Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a ¹ 0 are given by:
h
−b ± b2 − 4ac
2a
b
In any triangle ABC
C
Sine Rule
B
c
Volume of cone =
Area of triangle =
1
ab sin C
2
Volume of prism
= area of cross section × length
1 2
πr h
3
Curved surface area of cone = πrl
l
h
cross
section
length
r
Volume of cylinder = πr2h
Curved surface area
of cylinder = 2πrh
Volume of sphere =
4 3
πr
3
Surface area of sphere = 4πr2
r
r
h
2
DO NOT WRITE IN THIS AREA
A
Cosine Rule a2 = b2 + c2 – 2bccos A
DO NOT WRITE IN THIS AREA
a
b
a
b
c
=
=
sin A sin B sin C
DO NOT WRITE IN THIS AREA
Trigonometry
DO NOT WRITE IN THIS AREA
x=
1
(a + b)h
2
Area of trapezium =
DO NOT WRITE IN THIS AREA
Formulae sheet – Higher Tier
DO NOT WRITE IN THIS AREA
International GCSE Mathematics
*P59017A0228*
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Answer ALL TWENTY ONE questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1
(a) Factorise fully 4p + 6pq
(2)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(b) Expand and simplify (e + 3)(e – 5)
(2)
(c) Solve y =
2y + 1
5
Show clear algebraic working.
y=
(3)
(Total for Question 1 is 7 marks)
*P59017A0328*
3
Turn over
2
A
DO NOT WRITE IN THIS AREA
10
8
6
B
DO NOT WRITE IN THIS AREA
y
4
2
4
6
8
x
(a) Describe fully the single transformation that maps triangle A onto triangle B.
 2
(b) On the grid, translate triangle A by the vector  
 −5
Label the new triangle C.
4
*P59017A0428*
(3)
DO NOT WRITE IN THIS AREA
O
DO NOT WRITE IN THIS AREA
–2
DO NOT WRITE IN THIS AREA
–4
DO NOT WRITE IN THIS AREA
2
(1)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
4
The table gives information about the price of gold.
Price of one ounce of
gold (dollars)
1st February 2016
1st March 2016
1126.50
1236.50
(a) Work out the percentage increase in the price of gold between 1st February 2016 and
1st March 2016
Give your answer correct to 3 significant figures.
%
(3)
The price of one ounce of gold on 1st February 2016 was 1126.50 dollars.
The price of gold increased by 19% from 1st February 2016 to 1st July 2016
(b) Work out the price of one ounce of gold on 1st July 2016
Give your answer correct to the nearest dollar.
(3)
dollars
(Total for Question 4 is 6 marks)
*P59017A0728*
7
Turn over
D
Diagram NOT
accurately drawn
(30x – 5)°
(4x + 15)°
B
E
(20x + 45)°
A
F
DO NOT WRITE IN THIS AREA
C
DO NOT WRITE IN THIS AREA
5
BCD and AFE are straight lines.
*P59017A0828*
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
8
DO NOT WRITE IN THIS AREA
(Total for Question 5 is 5 marks)
DO NOT WRITE IN THIS AREA
Show that BCD is parallel to AFE.
Give reasons for your working.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
6
(a) Complete the table of values for y = x2 – 5x + 6
x
0
y
6
1
2
3
4
0
0
2
5
(1)
(b) On the grid, draw the graph of y = x2 – 5x + 6 for 0  x  5
y
7
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
6
5
4
3
2
1
O
1
2
3
4
5
x
–1
–2
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(2)
(c) By drawing a suitable straight line on the grid, find estimates for the solutions of the
equation
x2 – 5x = x – 7
(3)
(Total for Question 6 is 6 marks)
*P59017A0928*
9
Turn over
Volume (km3)
Arctic Ocean
1.88 ´ 107
Atlantic Ocean
3.10 ´ 108
Indian Ocean
2.64 ´ 108
Southern Ocean
7.18 ´ 107
DO NOT WRITE IN THIS AREA
Ocean
(a) Write 7.18 ´ 107 as an ordinary number.
DO NOT WRITE IN THIS AREA
The table shows the volumes, in km3, of four oceans.
(1)
(c) Write 9 880 000 in standard form.
DO NOT WRITE IN THIS AREA
The volume of the South China Sea is 9 880 000 km3
DO NOT WRITE IN THIS AREA
(2)
km3
DO NOT WRITE IN THIS AREA
(b) Calculate the total volume of these four oceans.
DO NOT WRITE IN THIS AREA
7
(1)
(Total for Question 7 is 4 marks)
10
*P59017A01028*
The diagram shows an isosceles triangle.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
8
Diagram NOT
accurately drawn
x cm
x cm
5 cm
The area of the triangle is 12 cm2
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Work out the perimeter of the triangle.
Give your answer correct to 3 significant figures.
cm
(Total for Question 8 is 4 marks)
*P59017A01128*
11
Turn over
Frequency
0 < s  10
3
10 < s  20
16
20 < s  30
24
30 < s  40
10
40 < s  50
5
50 < s  60
2
DO NOT WRITE IN THIS AREA
Speed (s km/h)
DO NOT WRITE IN THIS AREA
The table shows information about the speeds of 60 cycles.
0 < s  10
0 < s  20
0 < s  30
0 < s  40
0 < s  50
DO NOT WRITE IN THIS AREA
Cumulative
frequency
DO NOT WRITE IN THIS AREA
Speed (s km/h)
DO NOT WRITE IN THIS AREA
(a) Complete the cumulative frequency table.
DO NOT WRITE IN THIS AREA
9
0 < s  60
(1)
12
*P59017A01228*
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(b) On the grid, draw a cumulative frequency graph for your table.
60
50
40
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Cumulative
frequency
30
20
10
0
0
10
20
30
40
50
60
Speed (km/h)
(2)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(c) Use your graph to find an estimate for the interquartile range of the speeds.
(2)
km/h
(Total for Question 9 is 5 marks)
*P59017A01328*
13
Turn over
8 cm
DO NOT WRITE IN THIS AREA
B
Diagram NOT
accurately drawn
C
A
20°
13 cm
D
The point C lies on BD.
AD = 13 cm BC = 8 cm angle ADB = 90° angle CAD = 20°
DO NOT WRITE IN THIS AREA
10 Here is triangle ABD.
14
*P59017A01428*
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(Total for Question 10 is 5 marks)
DO NOT WRITE IN THIS AREA
°
DO NOT WRITE IN THIS AREA
Calculate the size of angle BAC.
Give your answer correct to 1 decimal place.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
11 Express
5 x+2
as a single fraction in its simplest terms.
−
3
2x
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(Total for Question 11 is 3 marks)
*P59017A01528*
15
Turn over
DO NOT WRITE IN THIS AREA
dy
=
dx
DO NOT WRITE IN THIS AREA
1
12 The curve C has equation y = x3 − 9 x + 1
3
dy
(a) Find
dx
(2)
16
*P59017A01628*
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(Total for Question 12 is 5 marks)
DO NOT WRITE IN THIS AREA
(3)
DO NOT WRITE IN THIS AREA
(b) Find the range of values of x for which C has a negative gradient.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
13 All the students in Year 11 at a school must study at least one of Geography (G), History (H)
and Religious Studies (R).
In Year 11 there are 65 students.
Of these students
15 study Geography, History and Religious Studies
21 study Geography and History
16 study Geography and Religious Studies
30 study Geography
18 study only Religious Studies
37 study Religious Studies
(a) Using this information, complete the Venn diagram to show the number of students in
each region of the Venn diagram.
E
H
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
G
R
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(3)
A student in Year 11 who studies both History and Religious Studies is chosen at random.
(b) Work out the probability that this student does not study Geography.
(2)
(Total for Question 13 is 5 marks)
*P59017A01728*
17
Turn over
DO NOT WRITE IN THIS AREA
(b) Work out the value of T when r = 6
DO NOT WRITE IN THIS AREA
(3)
DO NOT WRITE IN THIS AREA
(a) Find a formula for T in terms of r
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
T = 21.76 when r = 4
DO NOT WRITE IN THIS AREA
14 T is directly proportional to the cube of r
(1)
(Total for Question 14 is 4 marks)
18
*P59017A01828*
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
15 The total surface area of a solid hemisphere is equal to the curved surface area of a cylinder.
The radius of the hemisphere is r cm.
The radius of the cylinder is twice the radius of the hemisphere.
Given that
volume of hemisphere : volume of cylinder = 1 : m
find the value of m.
m=
(Total for Question 15 is 4 marks)
*P59017A01928*
19
Turn over
x
where x ≠ y
ym
DO NOT WRITE IN THIS AREA
find the value of m.
m=
(1)
(Total for Question 16 is 4 marks)
20
DO NOT WRITE IN THIS AREA
=
(3)
m
DO NOT WRITE IN THIS AREA
 y
(b) Given that 

