83
 109n  3 
1 M1 For dealing with 8−⅓ (shown as ½ or
e.g. or 0.5 × 10-3n oe or
2 10 3n 0.5) and (109n) −⅓ shown as 10−3n
 3 1 1

 8  0.5 and (10 9n 3
)  103n  oe
 
5 × 10-3n – 1 3 A1 5 × 10-(3n + 1)
Total 3 marks
23 4 r 2 16 16 M1 4 r 2
  r 2   or 3 r 2   allow   r 2  16.755...
2 3 3 2
4 A1 (allow 1.33... or better)
r = oe
3
1 4  4 
3 M1 dep on 1st M1 (need not include 
   " " )
2 3  3 
128
or answer of  (=4.96(44…))
81
128 4 A1 47
1 (accept 1.58(024…)
81 81
Total 4 marks

Pearson Education Limited. Registered company number 872828

with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom
Write your name here
Surname Other names

Centre Number Candidate Number

Pearson Edexcel
International GCSE

Mathematics A
Paper 4HR

Higher Tier
Thursday 8 June 2017 – Morning Paper Reference

Time: 2 hours 4MA0/4HR

You must have: Total Marks
Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser, calculator. Tracing paper may be used.

Advice
• Check
Read each question carefully before you start to answer it.
• your answers if you have time at the end.

Turn over

1/1/1/1/
*P48489A0124*
International GCSE MATHEMATICS
FORMULAE SHEET – HIGHER TIER

DO NOT WRITE IN THIS AREA

Pythagoras’ Volume of cone = 1
r 2h Volume of sphere = 4
r3
3 3
Theorem
c Curved surface area of cone = rl Surface area of sphere = 4 r 2
b
r
a l
h
a2 + b2 = c2
r

adj = hyp cos

hyp opp = hyp sin
opp opp = adj tan In any triangle ABC
C
adj opp
or sin b a
hyp

DO NOT WRITE IN THIS AREA

adj A B
cos c
hyp

opp a b c
tan Sine rule:
adj sin A sin B sin C

Cosine rule: a2 b2 + c 2 2bc cos A

1
Area of triangle 2 ab sin C
cross
section
h
lengt
Volume of prism = area of cross section length

Area of a trapezium = 12 (a + b)h

r Circumference of circle = 2 r a
DO NOT WRITE IN THIS AREA

Area of circle = r 2 h

r
The Quadratic Equation
Volume of cylinder = r h 2 The solutions of ax2 + bx + c 0,
h where a 0, are given by
Curved surface area
of cylinder = 2 rh b + b2 4ac
x
2a

2
*P48489A0224*
Answer ALL TWENTY FOUR questions.

Write your answers in the spaces provided.

DO NOT WRITE IN THIS AREA

You must write down all the stages in your working.

1 Here is a list of ingredients to make 12 chocolate cupcakes.

Chocolate cupcakes
Ingredients for 12 cupcakes

110 g butter
100 g sugar
75 g flour
25 g cocoa
2 eggs

James wants to make exactly 30 cupcakes.

(a) How much butter does James need?
DO NOT WRITE IN THIS AREA

....................................................... g
(2)
Sophie made some chocolate cupcakes for a party.
She used 375 g of sugar.
(b) How many cupcakes did Sophie make?
DO NOT WRITE IN THIS AREA

.......................................................

(2)

(Total for Question 1 is 4 marks)

3
*P48489A0324* Turn over
2 E = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
A = {multiples of 5}

DO NOT WRITE IN THIS AREA

B = {odd numbers}
(a) List the members of the set
(i) A B

.......................................................

(ii) A B

.......................................................

(2)
The set C has 6 members and B C =
(b) List the members of set C.

DO NOT WRITE IN THIS AREA

.......................................................

(2)

(Total for Question 2 is 4 marks)

17.7 × 5.8
3 (a) Work out the value of
3.4 + 5.3

Write down all the figures on your calculator display.

DO NOT WRITE IN THIS AREA

.......................................................

(2)
(b) Give your answer to part (a) correct to 3 significant figures.

.......................................................

(1)

(Total for Question 3 is 3 marks)

4
*P48489A0424*
4 The diagram shows a cuboid and a triangular prism.

Diagram NOT
DO NOT WRITE IN THIS AREA

accurately drawn
7 cm
7.5 cm

4.2 cm x cm
10 cm 5 cm

The volume of the cuboid is equal to the volume of the triangular prism.
Work out the value of x.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 4 is 4 marks)

5
*P48489A0524* Turn over
5 D ([SDQG íc)

DO NOT WRITE IN THIS AREA

.......................................................

(1)
(b) Factorise y2 + 8y

.......................................................

(1)
(c) Expand and simplify (x + 7)(xí

.......................................................

(2)
(d) Solve 5pí p

DO NOT WRITE IN THIS AREA

p = .......................................................
(2)
(e) Simplify y7 × y4

.......................................................

(1)
(f) Simplify h12 ÷ h4
DO NOT WRITE IN THIS AREA

.......................................................

(1)
(g) Simplify (e5)3

.......................................................

(1)

(Total for Question 5 is 9 marks)

6
*P48489A0624*
6 The frequency table shows information about the distances 60 office workers travel to
work each day.
DO NOT WRITE IN THIS AREA

Distance travelled (d km) Frequency

0 d - 10 5

10 d - 20 12

20 d - 30 17

30 d - 40 20

40 d - 50 6

(a) Write down the modal class.

.......................................................

