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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.
• 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.
• Checkanswer
Try to every question.
• your answers if you have time at the end.

Turn over

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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

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Answer ALL TWENTY FOUR questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

1 (a) Simplify a7 × a 4

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

(1)
(b) Simplify w 15 ÷ w 3

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

(1)
(c) Simplify (8x 5y 3)2

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

(2)
(d) Make t the subject of c = t 3 – 8v

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

(2)

(Total for Question 1 is 6 marks)

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2 Danil, Gabriel and Hadley share some money in the ratios 3 : 5 : 9
The difference between the amount of money that Gabriel receives and the amount of
money that Hadley receives is 196 euros.
Work out the amount of money that Danil receives.

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

(Total for Question 2 is 3 marks)

3 The diagram shows triangle ABC

A B
Diagram NOT
accurately drawn
8.4 cm 65°

Work out the length of the side AB

Give your answer correct to 3 significant figures.

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

(Total for Question 3 is 3 marks)

4
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4 Sarah makes and sells mugs.

One day she makes 150 mugs.
Her total cost for making these mugs is £1140
Of these mugs
2
are small mugs
5
32% are medium mugs
and the rest are large mugs
Here is Sarah’s price list for selling each mug.

MUGS
Small  £8.50
Medium £11.20
Large £14.20

Sarah sells all 150 mugs.

Work out her percentage profit.
Give your answer correct to the nearest whole number.

...................................................... %

(Total for Question 4 is 5 marks)

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5 Jenny has six cards.
Each card has a whole number written on it so that

the smallest number is 5

the largest number is 24
the median of the six numbers is 14
the mode of the six numbers is 8
Jenny arranges her cards so that the numbers are in order of size.

5 24
.............. .............. .............. ..............

(a) For the remaining four cards, write on each dotted line a number that could be on
the card.

(3)
A basketball team plays 6 games.
After playing 5 games, the team has a mean score of 21 points per game.
After playing 6 games, the team has a mean score of 23 points per game.
(b) Work out the number of points the team scored in its 6th game.

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

(3)
(Total for Question 5 is 6 marks)

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6 (a) Solve the inequality 5x – 7  2

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

(2)

(b) (i) Factorise y 2 – 2y – 35

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

(2)

(ii) Hence, solve y 2 – 2y – 35 = 0

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

(1)

(Total for Question 6 is 5 marks)

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7 E = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
A ∩ B = {5, 10, 15}
B¢ = {7, 8, 9, 11, 12, 13, 14}
A¢ = {4, 6, 7, 8, 14}
Complete the Venn diagram for this information.

A B

(Total for Question 7 is 3 marks)

8 a = 4.2 × 10–24 b = 3 × 10145
Work out the value of a × b
Give your answer in standard form.

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

(Total for Question 8 is 2 marks)

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9 The diagram shows isosceles triangle ABC

A
Diagram NOT
17.5 cm 17.5 cm accurately drawn

B C
28 cm

AB = AC = 17.5 cm BC = 28 cm
Calculate the area of triangle ABC

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

(Total for Question 9 is 4 marks)

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10 The straight line L has equation  2y + 7x = 10
(a) Find the gradient of L

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

(2)
(b) Find the coordinates of the point where L crosses the y‑axis.

(. . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . )
(1)

(Total for Question 10 is 3 marks)

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11 Himari invests 200 000 yen for 3 years in a savings account paying compound interest.
The rate of interest is 1.8% for the first year and x% for each of the second year and the
third year.
The value of the investment at the end of the third year is 209 754 yen.
Work out the value of x
Give your answer correct to one decimal place.

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

(Total for Question 11 is 3 marks)

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12 The table gives information about the times, in minutes, taken by 80 customers to do
their shopping in a supermarket.

Time taken (t minutes) Frequency

 0 < t  10  7

10 < t  20 26

20 < t  30 24

30 < t  40 14

40 < t  50  7

50 < t  60  2

(a) Complete the cumulative frequency table.

Cumulative
Time taken (t minutes)
frequency

0 < t  10

0 < t  20

0 < t  30

0 < t  40

0 < t  50

0 < t  60
(1)
(b) On the grid opposite, draw a cumulative frequency graph for your table.

12
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80

70

60

50

Cumulative
frequency
40

30

20

10

0
0 10 20 30 40 50 60
Time taken (minutes)
(2)
(c) Use your graph to find an estimate for the median time taken.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . minutes
(1)
One of the 80 customers is chosen at random.
(d) Use your graph to find an estimate for the probability that the time taken by this
customer was more than 42 minutes.

