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Candidate surname Other names

Mr. Demerdash
Centre Number Candidate Number
Pearson Edexcel
International GCSE

Thursday 6 June 2019

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

Mathematics A
Level 1/2
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.
• 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.
• Anything
You must NOT write anything on the formulae page.
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.
• your answers if you have time at the end.
Check

Turn over

P60261A
©2019 Pearson Education Ltd.

1/1/1/
*P60261A0124*
 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 v
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 = ʌU h = area of cross section ulength
3
Curved surface area of cone = ʌUO

O cross
h section

length
U
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Volume of cylinder = ʌU2h 4 3

Curved surface area Volume of sphere = ʌU
3
of cylinder = 2ʌUK
Surface area of sphere = 4ʌU2
U

U
h

2
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 Answer ALL TWENTY TWO questions.

Write your answers in the spaces provided.

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You must write down all the stages in your working.

1 (a)

í í í 0 1 2 3 4 5 x

Write down the inequality shown on the number line.

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

(1)
(b) Solve the inequality 4yí- y + 8
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.......................................................

(2)

(Total for Question 1 is 3 marks)

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 2 ABC and DEF are similar triangles.

A D
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Diagram NOT
12 cm accurately drawn

B
16 cm E
C
40 cm
F

(a) Work out the length of DE.

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....................................................... cm
(2)
The area of triangle DEF is 525 cm2
(b) Find the area of triangle DEF in m2

....................................................... m2
(2)
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(Total for Question 2 is 4 marks)

5
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3 A football team played 55 games.
Each game was won, drawn or lost.
number of games won : number of games drawn : number of games lost = 6 : 3 : 2

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Work out how many more games the team won than the team lost.

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

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(Total for Question 7 is 3 marks)

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 4 A = 32 × 5 4 × 7 B = 34 × 53 × 7 × 11
(a) Find the highest common factor (HCF) of A and B.
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.......................................................

(2)
(b) Find the lowest common multiple (LCM) of A and B.
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.......................................................

(2)

(Total for Question 8 is 4 marks)

5 (a) Write 840 000 in standard form.

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

(1)
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(b) Work out (6 × 107) ÷ (8 × 10í)

Give your answer in standard form.

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

(2)

(Total for Question 9 is 3 marks)

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6 Sandeep recorded the length of time, in minutes, that each of 100 adults went for a walk
one Saturday afternoon.

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The cumulative frequency table gives information about these times.

Cumulative
Time (t minutes)
frequency
30  t - 40 6

30  t - 50 20

30  t - 60 56

30  t - 70 84

30  t - 80 95

30  t - 90 100

(a) On the grid, draw a cumulative frequency graph for the information in the table.

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100

80

60
Cumulative
frequency

40
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20

0
30 40 50 60 70 80 90

Time (minutes)
(2)

10
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 (b) Use your graph to find an estimate for the median length of time that these adults
went for a walk.
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....................................................... minutes
(2)
One of the 100 adults is chosen at random.
(c) Use your graph to find an estimate for the probability that this adult went for a walk
for more than 72 minutes.
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.......................................................

(3)

(Total for Question 13 is 7 marks)

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

B
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C Diagram NOT
accurately drawn

98°

A
D

AOC is a diameter of the circle.

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Angle AOD = 98°

Work out the size of angle DBC.
Give a reason for each stage in your working.
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°
.......................................................

(Total for Question 15 is 4 marks)

13
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8 The following table gives values of x and y where y is inversely proportional to the
square of x.

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x 1.5 2 3 4
y 16 9 4 2.25

(a) Find a formula for y in terms of x.

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

(3)
Given that x  0
(b) find the value of x when y = 144

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

(2) DO NOT WRITE IN THIS AREA

(Total for Question 16 is 5 marks)

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 9 The table gives information about the first six terms of a sequence of numbers.
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Term number 1 2 3 4 5 6
1× 2 2×3 3×4 4×5 5×6 6×7
Term of sequence
2 2 2 2 2 2

Prove algebraically that the sum of any two consecutive terms of this sequence is always
a square number.
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(Total for Question 17 is 4 marks)

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10 The functions f and g are defined as

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f(x) = and g(x) = xí
4x − 3

(a) State which value of x must be excluded from any domain of the function f.

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

(1)
(b) Find fg(x).
Simplify your answer.

