Mr.

Seif Atef 302

www.dynamicpapers.com
Please check the examination details below before entering your candidate information
Candidate surname Other names

Centre Number Candidate Number

Pearson Edexcel
International GCSE

Tuesday 3 November 2020

Morning (Time: 2 hours) Paper Reference 4MA1/1H

Mathematics A
Paper 1H
Higher Tier

You must have: Total Marks

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

Instructions
• Use black ink or ball-point pen.
• candidate
Fill in the boxes at the top of this page with your name, centre number and
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

P62652A
©2020 Pearson Education Ltd.

1/1/1/1/
*P62652A0128*
Mr. Seif Atef 303

International GCSE Mathematics

Formulae sheet – Higher Tier

DO NOT WRITE IN THIS AREA

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

DO NOT WRITE IN THIS AREA

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
DO NOT WRITE IN THIS AREA

Volume of cylinder = πr2h 4 3

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

r
h

2
*P62652A0228*
Mr. Seif Atef 304

Answer ALL TWENTY FIVE 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 numbers from 1 to 14 are shown in the Venn diagram.

E
9
A 1 B
2 13
8
6 3
4 11
14
12
10 7
5
DO NOT WRITE IN THIS AREA

(a) List the members of the set A ∩ B

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

(1)
(b) List the members of the set Bʹ

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

(1)
A number is picked at random from the numbers in the Venn diagram.
(c) Find the probability that this number is in set A but is not in set B.
DO NOT WRITE IN THIS AREA

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

(2)

(Total for Question 1 is 4 marks)

3
*P62652A0328* Turn over
Mr. Seif Atef 305

2 Toy cars are made in a factory.

The toy cars are made for 15 hours each day.
5 toy cars are made every 12 seconds.

DO NOT WRITE IN THIS AREA

For the toy cars made each day, the probability of a toy car being faulty is 0.002
Work out an estimate of the number of faulty toy cars that are made each day.

DO NOT WRITE IN THIS AREA

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

(Total for Question 2 is 4 marks)

DO NOT WRITE IN THIS AREA

4
*P62652A0428*
Mr. Seif Atef 306

3 On the grid, draw the graph of y = 7 – 4x for values of x from −2 to 3

DO NOT WRITE IN THIS AREA

y
16

14

12

10

8
DO NOT WRITE IN THIS AREA

−2 −1 O 1 2 3 x

−2

−4
DO NOT WRITE IN THIS AREA

−6

−8

(Total for Question 3 is 3 marks)

5
*P62652A0528* Turn over
Mr. Seif Atef 307

4 Here is a list of six numbers written in order of size.

4 7 x 10 y y

DO NOT WRITE IN THIS AREA

The numbers have
a median of 9
a mean of 11
Find the value of x and the value of y.

DO NOT WRITE IN THIS AREA

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

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

(Total for Question 4 is 4 marks)

6
*P62652A0628*
Mr. Seif Atef 308

5 (a) Write 5.7 × 10–3 as an ordinary number.

DO NOT WRITE IN THIS AREA

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

(1)
(b) Write 800 000 in standard form.

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

(1)

3 × 105 − 2.7 × 104

(c) Work out
6 × 10 −2
DO NOT WRITE IN THIS AREA

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

(2)

(Total for Question 5 is 4 marks)

6 A rocket travelled 100 km at an average speed of 28 440 km/h.

Work out how long it took the rocket to travel the 100 km.
Give your answer in seconds, correct to the nearest second.
DO NOT WRITE IN THIS AREA

. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. . .. .. . .. . . .. .. . . .. . . . .. . . seconds

(Total for Question 6 is 3 marks)

7
*P62652A0728* Turn over
Mr. Seif Atef 309

7 (a) Solve 5(4 – x) = 7 – 3x

Show clear algebraic working.

DO NOT WRITE IN THIS AREA

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

DO NOT WRITE IN THIS AREA

(b) Factorise fully 16m3g3 + 24m2g5

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

(2)
(c) (i) Factorise y2 – 2y – 48

DO NOT WRITE IN THIS AREA

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

(2)
(ii) Hence, solve y2 – 2y – 48 = 0

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

(1)

(Total for Question 7 is 8 marks)

8
*P62652A0828*
Mr. Seif Atef 310

8 Here is a 10-sided polygon.

Diagram NOT
DO NOT WRITE IN THIS AREA

accurately drawn
148°

150° 150°

168° 168°

134° 134°

125°
125°
DO NOT WRITE IN THIS AREA

x°

Work out the value of x.