(1)

(b) Work out an estimate for the mean distance travelled to work by these office workers.
Give your answer correct to 1 decimal place.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

...................................................... km
(4)

(Total for Question 6 is 5 marks)

7
*P48489A0724* Turn over
7 (a) Solve the inequality 4x + 13 . 27

DO NOT WRITE IN THIS AREA

.......................................................

(2)
(b) On the number line, represent the inequality y .í

y
í í í 0 1 2 3
(1)

DO NOT WRITE IN THIS AREA

n is an integer.
(c) Write down all the values of nWKDWVDWLVI\ í n - 2

.......................................................

(2)

(Total for Question 7 is 5 marks)

DO NOT WRITE IN THIS AREA

8
*P48489A0824*
8

Diagram NOT
DO NOT WRITE IN THIS AREA

accurately drawn
18 cm
13 cm

x cm
Work out the value of x.
Give your answer correct to 3 significant figures.
DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 8 is 3 marks)

DO NOT WRITE IN THIS AREA

9
*P48489A0924* Turn over
9 Solve the simultaneous equations.
5xíy = 9.5

DO NOT WRITE IN THIS AREA

4x + 2y = 13
Show clear algebraic working.

DO NOT WRITE IN THIS AREA

x = .........................................

y = .........................................
DO NOT WRITE IN THIS AREA

(Total for Question 9 is 3 marks)

10
*P48489A01024*
10 2.2 × 107 passengers passed through Beijing Capital International Airport in 2014.
(a) Write 2.2 × 107 as an ordinary number.
DO NOT WRITE IN THIS AREA

.......................................................

(1)
950 000 tonnes of cargo traffic passed through Tokyo International Airport in 2014.
(b) Write 950 000 as a number in standard form.
DO NOT WRITE IN THIS AREA

.......................................................

(1)

(Total for Question 10 is 2 marks)

11 Mabintou invested $7500 for 3 years at 4% per year compound interest.

Calculate the value of her investment at the end of 3 years.
DO NOT WRITE IN THIS AREA

$ .......................................................

(Total for Question 11 is 3 marks)

11
*P48489A01124* Turn over
12 The straight line L is shown on the grid.
y

DO NOT WRITE IN THIS AREA

3
2
L
1

–2 –1 O 1 2 3 4 5 x
–1

–2

–3

(a) Find an equation of L.

DO NOT WRITE IN THIS AREA

.......................................................

(2)
(b) Find an equation of the line that is parallel to L and passes through the point (5, 4)

DO NOT WRITE IN THIS AREA

.......................................................

(2)

(Total for Question 12 is 4 marks)

12
*P48489A01224*
13 The diagram shows triangle ABC.

B
DO NOT WRITE IN THIS AREA

Diagram NOT
x accurately drawn

15 cm
9 cm

A 5 cm D C

AB = 9 cm BC = 15 cm
D is the point on AC such that AD = 5 cm.
Angle BAC = 90°
Calculate the size of angle x.
DO NOT WRITE IN THIS AREA

Give your answer to the nearest degree.

DO NOT WRITE IN THIS AREA

°
.......................................................

(Total for Question 13 is 4 marks)

13
*P48489A01324* Turn over
5 − x x −1
14 Solve − =1
2 3

DO NOT WRITE IN THIS AREA

Show clear algebraic working.

DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 14 is 4 marks)

14
*P48489A01424*
15
B
DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn
A

61° 53°
E D F

A, B, C and D are points on a circle.

EDF is the tangent to the circle at D.
Angle ADE = 61° and angle CDF = 53°
DO NOT WRITE IN THIS AREA

(a) (i) Write down the size of angle ACD.

°
.......................................................

(ii) Give a reason for your answer.

. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)
(b) Work out the size of angle ABC.
DO NOT WRITE IN THIS AREA

°
.......................................................

(2)

(Total for Question 15 is 4 marks)

15
*P48489A01524* Turn over
16 Here are six cards.
Each card has a number on it.

DO NOT WRITE IN THIS AREA

1 3 3 3 4 4

The cards are turned over to hide their numbers and are then mixed up.
Malachi takes at random two of the cards and turns them over to show their numbers.
(a) Calculate the probability that the number 4 is on both of the cards Malachi takes.

DO NOT WRITE IN THIS AREA

.......................................................

(2)
(b) Calculate the probability that the sum of the numbers on the two cards Malachi takes
is an even number.

DO NOT WRITE IN THIS AREA

.......................................................

(3)

(Total for Question 16 is 5 marks)

16
*P48489A01624*
17 Solve 11x2íxí
Show your working clearly.
Give your solutions correct to 2 decimal places.
DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 17 is 3 marks)

DO NOT WRITE IN THIS AREA

18 A is directly proportional to x2
A = 480 when x = 5
Find the value of A when x = 1.5
DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 18 is 3 marks)

17
*P48489A01724* Turn over
19 The table gives information about the time taken by each of 600 people to reach their
holiday destination.

DO NOT WRITE IN THIS AREA

Time taken (t minutes) Frequency

0 t - 100 120

100 t - 150 140

150 t - 300 240

300 t - 500 80

500 t - 600 20

(a) Use the information in the table to complete the histogram.

DO NOT WRITE IN THIS AREA

Frequency
density

0
0 100 200 300 400 500 600
Time taken (minutes)
(3)
(b) Work out an estimate for the number of people who took more than 200 minutes to
reach their holiday destination.
DO NOT WRITE IN THIS AREA

.......................................................