 x
−5
DO NOT WRITE IN THIS AREA
Simplify your answer.
DO NOT WRITE IN THIS AREA
a + 4b
where a is an integer and b is a prime number.
a − 4b
DO NOT WRITE IN THIS AREA
16 (a) Rationalise the denominator of
*P59017A02028*
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
17 Here is triangle ABC.
C
5.3 cm
B
Diagram NOT
accurately drawn
110°
4.1 cm
x°
A
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Calculate the value of x.
Give your answer correct to 3 significant figures.
(Total for Question 17 is 5 marks)
*P59017A02128*
21
Turn over
DO NOT WRITE IN THIS AREA
y
4
2
−8
−6
−4
−2
O
2
4
6
8
DO NOT WRITE IN THIS AREA
18 The graph of y = f(x) is shown on the grid.
x
1 
(a) On the grid above, sketch the graph of y = f  x
2 
22
*P59017A02228*
DO NOT WRITE IN THIS AREA
−8
DO NOT WRITE IN THIS AREA
−6
DO NOT WRITE IN THIS AREA
−4
DO NOT WRITE IN THIS AREA
−2
(2)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
The graph of y = f(x + k) is shown on the grid below.
y
4
2
−8
−6
−4
−2
O
2
4
6
8
x
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
−2
−4
−6
−8
(b) Write down the value of k
(1)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(Total for Question 18 is 3 marks)
*P59017A02328*
23
Turn over
(Total for Question 19 is 5 marks)
24
*P59017A02428*
DO NOT WRITE IN THIS AREA
(4)
DO NOT WRITE IN THIS AREA
g–1 : x 
DO NOT WRITE IN THIS AREA
(b) Express the inverse function g–1 in the form g–1 : x 
DO NOT WRITE IN THIS AREA
(1)
DO NOT WRITE IN THIS AREA
(a) Write down the range of g–1
DO NOT WRITE IN THIS AREA
19 g is the function with domain x  –3 such that g(x) = x2 + 6x
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
20 A bowl contains n pieces of fruit.
Of these, 4 are oranges and the rest are apples.
Two pieces of fruit are going to be taken at random from the bowl.
1
The probability that the bowl will then contain (n – 6) apples is
3
Work out the value of n
Show your working clearly.
(Total for Question 20 is 6 marks)
*P59017A02528*
25
Turn over
26
*P59017A02628*
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
TOTAL FOR PAPER IS 100 MARKS
DO NOT WRITE IN THIS AREA
(Total for Question 21 is 4 marks)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Prove that the common difference of the sequence is 12
DO NOT WRITE IN THIS AREA
21 (2x + 23), (8x + 2) and (20x – 52) are three consecutive terms of an arithmetic sequence.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
BLANK PAGE
*P59017A02728*
27
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
*P59017A02828*
28
DO NOT WRITE IN THIS AREA
BLANK PAGE
Please check the examination details below before entering your candidate information
Candidate surname
Pearson Edexcel
International GCSE
Other names
Centre Number
Candidate Number
Tuesday 7 January 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, compasses,
pen, HB pencil, eraser, calculator. Tracing paper may be used.
Instructions
black ink or ball-point pen.
• Use
Fill in the boxes at the top of this page with your name,
• centre
number and candidate number.
Answer
questions.
• Withoutallsufficient
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
total mark for this paper is 100.
• The
marks for each question are shown in brackets
• The
– use this as a guide as to how much time to spend on each question.
Advice
each question carefully before you start to answer it.
• Read
Check
• your answers if you have time at the end.
Turn over
P59756A
©2020 Pearson Education Ltd.
1/1/1/
*P59756A0128*
International GCSE Mathematics
Formulae sheet – Higher Tier
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a ¹ 0 are given by:
x=
1
(a + b)h
2
Area of trapezium =
h
−b ± b2 − 4ac
2a
b
Trigonometry
In any triangle ABC
C
Sine Rule
a
b
A
Volume of cone =
Cosine Rule a2 = b2 + c2 – 2bccos A
B
c
a
b
c
=
=
sin A sin B sin C
Area of triangle =
1
ab sin C
2
Volume of prism
= area of cross section × length
1 2
πr h
3
Curved surface area of cone = πrl
l
h
cross
section
length
r
Volume of cylinder = πr2h
Curved surface area
of cylinder = 2πrh
Volume of sphere =
4 3
πr
3
Surface area of sphere = 4πr2
r
r
h
2
*P59756A0228*
Answer all TWENTY TWO questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1
The point A has coordinates (5, −4)
The point B has coordinates (13, 1)
(a) Work out the coordinates of the midpoint of AB.
(. . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
(2)
Line L has equation y = 2 − 3x
(b) Write down the gradient of line L.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
Line L has equation y = 2 − 3x
(c) Does the point with coordinates (100, −302) lie on line L?
You must give a reason for your answer.
............................ ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
............................ ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
............................ ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 1 is 4 marks)
*P59756A0328*
3
Turn over
2
Find the lowest common multiple (LCM) of 28 and 105
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 2 is 2 marks)
4
*P59756A0428*
3
The diagram shows a shape.
Diagram NOT
accurately drawn
12 cm
6 cm
9 cm
x cm
The shape has area 129 cm2
Work out the value of x.
x = .......................................................
(Total for Question 3 is 4 marks)
*P59756A0528*
5
Turn over
4
The table shows information about the weights, in kilograms, of 40 babies.
Weight (w kg)
Frequency
2<w3
12
3<w4
16
4<w5
9
5<w6
2
6<w7
1
(a) Write down the modal class.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(b) Work out an estimate for the mean weight of the 40 babies.
.......................................................
(4)
kg
One of the 40 babies is going to be chosen at random.
(c) Find the probability that this baby has a weight of more than 5 kg.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 4 is 7 marks)
6
*P59756A0628*
5
120 children go on an activity holiday.
The ratio of the number of girls to the number of boys is 3 : 5
On Sunday, all the children either go sailing or go climbing.
16
of the boys go climbing.
25
Twice as many girls go sailing as go climbing.
Work out how many children go sailing on Sunday.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 5 is 6 marks)
*P59756A0728*
7
Turn over
6
(a) Write 7.8 × 10−4 as an ordinary number.
..................................................................................
(1)
(b) Work out
5.6 × 104 + 7 × 103
2.8 × 10 −3
Give your answer in standard form.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 6 is 3 marks)
7
(a) Expand and simplify (m − 8)(m + 5)
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(b) Factorise fully 5y + 20y2
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
8
*P59756A0828*
(c) Simplify ( p2 + 3)0
.......................................................
(1)
9−x
2
Show clear algebraic working.
(d) Solve 3(2x − 5) =
x = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(4)
(Total for Question 7 is 9 marks)
*P59756A0928*
9
Turn over
8
y
11
10
9
8
7
6
5
4
3
2
1
O
1
2
3
4
5
6
7
8
9
On the grid, enlarge the shaded shape with scale factor
10
11
12
13
14
15
1
and centre (1, 2)
2
(Total for Question 8 is 2 marks)
10
*P59756A01028*
16 x
9
Here is a right-angled triangle.
Diagram NOT
accurately drawn
P
63°
24.3 cm
R
Q
Calculate the length of PQ.
Give your answer correct to 3 significant figures.
.......................................................
cm
(Total for Question 9 is 3 marks)
*P59756A01128*
11
Turn over
10 The shaded region in the diagram is bounded by three lines.
The equation of one of the lines is given.
y
6
4
2
−6
−4
−2
2
O
−2
y=
4
6 x
1
x−2
3
−4
−6
Write down the three inequalities that define the shaded region.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 10 is 3 marks)
12
*P59756A01228*
11 Max invests $6000 in a savings account for 3 years.
The account pays compound interest at a rate of 1.5% per year for the first 2 years.
The compound interest rate changes for the third year.
At the end of 3 years, there is a total of $6311.16 in the account.
Work out the compound interest rate for the third year.
Give your answer correct to 1 decimal place.
.......................................................
%
(Total for Question 11 is 3 marks)
*P59756A01328*
13
Turn over
12 A total of 80 men and women took part in a race.
The cumulative frequency graph gives information about the times, in minutes, they took
for the race.
80
70
60
50
Cumulative
frequency
40
30
20
10
0
20
30
40
50
60
Time (minutes)
14
*P59756A01428*
70
(a) Use the graph to find an estimate for the interquartile range.
.......................................................
(2)
minutes
60% of the men took 50 minutes or less for the race.
No women took 50 minutes or less for the race.
(b) Work out an estimate for the number of men who took part in the race.
.......................................................
(3)
(Total for Question 12 is 5 marks)
*P59756A01528*
15
Turn over
13 The diagram shows a solid cube.
The cube is placed on a table so that the whole of one face of the cube is in contact with
the table.
w cm
w cm
Diagram NOT
accurately drawn
w cm
The cube exerts a force of 56 newtons on the table.
The pressure on the table due to the cube is 0.14 newtons/cm2
pressure =
force
area
Work out the volume of the cube.
.......................................................
(Total for Question 13 is 4 marks)
16
*P59756A01628*
cm3
14 The diagram shows parallelogram EFGH.
14.7 cm
F
G
106°
Diagram NOT
accurately drawn
9.3 cm
E
H
EF = 9.3 cm
FG = 14.7 cm
Angle EFG = 106°
(a) Work out the area of the parallelogram.
Give your answer correct to 3 significant figures.
.......................................................
cm2
.......................................................
cm
(2)
(b) Work out the length of the diagonal EG of the parallelogram.
Give your answer correct to 3 significant figures.
(3)
(Total for Question 14 is 5 marks)
*P59756A01728*
17
Turn over
15
Diagram NOT
accurately drawn
(x + 1) cm
(3 − x) cm
(2x + 5) cm
The diagram shows a cuboid of volume V cm3
(a) Show that V = 15 + 16x − x2 − 2x3
(3)
18
*P59756A01828*
There is a value of x for which the volume of the cuboid is a maximum.
(b) Find this value of x.
Show your working clearly.
Give your answer correct to 3 significant figures.
x = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(5)
(Total for Question 15 is 8 marks)
*P59756A01928*
19
Turn over
16 P =
2a − c
d
a = 58.4 correct to 3 significant figures.
c = 20 correct to 2 significant figures.
d = 3.6 correct to 2 significant figures.
Work out the upper bound for the value of P.
Show your working clearly.
Give your answer correct to 2 decimal places.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 16 is 3 marks)
20
*P59756A02028*
17 (a) Show that
(6 + 2 12 ) = 12 (7 + 4 3 )
2
Show each stage of your working.
(3)
 27 a12 
(b) Simplify fully  15 
 t 
2
−
3
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 17 is 6 marks)
*P59756A02128*
21
Turn over
18 There are 16 sweets in a bowl.
4 of the sweets are blackcurrant.
5 of the sweets are lemon.
7 of the sweets are orange.
Anna, Ravi and Sam each take at random one sweet from the bowl.
Work out the probability that the 5 lemon sweets are still in the bowl.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 18 is 4 marks)
22
*P59756A02228*
19 The diagram shows a cuboid ABCDEFGH.
A
B
D
C
Diagram NOT
accurately drawn
6 cm
F
G
5 cm
E
9 cm
H
EH = 9 cm, HG = 5 cm and GB = 6 cm.
Work out the size of the angle between AH and the plane EFGH.
Give your answer correct to 3 significant figures.
.......................................................
°
(Total for Question 19 is 4 marks)
*P59756A02328*
23
Turn over
20 The curve C has equation y = 4(x − 1)2 − a where a > 4
Using the axes below, sketch the curve C.
On your sketch show clearly, in terms of a,
(i) the coordinates of any points of intersection of C with the coordinate axes,
(ii) the coordinates of the turning point.
y
O
x
(Total for Question 20 is 4 marks)
24
*P59756A02428*
21 The functions f and g are such that
f(x) = x2 − 2x g(x) = x + 3
The function h is such that h(x) = fg(x) for x  −2
Express the inverse function h−1(x) in the form h−1(x) = …
h−1(x) = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 21 is 5 marks)
*P59756A02528*
25
Turn over
22 Triangle HJK is isosceles with HJ = HK and JK =
80
H is the point with coordinates (−4, 1)
J is the point with coordinates ( j, 15) where j < 0
K is the point with coordinates (6, k)
M is the midpoint of JK.
The gradient of HM is 2
Find the value of j and the value of k.
26
*P59756A02628*
j = .......................................................
k = .......................................................
(Total for Question 22 is 6 marks)
TOTAL FOR PAPER IS 100 MARKS
*P59756A02728*
27
BLANK PAGE
28
*P59756A02828*
Please check the examination details below before entering your candidate information
Candidate surname
Pearson Edexcel
International GCSE
Other names
Centre Number
Candidate Number
Thursday 7 January 2021
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, compasses,
pen, HB pencil, eraser, calculator. Tracing paper may be used.
Instructions
black ink or ball‑point pen.
• Use
Fill
in
boxes at the top of this page with your name,
• centrethe
number and candidate number.
all questions.
• Answer
sufficient working, correct answers may be awarded no marks.
• Without
Answer
the
in the spaces provided
• – there may questions
be more space than you need.
may be used.
• Calculators
must NOT write anything on the formulae page.
• You
Anything you write on the formulae page will gain NO credit.
Information
total mark for this paper is 100.
• The
marks for each question are shown in brackets
• The
– use this as a guide as to how much time to spend on each question.
Advice
each question carefully before you start to answer it.
• Read
• Check your answers if you have time at the end.
Turn over
P66297A
©2021 Pearson Education Ltd.
1/1/1/
*P66297A0128*
International GCSE Mathematics
Formulae sheet – Higher Tier
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a ¹ 0 are given by:
x=
1
(a + b)h
2
Area of trapezium =
h
−b ± b2 − 4ac
2a
b
Trigonometry
In any triangle ABC
C
Sine Rule
A
B
c
Volume of cone =
Cosine Rule a2 = b2 + c2 – 2bccos A
a
b
a
b
c
=
=
sin A sin B sin C
Area of triangle =
1
ab sin C
2
Volume of prism
= area of cross section × length
1 2
πr h
3
Curved surface area of cone = πrl
l
h
cross
section
length
r
Volume of cylinder = πr2h
Curved surface area
of cylinder = 2πrh
Volume of sphere =
4 3
πr
3
Surface area of sphere = 4πr2
r
r
h
2
*P66297A0228*
Answer ALL TWENTY FOUR questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1
Pieter owns a currency conversion shop.
Last Monday, Pieter changed a total of 20 160 rand into a number of different currencies.
He changed
3
of the 20 160 rand into euros.
10
He changed the rest of the rands into dollars, rupees and francs in the ratios 9 : 5 : 2
Pieter changed more rands into dollars than he changed into francs.
Work out how many more.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .
rand
(Total for Question 1 is 4 marks)
*P66297A0328*
3
Turn over
2
The table gives information about the speeds, in kilometres per hour, of 80 motorbikes
as each pass under a bridge.
Speed
(s kilometres per hour)
Frequency
40 < s  50
10
50 < s  60
16
60 < s  70
19
70 < s  80
23
80 < s  90
12
(a) Write down the modal class.
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(b) Work out an estimate for the mean speed of the motorbikes as they pass under the bridge.
Give your answer correct to 3 significant figures.
......................................................
kilometres per hour
(4)
(Total for Question 2 is 5 marks)
4
*P66297A0428*
3
The diagram shows a container for water in the shape of a prism.
Diagram NOT
accurately drawn
30 cm
20 cm
40 cm
60 cm
125 cm
85 cm
The rectangular base of the prism, shown shaded in the diagram, is horizontal.
The container is completely full of water.
Tuah is going to use a pump to empty the water from the container so that the volume of
water in the container decreases at a constant rate.
The pump starts to empty water from the container at 10 30 and at 12 00 the water level
in the container has dropped by 20 cm.
Find the time at which all the water has been pumped out of the container.
......................................................
(Total for Question 3 is 4 marks)
*P66297A0528*
5
Turn over
4
E = {20, 21, 22, 23, 24, 25, 26, 27, 28, 29}
A = {odd numbers}
B = {multiples of 3}
List the members of the set
(i) A ∩ B
...........................................................................................................
(1)
(ii) A ∪ B
...........................................................................................................
(1)
(Total for Question 4 is 2 marks)
6
*P66297A0628*
5
(a) Factorise fully 15y 4 + 20uy 3
......................................................
(b) Solve
4 – 3x =
(2)
5 − 8x
4
Show clear algebraic working.
x = ......................................................
(3)
(Total for Question 5 is 5 marks)
6
(a) Write 2 840 000 000 in standard form.
......................................................
(1)
(b) Write 2.5 × 10–4 as an ordinary number.
......................................................
(1)
(Total for Question 6 is 2 marks)
*P66297A0728*
7
Turn over
7
Chen invests 40 000 yuan in a fixed-term bond for 3 years.
The fixed-term bond pays compound interest at a rate of 3.5% each year.
(a) Work out the value of Chen’s investment at the end of 3 years.
Give your answer to the nearest yuan.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
(3)
yuan
Wang invested P yuan.
The value of his investment decreased by 6.5% each year.
At the end of the first year, the value of Wang’s investment was 30 481 yuan.
(b) Work out the value of P.
P = . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 7 is 6 marks)
8
*P66297A0828*
8
The region, shown shaded in the diagram, is a path.
Diagram NOT
accurately drawn
2m
O
7m
The boundary of the path is formed by two semicircles, with the same centre O, and two
straight lines.
The inner semicircle has a radius of 7 metres.
The path has a width of 2 metres.
Work out the perimeter of the path.
Give your answer correct to one decimal place.
......................................................
m
(Total for Question 8 is 3 marks)
*P66297A0928*
9
Turn over
9
(a) Simplify
(2x 3y 5)4
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(b) (i) Factorise
x 2 + 5x – 36
......................................................
(2)
(ii) Hence, solve x 2 + 5x – 36 = 0
......................................................
(1)
(Total for Question 9 is 5 marks)
10
*P66297A01028*
10 Here is isosceles triangle ABC.
A
Diagram NOT
accurately drawn
65°
D
16 cm
B
C
D is the midpoint of AC and DB = 16 cm.
Angle DAB = 65°
Work out the perimeter of triangle ABC.
Give your answer correct to one decimal place.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .
cm
(Total for Question 10 is 4 marks)
*P66297A01128*
11
Turn over
11 The cumulative frequency graph gives information about the weights, in grams, of
90 bags of sweets.
90
80
70
60
Cumulative
frequency
50
40
30
20
10
0
120
130
140
150
160
170
Weight (grams)
12
*P66297A01228*
180
(a) Find an estimate for the median of the weights of these bags of sweets.
......................................................
(2)
grams
Roberto sells the bags of sweets to raise money for charity.
Bags with a weight greater than d grams are labelled large bags and sold for 3.75 euros
each bag.
The total amount of money he receives by selling all the large bags is 93.75 euros.
(b) Find the value of d.
d = ......................................................
(3)
(Total for Question 11 is 5 marks)
*P66297A01328*
13
Turn over
4
3
as a single fraction.
−
x − 2 x +1
Give your answer in its simplest form.
12 (a) Express
......................................................
(3)
(b) Expand and simplify 2x(x – 5)(x – 3)
......................................................
(3)
(Total for Question 12 is 6 marks)
14
*P66297A01428*
13 Point A has coordinates (5, 8)
Point B has coordinates (9, –4)
(a) Work out the gradient of AB.
......................................................
(2)
The straight line L has equation y = –4x + 5
(b) Write down the gradient of a straight line that is perpendicular to L.
......................................................
(1)
(Total for Question 13 is 3 marks)
*P66297A01528*
15
Turn over
14 Ding is going to play one game of snooker against each of two of his friends, Marco
and Judd.
The probability tree diagram gives information about the probabilities that Ding will
win or lose each of these two games.
Ding against
Marco
0.6
0.4
Ding against
Judd
0.9
Ding wins
0.1
Ding loses
0.25
Ding wins
0.75
Ding loses
Ding wins
Ding loses
(a) Work out the probability that Ding will win both games.
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(b) Work out the probability that Ding will win exactly one of the games.
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 14 is 5 marks)
16
*P66297A01628*
15
a=
v−u
t
v = 9.6 correct to 1 decimal place
u = 3.8 correct to 1 decimal place
t = 1.84 correct to 2 decimal places
Calculate the upper bound for the value of a.
Give your answer as a decimal correct to 2 decimal places.
Show your working clearly.
......................................................
(Total for Question 15 is 3 marks)
*P66297A01728*
17
Turn over
16 The diagram shows the positions of three ships, A, B and C.
North
Diagram NOT
accurately drawn
B
150 m
North
120°
A
275 m
C
Ship B is due north of ship A.
The bearing of ship C from ship A is 120°
Calculate the bearing of ship C from ship B.
Give your answer correct to the nearest degree.
18
*P66297A01828*
......................................................
(Total for Question 16 is 5 marks)
*P66297A01928*
19
Turn over
°
17 A solid, S, is made from a hemisphere and a cylinder.
The centre of the circular face of the hemisphere and the centre of the top face of the
cylinder are at the same point.
Diagram NOT
accurately drawn
x cm
(20 – 4x) cm
The radius of the cylinder and the radius of the hemisphere are both x cm.
The height of the cylinder is (20 – 4x) cm.
1
The volume of S is V cm3 where V = πy
3
Find the maximum value of y.
Show clear algebraic working.
20
*P66297A02028*
......................................................
(Total for Question 17 is 5 marks)
18 Given that (8 –
x )(5 +
x ) = y x + 21 where x is a prime number and y is an integer,
find the value of x and the value of y.
Show each stage of your working clearly.
x = ......................................................
y = ......................................................
(Total for Question 18 is 3 marks)
*P66297A02128*
21
Turn over
19 Solve the simultaneous equations
x 2 – 9y – x = 2y 2 – 12
x + 2y – 1 = 0
Show clear algebraic working.
............................................................................................................
(Total for Question 19 is 5 marks)
22
*P66297A02228*
20 A and B are two similar solids.
A
Diagram NOT
accurately drawn
B
A has a volume of 1836 cm3
B has a volume of 4352 cm3
B has a total surface area of 1120 cm2
Work out the total surface area of A.
......................................................
cm2
(Total for Question 20 is 3 marks)
*P66297A02328*
23
Turn over
21 A curve has equation y = f(x)
The coordinates of the minimum point on this curve are (–9, 15)
(a) Write down the coordinates of the minimum point on the curve with equation
(i) y = f(x + 3)
(. . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
(ii) y =
1
f(x)
3
(. . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
(2)
The graph of y = a cos (x + b)° for 0  x  360 is drawn on the grid below.
2
1
O
180
360
–1
–2
Given that a > 0 and that 0 < b < 360
(b) find the value of a and the value of b.
a = ......................................................
b = ......................................................
(2)
(Total for Question 21 is 4 marks)
24
*P66297A02428*
22 The function f is such that f(x) = x 2 – 8x + 5 where x  4
Express the inverse function f –1 in the form f –1(x) = ...
f –1(x) = . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 22 is 3 marks)
*P66297A02528*
25
Turn over
23 OAB is a triangle.
M
A
B
P
N
O
→
→
OA = 2a and OB = 2b
M is the midpoint of AB.
N is the point on OB such that ON : NB = 2 : 1
P is the point on AN such that OPM is a straight line.
Use a vector method to find OP : PM
Show your working clearly.
26
*P66297A02628*
Diagram NOT
accurately drawn
......................................................
(Total for Question 23 is 6 marks)
Turn over for Question 24
*P66297A02728*
27
Turn over
24 An arithmetic series has first term a and common difference d.
The sum of the first 2n terms of the series is four times the sum of the first n terms of
the series.
Find an expression for a in terms of d.
Show your working clearly.
a = . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 24 is 4 marks)
TOTAL FOR PAPER IS 100 MARKS
28
*P66297A02828*
Please check the examination details below before entering your candidate information
Candidate surname
Centre Number
Other names
Candidate Number
Pearson Edexcel International GCSE
Paper
reference
Time 2 hours
Mathematics A
4MA1/1H
 
