Please check the examination details below before entering your candidate information

Candidate surname Other names

Mr. Demerdash
Centre Number Candidate Number
Pearson Edexcel
International GCSE

Wednesday 15 January 2020

Morning (Time: 2 hours) Paper Reference 4MA1/2HR

Mathematics A
Paper 2HR
Higher Tier

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 89
• 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.
• your answers if you have time at the end.
Check

Turn over

*P59817A0128*
P59817A
©2020 Pearson Education Ltd.

1/1/1/1/
 International GCSE Mathematics

Formulae sheet – Higher Tier

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Arithmetic series 1
n Area of trapezium = (a + b)h
Sum to n terms, Sn = [2a + (n – 1)d] 2
2
The quadratic equation a

The solutions of ax2 + bx + c = 0 where

a ¹ 0 are given by: h

−b ± b2 − 4ac
x=
2a b

Trigonometry In any triangle ABC

C a b c
Sine Rule = =
sin A sin B sin C

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b a Cosine Rule a2 = b2 + c2 – 2bccos A
1
Area of triangle = ab sin C
A B 2
c

1 2 Volume of prism
Volume of cone = πr h = area of cross section × length
3
Curved surface area of cone = πrl

l cross
h section

length
r
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Volume of cylinder = πr2h DO NOT WRITE IN THIS AREA

4 3
Curved surface area Volume of sphere = πr
3
of cylinder = 2πrh
Surface area of sphere = 4πr2
r

r
h

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*P59817A0228*
 Answer ALL TWENTY SIX questions.

Write your answers in the spaces provided.

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You must write down all the stages in your working.

1 (a) Write 517 × 52 as a single power of 5

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

(1)
(b) Write 800 as a product of its prime factors.
Show your working clearly.
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(Total for Question 1 is 3 marks)

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2 The table gives information about the amount of money, in £, that Fiona spent in a
grocery store each week during 2019

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Amount spent (£x) Frequency

0  x <   20 5

20  x <   40 11

40  x <   60 8

60  x <   80 19

80  x < 100 9

Work out an estimate for the total amount of money that Fiona spent in the grocery store
during 2019

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

(Total for Question 2 is 3 marks)

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 3 Use ruler and compasses only to construct the perpendicular bisector of the line AB.
You must show all your construction lines.
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A
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B
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(Total for Question 3 is 2 marks)

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4 Solve the simultaneous equations
3x + 5y = 6
7x – 5y = –11

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Show clear algebraic working.

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

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

(Total for Question 4 is 3 marks)

5 Hamish buys a new car for $20 000

The car depreciates in value by 19% each year.
Work out the value of the car at the end of 3 years.
Give your answer to the nearest $.

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

(Total for Question 5 is 3 marks)

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 6 The diagram shows a box in the shape of a cuboid.

Diagram NOT
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accurately drawn

x cm
1.2 cm

The box is put on a table.

The face of the box in contact with the table has length 1.2 metres and width x metres.
The force exerted by the box on the table is 27 newtons.
The pressure on the table due to the box is 30 newtons/m2

force
pressure =
area
Work out the value of x.
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x= .......................................................

(Total for Question 6 is 3 marks)

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7 The table shows information about the surface area of each of the world’s oceans.

Surface area in

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Ocean
square kilometres
Pacific 1.56 × 108

Indian 6.86 × 107

Southern 2.03 × 107

Arctic 1.41 × 107

Atlantic 1.06 × 108

(a) Work out the difference, in square kilometres, between the surface area of the
Atlantic Ocean and the surface area of the Indian Ocean.
Give your answer in standard form.

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....................................................... square kilometres
(2)
The surface area of the Pacific Ocean is k times the surface area of the Arctic Ocean.
(b) Work out the value of k.
Give your answer correct to the nearest whole number.
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k= . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(Total for Question 7 is 3 marks)

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 8 (a) Write down the integer values of x that satisfy the inequality –2 < x  4
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..................................................................................

(2)
The region R, shown shaded in the diagram, is bounded by three straight lines.

y
Diagram NOT
y=x–3 accurately drawn
y=6

R
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O x
x+y=5

(b) Write down the three inequalities that define the region R.
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.......................................................

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

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

(2)

(Total for Question 8 is 4 marks)

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 9
G F
Diagram NOT
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7 cm accurately drawn
B C

h cm H E
10 cm
A 12 cm D

The diagram shows a prism ABCDEFGH in which ABCD is a trapezium with BC parallel
to AD and CDEF is a rectangle.
BC = 7 cm     AD = 12 cm     DE = 10 cm
The height of trapezium ABCD is h cm
The volume of the prism is 608 cm3
Work out the value of h.
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h= .......................................................

(Total for Question 9 is 3 marks)

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10 Max kept a record of the marks he scored in each of the 11 spelling tests he took one term.
Here are his marks.

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18     5     7     12     11     18     15     16     17     13     14
Find the interquartile range of the marks.