(2)

(Total for Question 19 is 5 marks)

18
*P48489A01824*
20 The functions f and g are such that
1
DO NOT WRITE IN THIS AREA

f (x) = and g(x) = 2x + 3

x+5

(a) State which value of x must be excluded from any domain of f.

.......................................................

(1)
(b) Find g(10)

.......................................................

(1)
DO NOT WRITE IN THIS AREA

F &DOFXODWHJI í

.......................................................

(2)
(d) Express the inverse function gí in the form gí(x) = …
DO NOT WRITE IN THIS AREA

gí(x) = .......................................................

(2)

(Total for Question 20 is 6 marks)

19
*P48489A01924* Turn over
21 A

DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn

O W B

OAB is a triangle.
X is the midpoint of OA and W is the midpoint of OB.
Y is the point on AW such that AY : YW = 2 : 1
ĺ ĺ
OX = 3a and OW = 3b

DO NOT WRITE IN THIS AREA

(a) Express in terms of a and b
ĺ
(i) AW

.......................................................

ĺ
(ii) AY

.......................................................

ĺ
(iii) XB

.......................................................

(3)
(b) Show by a vector method that XYB is a straight line.
DO NOT WRITE IN THIS AREA

(2)

(Total for Question 21 is 5 marks)

20
*P48489A02024*
22 ABCDEFGH is a cuboid.
A 16 cm B Diagram NOT
DO NOT WRITE IN THIS AREA

accurately drawn

D C

F G

15 cm
E M H

AB = 16 cm and HG = 15 cm.
M is the midpoint of EH.
BM makes an angle of 24° with the base EFGH.
Calculate the height, BG, of the cuboid.
Give your answer correct to 3 significant figures.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

....................................................... cm

(Total for Question 22 is 4 marks)

21
*P48489A02124* Turn over
v−u
23 t =
a

DO NOT WRITE IN THIS AREA

v = 27.3 correct to 3 significant figures.
u = 18 correct to 2 significant figures.
a = 9.81 correct to 3 significant figures.
Work out the lower bound for the value of t.
Show your working clearly.
Give your answer correct to 3 significant figures.

DO NOT WRITE IN THIS AREA

.......................................................

(Total for Question 23 is 3 marks)

22
*P48489A02224*
24 The diagram shows triangle KLM.
K
DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn
10.4 cm 12.6 cm

L P M
18 cm

KLP is a sector of a circle with centre L and radius 10.4 cm.

The region of the triangle outside the sector is shown shaded in the diagram.
Calculate the area of the shaded region.
Give your answer correct to 3 significant figures.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . cm2

(Total for Question 24 is 5 marks)

TOTAL FOR PAPER IS 100 MARKS

23
*P48489A02324*
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

*P48489A02424*
Do NOT write on this page
BLANK PAGE

24
Mark Scheme (Results)

Summer 2017

Pearson Edexcel International GCSE

In Mathematics A (4MA0) Paper 4HR
Edexcel and BTEC Qualifications

Edexcel and BTEC qualifications come from Pearson, the world’s

Our website subject pages hold useful resources, support material

www.edexcel.com/contactus

Pearson: helping people progress, everywhere

Summer 2017
Publications Code 4MA0_4HR_1706_MS
All the material in this publication is copyright
© Pearson Education Ltd 2017
General Marking Guidance
 All candidates must receive the same treatment. Examiners
must mark the first candidate in exactly the same way as they
mark the last.
 Mark schemes should be applied positively. Candidates must
be rewarded for what they have shown they can do rather
than penalised for omissions.
 Examiners should mark according to the mark scheme not
according to their perception of where the grade boundaries
may lie.
 There is no ceiling on achievement. All marks on the mark
scheme should be used appropriately.
 All the marks on the mark scheme are designed to be
awarded. Examiners should always award full marks if
deserved, i.e. if the answer matches the mark scheme.
Examiners should also be prepared to award zero marks if the
candidate’s response is not worthy of credit according to the
mark scheme.
 Where some judgement is required, mark schemes will
provide the principles by which marks will be awarded and
exemplification may be limited.
 When examiners are in doubt regarding the application of the
mark scheme to a candidate’s response, the team leader must
be consulted.
 Crossed out work should be marked UNLESS the candidate
has replaced it with an alternative response.
 Types of mark
o M marks: method marks
o A marks: accuracy marks
o B marks: unconditional accuracy marks (independent of
M marks)
 Abbreviations
o cao – correct answer only
o ft – follow through
o isw – ignore subsequent working
o SC - special case
o oe – or equivalent (and appropriate)
o dep – dependent
o indep – independent
o eeoo – each error or omission
 No working
If no working is shown then correct answers normally score
full marks
If no working is shown then incorrect (even though nearly
correct) answers score no marks.
 With working
If there is a wrong answer indicated on the answer line always
check the working in the body of the script (and on any
diagrams), and award any marks appropriate from the mark
scheme.
If it is clear from the working that the “correct” answer has
been obtained from incorrect working, award 0 marks.
Any case of suspected misread loses A (and B) marks on that
part, but can gain the M marks.
If working is crossed out and still legible, then it should be
given any appropriate marks, as long as it has not been
replaced by alternative work.
If there is a choice of methods shown, then no marks should
be awarded, unless the answer on the answer line makes
clear the method that has been used.
If there is no answer on the answer line then check the
working for an obvious answer.
 Ignoring subsequent work
It is appropriate to ignore subsequent work when the
additional work does not change the answer in a way that is
inappropriate for the question: eg. Incorrect cancelling of a
fraction that would otherwise be correct.
It is not appropriate to ignore subsequent work when the
additional work essentially makes the answer incorrect eg
algebra.
Transcription errors occur when candidates present a correct
answer in working, and write it incorrectly on the answer line;
mark the correct answer.
 Parts of questions
Unless allowed by the mark scheme, the marks allocated to
one part of the question CANNOT be awarded in another.
International GCSE Maths
Apart from questions 9, 14, 17, 21b and 23 (where the mark scheme states otherwise) the correct answer, unless clearly obtained from an
incorrect method, should be taken to imply a correct method.
Q Working Answer Mark Notes
1 (a) 30 30 2 M1 Accept 9.16(666...) rounded or
Eg 110 or 2.5 110 or or 2.5 or
truncated to at least 3 SF
12 12
110 110
 30 or 9.16(666...) × 30 or or 9.16(666...) oe
12 12
A1
275