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
black ink or ball-point pen.
• Use
Fill
in
boxes at the top of this page with your name,
• centrethe
number and candidate number.
all questions.
• Answer
the questions in the spaces provided
• Answer
– there may be more space than you need.
may be used.
• Calculators
must NOT write anything on the formulae page.
• You
Anything you write on the formulae page will gain NO credit.
Information
total mark for this paper is 100.
• The
marks for each question are shown in brackets
• The
– use this as a guide as to how much time to spend on each question.
Advice
each question carefully before you start to answer it.
• Read
Try
to
every question.
• Checkanswer
• your answers if you have time at the end.
Turn over
P69196A
©2022 Pearson Education Ltd.
L:1/1/1/1/
*P69196A0128*
International GCSE Mathematics
Formulae sheet – Higher Tier
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a ¹ 0 are given by:
h
−b ± b2 − 4ac
2a
x=
b
Trigonometry
In any triangle ABC
C
Sine Rule
a
b
A
a
b
c
=
=
sin A sin B sin C
Cosine Rule a2 = b2 + c2 – 2bccos A
B
c
Volume of cone =
1
(a + b)h
2
Area of trapezium =
Area of triangle =
1
ab sin C
2
Volume of prism
= area of cross section × length
1 2
πr h
3
Curved surface area of cone = πrl
l
h
cross
section
length
r
Volume of cylinder = πr2h
Curved surface area
of cylinder = 2πrh
4 3
πr
3
Volume of sphere =
Surface area of sphere = 4πr2
r
r
h
2
*P69196A0228*

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)

*P69196A0328*
3
Turn over
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
B
A
8.4 cm
Diagram NOT
accurately drawn
65°
C
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
*P69196A0428*

4
Sarah makes and sells mugs.
One day she makes 150 mugs.
Her total cost for making these mugs is £1140
Of these mugs
and
2
are small mugs
5
32% are medium mugs
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)

*P69196A0528*
5
Turn over
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)
6
*P69196A0628*

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)

*P69196A0728*
7
Turn over
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.
E
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)
8
*P69196A0828*

9
The diagram shows isosceles triangle ABC
A
17.5 cm
B
AB = AC = 17.5 cm
Diagram NOT
accurately drawn
17.5 cm
28 cm
C
BC = 28 cm
Calculate the area of triangle ABC
......................................................
cm2
(Total for Question 9 is 4 marks)

*P69196A0928*
9
Turn over
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)
10
*P69196A01028*

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)

*P69196A01128*
11
Turn over
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.
Time taken (t minutes)
Cumulative
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
*P69196A01228*

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.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .
(1)
minutes
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)

*P69196A01328*
13
Turn over
13 (a) Expand and simplify
5x(x + 2)(3x – 4)
.................................................................................
(b) Simplify completely
 16 w8 
 y 20 
−
(3)
3
4
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 13 is 6 marks)
14
*P69196A01428*

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
....................
7
12
sunflower
....................
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)

*P69196A01528*
15
Turn over
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
*P69196A01628*

16 The diagram shows a circle with centre O
A
B
55°
C
Diagram NOT
accurately drawn
O
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)

*P69196A01728*
17
Turn over
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)
18
*P69196A01828*

18 A = w –
x2
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)

*P69196A01928*
19
Turn over
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)
20
*P69196A02028*

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)

*P69196A02128*
21
Turn over
21 The diagram shows the prism ABCDEFGHJK with horizontal base AEFG
J
C
H
B
A
D
G
K
M
Diagram NOT
accurately drawn
F
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
find the value of T, giving your answer in the form
are integers.
22
p+ q
17
where p and q
*P69196A02228*

T = ......................................................
(Total for Question 21 is 5 marks)
Turn over for Question 22

*P69196A02328*
23
Turn over
22 The diagram shows triangle OAB
B
Diagram NOT
accurately drawn
M
P
N
O
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
*P69196A02428*

→
OP = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 22 is 5 marks)
Turn over for Question 23

*P69196A02528*
25
Turn over
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)
26
*P69196A02628*