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

(Total for Question 10 is 3 marks)

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 11 A
Diagram NOT
accurately drawn
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9 cm

C 8 cm
P
D
6 cm

APB and CPD are chords of a circle.

AP = 9 cm PB = 6 cm CP = 8 cm
Calculate the length of PD.
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....................................................... cm

(Total for Question 11 is 2 marks)

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12 Solve the inequality 5y2 – 17y  40

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

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(3)

(Total for Question 12 is 3 marks)

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 13 The diagram shows two similar vases, A and B.
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Diagram NOT
accurately drawn

13 cm
9 cm

A B

The height of vase A is 9 cm and the height of vase B is 13 cm.

Given that
surface area of vase A + surface area of vase B = 1800 cm2

calculate the surface area of vase A.

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

(Total for Question 13 is 4 marks)

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 14 The first term of an arithmetic series S is –6
The sum of the first 30 terms of S is 2865
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Find the 9th term of S.

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

(Total for Question 14 is 4 marks)

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 15 N is a multiple of 5
A=N+1
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B=N–1
Prove, using algebra, that A2 – B2 is always a multiple of 20
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(Total for Question 15 is 3 marks)

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16 The diagram shows trapezium OACB.

A 4b C

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Diagram NOT
accurately drawn

3a

O 6b B

→ → →
OA = 3a       OB = 6b       AC = 4b
N is the point on OC such that ANB is a straight line.
→
Find ON as a simplified expression in terms of a and b.

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(Total for Question 16 is 5 marks)

TOTAL FOR PAPER IS 100 MARKS

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*P59817A02628*
17 Brendon, Asha and Julie share some money in the ratios 3 : 2 : 6
The total amount of money that Asha and Julie receive is $36

Work out the amount of money that Brendon receives.

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

(Total for Question 17 is 3 marks)

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18 In a sale, the normal price of a hat is reduced by 15%
The sale price of the hat is 20.40 euros.
Work out the normal price of the hat.

...................................................... euros

(Total for Question 18is 3 marks)

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19 5 children are playing on a trampoline.
The mean weight of the 5 children is 28 kg.
2 of the children get off the trampoline.
The mean weight of these 2 children is 26.5 kg.
Work out the mean weight of the 3 children who remain on the trampoline.

...................................................... kg

(Total for Question 19 is 3 marks)

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20 Pablo made a solid gold statue.
He melted down some gold blocks and used the gold to make the statue.
Each block of gold was a cuboid, as shown below.

Diagram NOT
accurately drawn

1.5 cm 8 cm

2 cm

The mass of the statue is 5.73 kg.

The density of gold is 19.32 g/cm3
Work out the least number of gold blocks Pablo melted down in order to make the statue.
Show your working clearly.

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

(Total for Question 20 is 5 marks)

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21 The cumulative frequency graph gives information about the waiting times, in minutes,
of people with appointments at Hospital A.

60

50

40
Cumulative
frequency 30

20

10

0
0 10 20 30 40 50
Waiting time (minutes)

(a) Use the graph to find an estimate of the median waiting time at Hospital A.

...................................................... minutes
(1)
(b) Use the graph to find an estimate of the interquartile range of the waiting times at
Hospital A.

...................................................... minutes
(2)
At a different hospital, Hospital B, the median waiting time is 28 minutes and the
interquartile range of the waiting times is 19 minutes.
(c) Compare the waiting times at Hospital A with the waiting times at Hospital B.

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

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

(2)

(Total for Question 21 is 5 marks)

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*P58443A01224*
22

B Diagram NOT
accurately drawn
38°

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

Angle ABC = 38°
Work out the size of angle OAC.
Give a reason for each stage of your working.

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

(Total for Question 22 is 4 marks)

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23 The function f is such that fx)
( = (x − 4)2 for all values of x.
(a) Find f (1)

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

(1)
(b) State the range of the function f.

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

(1)
4
The function g is such that g(x) = x ≠ −3
x+3
(c) Work out fg(2)

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

(2)

(Total for Question 23 is 4 marks)

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*P58443A01724* Turn over
24 The diagram shows a frustum of a cone and a sphere.
The frustum is made by removing a small cone from a large cone.
The cones are similar.

Diagram NOT
accurately drawn
h cm

2h cm
r cm

r cm

The height of the small cone is h cm.

The height of the large cone is 2h cm.
The radius of the base of the large cone is r cm.
The radius of the sphere is r cm.
Given that the volume of the frustum is equal to the volume of the sphere,
find an expression for r in terms of h.
Give your expression in its simplest form.

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*P58443A02024*
 r = ......................................................

(Total for Question 24 is 5 marks)

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25 A particle moves along a straight line.
The fixed point O lies on this line.
The displacement of the particle from O at time t seconds, t  0, is s metres where

s = t 3 + 4t 2 − 5t + 7

At time T seconds the velocity of P is V m/s where V  −5

Find an expression for T in terms of V.

−4 + k + mV
Give your expression in the form where k and m are integers to be found.
3

T = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 25 is 6 marks)

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*P58443A02424*