(b) 375 2 M1 For a complete method

Eg 12 or 3.75 12 or Accept 8.33(333...) rounded to at
100
100 least 3 SF
375 ÷ or 375 ÷ 8.33(333...) or
12
12
 375 or 0.12  375
100 A1
45
Total 4 marks
2 (a) (i) 5, 15 1 B1
(ii) 5, 7, 9, 10, 11, 13, 15 1 B1
(b) 4, 6, 8, 10, 12, 14 2 B2 B2 for all correct and none
incorrect.
If not B2 then B1 for 4 or more
correct and no more than 1
incorrect.
Total 4 marks

3 (a) 2 M1 102.66 or 1.843(9...) or 7.143(9..)

14.37028405 A1 Accept 14.37(028......) rounded or
truncated to at least 4SF
(b) 14.4 1 B1 ft As long as from at least 4sf
Total 3 marks
4 10 × 4.2 × 7.5 or 315 (cm3) oe 4 M1 For volume of cuboid
Eg 0.5 × 7 × x × 5 or 17.5x oe M1 indep
For volume of triangular prism
10 × 4.2 × 7.5 = 0.5 × 7 × x × 5 or 17.5x = 315 M1 Dep on M2
oe or For a correct equation involving
10  4.2  7.5 "315" volume of cuboid and volume of
or oe
0.5  7  5 "17.5" prism or
For a correct expression for x
18 A1 18
SCB2 for For volume of cuboid =
315 and final answer = 9
Total 4 marks
5 (a) 12 – 28c 1 B1
(b) y(y + 8) 1 B1
(c) x² − 3x + 7x − 21 2 M1 For 3 correct terms
or for 4 correct terms ignoring signs
or for x² + 4x + c for any non-zero
value of c or for ... + 4x – 21
x² + 4x −21 A1 cao
(d) 5p – 3p = 9 or 2p = 9 or −9 = 3p – 5p or −9 = −2p 2 M1

4.5 A1 oe
9 1
eg or 4
2 2
(e) y11 1 B1
(f) h8 1 B1
(g) e15 1 B1
Total 9 marks
6 (a) 30 < d ≤ 40 1 B1 Accept 30  40
(b) 5×5 + 15×12 + 25×17 + 35×20 + 45×6 or 4 M2 f × d for at least 4 products with
25 + 180 + 425 + 700 + 270 or correct mid- interval values and
1600 intention to add.

If not M2 then award M1 for

d used consistently for at least 4
products within interval (including
end points) and intention to add
or
for at least 4 correct products with
correct mid-interval values with no
intention to add
25  180  425  700  270
or  
1600  M1 dep on M1 (ft their products)

5  12  17  20  6  60  NB: accept their 60 if addition of
frequencies is shown
26.7 A1 Accept 26.6 – 26.7 inclusive
Accept 27 if M3 awarded
Do not accept fractions or mixed
80 2
numbers, eg or 26
3 3
Total 5 marks
7 (a) 4x ≥ 27 – 13 or 4 x  14 2 M1 Accept an equation in place of an
or –4x ≤ 13 – 27 or 4 x  14 inequality or
accept wrong inequality sign or
accept 3.5 oe given as answer

A1 oe
x  3.5 Must be the final answer
(b) Correct line drawn 1 B1 For a closed circle at −1with line
that goes at least as far as 3 or
for a closed circle at −1with an
arrow on a line pointing to the
right
(c) −2, −1, 0, 1, 2 2 B2 B1 for list with one error or
omission:
e.g.
−2, −1, 0, 1, 2, 3;
−1, 0, 1, 2;
−2, −1, 1, 2;
−3, −2, −1, 0, 1, 2
SCB1 for −3, −2, −1, 0, 1
Total 5 marks
8 (x² =) 18² − 13² or 324 – 169 or 155 3 M1 Squaring and subtracting
(𝑥 =) √18² − 13² or √"155" M1dep for square rooting
12.4 A1 Accept 12.4 – 12.46 inclusive
Alternative Methods - Using Trigonometry

13 M2 For a complete method

Eg sin 1 ( ) and 18cos"46.2(382...)" oe or
18
13
cos 1 ( ) and 18sin"43.7(617...)" oe
18
A1 Accept 12.4 – 12.46 inclusive
Total 3 marks
9 Eg 9x = 22.5 or 18 y  27 or 18 y  27 or 3 M1 For a complete method to
5x – (13 – 4x) = 9.5 or 4x + 5x – 9.5 = 13 or eliminate one variable (condone
one arithmetic error)
 13  2 y 
5   2 y  9.5 or
 4 
 9.5  2 y 
4   2 y  13
 5 