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

*P69196A02728*
27
BLANK PAGE
28
*P69196A02828*

Write your name here
Surname
Other names
Pearson Edexcel
International GCSE
Centre Number
Candidate Number
Mathematics A
Level 1/2
Paper 1H
Higher Tier
Thursday 24 May 2018 – Morning
Time: 2 hours
Paper Reference
4MA1/1H
You must have:
Total Marks
Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser, calculator. Tracing paper may be used.
Instructions
black ink or ball-point pen.
• Use
Fill in the boxes at the top of this page with your name,
• centre
number and candidate number.
Answer
questions.
• Withoutallsufficient
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
total mark for this paper is 100.
• The
for each question are shown in brackets
• –Theusemarks
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
P54694A
©2018 Pearson Education Ltd.
1/1/1/1/
*P54694A0124*
International GCSE Mathematics
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a v0 are given by:
x=
1
(a + b)h
2
Area of trapezium =
h
−b ± b2 − 4ac
2a
b
Trigonometry
In any triangle ABC
C
Sine Rule
a
b
c
=
=
sin A sin B sin C
Cosine Rule a2 = b2 + c2 – 2bccos A
Area of triangle =
A
B
c
Volume of cone =
1
ab sin C
2
Volume of prism
= area of cross section ulength
1 2
ʌU h
3
Curved surface area of cone = ʌUO
O
h
DO NOT WRITE IN THIS AREA
a
b
cross
section
length
U
Volume of sphere =
4 3
ʌU
3
Surface area of sphere = 4ʌU2
U
U
h
*P54694A0224*
DO NOT WRITE IN THIS AREA
Volume of cylinder = ʌU2h
Curved surface area
of cylinder = 2ʌUK
2
DO NOT WRITE IN THIS AREA
Formulae sheet – Higher Tier
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Answer all TWENTY questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1
The table shows information about the weights, in kg, of 40 parcels.
Weight of parcel ( p kg)
Frequency
0p-1
19
1p-2
12
2p-3
5
3p-4
2
4p-5
2
(a) Write down the modal class.
.......................................................
(1)
(b) Work out an estimate for the mean weight of the parcels.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . .
kg
(4)
(Total for Question 1 is 5 marks)
*P54694A0324*
3
Turn over
2
There are some people in a cinema.
DO NOT WRITE IN THIS AREA
3
of the people in the cinema are children.
5
For the children in the cinema,
number of girls : number of boys = 2 : 7
There are 170 girls in the cinema.
Work out the number of adults in the cinema.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
.......................................................
(Total for Question 2 is 5 marks)
4
*P54694A0424*
DO NOT WRITE IN THIS AREA
3
(a) Simplify y 5 × y 9
.......................................................
(1)
(b) Simplify
(2m3)4
.......................................................
(2)
DO NOT WRITE IN THIS AREA
(c) Solve 5(x + 3) = 3x – 4
Show clear algebraic working.
x = .......................................................
(3)
DO NOT WRITE IN THIS AREA
(d) (i) Factorise x 2 + 2x – 24
.......................................................
(2)
(ii) Hence, solve x 2 + 2x – 24 = 0
.......................................................
(1)
(Total for Question 3 is 9 marks)
*P54694A0524*
5
Turn over
4
Here is a Venn diagram.
A
B
6
5
3
10
7
2
12
C
11
1
4
DO NOT WRITE IN THIS AREA
E
9
8
(a) Write down the numbers that are in the set
(i) A
(ii) B ∪ C
....................................................................
(2)
Brian writes down the statement A ∩ C = Ø
DO NOT WRITE IN THIS AREA
....................................................................
(b) Is Brian’s statement correct?
You must give a reason for your answer.
. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
One of the numbers in the Venn diagram is picked at random.
(c) Find the probability that this number is in set Cƍ
.......................................................
(2)
(Total for Question 4 is 5 marks)
6
*P54694A0624*
DO NOT WRITE IN THIS AREA
(1)
(a) Write 8 × 104 as an ordinary number.
.......................................................
(1)
(b) Work out (3.5 × 105) ÷ (7 × 108)
Give your answer in standard form.
.......................................................
(2)
(Total for Question 5 is 3 marks)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
5
*P54694A0724*
7
Turn over
6
DO NOT WRITE IN THIS AREA
Diagram NOT
accurately drawn
M
O
3.5 cm
P
9.7 cm
N
M, N and P are points on a circle, centre O.
MON is a diameter of the circle.
DO NOT WRITE IN THIS AREA
MP = 3.5 cm
PN = 9.7 cm
Angle MPN = 90q
Work out the circumference of the circle.
Give your answer correct to 3 significant figures.
(Total for Question 6 is 4 marks)
8
*P54694A0824*
cm
DO NOT WRITE IN THIS AREA
.......................................................
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
7
Chao bought a boat for HK$160 000
The value of the boat depreciates by 4% each year.
(a) Work out the value of the boat at the end of 3 years.
Give your answer correct to the nearest HK$.
HK$. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
Jalina gets a salary increase of 5%
Her salary after the increase is HK$252 000
DO NOT WRITE IN THIS AREA
(b) Work out Jalina’s salary before the increase.
HK$. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 7 is 6 marks)
*P54694A0924*
9
Turn over
8
A = 3 5 × 5 × 73
B = 23 × 3 × 74
.......................................................
(ii) Find the Lowest Common Multiple (LCM) of A and B.
(2)
A = 35 × 5 × 73
B = 23 × 3 × 74
C = 2 p × 5q × 7U
Given that
the HCF of B and C is 23 × 7
the LCM of A and C is 24 × 35 × 52 × 73
DO NOT WRITE IN THIS AREA
.......................................................
DO NOT WRITE IN THIS AREA
(a) (i) Find the Highest Common Factor (HCF) of A and B.
(b) find the value of p, the value of q and the value of U.
q = .......................................................
U = .......................................................
(2)
(Total for Question 8 is 4 marks)
10
*P54694A01024*
DO NOT WRITE IN THIS AREA
p = .......................................................
The diagram shows a right-angled triangle.
Diagram NOT
accurately drawn
72q
12.8 cm
Five of these triangles are put together to make a shape.
Diagram NOT
accurately drawn
Calculate the perimeter of the shape.
Give your answer correct to 3 significant figures.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
9
.......................................................
cm
(Total for Question 9 is 5 marks)
*P54694A01124*
11
Turn over
10 The cumulative frequency graph shows information about the length, in minutes, of each
of 80 films.
DO NOT WRITE IN THIS AREA
80
70
60
50
DO NOT WRITE IN THIS AREA
Cumulative
frequency
40
30
20
10
90
100
110
120
Length (minutes)
130
140
(a) Use the graph to find an estimate for the interquartile range.
.......................................................
(2)
12
*P54694A01224*
minutes
DO NOT WRITE IN THIS AREA
0
80
DO NOT WRITE IN THIS AREA
Clare says,
“More than 35% of these films are over 120 minutes long.”
(b) Is Clare correct?
Give a reason for your answer.
. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(Total for Question 10 is 5 marks)
*P54694A01324*
13
Turn over
11 (a) Expand and simplify
(2x – 1)(x + 3)(x – 5)
DO NOT WRITE IN THIS AREA
...................................................................................
(3)
DO NOT WRITE IN THIS AREA
(b) Solve 3x 2 + 6x – 5 = 0
Show your working clearly.
Give your solutions correct to 3 significant figures.
(3)
(Total for Question 11 is 6 marks)
14
*P54694A01424*
DO NOT WRITE IN THIS AREA
.......................................................
12 The diagram shows two straight lines drawn on a grid.
DO NOT WRITE IN THIS AREA
y
10
9
3y = 2x + 6
8
7
6
5
4
3
DO NOT WRITE IN THIS AREA
2
1
–2
–1 O
–1
1
2
3
4
5
6
–2
7
8
9
10 x
4x + 3y = 24
(a) Write down the solution of the simultaneous equations
3y = 2x + 6
4x + 3y = 24
x = .......................................................
DO NOT WRITE IN THIS AREA
y = .......................................................
(1)
(b) Show, by shading on the grid, the region defined by all five of the inequalities
x.0
y.0
x+y.4
3y - 2x + 6
4x + 3y - 24
Label the region R.
(3)
(Total for Question 12 is 4 marks)
*P54694A01524*
15
Turn over
13
DO NOT WRITE IN THIS AREA
L
Diagram NOT
accurately drawn
27q
O
N
Q
T
M
L, M and N are points on a circle, centre O.
QMT is the tangent to the circle at M.
(a) (i) Find the size of angle NOM.
q
(ii) Give a reason for your answer.
. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(b) (i) Find the size of angle NMQ.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .
q
(ii) Give a reason for your answer.
. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 13 is 4 marks)
16
*P54694A01624*
DO NOT WRITE IN THIS AREA
. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
14 The function f is such that
f (x) =
3x − 5
4
(a) Find f (–7)
.......................................................
(1)
(b) Express the inverse function f –1 in the form f –1(x) = ...
f –1(x) = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
The function g is such that
g (x) = 19 − x
DO NOT WRITE IN THIS AREA
(c) Find fg (3)
.......................................................
(2)
(d) Which values of x cannot be included in any domain of g?
.......................................................
(2)
(Total for Question 14 is 7 marks)
*P54694A01724*
17
Turn over
−
DO NOT WRITE IN THIS AREA
15 (a) Simplify fully
1
⎛ 256 x 20 ⎞ 4
⎜
⎟
⎝ y8 ⎠
.......................................................
(b) Express
1
9 x 2 − 25
−
1
as a single fraction in its simplest form.
6 x + 10
DO NOT WRITE IN THIS AREA
(2)
DO NOT WRITE IN THIS AREA
.......................................................
(3)
(Total for Question 15 is 5 marks)
18
*P54694A01824*
DO NOT WRITE IN THIS AREA
16 A frustum is made by removing a small cone from a large cone.
The cones are mathematically similar.
Diagram NOT
accurately drawn
h cm
U cm
U cm
Frustum
The large cone has base radius U cm and height h cm.
Given that
find an expression, in terms of h, for the height of the frustum.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
98
volume of frustum
=
volume of large cone 125
.......................................................
cm
(Total for Question 16 is 4 marks)
*P54694A01924*
19
Turn over
17 The diagram shows parallelogram ABCD.
y
Diagram NOT
accurately drawn
B
D
A
x
O
o ⎛ 2⎞
AB = ⎜ ⎟
⎝ 7⎠
DO NOT WRITE IN THIS AREA
C
o ⎛10⎞
AC = ⎜ ⎟
⎝ 11⎠
The point B has coordinates (5, 8)
(. . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . )
(3)
DO NOT WRITE IN THIS AREA
(a) Work out the coordinates of the point C.
The point E has coordinates (63, 211)
(b) Use a vector method to prove that ABE is a straight line.
DO NOT WRITE IN THIS AREA
(2)
(Total for Question 17 is 5 marks)
20
*P54694A02024*
DO NOT WRITE IN THIS AREA
18
y
O
(–2, –1)
x
The diagram shows the curve with equation y = f (x)
The coordinates of the minimum point of the curve are (–2, –1)
(a) Write down the coordinates of the minimum point of the curve with equation
(i) y = f (x – 5)
DO NOT WRITE IN THIS AREA
(. . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . )
1
(ii) y = f (x)
2
(. . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . )
(2)
The graph of y = a sin(x – b)q + c for –90 - x -450 is drawn on the grid below.
y
3
2
1
DO NOT WRITE IN THIS AREA
–90
O
90
180
270
360
450 x
–1
(b) Find the value of a, the value of b and the value of c.
a = .......................................................
b = .......................................................
c = .......................................................
(3)
(Total for Question 18 is 5 marks)
*P54694A02124*
21
Turn over
19 Jack plays a game with two fair spinners, A and B.
Jack spins both spinners.
He wins the game if one spinner lands on an odd number and the other spinner lands on
an even number.
Jack plays the game twice.
Work out the probability that Jack wins the game both times.
DO NOT WRITE IN THIS AREA
Spinner A can land on the number 2 or 3 or 5 or 7
Spinner B can land on the number 2 or 3 or 4 or 5 or 6
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
.......................................................
(Total for Question 19 is 4 marks)
22
*P54694A02224*
AB = AC
A has coordinates (4, 37)
B and C lie on the line with equation 3y = 2x + 12
Find an equation of the line of symmetry of triangle ABC.
Give your answer in the form px + qy = U where p, q and U are integers.
Show clear algebraic working.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
20 ABC is an isosceles triangle such that
.......................................................
(Total for Question 20 is 5 marks)
TOTAL FOR PAPER IS 100 MARKS
*P54694A02324*
23
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
*P54694A02424*
24
DO NOT WRITE IN THIS AREA
BLANK PAGE
Please check the examination details below before entering your candidate information
Candidate surname
Pearson Edexcel
International GCSE
Other names
Centre Number
Candidate Number
Tuesday 21 May 2019
Morning (Time: 2 hours)
Paper Reference 4MA1/1H
Mathematics A
Level 1/2
Paper 1H
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
black ink or ball-point pen.
• Use
in the boxes at the top of this page with your name, centre number and
• Fill
candidate number.
all questions.
• Answer
sufficient working, correct answers may be awarded no marks.
• Without
the questions in the spaces provided
• Answer
– there may be more space than you need.
may be used.
• Calculators
must NOT write anything on the formulae page.
• You
Anything you write on the formulae page will gain NO credit.
Information
total mark for this paper is 100.
• The
marks for each question are shown in brackets
• The
– use this as a guide as to how much time to spend on each question.
Advice
each question carefully before you start to answer it.
• Read
Check
• your answers if you have time at the end.
Turn over
P58365A
©2019 Pearson Education Ltd.
1/1/1/1/
*P58365A0124*
International GCSE Mathematics
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a v0 are given by:
x=
1
(a + b)h
2
Area of trapezium =
h
−b ± b2 − 4ac
2a
b
In any triangle ABC
Trigonometry
C
Sine Rule
a
b
c
=
=
sin A sin B sin C
Cosine Rule a2 = b2 + c2 – 2bccos A
Area of triangle =
A
B
c
Volume of cone =
1
ab sin C
2
Volume of prism
= area of cross section ulength
1 2
ʌU h
3
Curved surface area of cone = ʌUO
O
h
DO NOT WRITE IN THIS AREA
a
b
cross
section
length
U
Volume of sphere =
4 3
ʌU
3
Surface area of sphere = 4ʌU2
U
U
h
*P58365A0224*
DO NOT WRITE IN THIS AREA
Volume of cylinder = ʌU2h
Curved surface area
of cylinder = 2ʌUK
2
DO NOT WRITE IN THIS AREA
Formulae sheet – Higher Tier
Write your answers in the spaces provided.
You must write down all the stages in your working.
1
Show that 4
2
1
1
÷1 =4
3
9
5
(Total for Question 1 is 3 marks)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Answer ALL TWENTY FOUR questions.
*P58365A0324*
3
Turn over
2
DO NOT WRITE IN THIS AREA
Jalina left her home at 10 00 to cycle to a park.
On her way to the park, she stopped at a friend’s house and then continued her journey to
the park.
Here is the distance-time graph for her journey to the park.
25
20
15
Distance from
home (km)
10
DO NOT WRITE IN THIS AREA
5
0
10 00
11 00
12 00
13 00
14 00
15 00
Time
(a) On her journey to the park, did Jalina cycle at a faster speed before or after she
stopped at her friend’s house?
Give a reason for your answer.
. . . . . . . . . . . .................................................... ....................................... . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . .................................................... ....................................... . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
4
*P58365A0424*
DO NOT WRITE IN THIS AREA
. . . . . . . . . . . .................................................... ....................................... . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
Jalina stayed at the park for 45 minutes.
She then cycled, without stopping, at a constant speed of 16 km/h from the park back to