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

(2)
(Total for Question 12 is 6 marks)

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13 (a) Expand and simplify 5x(x + 2)(3x – 4)

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

(3)
3
−
(b) Simplify completely  16 w8  4
 y 20 

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

(3)

(Total for Question 13 is 6 marks)

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14 Aika has 2 packets of seeds, packet A and packet B

There are 12 seeds in packet A and 7 of these are sunflower seeds.
There are 15 seeds in packet B and 8 of these are sunflower seeds.
Aika is going to take at random a seed from packet A and a seed from packet B
(a) Complete the probability tree diagram.

packet A packet B
sunflower
....................

sunflower
7
12
....................

not sunflower

sunflower
....................

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

not sunflower

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

not sunflower
(2)
(b) Calculate the probability that Aika will take two sunflower seeds.

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

(2)

(Total for Question 14 is 4 marks)

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15 A is inversely proportional to C 2
A = 40 when C = 1.5
Calculate the value of C when A = 1000

C = . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 15 is 3 marks)

16
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16 The diagram shows a circle with centre O

A B
C Diagram NOT
55° accurately drawn

A, B and C are points on the circle so that the length of the arc ABC is 5 cm.
Given that angle AOC = 55°
work out the area of the circle.
Give your answer correct to one decimal place.

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

(Total for Question 16 is 4 marks)

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17 A and B are two similar vases.

Diagram NOT
accurately drawn

10 cm 15 cm

A B

Vase A has height 10 cm.

Vase B has height 15 cm.
The difference between the volume of vase A and the volume of vase B is 1197 cm3
Calculate the volume of vase A

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

(Total for Question 17 is 4 marks)

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x2
18 A = w –
y

w = 3.45 correct to 2 decimal places.

 x = 1.9 correct to 1 decimal place.
 y = 5 correct to the nearest whole number.
Work out the lower bound of the value of A
Show your working clearly.

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

(Total for Question 18 is 3 marks)

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19 Solve the simultaneous equations
3x 2 + y 2 – xy = 5
y = 2x – 3
Show clear algebraic working.

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

(Total for Question 19 is 5 marks)

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20 (a) Express  7 + 12x – 3x 2  in the form  a + b(x + c)2  where a, b and c are integers.

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

(3)
C is the curve with equation  y = 7 + 12x – 3x 2
The point A is the maximum point on C
(b) Use your answer to part (a) to write down the coordinates of A

(. . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . )
(1)

(Total for Question 20 is 4 marks)

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21 The diagram shows the prism ABCDEFGHJK with horizontal base AEFG

Diagram NOT
C accurately drawn
H
K

B
D
G M
F

A E

ABCDEis a cross section of the prism where

ABDE is a square
BCD is an equilateral triangle
EF = 2 × AE
M is the midpoint of GF so that JM is vertical.
Angle MAJ = y°
Given that tan y° = T
p+ q
find the value of T, giving your answer in the form where p and q
are integers. 17

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

(Total for Question 21 is 5 marks)

Turn over for Question 22

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22 The diagram shows triangle OAB

Diagram NOT
accurately drawn

M
N
P

A
→ →
OA = 8a OB = 6b

M is the point on OB such that OM : MB = 1 : 2

N is the midpoint of AB
P is the point of intersection of ON and AM
→
Using a vector method, find OP as a simplified expression in terms of a and b
Show your working clearly.

24
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→
OP = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(Total for Question 22 is 5 marks)

Turn over for Question 23

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23 The diagram shows a sketch of the curve with equation  y = f(x)

y (5, 7)

y = f(x)

O x

There is only one maximum point on the curve.

The coordinates of this maximum point are (5, 7)
Write down the coordinates of the maximum point on the curve with equation

 (i)   y = f(x + 9)

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

(ii)
   y = f(x) + 3

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

(Total for Question 23 is 2 marks)

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24 The curve C has equation  y = ax 3 + bx 2 – 12x + 6  where a and b are constants.

The point A with coordinates (2, –6) lies on C
The gradient of the curve at A is 16
Find the y coordinate of the point on the curve whose x coordinate is 3
Show clear algebraic working.

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

(Total for Question 24 is 6 marks)

TOTAL FOR PAPER IS 100 MARKS

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