Eg 5 × "2.5" – 2y = 9.5 or 5x – 2 × "1.5" = 9.5 M1 Dep on M1

For substituting the other variable
or starting again to eliminate the
other variable
A1 dep on M1
x = 2.5, y = 1.5 NB: candidates showing no correct
working score 0 marks.
Total 3 marks

10 (a) 22 000 000 1 B1

(b) 9.5 × 105 1 B1
Total 2 marks
11 7500 × 0.04 or 300 or 7500 × 1.04 or 7800 3 M1 For interest for first year or M2 for 7500⨯ 1.043
or 7500 × 1.04𝑛 (n > 1 ) for 7500 × 0.04 × 3 oe or 900 oe
or
for 7500 + 7500 × 0.04 × 3 oe
or an answer of 8400

4 4 M1 For a complete method

Eg 7500 + ⨯7500 + ⨯(7500 +
100 100
“300”)
4
+ ⨯(7500 + “300” + “312”) or
100

7500 + “300” + “312” + “324.48”

8436.48
A1 Accept answers in the range 8436 – 8437
NB: Answer in the range 936 -937 gets M2A0
Total 3 marks
12 (a) 2 M1 3
For (y=) x + c (c may be any
6
number or letter) or
For ( y ) mx  1 where m is non-
zero or for
3 3
Gradient = oe or m = oe
6 6
clearly stated
1 A1 For a fully a correct equation for L
y= x – 1 oe Eg
2
3
y  x  1 or 2y = x – 2 or
6
1
y – 1 = (x – 4) or
2
1
y − −2 = (x − − 2)
2
1 1
M1A0 for L = x – 1 or x – 1
2 2
(b) 1 1 2 M1ft For correct substitution of given
4 = " " × 5 + c or y  4  " "( x  5) coordinate into their equation
2 2
Follow through their gradient in (a)
1 1 A1 oe
y= x+1 1
2 2 Eg y  ( x  3)
2
1 1
SCB1 for (l =) x + 1
2 2
Total 4 marks
13 5 9 4 M1 For correct method to find angle
(Angle ABD =) tan−1( ) or (Angle ADB =) tan−1( ) or ABD or ADB or ABC or ACB or
9 5
9 9 for correct method to find side BD,
(Angle ABC =) cos−1( ) or (Angle ACB =) sin−1( ) AC or DC.
15 15
(BD =) 92  52 or (AC =) 152  92 (DC =) 152  92 -5

A1 For angle ABD = 29.(0546...) or

for angle ADB = 60.(9453...) or
for angle ABC = 53.(1301...) or
for angle ACB = 36.(8698...) or
For BD = 106 or10.(2956...) or
for AC = 12 or
for DC = 7
Accept rounded or truncated to at
least 2SF
9 5 M1 For a complete method to find x or
Eg (x =) cos−1( ) − tan−1( ) or sinx or cosx
15 9
(x =) 180  90  "29.(0546...)" "36.(8698...)" or
Accept 0.912  cosx  0.9152
152  "10.(2956...)"2  7 2
cos x  or cosx = 0.913(009) or
2 15  "10.(2956...)" Accept 0.407  sinx  0.413
7sin"36.(8698...)" 7sin"119.(054...)"
sinx = or sinx = or
106 15
sinx = 0.407(940...)
24 A1 Awrt 24
Total 4 marks
14 6(5  x) 6( x  1) 4 M1 For a clear intention to multiply
  6 × 1 or both sides by 6 or a multiple of 6
2 3
3(5− x) – 2(x – 1) = 6 or or to express LHS as a single
3(5  x)  2( x  1) fraction with denominator of 6 or a
( 1) or multiple of 6 or to express LHS as
6
the sum of 2 fractions with
3(5  x) 2( x  1)
 ( 1) denominator of 6 or a multiple of 6
6 6
15 – 3x – 2x +2 = 6 or M1 Expanding brackets in a correct
15  3x  2 x  2 equation.
1
6
15  3x 2 x  2
 1
6 6
Eg −3x – 2x = 6 – 2 – 15 or −5x = −11 or M1 dep on both preceding marks for a
3x + 2x = 15 + 2 – 6 or 5x = 11 correct rearrangement of a correct
equation with terms in x on one
side and numbers on the other.
2.2 A1 oe
Dependent on M2
Total 4 marks
15 (a)(i) 61° 1 B1
(ii) Alternate segment 1 B1 Dep on B1 for (a)(i)
theorem Accept alternate segment(s)
Accept angles in alternate
segments are equal or
Accept Angle between a chord and
a tangent is equal to the angle on
the circumference subtended/made
by the same chord
(b) 180 – (180−(61+53)) 2 M1 For 61 + 53 or 180 – 66
114° A1 cao
Total 4 marks
16 (a) 2 1 2 M1 For a complete method
× oe
6 5
A1 oe
2
Eg
30
1 Accept 0.066(666...) rounded or
15 truncated to at least 3 decimal
places
(b) 4 3 2 1 3 M1 One correct product that gives an
× or 0.4 or × or 0.066(666...) or even number
6 5 6 5
1 3 3 1 3 2 2 1
× or × or 0.1 or × or 0.2 or × or
6 5 6 5 6 5 6 5
0.066(666...)

