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Pearson Edexcel International GCSE

Time 2 hours
Paper
reference 4MA1/1H
Mathematics A
 

PAPER 1H
Higher Tier

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

Instructions
• Use black ink or ball-point pen.
• centrethe
Fill in 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.
• – there may questions
Answer the in the spaces provided
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.

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*P72437RA0132*
P72437RA
©2023 Pearson Education Ltd.

J:1/1/1/1/1/
 International GCSE Mathematics
Formulae sheet – Higher Tier

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

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

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
*P72437RA0232*
*P66297A0228* 
 Answer ALL TWENTY FOUR questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1 80 students entered a dancing competition.
The table gives information about the length of time, in minutes, for which each student
spent dancing.

Time (m) Frequency

0 < m  12 11

12 < m  24 25

24 < m  36 23

36 < m  48 15

48 < m  60 6

Work out an estimate for the mean length of time the students spent dancing.

...................................................... minutes

(Total for Question 1 is 4 marks)

3
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 Answer ALL TWENTY FIVE questions.
Write your answers in the spaces provided.
2.
You must write down all the stages in your working.

1 Write 2250 as a product of powers of its prime factors.

Show your working clearly.

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

(Total for Question 1 is 3 marks)

3
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3.
2 Here is a Venn diagram.

E
B
A C

6
7
8
11 5 15 10
13 12
14

(a) Write down the numbers that are in the set

(i) A

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

(1)
(ii) B ∪ C

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

(1)
Dominic writes down 9 ∉ C
(b) Explain why Dominic is correct.

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

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

(1)

(Total for Question 2 is 3 marks)

4
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4.
4 The diagram shows a shape made up of three semicircles, enclosing a
right‑angled triangle.

A Diagram NOT
accurately drawn

6 cm

C 6 cm B

AB, BC and CA are each the diameter of a semicircle.

BC = CA = 6 cm.
Work out the perimeter of the shape.
Give your answer correct to one decimal place.

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

(Total for Question 4 is 5 marks)

6
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5.
2 Here is a biased spinner.

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3 4

2 5
1

The table gives information about the probability that, when the spinner is spun once,
it will land on each number.

Number 1 2 3 4 5

Probability 2x 0.27 0.04 x 0.12

Alexis is going to spin the spinner 400 times.

Work out an estimate for the number of times the spinner will land on an odd number.

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

(Total for Question 2 is 4 marks)

4
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6.
5 In a box, there are only green sweets, orange sweets and yellow sweets.
There are 280 sweets in the box so that
the number of green sweets : the number of orange sweets = 2 : 3
and
the number of orange sweets : the number of yellow sweets = 1 : 5
Work out how many green sweets there are in the box.

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

(Total for Question 5 is 3 marks)

7
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7.
19 The acceleration, a, of an object is given by

v−u
a=
t
where

v = 45.23 correct to 2 decimal places
u = 5.12 correct to 2 decimal places
t = 8.5   correct to 2 significant figures
By considering bounds, work out the value of a to a suitable degree of accuracy.
Show your working clearly and give a reason for your answer.

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

(Total for Question 19 is 5 marks)

21
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8.
4 Divya and Yuan each pay for a holiday at a special offer price.

Divya’s holiday Yuan’s holiday

Normal price: $1600 Normal price: $1400

Special offer: Special offer:

16% off the normal price k % off the normal price

The amount that Divya pays is the same as the amount that Yuan pays.
Work out the value of k

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

(Total for Question 4 is 4 marks)

6
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9.
22 The first term of an arithmetic series is (2t + 1) where t > 0
The nth term of this arithmetic series is (14t – 5)
The common difference of the series is 3
The sum of the first n terms of the series can be written as p(qt – 1) r where p, q and r
are integers.
Find the value of p, the value of q and the value of r
Show clear algebraic working.

(3 marks)

26
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10.
24 OAED is a quadrilateral.

E
Diagram NOT
accurately drawn

7a + 3b

C B
A D
2b
2a
       O
→ → →
OA = 2a OB = 2b DE = 7a + 3b

AB : BD = 1 : 2
The point C on AB is such that OCE is a straight line.
Use a vector method to find the ratio of OC : CE

(4 marks)

30
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11.
7 (a) Write 9.32 × 10–5 as an ordinary number.