DO NOT WRITE IN THIS AREA

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

(Total for Question 8 is 4 marks)

9
*P62652A0928* Turn over
Mr. Seif Atef 311

9 In a sale, normal prices are reduced by 20%

A bag costs 1080 rupees in the sale.

DO NOT WRITE IN THIS AREA

Work out the normal price of the bag.

DO NOT WRITE IN THIS AREA

. .. .. .. . .. .. .. .. .. .. .. . .. .. .. .. . .. . . .. . .. . . .. . . .. . . .. . . rupees

(Total for Question 9 is 3 marks)

DO NOT WRITE IN THIS AREA

10
*P62652A01028*
Mr. Seif Atef 312

10 A = 2 × 343
B = 16 × 337
DO NOT WRITE IN THIS AREA

(a) Find the highest common factor (HCF) of A and B.

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

(1)
(b) Express the number A × B as a product of powers of its prime factors.
DO NOT WRITE IN THIS AREA

Give your answer in its simplest form.

DO NOT WRITE IN THIS AREA

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

(2)

(Total for Question 10 is 3 marks)

11
*P62652A01128* Turn over
Mr. Seif Atef 313

11 The diagram shows trapezium ABCD in which BC and AD are parallel.

B 8.4 cm C

DO NOT WRITE IN THIS AREA

Diagram NOT
accurately drawn

A 17.6 cm D

The trapezium has exactly one line of symmetry.

BC = 8.4 cm
AD = 17.6 cm
The trapezium has area 179.4 cm2
Work out the size of angle ABC.
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 6 marks)

12
*P62652A01228*
Mr. Seif Atef 314

12 Solve the simultaneous equations

7x – 2y = 34
DO NOT WRITE IN THIS AREA

3x + 5y = −3
Show clear algebraic working.
DO NOT WRITE IN THIS AREA

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

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

(Total for Question 12 is 4 marks)

DO NOT WRITE IN THIS AREA

13
*P62652A01328* Turn over
Mr. Seif Atef 315

13 Jan invests $8000 in a savings account.

The account pays compound interest at a rate of x % per year.

DO NOT WRITE IN THIS AREA

At the end of 6 years, there is a total of $8877.62 in the account.

Work out the value of x.

Give your answer correct to 2 decimal places.

DO NOT WRITE IN THIS AREA

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

(Total for Question 13 is 3 marks)

DO NOT WRITE IN THIS AREA

14
*P62652A01428*
Mr. Seif Atef 316

14 F is inversely proportional to the square of v.

Given that F = 6.5 when v = 4
DO NOT WRITE IN THIS AREA

find a formula for F in terms of v.

DO NOT WRITE IN THIS AREA

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

(Total for Question 14 is 3 marks)

DO NOT WRITE IN THIS AREA

15
*P62652A01528* Turn over
Mr. Seif Atef 317

15 Harry has two fair 5-sided spinners.

DO NOT WRITE IN THIS AREA

red red
red red
green green
green red
green red

Spinner A Spinner B

Harry is going to spin each spinner once.

(a) Complete the probability tree diagram.

Spinner A Spinner B

DO NOT WRITE IN THIS AREA

red
. .. .. .. .. .. . .. .. .. ..

red
..... ...............

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

green

red
.. .. .. . .. .. .. .. .. .. .

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

green

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

green

(2)

16
*P62652A01628*
Mr. Seif Atef 318

(b) Work out the probability that at least one of the spinners will land on green.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

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

(3)

(Total for Question 15 is 5 marks)

DO NOT WRITE IN THIS AREA

17
*P62652A01728* Turn over
Mr. Seif Atef 319

16

Diagram NOT

DO NOT WRITE IN THIS AREA

accurately drawn

58°
O
P

M
L

L, M, N and P are points on a circle, centre O

DO NOT WRITE IN THIS AREA

Angle MNP = 58°
(a) (i) Find the size of angle MLP

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

(ii) Give a reason for your answer.