her home.
(b) Show all this information on the distance-time graph.
(2)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(c) Work out Jalina’s average cycling speed, in kilometres per hour, for the complete
journey to the park and back.
Do not include the times when she was not cycling in your calculation.
Give your answer correct to 1 decimal place.
.......................................................
km/h
(3)
(Total for Question 2 is 6 marks)
*P58365A0524*
5
Turn over
3
(a) Simplify e9 ÷ e5
(1)
E 6LPSOLI\ ௘y2)8
.......................................................
(1)
(c) Expand and simplify (x + 9)(x – 2)
(2)
(d) Factorise fully 16c4p2 + 20cp3
DO NOT WRITE IN THIS AREA
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . .
DO NOT WRITE IN THIS AREA
.......................................................
.......................................................
(2)
(Total for Question 3 is 6 marks)
DO NOT WRITE IN THIS AREA
6
*P58365A0624*
DO NOT WRITE IN THIS AREA
4
(a) Complete the table of values for y = x2íxí
x
í
í
y
0
1
2
í
3
4
í
3
(2)
(b) On the grid, draw the graph of y = x2íxíIRUDOOYDOXHVRIxIURPíWR
y
10
DO NOT WRITE IN THIS AREA
8
6
4
2
DO NOT WRITE IN THIS AREA
í
í
O
1
2
3
4
x
í
í
í
(2)
(Total for Question 4 is 4 marks)
*P58365A0724*
7
Turn over
5
Becky has a biased 6-sided dice.
Number
1
2
3
4
5
6
Probability
2x
0.18
2x
3x
0.26
x
Becky is going to throw the dice 200 times.
Work out an estimate for the number of times that the dice will land on an even number.
DO NOT WRITE IN THIS AREA
The table gives information about the probability that, when the dice is thrown, it will
land on each number.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
.......................................................
(Total for Question 5 is 4 marks)
8
*P58365A0824*
The diagram shows a solid cuboid made from wood.
12 cm
8 cm
Diagram NOT
accurately drawn
5 cm
The wood has density 0.7 g/cm3
Work out the mass of the cuboid.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
6
.......................................................
grams
DO NOT WRITE IN THIS AREA
(Total for Question 6 is 3 marks)
*P58365A0924*
9
Turn over
7
(a) Write 5.7 × 106 as an ordinary number.
(1)
(b) Write 0.004 in standard form.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . .
(1)
DO NOT WRITE IN THIS AREA
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . .
2 × 104 + 3 × 105
(c) Work out
6.4 × 10 −2
(2)
(Total for Question 7 is 4 marks)
8
On 1st January 2016 Li bought a boat for $170 000
The value of the boat depreciates by 8% per year.
DO NOT WRITE IN THIS AREA
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . .
Work out the value of the boat on 1st January 2019
Give your answer correct to the nearest dollar.
(Total for Question 8 is 3 marks)
10
*P58365A01024*
DO NOT WRITE IN THIS AREA
$ .......................................................
DO NOT WRITE IN THIS AREA
9
The diagram shows a shape made from a right-angled triangle and a semicircle.
Diagram NOT
accurately drawn
A
C
6 cm
6 cm
B
AC is the diameter of the semicircle.
BA = BC = 6 cm
Angle ABC = 90°
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Work out the area of the shape.
Give your answer correct to 1 decimal place.
.......................................................
cm2
(Total for Question 9 is 5 marks)
*P58365A01124*
11
Turn over
10 A = 2n × 3 × 5m
DO NOT WRITE IN THIS AREA
Write 8A as a product of powers of its prime factors.
.......................................................
11 C = bía
a = 6 correct to the nearest integer
b = 15 correct to the nearest 5
Work out the upper bound for the value of C
Show your working clearly.
DO NOT WRITE IN THIS AREA
(Total for Question 10 is 2 marks)
DO NOT WRITE IN THIS AREA
.......................................................
(Total for Question 11 is 3 marks)
12
*P58365A01224*
.......................................................
(2)
4m + 9
ím
3
Show clear algebraic working.
(b) Solve
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
12 (a) Factorise 2x2íx + 6
m = .......................................................
(4)
DO NOT WRITE IN THIS AREA
(c) Write
4
y
in the form y b where b is a fraction.
y
.......................................................
(2)
(Total for Question 12 is 8 marks)
*P58365A01324*
13
Turn over
13 In group C, there are 6 girls and 8 boys.
In group D, there are 3 girls and 7 boys.
(a) Complete the probability tree diagram.
group C
group D
girl
....................
girl
DO NOT WRITE IN THIS AREA
A team is made by picking at random one child from group C and one child from group D.
....................
....................
boy
girl
....................
boy
....................
boy
(2)
DO NOT WRITE IN THIS AREA
....................
(b) Work out the probability that there are two boys in the team.
(2)
14
*P58365A01424*
DO NOT WRITE IN THIS AREA
.......................................................
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
After the first team has been picked, a second team is picked.
One child is picked at random from the children left in group C and one child is picked
at random from the children left in group D.
(c) Work out the probability that there are two boys in each of the two teams.
.......................................................
(3)
(Total for Question 13 is 7 marks)
14 E = {positive integers less than 20}
A = {x : x 12}
B = {x : 7 - x 16}
DO NOT WRITE IN THIS AREA
(a) List the members of A ∩ B
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(2)
C is a set such that C ⊂ A and n(C௘ Given that all members of C are even numbers,
(b) list the members of one possible set C.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 14 is 3 marks)
*P58365A01524*
15
Turn over
••
15 Use algebra to show that the recurring decimal 0.254 =
DO NOT WRITE IN THIS AREA
14
55
16 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.
(Total for Question 16 is 2 marks)
16
*P58365A01624*
DO NOT WRITE IN THIS AREA
.......................................................
DO NOT WRITE IN THIS AREA
(Total for Question 15 is 2 marks)
DO NOT WRITE IN THIS AREA
17 A and B are two similar vases.
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
DO NOT WRITE IN THIS AREA
(a) Work out the surface area of vase B.
.......................................................
cm2
(2)
Vase B has a volume of V cm3
DO NOT WRITE IN THIS AREA
(b) Find in terms of V, an expression for the volume, in cm3, of vase A.
.......................................................
cm3
(2)
(Total for Question 17 is 4 marks)
*P58365A01724*
17
Turn over
18 The diagram shows triangle PQR.
DO NOT WRITE IN THIS AREA
Diagram NOT
accurately drawn
P
17.8 cm
36°
R
Q
26.3 cm
Calculate the length of PR.
Give your answer correct to 3 significant figures.
DO NOT WRITE IN THIS AREA
.......................................................
cm
(Total for Question 18 is 3 marks)
DO NOT WRITE IN THIS AREA
18
*P58365A01824*
DO NOT WRITE IN THIS AREA
19 The table gives information about the heights of some trees.
Height (h metres)
Frequency
0 h - 20
15
20 h - 35
48
35 h - 40
21
40 h - 50
16
On the grid, draw a histogram for this information.
5
DO NOT WRITE IN THIS AREA
4
3
Frequency
density
2
1
DO NOT WRITE IN THIS AREA
0
0
10
20
30
40
50
Height (h metres)
(Total for Question 19 is 3 marks)
*P58365A01924*
19
Turn over
20
DO NOT WRITE IN THIS AREA
B
Diagram NOT
accurately drawn
A
C
V
71°
D
T
DO NOT WRITE IN THIS AREA
A, B, C and D are points on a circle.
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.
DO NOT WRITE IN THIS AREA
.......................................................
(Total for Question 20 is 5 marks)
20
*P58365A02024*
°
DO NOT WRITE IN THIS AREA
21 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.
Diagram NOT
accurately drawn
The hemisphere and the cylinder have the same radius.
Given that the solid has volume 792ʌ cm3
work out the height of the solid.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
The ratio of the radius of the cylinder to the height of the cylinder is 1 : 3
.......................................................
cm
(Total for Question 21 is 5 marks)
*P58365A02124*
21
Turn over
22 The graph of y = sinx° for 0 - x - 360 is drawn on the grid.
DO NOT WRITE IN THIS AREA
y
3
2
1
O
60
120
180
240
300
360 x
í
í
(a) On the grid, draw the graph of y = 2sin(x + 30)° for 0 - x - 360
(2)
DO NOT WRITE IN THIS AREA
í
(b) (i) Write x2íx + 10 in the form (xía)2 + b where a and b are integers.
(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 22 is 6 marks)
22
*P58365A02224*
DO NOT WRITE IN THIS AREA
.......................................................
B is the point with coordinates (10, 19)
D is the point with coordinates (2, 7)
Find an equation of the line AC.
Give your answer in the form py + qx = U where p, q and U are integers.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
23 ABCD is a kite with AB = AD and CB = CD.
.......................................................
(Total for Question 23 is 5 marks)
*P58365A02324*
23
Turn over
24 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
DO NOT WRITE IN THIS AREA
s = t3ít2 + 5tí
Find the value of t for which the acceleration of P is 3 m/s2
DO NOT WRITE IN THIS AREA
(Total for Question 24 is 4 marks)
TOTAL FOR PAPER IS 100 MARKS
24
*P58365A02424*
DO NOT WRITE IN THIS AREA
t = .......................................................
Please check the examination details below before entering your candidate information
Candidate surname
Pearson Edexcel
International GCSE
Time 2 hours
Other names
Centre Number
Candidate Number
Paper
reference
4MA1/1H
Mathematics A
PAPER 1H
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
black ink or ball-point pen.
• Use
Fill in the boxes at the top of this page with your name,
• centre
number and candidate number.
Answer
questions.
• Withoutallsufficient
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
total mark for this paper is 100.
• The
The
for each question are shown in brackets
• – usemarks
this as a guide as to how much time to spend on each question.
Advice
each question carefully before you start to answer it.
• Read
Check
your answers if you have time at the end.
• Good luck
with your examination.
•
Turn over
P65914A
©2021 Pearson Education Ltd.
1/1/1/1/1/1/
*P65914A0128*
International GCSE Mathematics
Formulae sheet – Higher Tier
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a ¹ 0 are given by:
x=
1
(a + b)h
2
Area of trapezium =
h
−b ± b2 − 4ac
2a
b
Trigonometry
In any triangle ABC
C
Sine Rule
a
b
A
Volume of cone =
Cosine Rule a2 = b2 + c2 – 2bccos A
B
c
a
b
c
=
=
sin A sin B sin C
Area of triangle =
1
ab sin C
2
Volume of prism
= area of cross section × length
1 2
πr h
3
Curved surface area of cone = πrl
l
h
cross
section
length
r
Volume of cylinder = πr2h
Curved surface area
of cylinder = 2πrh
Volume of sphere =
4 3
πr
3
Surface area of sphere = 4πr2
r
r
h
2
*P65914A0228*
Answer all TWENTY SIX questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1
A plane flew from Madrid to Dubai.
The distance the plane flew was 5658 km.
The flight time was 8 hours 12 minutes.
Work out the average speed of the plane.
.......................................................
km/h
(Total for Question 1 is 3 marks)
2
Here are the first 4 terms of an arithmetic sequence.
85 79 73 67
Find an expression, in terms of n, for the nth term of the sequence.
.......................................................
(Total for Question 2 is 2 marks)
*P65914A0328*
3
Turn over
3
A
x cm
B
Diagram NOT
accurately drawn
8 cm
14 cm
E
C
13 cm
D
The diagram shows the shape ABCDE.
The area of the shape is 91.8 cm²
Work out the value of x.
x = . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 3 is 4 marks)
4
*P65914A0428*
4
On a farm there are chickens, ducks and pigs.
The ratio of the number of chickens to the number of ducks is 7 : 2
The ratio of the number of ducks to the number of pigs is 5 : 9
There are 36 pigs on the farm.
Work out the number of chickens on the farm.
.......................................................
(Total for Question 4 is 3 marks)
*P65914A0528*
5
Turn over
5
(a) Expand and simplify 3x(2x + 3) – x(3x + 5)
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(b) Make t the subject of the formula p = at – d
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
n
w ×w
= w10
3
w
(c) work out the value of n.
Given that
5
n = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 5 is 6 marks)
6
*P65914A0628*
6
Grace has a biased 5-sided spinner.
orange
pink
green
red
blue
Grace is going to spin the arrow on the spinner once.
The table below gives the probabilities that the spinner will land on red or on blue or on green.
Colour
Red
Blue
Green
Probability
0.20
0.12
0.08
Orange
Pink
The probability that the spinner will land on orange is 3 times the probability that the
spinner will land on pink.
(a) Work out the probability that the spinner will land on orange.
.......................................................
(3)
Grace spins the arrow on the spinner 150 times.
(b) Work out an estimate for the number of times the spinner lands on blue.
.......................................................
(2)
(Total for Question 6 is 5 marks)
*P65914A0728*
7
Turn over
−4  2y < 6
7
y is an integer.
(a) Write down all the possible values of y.
....................................................................
(2)
(b) Solve the inequality 7t – 3  2t + 31
Show your working clearly.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 7 is 4 marks)
8
*P65914A0828*
8
The table shows the populations of five countries.
Country
Population
China
1.4 × 109
Germany
8.2 × 107
Sweden
9.9 × 106
Fiji
9.1 × 105
Malta
4.3 × 105
(a) Work out the difference between the population of China and the population of Germany.
Give your answer in standard form.
.......................................................
(2)
Given that
population of Fiji =
1
× population of Sweden
k
(b) work out the value of k.
Give your answer correct to the nearest whole number.
k = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 8 is 4 marks)
*P65914A0928*
9
Turn over
(a) Factorise fully 25a4c7d + 45a9c3h
9
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(b) Solve (2x + 5)2 = (2x + 3)(2x – 1)
x = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 9 is 5 marks)
10 Jethro has sat 5 tests.
Each test was marked out of 100 and Jethro’s mean mark for the 5 tests is 74
Jethro has to sit one more test that is also to be marked out of 100
Jethro wants his mean mark for all 6 tests to be at least 77
Work out the least mark that Jethro needs to get for the last test.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 10 is 3 marks)
10
*P65914A01028*
11
2 × 16 = 2 x
(a) Find the value of x.
Show your working clearly.
x = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(11−6 )5
= 11n
4
11
(b) Find the value of n.
Show your working clearly.
n = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 11 is 4 marks)
*P65914A01128*
11
Turn over
12 The diagram shows a sector of a circle with radius 7 cm.
Diagram NOT
accurately drawn
7 cm
50°
Work out the length of the arc of the sector.
Give your answer correct to one decimal place.
.......................................................
(Total for Question 12 is 2 marks)
12
*P65914A01228*
cm
13 Expand and simplify 4x(3x + 1)(2x – 3)
Show your working clearly.
.......................................................
(Total for Question 13 is 3 marks)
14 Here is the number of goals that Henri’s team scored one summer in each water polo match.
5 8 9 11 13 13 14 15 16 17 20
Find the interquartile range of the numbers of goals.
Show your working clearly.
.......................................................
(Total for Question 14 is 2 marks)
*P65914A01328*
13
Turn over
15 P, Q and R are points on a circle, centre O.
TRV is the tangent to the circle at R.
Q
V
Diagram NOT
accurately drawn
238°
60°
O
R
P
T
Reflex angle POR = 238°
Angle QRV = 60°
Calculate the size of angle OPQ.
Give a reason for each stage of your working.
.......................................................