4 3 2 1 M1 Sum of correct products

× + × or
6 5 6 5
1 3 3 1 3 2 2 1
× + × + × + ×
6 5 6 5 6 5 6 5
A1 oe
7 Accept 0.466(666...) rounded or
15 truncated to at least 3 decimal
places
With Replacement
4 4 2 2
 or 0.444(444) or  or 0.111(111...) or M1
6 6 6 6
1 3 3 1 2 2
 or  or 0.083(333...) or  or 0.111(111...) or
6 6 6 6 6 6
3 3 1 1
 or 0.25 or  or 0.027(777...)
6 6 6 6

4 4 2 2 M1
 +  oe or
6 6 6 6
1 3 3 1 2 2 3 3 1 1
 +  +  +  +  oe or
6 6 6 6 6 6 6 6 6 6
5
or or 0.555(555...)
9

Alternative method 3
2 4 4 2
1 − ( × + × ) oe M2
6 5 6 5
A1 oe
7
Accept 0.466(666...) rounded or
15 truncated to at least 3 decimal
places
Total 5 marks
17 3  9  220 3  9  220 3 M2 Or for
or or
22 2 11   3  (3)2  4 11 5
(allow
3  (3) 2  220 3  (3) 2  220 2 11
or partial correct evaluation)
2 11 22
NB: denominator must be 2×11 or 22 and there must be 3  229
and
evidence for correct order of operations in the numerator 22
Do not accept sign error or omission of brackets
If not M2 then

M1 for

− − 3 ± √(−3)2 − 4(11)(−5)
2 × 11

Condone one sign error in

substitution;
Condone omission of brackets
Allow partial correct evaluation

0.82 and A1 for awrt 0.82 and awrt −0.55

−0.55
Award M2 A1 for awrt 0.82, −0.55
with sufficient correct working that
would gain at least M1

Alternative scheme
3 229 M1
11[(x − 22)² − 484] oe
3 229 M1
 oe
22 484
0.82 and A1 for awrt 0.82 and awrt −0.55
−0.55 Award M2 A1 for awrt 0.82, −0.55
with sufficient correct working that
would gain at least M1
Total 3 marks

18 480 = k × 5² or 480  k × 5² oe or 3 M1
480
or (k ) 2 or (k =) 19.2 oe
5
480
k  2 or k  19.2 oe
5
“19.2” × 1.5² M1 Dep on M1
or for A = 19.2x² oe
43.2 A1 oe
Total 3 marks
19 (a) Frequency densities: 1.2, 2.8, 1.6, 0.4, 0.2 3 M1 For 3 or more correctly calculated
freq densities or
For a correct scale indicated or
1 small square = 1 (person)
1 big square = 25 (people)
M1 For at least 2 additional correct
bars (with or without scale)
Implies first M1
A fully A1 All 4 additional bars correct
correct
histogram
(b) 100 2 M1 A fully complete method to find
× 240 + 100 or 1.6 × 100 + 100 or “160” + 100 the number of people who took
150
oe from 200 to 300 minutes + 100
1
or 600  (120  140   240) or
3
600  (120  140  50 1.6)) or 600  340 oe
260 A1
Total 5 marks
20 (a) −5 1 B1
(b) 23 1 B1
(c) 1 1 2
(f(−7)) = or (f(−7)) =  or M1
7  5 2
 1  1
2   3 or 2    3
 7  5  2
2 A1
(d) x 3 2 M1
x  3  2 y or  y  or
2 2
y 3
y  3  2 x or  x  or
2 2
y 3 y 3
or 
2 2 2

x3 A1 oe
x 3
2 Eg 
2 2
Total 6 marks
21 (a) (i) 3b – 6a 1 B1 Oe
Need not be simplified
Mark the final answer
(ii) 2b – 4a 1 B1ft 2
oe eg 3(‘3b −6a’)
Need not be simplified
Mark the final answer
(iii) 6b – 3a 1 B1 oe
Need not be simplified
Mark the final answer
(b) Eg XY = 2b – a oe or YB = 4b – 2a 2 M1 Work out XY or YX or YB or BY
shown A1 Dep on M1
Correct conclusion from correct
simplified vectors
Eg XB  3 XY or YB  2 XY or
XB  1.5YB
or XB and XY are parallel
or YB and XY are parallel
or XB and YB are parallel
Total 5 marks
22 4 B1 Identifying correct triangle
√82 + 15² or √289 or 17 M1 Complete method to find MG
BG BG M1 Dep
Eg tan24 = or tan24 = For a correct equation involving
8  15
2 2 17
BG or a correct expression for BG
BG 82  152 BG 17 Implies B1
or  or 
sin 24 sin(90  24) sin 24 sin66
17
(BG =) 17tan24 or (BG=)  sin 24
sin66
7.57 A1 Accept 7.56 – 7.57
Total 4 marks
23 27.25 or 27.35 or 17.5 or 18.5 or 9.805 or 3 B1 Accept 27.349̇ or 27.3499… or
9.815 18.49̇ or 18.499... or 9.8149̇ or
9.81499...
27.25  18.5 M1 LB  UB1
(t ) For oe where
9.815 UB2

27.25 ≤ LB < 27.3

and 18 < UB1 ≤ 18.5
and 9.81 < UB2 ≤ 9.815

0.891 A1 27.25  18.5

dep on seeing
9.815
Correct working must be seen
Accept 0.891 - 0.8915
Total 3 marks
24 Eg 12.6² = 10.4²+18²−2×10.4×18×cosL or 5 M1 Correct substitution into cosine
158.76 = 108.16 + 324 − 374.4 cosL rule to find L or