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

(c) Express the inverse function f í in the form f í(x) = …

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f í(x) = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)

16
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 Part of the curve with equation y = h(x) is shown on the grid.

y
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20

15

10

í í O 1 2 3 x
í

í

(d) Find an estimate for the gradient of the curve at the point where x í
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Show your working clearly.

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

(3)

(Total for Question 18 is 9 marks)

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11 The diagram shows two similar bottles, A and B.

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Diagram NOT
accurately drawn

A
B

Bottle A has surface area 240 cm2

Bottle B has surface area 540 cm2 and volume 2025 cm3
Work out the volume of bottle A.

....................................................... cm3 DO NOT WRITE IN THIS AREA

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(Total for Question 21 is 3 marks)

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

(Total for Question 23 is 6 marks)

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Turn over for Question 24

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DO NOT WRITE IN THIS AREA

You must write down all the stages in yourworking.

2
13 The diagram shows a cylinder.

Diagram NOT
accurately drawn
8.2 cm

10 cm
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The cylinder has radius 8.2 cm and height 10 cm.

The cylinder is empty.
Pam pours 1.5 litres of water into the cylinder.
Work out the depth of the water in the cylinder.
Give your answer correct to 1 decimal place.
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.................................................... cm

(Total for Question 1 is 3 marks)

3
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 13 Lorenzo increases all the prices on his restaurant menu by 8%
Before the increase, the price of a dessert was $4.25
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(a) Work out the price of the dessert after the increase.

$ .......................................................
(3)
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After the increase, the price of lasagne is $9.45

(b) Work out the price of lasagne before the increase.
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$ .......................................................
(3)

(Total for Question 6 is 6 marks)

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 14 There are 10 people in a lift.
These 10 people have a mean weight of 79.2 kg.
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3 of these people get out of the lift.

These 3 people have a mean weight of 68 kg.
Work out the mean weight of the 7 people left in the lift.
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.................................................... kg

(Total for Question 8 is 3 marks)

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

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

9
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15 3 years ago, the ratio of Tom’s age to Clemmie’s age was 2 : 7
Tom is now 15 years old and Clemmie is now x years old.
Find the value of x.

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

(Total for Question 11 is 3 marks)

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 16 A particle P is moving along a straight line.
The fixed point O lies on this line.
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At time t seconds, the displacement, s metres, of P from O is given by

s = 4t 3ít 2 + 5t
At time t seconds, the velocity of P is v m/s.
(a) Find an expression for v in terms of t.

v = .......................................................
(2)
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(b) Find the time at which the acceleration of the particle is 6 m/s2
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....................................................... seconds
(3)

(Total for Question 16 is 5 marks)

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17 The 25th term of an arithmetic series is 44.5
The sum of the first 30 terms of this arithmetic series is 765

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Find the 16th term of the arithmetic series.
Show your working clearly.

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

(Total for Question 19 is 5 marks)

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 18 a = 25 q 1014n where n is an integer.
3

Find an expression, in terms of n, for a 2

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Give your answer in standard form.

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

(Total for Question 20 is 3 marks)

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19 A curve has equation y = f(x)
There is only one maximum point on the curve.

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The coordinates of this maximum point are (4, 3)
(a) Write down the coordinates of the maximum point on the curve with equation
(i) y = f(x – 5)

(. . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
(ii) y = 3f(x)

(. . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
(2)
Here is the graph of y = a sin(bx)° for 0 - x - 360

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2–

1–

O–
–

90 180 270 360 x

–1 –

–2 –

(b) Find the value of a and the value of b.

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a = .......................................................

b = .......................................................
(2)

(Total for Question 21 is 4 marks)

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 20 Solve the simultaneous equations
2x2 + 3y2 = 5
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y = 2x + 1
Show clear algebraic working.
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..................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 22 is 5 marks)

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21
C

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B Diagram NOT
x accurately drawn

54°
A
F D

32°

B, C, D and F are points on a circle.

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ABC, AFD, BFE and CDE are straight lines.
Work out the size of angle x.
Show your working clearly.

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°
x = .......................................................

(Total for Question 23 is 4 marks)

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*P60260A02224*
 22
A P B
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Diagram NOT
a accurately drawn
Q

O c C
→ → →
OA = a OC = c AB = 2c
P is the point on AB such that AP : PB = 3 : 1
Q is the point on AC such that OQP is a straight line.

Use a vector method to find AQ : QC

Show your working clearly.
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AQ : QC = .......................................................

(Total for Question 24 is 5 marks)

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