Please check the examination details below before entering your candidate information

Candidate surname
Mr. Demerdash Other names

Centre Number Candidate Number

Pearson Edexcel
International GCSE

Thursday 6 June 2019

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

Mathematics A
Level 1/2
Paper 2H
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 107
• 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
• Check
Read each question carefully before you start to answer it.
• your answers if you have time at the end.

Turn over

P58371A
©2019 Pearson Education Ltd.

1/1/1/
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 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
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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 FOUR questions.
Write your answers in the spaces provided.
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You must write down all the stages in your working.

1 The table shows information about the heights, in cm, of 48 sunflowers in a garden centre.

Height of sunflower (h cm) Frequency

90  h - 100 8
100  h - 110 12
110  h - 120 15
120  h - 130 10
130  h - 140 3

Work out an estimate for the mean height of the sunflowers.

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

(Total for Question 1 is 4 marks)

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2 Use ruler and compasses to construct the perpendicular bisector of the line DE.
You must show all your construction lines.

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D E

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(Total for Question 2 is 2 marks)

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3 A cylinder has diameter 14 cm and height 20 cm.
Work out the volume of the cylinder.

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Give your answer correct to 3 significant figures.

cm3

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

(Total for Question 3 is 2 marks)

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 4 Josh buys and sells books for a living.
He buys 120 books for £4 each.
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1
He sells of the books for £5 each.
2
He sells 40% of the books for £7 each.
He sells the rest of the books for £8 each.
(a) Calculate Josh’s percentage profit.
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....................................................... %
(5)
One book that Josh owns had a value of £15 on the 1st May 2019
The value of this book had increased by 20% in the last year.
(b) Find the value of the book on the 1st May 2018
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£. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)

(Total for Question 4 is 8 marks)

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5 ABC and DEF are similar triangles.

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Diagram NOT
accurately drawn
B

19.5 cm
6 cm 15 cm

A 4.2 cm C

D F

(a) Work out the length of DF.

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....................................................... cm
(2)
(b) Work out the length of BC.

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

(Total for Question 5 is 4 marks)

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 6 30 students in a class sat a Mathematics test.
The mean mark in the test for the 30 students was 26.8
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13 of the 30 students in the class are boys.

The mean mark in the test for the boys was 25
Find the mean mark in the test for the girls.
Give your answer correct to 3 significant figures.
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.......................................................

(Total for Question 6 is 3 marks)

7 Change a speed of x kilometres per hour into a speed in metres per second.
Simplify your answer.
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....................................................... m/s

(Total for Question 7 is 3 marks)

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*P58371A0928* Turn over
8 Solve the simultaneous equations
x + 2y í

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3x – y = 16
Show clear algebraic working.

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

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

(Total for Question 8 is 3 marks)

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9 The table gives the average crowd attendance per match for each of five football clubs
for one season.

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Football club Average crowd attendance
Monaco 9.5 q 103
Chelsea 4.2 q 104
Juventus 3.9 q 104
Oxford United 8.3 q 103
Barcelona 7.7 q 104

(a) Find the difference between the average crowd attendance for Barcelona and the
average crowd attendance for Monaco.
Give your answer in standard form.

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

(2)

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Antonio says,

“The average crowd attendance for Chelsea is approximately 50 times that for Oxford United.”
(b) Is Antonio correct?
You must give a reason for your answer.

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

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

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

(2)
During last season the cost of a ticket to watch Seapron United increased by 15% and
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then decreased by 8%
(c) Work out the overall percentage change in the cost of a ticket to watch Seapron
United during last season.

....................................................... %
(2)

(Total for Question 9 is 6 marks)

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10 The table gives information about the times taken, in minutes, for 80 taxi journeys.

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Time taken (t minutes) Frequency
0t- 5 7
5  t - 10 10
10  t - 15 12
15  t - 20 19
20  t - 25 18
25  t - 30 14

(a) Complete the cumulative frequency table.

Time taken (t minutes) Cumulative frequency

0t- 5
0  t - 10

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0  t - 15
0  t - 20
0  t - 25
0  t - 30
(1)
(b) On the grid opposite, draw a cumulative frequency graph for your table.

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*P58371A01428*
 80
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70

60

50

Cumulative
40
frequency
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30

20

10

0
0 5 10 15 20 25 30
Time taken (minutes)
(2)
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(c) Use your graph to find an estimate for the median.

....................................................... minutes
(1)
(d) Use your graph to find an estimate for the interquartile range.

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

(Total for Question 10 is 6 marks)

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11 Here are two vectors.

→ ⎛ 6⎞ → ⎛ 1⎞

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AB = ⎜ ⎟ CB = ⎜ ⎟
⎝ −9⎠ ⎝ 3⎠
→
Find the magnitude of AC .