10.42 +12.62 −18²

For cosK = 2 ×10.4 ×12.6 oe
AND
12.6sin "102.(579…)"
−57.08 SinL = or
Note: cosK = (= −0.217(796…)) and K = 102.(579...) 18
262.08
374.6
cosM = 453.6 (= 0.825(837…)) and M = 34.3(264...) 182 +12.62 −10.4²
For cosM = 2 ×18 ×12.6 oe
AND
12.6sin "34.3(264…)"
SinL = 10.4
10.42 +182 −12.6² 273.4 A1 Rearranging cosine rule correctly.
Eg cosL = or cosL = or Accept L = 43°
2 ×10.4 ×18 374.4
cosL = 0.73(0235...) oe or L = 43.0(938...) Accept 43.0(938...) rounded or
truncated to at least 3 SF
"43.0  938... " M1 Dep on at least M1
(Area of sector =) × 𝜋 × 10.4² or 40.6(752...) Accept 40.5 – 40.7
360
B1 For (area of triangle=) 63.9(471…)
Accept 63.8 – 64.0
23.3 A1 Accept 23.2 – 23.3
Total 5 marks
Pearson Education Limited. Registered company number 872828
with its registered office at 80 Strand, London, WC2R 0RL, United Kingdom

June 2016 QP
No ratings yet
June 2016 QP
24 pages
Igcse A May 2016 Paper 3h
No ratings yet
Igcse A May 2016 Paper 3h
24 pages
June 2017 Maths
0% (1)
June 2017 Maths
24 pages
3HR QP
No ratings yet
3HR QP
24 pages
3HR January 2017 QP
No ratings yet
3HR January 2017 QP
24 pages
4MA0 3H Que 20180525
0% (1)
4MA0 3H Que 20180525
24 pages
Mathematics A: Paper 3H Higher Tier
No ratings yet
Mathematics A: Paper 3H Higher Tier
24 pages
4MA0 4H Que 20160119 PDF
No ratings yet
4MA0 4H Que 20160119 PDF
24 pages
4.june 2018.
No ratings yet
4.june 2018.
26 pages
January 2016 (R) QP 2
No ratings yet
January 2016 (R) QP 2
24 pages
Screenshot 1446-10-27 at 5.34.41 PM
No ratings yet
Screenshot 1446-10-27 at 5.34.41 PM
21 pages
Ilovepdf Merged
No ratings yet
Ilovepdf Merged
72 pages
07a 4MA0 4H (R) - January 2015
No ratings yet
07a 4MA0 4H (R) - January 2015
24 pages
4MA0 4HR Que 20150112
No ratings yet
4MA0 4HR Que 20150112
24 pages
Jun 2017 3h - Unlocked
No ratings yet
Jun 2017 3h - Unlocked
24 pages
4MA0 4HR Que 20160609 PDF
No ratings yet
4MA0 4HR Que 20160609 PDF
24 pages
IG Mathematics B - Question Paper 1 (Jun 2025)
No ratings yet
IG Mathematics B - Question Paper 1 (Jun 2025)
24 pages
Pdf24 Merged
No ratings yet
Pdf24 Merged
1,088 pages
January 2017 QP
No ratings yet
January 2017 QP
24 pages
IGCSE Maths Exam Paper
No ratings yet
IGCSE Maths Exam Paper
24 pages
June 19 2h
No ratings yet
June 19 2h
29 pages
Jan3hr 2016 - Unlocked
No ratings yet
Jan3hr 2016 - Unlocked
24 pages
4MA0 3HR Que 20160526 PDF
No ratings yet
4MA0 3HR Que 20160526 PDF
20 pages
Mathematics A: Paper 3HR Higher Tier
No ratings yet
Mathematics A: Paper 3HR Higher Tier
20 pages
June 19 2hr
No ratings yet
June 19 2hr
26 pages
2018 Summer 2H PDF
No ratings yet
2018 Summer 2H PDF
24 pages
Tuesday 21 May 2019: Mathematics
No ratings yet
Tuesday 21 May 2019: Mathematics
24 pages
p1 Mock 2-Numbered
No ratings yet
p1 Mock 2-Numbered
25 pages
Selected Questions 20200305 2HR
No ratings yet
Selected Questions 20200305 2HR
24 pages
03a International GCSE Mathematics A 4MA1 1H - May 2025 Examination Paper (PDF) 4
50% (2)
03a International GCSE Mathematics A 4MA1 1H - May 2025 Examination Paper (PDF) 4
28 pages
4MA1 Maths 2019 Jun 1H QP
No ratings yet
4MA1 Maths 2019 Jun 1H QP
24 pages
4MA0 3H Que 20120511
No ratings yet
4MA0 3H Que 20120511
24 pages
Questionpaper Paper1F January2018 IGCSE Edexcel Maths
No ratings yet
Questionpaper Paper1F January2018 IGCSE Edexcel Maths
24 pages
4ma1 2h Que 20240604
No ratings yet
4ma1 2h Que 20240604
28 pages
4MA0 3HR Que 20140110 PDF
No ratings yet
4MA0 3HR Que 20140110 PDF
20 pages
1MA0 2F Que 20151106
No ratings yet
1MA0 2F Que 20151106
28 pages
01a IGCSE Maths 4MB1 01 May 2023 Examination Paper PDF
0% (1)
01a IGCSE Maths 4MB1 01 May 2023 Examination Paper PDF
24 pages
Paper 1
No ratings yet
Paper 1
64 pages
Edexcel Igcse Maths Jan 2023 p2h
No ratings yet
Edexcel Igcse Maths Jan 2023 p2h
28 pages
4MA1 1FR Que 20190110
No ratings yet
4MA1 1FR Que 20190110
24 pages
GCSE Maths Higher Tier Guide
No ratings yet
GCSE Maths Higher Tier Guide
24 pages
Contentdampdfinternational GCSEMathematics B2016Exam Materials4mb1 01 Que 20230519 PDF
No ratings yet
Contentdampdfinternational GCSEMathematics B2016Exam Materials4mb1 01 Que 20230519 PDF