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

(1)
(b) Work out 3 × 105 – 6 × 104

Give your answer in standard form.

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

(2)
(c) Work out (3 × 1055) × (6 × 1065)
Give your answer in standard form.

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

(2)

(Total for Question 7 is 5 marks)

8
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12.
7 (a) Simplify g 9 ÷ g 2

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

(1)
(b) Expand 5k 2 (k 3 + 4)

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

(2)
(c) (i) Factorise x 2 − 2 x − 63

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

(2)
(ii) Hence, solve x 2 − 2 x − 63 = 0

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

(1)
(d) Solve the inequality 7  2 y  3 y  12

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

(3)
(Total for Question 7 is 9 marks)

8
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13.
12 Solve the simultaneous equations
4x + 3y = 9.6

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6x + 5y = 16.8
Show clear algebraic working.

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

y = . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 12 is 3
4 marks)

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12
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14.
10 R and T are points on a circle, centre O

M T Diagram NOT
R accurately drawn
52°

RT = 12 cm
M is the midpoint of RT
Angle ROM = 52°
Work out the area of the circle.
Give your answer correct to 3 significant figures.

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

(Total for Question 10 is 4 marks)

11
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15.
16 The function f is such that

2 5
f(x) =    where x ≠
3x − 5 3
 1
(a) Find f  
 3

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

(1)

(b) Find f –1(x)

f –1(x) = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
The function g is such that

g(x) = 5x 2 – 20x + 23

(c) Express g(x) in the form a(x – b)2 + c

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

(3)

(Total for Question 16 is 6 marks)

18
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16.
18 Solve    3(x – 2 3) = x + 2 3

Give your answer in the form a + b 3 where a and b are integers.

Show your working clearly.

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

(Total for Question 18 is 3

4 marks)

20
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17.
19 P is inversely proportional to y2
When y = 4, P = a
(a) Find a formula for P in terms of y and a

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

(3)
Given also that y is directly proportional to x
and when x = a, P = 4a
(b) find a formula for P in terms of x and a

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

(3)

(Total for Question 19 is 6 marks)

21
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18.
20 Here is a sketch of the curve y = a cos(x + b)° for 0  x  360

O 90 180 270 360 x

–1

–2

Given that 0 < b < 180

find the value of a and the value of b

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

b = ......................................................

(Total for Question 20 is 2 marks)

22
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19.
23 G is the point on the curve with equation y = 8x 2 – 14x – 6 where the gradient is 10
The straight line Q passes through the point G and is perpendicular to the tangent at G
Find an equation for Q
Give your answer in the form ax + by + c = 0 where a, b and c are integers.

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

(Total for Question 23 is 54 marks)

26
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 20.
21 There are 25 counters in a bag such that
6 counters are blue
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x counters are orange, where x > 9

the rest of the counters are pink
Maalam takes at random two of the counters from the bag.
22
The probability that Maalam takes one orange counter and one pink counter is
75
Calculate the probability that Maalam takes 2 pink counters from the bag.
Show clear algebraic working.
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 21 is 5 marks)

21
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21.
21 The curve T has equation y = x3 – 2x2 – 9x + 15
dy
(a) Find
dx

dy
= ......................................................
dx
(2)
(b) Find the range of values of x for which T has a positive gradient.
Give your values correct to 3 significant figures.
Show your working clearly.

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

(4)

(Total for Question 21 is 6 marks)

21
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22.
 4x2  7 x  2 
23 Simplify  x 2  4      2x
 x 
ax 2
Give your answer in the form where a, b and c are integers.
bx + c

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

(Total for Question 23 is 4 marks)

24
*P72792A02428* 
23.
25 Here is a triangle ABC

B
Diagram NOT
C accurately drawn

(2x – 1) cm
(2x + 1) cm
30°

The area of the triangle is (x2 + x – 3.75) cm2

Find the size of the largest angle in triangle ABC
Give your answer correct to the nearest degree.

(5 Marks)

26
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