(Total for Question 15 is 4 marks)
14
*P65914A01428*
°
16 Use algebra to show that the recurring decimal 0.281̇3̇ =
557
1980
(Total for Question 16 is 2 marks)
17 Using algebra, prove that, given any 3 consecutive even numbers, the difference between
the square of the largest number and the square of the smallest number is always
8 times the middle number.
(Total for Question 17 is 3 marks)
*P65914A01528*
15
Turn over
18 The table and histogram give information about the distance travelled, in order to get to
work, by each person working in a large store.
Distance (d km)
Frequency
0  d < 10
40
10  d < 15
15  d < 20
20  d < 30
30  d < 60
30
Frequency
density
0
16
0
10
20
30
40
Distance travelled (km)
50
*P65914A01628*
60
Using the information in the table and in the histogram,
(a) complete the table,
(2)
(b) complete the histogram.
(1)
One of the people working in the store is chosen at random.
(c) Work out an estimate for the probability that the distance travelled by this person, in
order to get to work, was greater than 25 km.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 18 is 5 marks)
*P65914A01728*
17
Turn over
19 The Venn diagram shows a universal set, E and sets A, B and C.
E
A
B
5
12
9
6
10
3
4
8
C
12, 5, 9, 10, 6, 3, 4 and 8 represent the numbers of elements.
Find
(i) n(A ∪ B)
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(ii) n(Aʹ ∩ Bʹ)
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(iii) n([A ∩ B] ∪ C)
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 19 is 3 marks)
18
*P65914A01828*
20 P =
t−w
y
t = 9.7 correct to 1 decimal place
w = 5.9 correct to 1 decimal place
y = 3 correct to 1 significant figure
Calculate the upper bound for the value of P.
Show your working clearly.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 20 is 3 marks)
*P65914A01928*
19
Turn over
21 Given that x =
5
5
and that y =
9y + 5
5a − 2
find an expression for x in terms of a.
Give your expression as a single fraction in its simplest form.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 21 is 4 marks)
20
*P65914A02028*
22 The diagram shows a triangular prism ABCDEF with a horizontal base ABEF.
D
C
12 cm
12 cm
F
Diagram NOT
accurately drawn
E
15 cm
A
10 cm
B
AC = BC = FD = ED = 12 cm AB = 10 cm BE = 15 cm
Calculate the size of the angle between AD and the base ABEF.
Give your answer correct to 3 significant figures.
......................................................
(Total for Question 22 is 4 marks)
*P65914A02128*
21
Turn over
°
23 The sum of the first N terms of an arithmetic series, S, is 292
The 2nd term of S is 8.5
The 5th term of S is 13
Find the value of N.
Show clear algebraic working.
N = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 23 is 5 marks)
22
*P65914A02228*
24 The functions f and g are defined as
f(x) = 5x2 − 10x + 7 where x  1
g(x) = 7x − 6
(a) Find fg(2)
.......................................................
(2)
(b) Express the inverse function f −1 in the form f −1 (x) = ...
f −1 (x) = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(4)
(Total for Question 24 is 6 marks)
*P65914A02328*
23
Turn over
25 The diagram shows two circles such that the region R, shown shaded in the diagram, is
the region common to both circles.
Diagram NOT
accurately drawn
A
4 cm
5 cm
O
50°
R
P
B
One of the circles has centre O and radius 5 cm.
The other circle has centre P and radius 4 cm.
Angle AOB = 50°
Calculate the area of region R.
Give your answer correct to 3 significant figures.
24
*P65914A02428*
......................................................
cm2
(Total for Question 25 is 6 marks)
Turn over for Question 26
*P65914A02528*
25
Turn over
26 OACB is a trapezium.
3b
A
2a
O
C
Diagram NOT
accurately drawn
P
5b
B
→
→
→
OA = 2a OB = 5b AC = 3b
The diagonals, OC and AB, of the trapezium intersect at the point P.
→
Find and simplify an expression, in terms of a and b, for OP
Show your working clearly.
26
*P65914A02628*
→
OP = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 26 is 5 marks)
TOTAL FOR PAPER IS 100 MARKS
*P65914A02728*
27
BLANK PAGE
28
*P65914A02828*
Please check the examination details below before entering your candidate information
Candidate surname
Pearson Edexcel
International GCSE
Other names
Centre Number
Candidate Number
Tuesday 19 May 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
black ink or ball-point pen.
• Use
in the boxes at the top of this page with your name, centre number and
• Fill
candidate number.
all questions.
• Answer
sufficient working, correct answers may be awarded no marks.
• Without
the questions in the spaces provided
• Answer
– there may be more space than you need.
may be used.
• Calculators
must NOT write anything on the formulae page.
• You
Anything you write on the formulae page will gain NO credit.
Information
total mark for this paper is 100.
• The
marks for each question are shown in brackets
• The
– use this as a guide as to how much time to spend on each question.
Advice
each question carefully before you start to answer it.
• Read
Check
• your answers if you have time at the end.
Turn over
P62652A
©2020 Pearson Education Ltd.
1/1/1/1/
*P62652A0128*
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a ¹ 0 are given by:
h
−b ± b2 − 4ac
2a
b
Trigonometry
In any triangle ABC
Sine Rule
B
c
Volume of cone =
Area of triangle =
1
ab sin C
2
Volume of prism
= area of cross section × length
1 2
πr h
3
Curved surface area of cone = πrl
l
h
cross
section
length
r
Volume of cylinder = πr2h
Curved surface area
of cylinder = 2πrh
Volume of sphere =
4 3
πr
3
Surface area of sphere = 4πr2
r
r
h
2
DO NOT WRITE IN THIS AREA
A
Cosine Rule a2 = b2 + c2 – 2bccos A
DO NOT WRITE IN THIS AREA
a
b
a
b
c
=
=
sin A sin B sin C
DO NOT WRITE IN THIS AREA
C
DO NOT WRITE IN THIS AREA
x=
1
(a + b)h
2
Area of trapezium =
DO NOT WRITE IN THIS AREA
Formulae sheet – Higher Tier
DO NOT WRITE IN THIS AREA
International GCSE Mathematics
*P62652A0228*
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Answer ALL TWENTY FIVE questions.
Write your answers in the spaces provided.
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
8
4
14
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
10
B
1
2
6
13
3
11
12
7
5
(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.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(c) Find the probability that this number is in set A but is not in set B.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 1 is 4 marks)
*P62652A0328*
3
Turn over
4
*P62652A0428*
DO NOT WRITE IN THIS AREA
(Total for Question 2 is 4 marks)
DO NOT WRITE IN THIS AREA
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
Work out an estimate of the number of faulty toy cars that are made each day.
DO NOT WRITE IN THIS AREA
For the toy cars made each day, the probability of a toy car being faulty is 0.002
DO NOT WRITE IN THIS AREA
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
2
On the grid, draw the graph of y = 7 – 4x for values of x from −2 to 3
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
3
y
16
14
12
10
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
8
6
4
2
−2
−1
O
1
2
3
x
−2
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
−4
−6
−8
(Total for Question 3 is 3 marks)
*P62652A0528*
5
Turn over
The numbers have
a median of 9
a mean of 11
Find the value of x and the value of y.
(Total for Question 4 is 4 marks)
6
*P62652A0628*
DO NOT WRITE IN THIS AREA
y = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
x = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
4 7 x 10 y y
DO NOT WRITE IN THIS AREA
Here is a list of six numbers written in order of size.
DO NOT WRITE IN THIS AREA
4
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
5
(a) Write 5.7 × 10–3 as an ordinary number.
.......................................................
(1)
(b) Write 800 000 in standard form.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(c) Work out
3 × 105 − 2.7 × 104
6 × 10 −2
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(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.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .
seconds
(Total for Question 6 is 3 marks)
*P62652A0728*
7
Turn over
(c) (i) Factorise y2 – 2y – 48
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(ii) Hence, solve y2 – 2y – 48 = 0
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 7 is 8 marks)
8
*P62652A0828*
DO NOT WRITE IN THIS AREA
(2)
DO NOT WRITE IN THIS AREA
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
(b) Factorise fully 16m3g3 + 24m2g5
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
x = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
DO NOT WRITE IN THIS AREA
7 (a) Solve 5(4 – x) = 7 – 3x
Show clear algebraic working.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
8
Here is a 10-sided polygon.
148°
150°
150°
168°
168°
134°
134°
125°
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
125°
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Diagram NOT
accurately drawn
x°
Work out the value of x.
x = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 8 is 4 marks)
*P62652A0928*
9
Turn over
Work out the normal price of the bag.
10
*P62652A01028*
DO NOT WRITE IN THIS AREA
(Total for Question 9 is 3 marks)
rupees
DO NOT WRITE IN THIS AREA
.......................................................
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
A bag costs 1080 rupees in the sale.
DO NOT WRITE IN THIS AREA
In a sale, normal prices are reduced by 20%
DO NOT WRITE IN THIS AREA
9
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
10 A = 2 × 343
B = 16 × 337
(a) Find the highest common factor (HCF) of A and B.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(1)
(b) Express the number A × B as a product of powers of its prime factors.
Give your answer in its simplest form.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 10 is 3 marks)
*P62652A01128*
11
Turn over
A
8.4 cm
C
DO NOT WRITE IN THIS AREA
B
Diagram NOT
accurately drawn
D
17.6 cm
The trapezium has exactly one line of symmetry.
BC = 8.4 cm
AD = 17.6 cm
DO NOT WRITE IN THIS AREA
11 The diagram shows trapezium ABCD in which BC and AD are parallel.
The trapezium has area 179.4 cm2
12
*P62652A01228*
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(Total for Question 11 is 6 marks)
°
DO NOT WRITE IN THIS AREA
.......................................................
DO NOT WRITE IN THIS AREA
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
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
12 Solve the simultaneous equations
7x – 2y = 34
3x + 5y = −3
Show clear algebraic working.
x = .......................................................
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
y = .......................................................
(Total for Question 12 is 4 marks)
*P62652A01328*
13
Turn over
14
*P62652A01428*
DO NOT WRITE IN THIS AREA
(Total for Question 13 is 3 marks)
DO NOT WRITE IN THIS AREA
x = ........................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
Work out the value of x.
Give your answer correct to 2 decimal places.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
At the end of 6 years, there is a total of $8877.62 in the account.
DO NOT WRITE IN THIS AREA
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
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
14 F is inversely proportional to the square of v.
Given that F = 6.5 when v = 4
find a formula for F in terms of v.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 14 is 3 marks)
*P62652A01528*
15
Turn over
green
green
red
red
red
green
green
red
red
Spinner A
DO NOT WRITE IN THIS AREA
red
Spinner B
DO NOT WRITE IN THIS AREA
15 Harry has two fair 5-sided spinners.
Harry is going to spin each spinner once.
(a) Complete the probability tree diagram.
Spinner A
....................
....................
green
red
DO NOT WRITE IN THIS AREA
red
DO NOT WRITE IN THIS AREA
....................
DO NOT WRITE IN THIS AREA
red
DO NOT WRITE IN THIS AREA
Spinner B
....................
....................
green
....................
green
(2)
16
*P62652A01628*
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(b) Work out the probability that at least one of the spinners will land on green.
.......................................................
(3)
(Total for Question 15 is 5 marks)
*P62652A01728*
17
Turn over
DO NOT WRITE IN THIS AREA
Diagram NOT
accurately drawn
N
58°
O
P
DO NOT WRITE IN THIS AREA
16
M
L
°
(ii) Give a reason for your answer.
............................ ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
............................ ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
DO NOT WRITE IN THIS AREA
.......................................................
DO NOT WRITE IN THIS AREA
(a) (i) Find the size of angle MLP
DO NOT WRITE IN THIS AREA
Angle MNP = 58°
DO NOT WRITE IN THIS AREA
L, M, N and P are points on a circle, centre O
(b) Find the size of the reflex angle MOP
.......................................................
(2)
(Total for Question 16 is 4 marks)
18
*P62652A01828*
°
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
17 A metal block has a mass of 5 kg, correct to the nearest 50 grams.
The block has a volume of (1.84 × 10 –3 ) m3, correct to 3 significant f igures.
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.
.......................................................
kg/m3
(Total for Question 17 is 4 marks)
*P62652A01928*
19
Turn over
Frequency
10 < h  20
35
20 < h  35
45
35 < h  50
75
50 < h  70
40
70 < h  80
8
DO NOT WRITE IN THIS AREA
Height (h cm)
DO NOT WRITE IN THIS AREA
18 The table gives information about the heights, in centimetres, of some plants.
30
40
50
60
70
80
Height (h cm)
(3)
20
*P62652A02028*
DO NOT WRITE IN THIS AREA
20
DO NOT WRITE IN THIS AREA
10
DO NOT WRITE IN THIS AREA
0
DO NOT WRITE IN THIS AREA
(a) On the grid, draw a histogram for this information.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(b) Work out an estimate for the number of these plants with a height greater than 40 cm.
.......................................................
(2)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(Total for Question 18 is 5 marks)
19 Without using a calculator, rationalise the denominator of
Simplify your answer.
You must show each stage of your working.
6
3− 7
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 19 is 3 marks)
*P62652A02128*
21
Turn over
22
*P62652A02228*
DO NOT WRITE IN THIS AREA
(Total for Question 20 is 3 marks)
cm3
DO NOT WRITE IN THIS AREA
.......................................................
DO NOT WRITE IN THIS AREA
Work out the volume of shape S.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Shape R has surface area 108 cm2 and volume 135 cm3
Shape S has surface area 300 cm2
DO NOT WRITE IN THIS AREA
20 R and S are two similar solid shapes.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
21 Express
1
9x2 − 4
7
× 2
−
3 x − 2 3 x − 13 x − 10 x − 1
as a single fraction in its simplest form.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 21 is 5 marks)
*P62652A02328*
23
Turn over
24
*P62652A02428*
DO NOT WRITE IN THIS AREA
(Total for Question 22 is 4 marks)
DO NOT WRITE IN THIS AREA
(. . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
DO NOT WRITE IN THIS AREA
Find the exact coordinates of the point where the line through B and D intersects the y-axis.
DO NOT WRITE IN THIS AREA
The points A and C both lie on the line with equation 2y + 7x = 20
DO NOT WRITE IN THIS AREA
The diagonals, AC and BD, intersect at the point M.
The coordinates of M are (6, −11)
DO NOT WRITE IN THIS AREA
22 ABCD is a rhombus.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
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)
*P62652A02528*
25
Turn over
26
*P62652A02628*
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(Total for Question 24 is 4 marks)
DO NOT WRITE IN THIS AREA
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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
8 15 22 29 36
DO NOT WRITE IN THIS AREA
24 Here are the first five terms of an arithmetic sequence.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