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

(Total for Question 11 is 3 marks)

3x − 2
12 Make x the subject of the formula y =
x +1

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

(Total for Question 12 is 4 marks)

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13 y is directly proportional to the cube of x
y = 20 h when x = h (h ≠ 0)

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(a) Find a formula for y in terms of x and h

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

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(b) Find x in terms of h when y = 67.5 h
Give your answer in its simplest form.

x =. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
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(Total for Question 13 is 5 marks)

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 14 The diagram shows a solid cuboid.

Diagram NOT
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accurately drawn

(12 – 3x) cm

x cm

x cm

The total surface area of the cuboid is A cm2

Find the maximum value of A.
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.......................................................

(Total for Question 14 is 5 marks)

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15 ABCD is a quadrilateral.

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Diagram NOT
accurately drawn
39°
26 cm

D
B 95°

47°

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The area of triangle ACD is 250 cm2
Calculate the area of the quadrilateral ABCD.
Show your working clearly.
Give your answer correct to 3 significant figures.

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

(Total for Question 15 is 6 marks)

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16 The function f is such that f (x) = 3x – 2
(a) Find f (5)

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

(1)
The function g is such that g(x) = 2x2 – 20x + 9 where x . 5
(b) Express the inverse function g–1 in the form g–1(x) = ...

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g–1(x) = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(4)

(Total for Question 16 is 5 marks)

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 17 The diagram shows a solid cuboid made from wood.

12 cm
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Diagram NOT
8 cm accurately drawn

5 cm

The wood has density 0.7 g/cm3

Work out the mass of the cuboid.
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....................................................... grams

(Total for Question 17 is 3 marks)

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18 (a) Write 5.7 × 106 as an ordinary number.

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

(1)
(b) Write 0.004 in standard form.

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

(1)
2 × 104 + 3 × 105
(c) Work out
6.4 × 10 −2

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

(2)

(Total for Question 18 is 4 marks)

19 On 1st January 2016 Li bought a boat for $170 000

The value of the boat depreciates by 8% per year.
Work out the value of the boat on 1st January 2019
Give your answer correct to the nearest dollar.

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

(Total for Question 19 is 3 marks)

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20 A = 2n × 3 × 5m
Write 8A as a product of powers of its prime factors.

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

(Total for Question 20 is 2 marks)

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

7 10 13 16 19

Find the sum of the first 100 terms of this sequence.

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

(Total for Question 21 is 2 marks)

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 22 A and B are two similar vases.
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Diagram NOT
accurately drawn

A B

Vase A has height 24 cm.

Vase B has height 36 cm.
Vase A has a surface area of 960 cm2
(a) Work out the surface area of vase B.
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....................................................... cm2
(2)
Vase B has a volume of V cm3
(b) Find in terms of V, an expression for the volume, in cm3, of vase A.
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....................................................... cm3
(2)

(Total for Question 22 is 4 marks)

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23

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Diagram NOT
accurately drawn

C V

71°
D

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

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TDV is the tangent to the circle at D.
AB = AD
Angle ADT = 71°
Work out the size of angle BCD.
Give a reason for each stage of your working.

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

(Total for Question 23 is 5 marks)

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 24 A solid is made from a hemisphere and a cylinder.
The plane face of the hemisphere coincides with the upper plane face of the cylinder.
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Diagram NOT
accurately drawn

The hemisphere and the cylinder have the same radius.

The ratio of the radius of the cylinder to the height of the cylinder is 1 : 3
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Given that the solid has volume 792ʌ cm3

work out the height of the solid.
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....................................................... cm

(Total for Question 24 is 5 marks)

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25 The graph of y = sinx° for 0 - x - 360 is drawn on the grid.
y

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3

O
60 120 180 240 300 360 x

í

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í

í

(a) On the grid, draw the graph of y = 2sin(x + 30)° for 0 - x - 360
(2)

(b) (i) Write x2íx + 10 in the form (xía)2 + b where a and b are integers.

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

(2)
(ii) Hence, describe fully the single transformation that maps the curve with equation
y = x2 onto the curve with equation y = x2íx + 10

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

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

(2)

(Total for Question 25 is 6 marks)

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*P58365A02224*
26 A particle P is moving along a straight line that passes through the fixed point O.
The displacement, s metres, of P from O at time t seconds is given by

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s = t3ít2 + 5tí

Find the value of t for which the acceleration of P is 3 m/s2

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t = .......................................................

(Total for Question 26 is 4 marks)

TOTAL FOR PAPER IS 100 MARKS

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*P58365A02424*