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

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

(2)
(b) Find the size of the reflex angle MOP

DO NOT WRITE IN THIS AREA

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

(2)

(Total for Question 16 is 4 marks)

18
*P62652A01828*
Mr. Seif Atef 320

17 A metal block has a mass of 5 kg, correct to the nearest 50 grams.

–3
The block has a volume of (1.84 × 10 ) m3, correct to 3 significant f igures.
DO NOT WRITE IN THIS AREA

Work out the upper bound for the density of the block.
Give your answer in kg /m3 correct to 1 decimal place.
Show your working clearly.
DO NOT WRITE IN THIS AREA

.. .. .. .. .. . .. .. .. .. .. .. .. . .. .. . .. . . .. .. . . . .. . . .. . . .. . . . kg/m3

(Total for Question 17 is 4 marks)

DO NOT WRITE IN THIS AREA

19
*P62652A01928* Turn over
Mr. Seif Atef 321

18 The table gives information about the heights, in centimetres, of some plants.

DO NOT WRITE IN THIS AREA

Height (h cm) Frequency

10 < h  20 35

20 < h  35 45

35 < h  50 75

50 < h  70 40

70 < h  80 8

(a) On the grid, draw a histogram for this information.

DO NOT WRITE IN THIS AREA

DO NOT WRITE IN THIS AREA

0
10 20 30 40 50 60 70 80

Height (h cm)
(3)

20
*P62652A02028*
Mr. Seif Atef 322

(b) Work out an estimate for the number of these plants with a height greater than 40 cm.
DO NOT WRITE IN THIS AREA

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

(2)

(Total for Question 18 is 5 marks)

DO NOT WRITE IN THIS AREA

6
19 Without using a calculator, rationalise the denominator of
3− 7
Simplify your answer.
You must show each stage of your working.
DO NOT WRITE IN THIS AREA

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

(Total for Question 19 is 3 marks)

21
*P62652A02128* Turn over
Mr. Seif Atef 323

20 R and S are two similar solid shapes.

Shape R has surface area 108 cm2 and volume 135 cm3

DO NOT WRITE IN THIS AREA

Shape S has surface area 300 cm2
Work out the volume of shape S.

DO NOT WRITE IN THIS AREA

. .. .. .. .. . .. .. .. .. .. .. .. . .. . .. . . .. .. . . .. . . . .. . . .. . . .. . . cm3

(Total for Question 20 is 3 marks)

DO NOT WRITE IN THIS AREA

22
*P62652A02228*
Mr. Seif Atef 324

21 Express

9x2 − 4
DO NOT WRITE IN THIS AREA

1 7
× 2 −
3 x − 2 3 x − 13 x − 10 x − 1

as a single fraction in its simplest form.

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

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

(Total for Question 21 is 5 marks)

23
*P62652A02328* Turn over
Mr. Seif Atef 325

22 ABCD is a rhombus.
The diagonals, AC and BD, intersect at the point M.

DO NOT WRITE IN THIS AREA

The coordinates of M are (6, −11)
The points A and C both lie on the line with equation 2y + 7x = 20

Find the exact coordinates of the point where the line through B and D intersects the y-axis.

DO NOT WRITE IN THIS AREA

DO NOT WRITE IN THIS AREA

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

(Total for Question 22 is 4 marks)

24
*P62652A02428*
Mr. Seif Atef 326

23 Curve C has equation y = px3 − mx where p and m are positive integers.

Find the range of values of x, in terms of p and m, for which the gradient of C is negative.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA

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

(Total for Question 23 is 4 marks)

DO NOT WRITE IN THIS AREA

25
*P62652A02528* Turn over
Mr. Seif Atef 327

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

8 15 22 29 36

DO NOT WRITE IN THIS AREA

Work out the sum of all the terms from the 50th term to the 100th term inclusive.

DO NOT WRITE IN THIS AREA

DO NOT WRITE IN THIS AREA

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

(Total for Question 24 is 4 marks)

26
*P62652A02628*
Mr. Seif Atef 328

25 The curve with equation y = g(x) is transformed to the curve with equation y = −g(x) by
the single transformation T.
DO NOT WRITE IN THIS AREA

(a) Describe fully the transformation T.

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

(1)
The diagram shows the graph of y = f(x)

y
6

2
DO NOT WRITE IN THIS AREA

−2 O 2 4 6 8 10 x

−2

−4

−6

(b) On the grid, draw the graph of y = 2f(x – 1)

DO NOT WRITE IN THIS AREA

(2)

(Total for Question 25 is 3 marks)

TOTAL FOR PAPER IS 100 MARKS

27
*P62652A02728*
 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

*P62652A02828*
BLANK PAGE
329
Mr. Seif Atef

28