25 The curve with equation y = g(x) is transformed to the curve with equation y = −g(x) by
the single transformation T.
(a) Describe fully the transformation T.
............................ ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
The diagram shows the graph of y = f(x)
y
6
4
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
2
−2
O
2
4
6
8
10 x
−2
−4
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
−6
(b) On the grid, draw the graph of y = 2f(x – 1)
(2)
(Total for Question 25 is 3 marks)
TOTAL FOR PAPER IS 100 MARKS
*P62652A02728*
27
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
*P62652A02828*
28
DO NOT WRITE IN THIS AREA
BLANK PAGE
Please check the examination details below before entering your candidate information
Candidate surname
Other names
Centre Number
Candidate Number
Paper
reference
4MA1/1H
Pearson Edexcel
International GCSE
Time 2 hours
Mathematics A
PAPER 1H
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
black ink or ball-point pen.
• Use
in the boxes at the top of this page with your name,
• Fill
centre number and candidate number.
all questions.
• Answer
sufficient working, correct answers may be awarded no marks.
• Without
the questions in the spaces provided
• Answer
– there may be more space than you need.
may be used.
• Calculators
must NOT write anything on the formulae page.
• You
Anything you write on the formulae page will gain NO credit.
Information
total mark for this paper is 100.
• The
The
for each question are shown in brackets
• – usemarks
this as a guide as to how much time to spend on each question.
Advice
each question carefully before you start to answer it.
• Read
Check
your answers if you have time at the end.
• Good luck
with your examination.
•
Turn over
P65915RA
©2021 Pearson Education Ltd.
1/1/1/1/1/1
*P65915RA0124*
International GCSE Mathematics
Formulae sheet – Higher Tier
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a ¹ 0 are given by:
x=
1
(a + b)h
2
Area of trapezium =
h
-b ± b2 - 4ac
2a
b
Trigonometry
In any triangle ABC
C
Sine Rule
a
b
A
Volume of cone =
Cosine Rule a2 = b2 + c2 – 2bccos A
B
c
a
b
c
=
=
sin A sin B sin C
Area of triangle =
1
ab sin C
2
Volume of prism
= area of cross section × length
1 2
πr h
3
Curved surface area of cone = πrl
l
h
cross
section
length
r
Volume of cylinder = πr2h
Curved surface area
of cylinder = 2πrh
Volume of sphere =
4 3
πr
3
Surface area of sphere = 4πr2
r
r
h
2
*P65915RA0224*
Answer ALL TWENTY questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1
(a) Simplify e8 ÷ e 2
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(b) Expand and simplify (x – 3)(x + 1)
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 1 is 3 marks)
2
Here is a right-angled triangle.
30 cm
52 cm
h cm
Diagram NOT
accurately drawn
Calculate the value of h.
Give your answer correct to 3 significant figures.
h = . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 2 is 3 marks)
*P65915RA0324*
3
Turn over
3
There are 54 fish in a tank.
Some of the fish are white and the rest of the fish are red.
Jeevan takes at random a fish from the tank.
4
The probability that he takes a white fish is
9
(a) Work out the number of white fish originally in the tank.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
Jeevan puts the fish he took out, back into the tank.
He puts some more white fish into the tank.
Jeevan takes at random a fish from the tank.
1
The probability that he takes a white fish is now
2
(b) Work out the number of white fish Jeevan put into the tank.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 3 is 4 marks)
4
*P65915RA0424*
4
The diagram shows the front of a wooden door with a semicircular glass window.
Diagram NOT
accurately drawn
0.5 m
2m
0.75 m
Julie wants to apply 2 coats of wood varnish to the front of the door, shown shaded in
the diagram.
250 millilitres of wood varnish covers 4 m2 of the wood.
Work out how many millilitres of wood varnish Julie will need.
Give your answer correct to the nearest millilitre.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . .
millilitres
(Total for Question 4 is 5 marks)
*P65915RA0524*
5
Turn over
5
Yasmin has some identical rectangular tiles.
Each tile is L cm by W cm.
Diagram NOT
accurately drawn
L cm
W cm
Using 9 of her tiles, Yasmin makes rectangle ABCD, shown in the diagram below.
A
B
Diagram NOT
accurately drawn
D
C
The area of ABCD is 1620 cm2
Work out the value of L and the value of W.
L = .............................
W = .............................
(Total for Question 5 is 5 marks)
6
*P65915RA0624*
6
Alison buys 5 apples and 3 pears for a total cost of $1.96
Greg buys 3 apples and 2 pears for a total cost of $1.22
Michael buys 10 apples and 10 pears.
Work out how much Michael pays for his 10 apples and 10 pears.
Show your working clearly.
$. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 6 is 5 marks)
7
Write 3.6 ´ 103 as a product of powers of its prime factors.
Show your working clearly.
......................................................
(Total for Question 7 is 3 marks)
*P65915RA0724*
7
Turn over
8
In 2018, the population of Sydney was 5.48 million.
This was 22% of the total population of Australia.
Work out the total population of Australia in 2018
Give your answer correct to 3 significant figures.
......................................................
million
(Total for Question 8 is 3 marks)
(i) Solve the inequalities –7  2x – 3 < 5
9
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(ii) On the number line, represent the solution set to part (i)
–6 –5 –4 –3 –2 –1
0
1
2
3
4
5
6 x
(2)
(Total for Question 9 is 5 marks)
8
*P65915RA0824*
10 A solid aluminium cylinder has radius 10 cm and height h cm.
Diagram NOT
accurately drawn
10 cm
h cm
The mass of the cylinder is 5.4 kg.
The density of aluminium is 0.0027 kg/cm3
Calculate the value of h.
Give your answer correct to one decimal place.
h = . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 10 is 5 marks)
*P65915RA0924*
9
Turn over
11 The table gives information about the times taken by 90 runners to complete a 10 km race.
Time (t minutes)
Frequency
25 < t  35
12
35 < t  45
24
45 < t  55
28
55 < t  65
12
65 < t  75
10
75 < t  85
4
(a) Complete the cumulative frequency table.
Time (t minutes)
Cumulative frequency
25 < t  35
12
25 < t  45
25 < t  55
25 < t  65
25 < t  75
25 < t  85
10
*P65915RA01024*
(1)
(b) On the grid below, draw a cumulative frequency graph for your table.
90
80
70
60
Cumulative
frequency 50
40
30
20
10
0
25
35
45
55
65
Time (t minutes)
75
85
(2)
Any runner who completed the race in a time T minutes such that 42 < T  52 minutes
was awarded a silver medal.
(c) Use your graph to find an estimate for the number of runners who were awarded a
silver medal.
.......................................................
(2)
runners
(Total for Question 11 is 5 marks)
*P65915RA01124*
11
Turn over
12 The diagram shows a vertical cliff with a vertical radio mast on top of the cliff and a
buoy in the sea.
A
Diagram NOT
accurately drawn
100 m
20°
B
dm
The height of the cliff is 100 metres.
The buoy is at the point B that is d metres from the base of the cliff.
The angle of elevation from B to the top of the cliff is 20°
(a) Calculate the value of d.
Give your answer correct to 3 significant figures.
d = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
The point A at the top of the radio mast is vertically above the top of the cliff.
The angle of elevation from B to A is 25°
(b) Calculate the height of the radio mast.
Give your answer correct to 3 significant figures.
.......................................................
(3)
(Total for Question 12 is 6 marks)
12
*P65915RA01224*
m
13 Here is a triangle XYZ.
X
130°
Y
16 cm
Diagram NOT
accurately drawn
25°
Z
The length XZ and the angles YXZ and XYZ are each given correct to 2 significant figures.
Calculate the upper bound for the length YZ.
Give your answer correct to one decimal place.
Show your working clearly.
.......................................................
cm
(Total for Question 13 is 3 marks)
*P65915RA01324*
13
Turn over
14 ABCDEF and GHIJKL are regular hexagons each with centre O.
H
G
A
B
a
L
F
Diagram NOT
accurately drawn
b
C
O
E
K
I
D
J
GHIJKL is an enlargement of ABCDEF, with centre O and scale factor 2
→
→
OA = a OB = b
(a) Write the following vectors, in terms of a and b.
Simplify your answers.
→
(i) AB
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
→
(ii) KI
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
→
(iii) LD
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
14
*P65915RA01424*
The triangle OAB has an area of 5 cm2
(b) Calculate the area of the shaded region.
.......................................................
(3)
cm2
(Total for Question 14 is 8 marks)
*P65915RA01524*
15
Turn over
15 Magnus and Garry play 2 games of chess against each other.
2
The probability that Magnus beats Garry in any game is
9
4
The probability that any game between Magnus and Garry is drawn is
9
The result of any game is independent of the result of any other game.
(a) Complete the probability tree diagram.
First game
Second game
....................
....................
Magnus wins
2
9
4
9
Game drawn
Magnus wins
Game drawn
....................
Magnus loses
....................
Magnus wins
....................
Game drawn
....................
Magnus loses
....................
Magnus wins
....................
Magnus loses
....................
....................
Game drawn
Magnus loses
(2)
16
*P65915RA01624*
For each game of chess,
the winner gets 2 points and the loser gets 0 points,
when the game is drawn, each player gets 1 point.
(b) Work out the probability that, after 2 games, Magnus and Garry have the same
number of points.
.......................................................
(3)
Magnus and Garry now play a third game of chess.
(c) Work out the probability that, after 3 games, Magnus and Garry have the same
number of points.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 15 is 8 marks)
*P65915RA01724*
17
Turn over
16 There are 32 students in a class.
In one term these 32 students each took a test in Maths (M), in English (E) and in French (F).
25 students passed the test in Maths.
20 students passed the test in English.
14 students passed the test in French.
18 students passed the tests in Maths and English.
11 students passed the tests in Maths and French.
4 students failed all three tests.
x students passed all three tests.
The incomplete Venn diagram gives some more information about the results of the 32 students.
E
M
E
3
2
F
(a) Use all the given information about the results of students who passed the test in Maths
to find the value of x.
x = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
18
*P65915RA01824*
(b) Use your value of x to complete the Venn diagram to show the number of students in
each subset.
E
M
E
3
2
F
(2)
A student who passed the test in Maths is chosen at random.
(c) Find the probability that this student failed the test in French.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 16 is 5 marks)
*P65915RA01924*
19
Turn over
17 (a) Factorise 6y2 – y – 5
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(b) Make f the subject of w =
2f +3
8- f
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(c) Express 4x2 – 8x + 7 in the form a(x + b)2 + c where a, b and c are integers.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 17 is 8 marks)
20
*P65915RA02024*
18 0.4 x is a recurring decimal.
x is a whole number such that 1  x  9
●
Find, in terms of x, the recurring decimal 0.4x as a fraction.
Give your fraction in its simplest form.
Show clear algebraic working.
●
.......................................................
(Total for Question 18 is 3 marks)
*P65915RA02124*
21
Turn over
19 ABCED is a five-sided shape.
E
D
Diagram NOT
accurately drawn
C
y cm
A
x cm
B
ABCD is a rectangle.
CED is an equilateral triangle.
AB = x cm BC = y cm
The perimeter of ABCED is 100 cm.
The area of ABCED is R cm2
(a) Show that R =
x
200 6 3 x
4
(3)
22
*P65915RA02224*
(b) (i) Find the value of x for which R has its maximum value.
p
Give your answer in the form
where p and q are integers.
q- 3
x = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(ii) Explain why the maximum value of R is given by this value of x.
............................ ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
............................ ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
............................ ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 19 is 6 marks)
Turn over for Question 20
*P65915RA02324*
23
Turn over
20 The straight line L passes through point A (– 6, 2) and point B (5, 3)
The straight line M is perpendicular to L and passes through the midpoint of A and B.
The line M intersects the line x = – 1 at point C.
Calculate the area of triangle ABC.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 20 is 7 marks)
TOTAL FOR PAPER IS 100 MARKS
24
*P65915RA02424*
International GCSE Mathematics
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a ¹ 0 are given by:
x=
1
(a + b)h
2
Area of trapezium =
h
−b ± b2 − 4ac
2a
b
In any triangle ABC
Trigonometry
C
Sine Rule
A
Volume of cone =
Cosine Rule a2 = b2 + c2 – 2bccos A
B
c
a
b
c
=
=
sin A sin B sin C
Area of triangle =
1
ab sin C
2
Volume of prism
= area of cross section × length
1 2
πr h
3
Curved surface area of cone = πrl
l
h
DO NOT WRITE IN THIS AREA
a
b
cross
section
length
r
Volume of sphere =
4 3
πr
3
Surface area of sphere = 4πr2
r
r
h
*P59019A0224*
DO NOT WRITE IN THIS AREA
Volume of cylinder = πr2h
Curved surface area
of cylinder = 2πrh
2
DO NOT WRITE IN THIS AREA
Formulae sheet – Higher Tier
Write your answers in the spaces provided.
You must write down all the stages in your working.
1
A plane has a length of 73 metres.
A scale model is made of the plane.
The scale of the model is 1 : 200
Work out the length of the scale model.
Give your answer in centimetres.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Answer ALL TWENTY THREE questions.
cm
(Total for Question 1 is 3 marks)
2
Here are the first five terms of an arithmetic sequence.
7 11 15 19 23
DO NOT WRITE IN THIS AREA
Write down an expression, in terms of n, for the nth term of this sequence.
(Total for Question 2 is 2 marks)
*P59019A0324*
3
Turn over
3
There are 90 counters in a bag.
Each counter in the bag is either red or blue so that
Li is going to put some more red counters in the bag so that
the probability of taking at random a red counter from the bag is
Work out the number of red counters that Li is going to put in the bag.
1
3
DO NOT WRITE IN THIS AREA
the number of red counters : the number of blue counters = 2 : 13
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(Total for Question 3 is 4 marks)
4
*P59019A0424*
E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = {odd numbers}
A ∩ B = {1, 3}
A ∪ B = {1, 2, 3, 4, 5, 6, 7, 9, 11, 12}
Draw a Venn diagram to show this information.
E
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
4
DO NOT WRITE IN THIS AREA
(Total for Question 4 is 4 marks)
*P59019A0524*
5
Turn over
5
DO NOT WRITE IN THIS AREA
Calvin has 12 identical rectangular tiles.
He arranges the tiles to fit exactly round the edge of a shaded rectangle, as shown in the
diagram below.
Diagram NOT
accurately drawn
67 cm
123 cm
Work out the area of the shaded rectangle.
DO NOT WRITE IN THIS AREA
(Total for Question 5 is 5 marks)
6
*P59019A0624*
DO NOT WRITE IN THIS AREA
cm2
DO NOT WRITE IN THIS AREA
6
(a) Find the highest common factor (HCF) of 96 and 120
(2)
A = 23 ´ 5 ´ 72 ´ 11
B = 24 ´ 7 ´ 11
C = 3 ´ 52
(2)
(Total for Question 6 is 4 marks)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(b) Find the lowest common multiple (LCM) of A, B and C.
*P59019A0724*
7
Turn over
7
Jenny invests $8500 for 3 years in a savings account.
She gets 2.3% per year compound interest.
DO NOT WRITE IN THIS AREA
(a) How much money will Jenny have in her savings account at the end of 3 years?
Give your answer correct to the nearest dollar.
(3)
Rami bought a house on 1st January 2015
In 2015, the house increased in value by 15%