24 pages
4MA0 3HR Que 20180525
No ratings yet
4MA0 3HR Que 20180525
24 pages
4MA0 4H Que 20160609
No ratings yet
4MA0 4H Que 20160609
24 pages
1MA1 1H Que 20230520
100% (1)
1MA1 1H Que 20230520
26 pages
Mathematics A: Pearson Edexcel GCSE
No ratings yet
Mathematics A: Pearson Edexcel GCSE
28 pages
4ma1 2h Que 20230118
No ratings yet
4ma1 2h Que 20230118
28 pages
GCSE Maths Exam Instructions
No ratings yet
GCSE Maths Exam Instructions
28 pages
3 Hnov 2018
No ratings yet
3 Hnov 2018
20 pages
Igcse A January 2017 Paper 3h
No ratings yet
Igcse A January 2017 Paper 3h
24 pages
Provisional Answer Key 09 03 2025
No ratings yet
Provisional Answer Key 09 03 2025
9 pages
Diagnostic Test Natural Science 4 Primaria Byme 5 PDF Free
0% (1)
Diagnostic Test Natural Science 4 Primaria Byme 5 PDF Free
2 pages
TG KPWKP 2019 1ST Quarter
0% (1)
TG KPWKP 2019 1ST Quarter
109 pages
Alfa Tau English
No ratings yet
Alfa Tau English
55 pages
Penetration Tester Resume
No ratings yet
Penetration Tester Resume
2 pages
Key Elements of Drama & Theater
0% (1)
Key Elements of Drama & Theater
24 pages
Distributed Leadership Pamphlet
No ratings yet
Distributed Leadership Pamphlet
31 pages
IAPM
No ratings yet
IAPM
1 page
Does Your Name Determine Your Destiny
No ratings yet
Does Your Name Determine Your Destiny
3 pages
Immediate Access Entrepreneurship 12th Edition Hisrich Verified PDF Download
0% (3)
Immediate Access Entrepreneurship 12th Edition Hisrich Verified PDF Download
405 pages
Knowledge Management Toolkit The Practical Techniques For Building A Knowledge Management System Amrit Tiwana Download Instantly
No ratings yet
Knowledge Management Toolkit The Practical Techniques For Building A Knowledge Management System Amrit Tiwana Download Instantly
330 pages
Packet Tracer Reference For Network Administrators and Academy Instructors
No ratings yet
Packet Tracer Reference For Network Administrators and Academy Instructors
13 pages
Intermediate Financial Management 13th Edition Eugene F Brigham Phillip R Daves Ebook and TestBank Bundle Full Version
No ratings yet
Intermediate Financial Management 13th Edition Eugene F Brigham Phillip R Daves Ebook and TestBank Bundle Full Version
344 pages
Detailed Lesson Plan - Lesson 3 - Monreal
No ratings yet
Detailed Lesson Plan - Lesson 3 - Monreal
16 pages
Applied Economics Week1
No ratings yet
Applied Economics Week1
6 pages
Btech Regulations 2015 16
100% (1)
Btech Regulations 2015 16
23 pages
Grad Viewbook 2024-25 - EN - V19 - Single Page
No ratings yet
Grad Viewbook 2024-25 - EN - V19 - Single Page
26 pages
State Common Entrance Test Cell, Maharashtra State, Mumbai
No ratings yet
State Common Entrance Test Cell, Maharashtra State, Mumbai
2 pages
Ancient Greek Inscriptions
100% (2)
Ancient Greek Inscriptions
200 pages
Quay Container Crane Productivity Effectiveness Analysis Case Study PT Jakarta International Container Terminal
No ratings yet
Quay Container Crane Productivity Effectiveness Analysis Case Study PT Jakarta International Container Terminal
9 pages
Pastoral Counseling Research Work Report 1
No ratings yet
Pastoral Counseling Research Work Report 1
24 pages
Day 2
No ratings yet
Day 2
2 pages
Manual of Surgical Pathology Expert Consult Online and Print Expert Consult Title Online Print Third Edition Susan C. Lester MD PHD Instant Download
No ratings yet
Manual of Surgical Pathology Expert Consult Online and Print Expert Consult Title Online Print Third Edition Susan C. Lester MD PHD Instant Download
121 pages
Philosophical Underpinnings of Research
100% (3)
Philosophical Underpinnings of Research
20 pages
Ckad 7
No ratings yet
Ckad 7
19 pages
Plurality of English
100% (1)
Plurality of English
5 pages
Physics: Center of Mass & Momentum
No ratings yet
Physics: Center of Mass & Momentum
6 pages
Aptitude Quiz for Competitive Exams
No ratings yet
Aptitude Quiz for Competitive Exams
1 page
CS353 Fall2024 Syllabus
No ratings yet
CS353 Fall2024 Syllabus
2 pages
Alabama State Policy Grading Rubric
No ratings yet
Alabama State Policy Grading Rubric
3 pages