In 2016, the house decreased in value by 8%
On 1st January 2017, the value of the house was $687 700
(b) What was the value of the house on 1st January 2015?
(3)
(Total for Question 7 is 6 marks)
8
*P59019A0824*
DO NOT WRITE IN THIS AREA
$
DO NOT WRITE IN THIS AREA
$
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
8
A block of wood has a mass of 3.5 kg.
The wood has density 0.65 kg/m3
(a) Work out the volume of the block of wood.
Give your answer correct to 3 significant figures.
(3)
m3
(b) Change a speed of 630 kilometres per hour to a speed in metres per second.
(3)
m/s
(Total for Question 8 is 6 marks)
*P59019A0924*
9
Turn over
9
Solve the simultaneous equations
DO NOT WRITE IN THIS AREA
4x + 5y = 4
2x – y = 9
Show clear algebraic working.
y=
(Total for Question 9 is 3 marks)
DO NOT WRITE IN THIS AREA
x=
DO NOT WRITE IN THIS AREA
10
*P59019A01024*
11 Twenty students took a Science test and a Maths test.
The table gives information about their results.
Median
Interquartile range
Science
27
18
Maths
24.5
11
Use this information to compare the Science test results with the Maths test results.
Write down two comparisons.
DO NOT WRITE IN THIS AREA
Both tests were marked out of 50
1.
2.
DO NOT WRITE IN THIS AREA
(Total for Question 11 is 2 marks)
DO NOT WRITE IN THIS AREA
12
*P59019A01224*
DO NOT WRITE IN THIS AREA
12 (a) Simplify n0
(1)
(b) Simplify (3x2y5)3
(2)
(2)
(d) Make r the subject of m =
6a + r
5r
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(c) Factorise fully 2e2 – 18
(4)
(Total for Question 12 is 9 marks)
*P59019A01324*
13
Turn over
13 The frequency table gives information about the numbers of mice in some nests.
Frequency
5
4
6
13
7
16
8
x
9
6
DO NOT WRITE IN THIS AREA
Number of mice
The mean number of mice in a nest is 7
Work out the value of x.
DO NOT WRITE IN THIS AREA
(Total for Question 13 is 4 marks)
14
*P59019A01424*
DO NOT WRITE IN THIS AREA
x=
DO NOT WRITE IN THIS AREA
14 Marcus plays two games of tennis.
For each game, the probability that Marcus wins is 0.35
(a) Complete the probability tree diagram.
First game
Second game
Marcus
wins
0.35
Marcus
wins
Marcus
does not
win
Marcus
does not
win
Marcus
does not
win
(2)
(b) Work out the probability that Marcus wins at least one of the two games of tennis.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Marcus
wins
(3)
(Total for Question 14 is 5 marks)
*P59019A01524*
15
Turn over
15 The diagram shows a trapezium.
Diagram NOT
accurately drawn
(2x – 3)
(3x – 2)
All measurements shown on the diagram are in centimetres.
DO NOT WRITE IN THIS AREA
(x + 5)
The area of the trapezium is 133 cm2
(a) Show that 8x2 – 6x – 275 = 0
DO NOT WRITE IN THIS AREA
(3)
(b) Find the value of x.
Show your working clearly.
(3)
(Total for Question 15 is 6 marks)
16
*P59019A01624*
DO NOT WRITE IN THIS AREA
x=
DO NOT WRITE IN THIS AREA
16 The diagram shows two mathematically similar vases, A and B.
Diagram NOT
accurately drawn
A
B
A has a volume of 405 cm3
B has a volume of 960 cm3
B has a surface area of 928 cm2
DO NOT WRITE IN THIS AREA
Work out the surface area of A.
cm2
DO NOT WRITE IN THIS AREA
(Total for Question 16 is 3 marks)
*P59019A01724*
17
Turn over
17 f is the function such that f(x) = 4 – 3x
(1)
g is the function such that g( x) =
1
1 − 2x
(b) Find the value of x that cannot be included in any domain of g
DO NOT WRITE IN THIS AREA
(a) Work out f(5)
(1)
DO NOT WRITE IN THIS AREA
(c) Work out fg(−1.5)
(Total for Question 17 is 4 marks)
18
*P59019A01824*
DO NOT WRITE IN THIS AREA
(2)
a
m−x
x=8
correct to 1 significant figure
a = 4.6 correct to 2 significant figures
m = 20 correct to the nearest 10
Calculate the lower bound of P.
Show your working clearly.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
18 P =
DO NOT WRITE IN THIS AREA
(Total for Question 18 is 4 marks)
*P59019A01924*
19
Turn over
19 The histogram shows information about the numbers of minutes some people waited to
be served at a Post Office.
DO NOT WRITE IN THIS AREA
5
4
3
Frequency
density
2
0
0
5
10
15
20
25
30
Number of minutes
Work out an estimate for the proportion of these people who waited longer than 20 minutes
to be served.
DO NOT WRITE IN THIS AREA
1
DO NOT WRITE IN THIS AREA
(Total for Question 19 is 3 marks)
20
*P59019A02024*
DO NOT WRITE IN THIS AREA
20
A
Diagram NOT
accurately drawn
D
B
x°
P
C
Q
A, B, C and D are points on a circle.
PCQ is a tangent to the circle.
AB = CB.
Prove that angle CDA = 2x°
Give reasons for each stage in your working.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Angle BCQ = x°
(Total for Question 20 is 5 marks)
*P59019A02124*
21
Turn over
21 Line L has equation 4y – 6x = 33
Line M goes through the point A (5, 6) and the point B (−4, k)
DO NOT WRITE IN THIS AREA
L is perpendicular to M.
Work out the value of k.
DO NOT WRITE IN THIS AREA
(Total for Question 21 is 4 marks)
DO NOT WRITE IN THIS AREA
22
*P59019A02224*
22 The diagram shows a cone.
DO NOT WRITE IN THIS AREA
V
A
Diagram NOT
accurately drawn
B
AB is a diameter of the cone.
V is the vertex of the cone.
Given that
work out the size of angle AVB.
Give your answer correct to 1 decimal place.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
the area of the base of the cone : the total surface area of the cone = 3 : 8
°
(Total for Question 22 is 6 marks)
*P59019A02324*
23
Turn over
DO NOT WRITE IN THIS AREA
23 ABCD is a trapezium.
→
→
DC = 3AB
→  −2
→  −1
DA =   DB =  
 3
 7
→
Find the exact magnitude of BC
DO NOT WRITE IN THIS AREA
TOTAL FOR PAPER IS 100 MARKS
24
*P59019A02424*
DO NOT WRITE IN THIS AREA
(Total for Question 23 is 5 marks)
Please check the examination details below before entering your candidate information
Candidate surname
Pearson Edexcel
International GCSE
Other names
Centre Number
Candidate Number
Wednesday 15 January 2020
Morning (Time: 2 hours)
Paper Reference 4MA1/2H
Mathematics A
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
black ink or ball-point pen.
• Use
Fill in the boxes at the top of this page with your name,
• centre
number and candidate number.
Answer
questions.
• Withoutallsufficient
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
total mark for this paper is 100.
• The
marks for each question are shown in brackets
• The
– 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
P59762A
©2020 Pearson Education Ltd.
1/1/
*P59762A0128*
International GCSE Mathematics
Formulae sheet – Higher Tier
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a ¹ 0 are given by:
x=
1
(a + b)h
2
Area of trapezium =
h
−b ± b2 − 4ac
2a
b
Trigonometry
In any triangle ABC
C
Sine Rule
a
b
A
Volume of cone =
Cosine Rule a2 = b2 + c2 – 2bccos A
B
c
a
b
c
=
=
sin A sin B sin C
Area of triangle =
1
ab sin C
2
Volume of prism
= area of cross section × length
1 2
πr h
3
Curved surface area of cone = πrl
l
h
cross
section
length
r
Volume of cylinder = πr2h
Curved surface area
of cylinder = 2πrh
Volume of sphere =
4 3
πr
3
Surface area of sphere = 4πr2
r
r
h
2
*P59762A0228*
Answer ALL TWENTY SIX questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1
x9
x2
(a) Simplify
.......................................................
(1)
(b) Write
7 ×7
73
8
4
as a single power of 7
.......................................................
(2)
(Total for Question 1 is 3 marks)
2
Change 32.4 m3 into cm3
.......................................................
cm3
(Total for Question 2 is 2 marks)
*P59762A0328*
3
Turn over
3
Show that
4
7
4
2
+3 =8
15
5
3
(Total for Question 3 is 3 marks)
4
*P59762A0428*
4
The diagram shows a triangle.
30°
(4x + 10)°
Diagram NOT
accurately drawn
(x + 20)°
Work out the value of x.
x = .......................................................
(Total for Question 4 is 4 marks)
*P59762A0528*
5
Turn over
5
Use ruler and compasses to construct the bisector of angle BAC.
You must show all your construction lines.
B
A
C
(Total for Question 5 is 2 marks)
6
*P59762A0628*
6
A bag contains only red beads, blue beads, green beads and yellow beads.
The table gives the probabilities that, when a bead is taken at random from the bag,
the bead will be blue or the bead will be yellow.
Colour
Probability
red
blue
green
yellow
0.24
0.31
The probability that the bead will be green is twice the probability that the bead will be red.
Sofia takes at random a bead from the bag.
She writes down the colour of the bead and puts the bead back into the bag.
She does this 180 times.
Work out an estimate for the number of times she takes a red bead from the bag.
.......................................................
(Total for Question 6 is 4 marks)
*P59762A0728*
7
Turn over
7
(a) Solve the inequality
2x + 7 > 4
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(b) Solve
x 2 – 3x – 40 = 0
Show clear algebraic working.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 7 is 5 marks)
8
*P59762A0828*
8
The table shows the cost, in euros, of Brigitte’s car insurance in each of the years 2016,
2017 and 2018
Year
2016
2017
2018
Cost of insurance (euros)
500
545
592
Brigitte says,
“The percentage increase in the cost of my car insurance from 2017 to 2018 is more than
the percentage increase in the cost of my car insurance from 2016 to 2017”
(a) Is Brigitte correct?
You must show how you get your answer.
(4)
Henri wants to insure his car.
He gets a discount of 15% off the normal price.
Henri pays 952 euros for his car insurance after the discount.
(b) Work out the discount that Henri gets.
.......................................................
(3)
euros
(Total for Question 8 is 7 marks)
*P59762A0928*
9
Turn over
9
The density of gold is 19.3 g/cm3
A gold bar has volume 150 cm3
Work out the mass of the gold bar.
.......................................................
g
(Total for Question 9 is 2 marks)
10 Change a speed of 50 metres per second to a speed in kilometres per hour.
.......................................................
kilometres per hour
(Total for Question 10 is 3 marks)
10
*P59762A01028*
11 The diagram shows a shaded shape ABCD made from a semicircle ABC and a
right‑angled triangle ACD.
B
A
C
17 cm
Diagram NOT
accurately drawn
15 cm
D
AC is the diameter of the semicircle ABC.
Work out the perimeter of the shaded shape.
Give your answer correct to 3 significant figures.
.......................................................
cm
(Total for Question 11 is 5 marks)
*P59762A01128*
11
Turn over
12 Astrid wants to buy some oil.
She can buy the oil from either Dane Oil or Arctic Oil.
Here is information about the price that each company will charge Astrid.
Dane Oil
Arctic Oil
(4.2 × 105) litres
for
2 500 000 Krone
(8.6 × 105) litres
for
770 000 Dollars
Astrid wants to get the better value for money for the oil.
1 Dollar = 6.57 Krone
From which company should she buy her oil, Dane Oil or Arctic Oil?
You must show your working.
(Total for Question 12 is 4 marks)
12
*P59762A01228*
13
B
28°
C
A
O
Diagram NOT
accurately drawn
32°
D
A, B, C and D are points on a circle, centre O.
AOD is a diameter of the circle.
Angle CBD = 28°
Angle BDA = 32°
Find the size of angle BDC.
Give a reason for each stage of your working.
.......................................................
°
(Total for Question 13 is 4 marks)
*P59762A01328*
13
Turn over
14 There are 20 glasses in a cupboard.
13 of the glasses are large
7 of the glasses are small
Roberto takes at random two glasses from the cupboard.
(a) Complete the probability tree diagram.
large
....................
large
....................
....................
small
large
....................
....................
small
....................
small
(2)
(b) Work out the probability that Roberto takes two small glasses.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 14 is 4 marks)
14
*P59762A01428*
15 Here are six graphs.
Graph B
Graph A
y
y
O
y
O
x
y
O
x
Graph E
Graph D
O
Graph C
Graph F
y
O
x
x
y
x
O
x
Complete the table below with the letter of the graph that could represent each given
equation.
Write your answers on the dotted lines.
Equation
y=
2
x2
y=–
1 3
x
2
y=–
5
x
Graph
............................
............................
............................
(Total for Question 15 is 3 marks)
*P59762A01528*
15
Turn over
16 Make x the subject of y =
x +1
x−4
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 16 is 4 marks)
16
*P59762A01628*
17 Prove that the difference between two consecutive square numbers is always an odd number.
Show clear algebraic working.
(Total for Question 17 is 3 marks)
*P59762A01728*
17
Turn over
18 The histogram gives information about the times, in minutes, that some customers spent
in a supermarket.
5
4
3
Frequency
density
2
1
0
0
10
20
30
Time (minutes)
40
50
(a) Work out an estimate for the proportion of these customers who spent between
17 minutes and 35 minutes in the supermarket.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
18
*P59762A01828*
One of the customers is selected at random.
Given that this customer had spent more than 30 minutes in the supermarket,
(b) find the probability that this customer spent more than 36 minutes in the supermarket.
.......................................................
(2)
(Total for Question 18 is 5 marks)
19 (a) Write down an equation of a line that is parallel to the line with equation y = 7 – 4x
.......................................................
(1)
The line L passes through the points with coordinates (–3, 1) and (2, –2)
(b) Find an equation of the line that is perpendicular to L and passes through the point
with coordinates (–6, 4)
Give your answer in the form ax + by + c = 0 where a, b and c are integers.
.......................................................
(4)
(Total for Question 19 is 5 marks)
*P59762A01928*
19
Turn over
20 The area of a rectangle is 18 cm2
The length of the rectangle is
( 7 + 1) cm.
Without using a calculator and showing each stage of your working,
find the width of the rectangle.
Give your answer in the form a b + c where a, b and c are integers.
.......................................................
(Total for Question 20 is 3 marks)
20
*P59762A02028*
cm
21 The diagram shows a sketch of part of the curve with equation y = f(x)
y
(4, 6)
y = f(x)
O
x
There is one maximum point on this curve.
The coordinates of this maximum point are (4, 6)
(a) Write down the coordinates of the maximum point on the curve with equation
(i) y = f(x + 4)
(. . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
(ii) y = f(2x)
(. . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
(2)
The equation of a curve C is y = x 2 + 3x + 4
 4
The curve C is transformed to curve S under the translation  
 6
(b) Find an equation of curve S.
You do not need to simplify the equation.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 21 is 4 marks)
*P59762A02128*
21
Turn over
22 The line with equation y = x + 2 intersects the curve with equation x 2 + y 2 – 2y = 24 at
the points A and B.
Find the coordinates of A and B.
Show clear algebraic working.
(. . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
(. . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
(Total for Question 22 is 5 marks)
22
*P59762A02228*
23
B
4a
M
Diagram NOT
accurately drawn
P
A
2b
C
ABC is a triangle.
The midpoint of BC is M.
P is a point on AM.
→
AB = 4a
→
AC = 2b
→ 3
3
AP = a + b
2
4
Find the ratio AP : PM
.......................................................
(Total for Question 23 is 3 marks)
*P59762A02328*
23
Turn over
24 Express
3 
9 x − 4 x3
 4
−

 ÷ 2
2x − 5 2x − 3
6 x − 17 x + 5
as a single fraction in its simplest form.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 24 is 4 marks)
24
*P59762A02428*
25 Mario is going to save $50 in the year 2021
He is going to continue to save, up to and including the year 2070, by increasing the
amount he saves each year by $k
Mario will save a total of $33 125 from 2021 to 2070
Work out the value of k.
k = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 25 is 3 marks)
*P59762A02528*
25
Turn over
26 Here is a sector, AOB, of a circle with centre O and angle AOB = x°
O
Diagram NOT
accurately drawn
x°
A
B
The sector can form the curved surface of a cone by joining OA to OB.
O
Diagram NOT
accurately drawn
25 cm
AB
The height of the cone is 25 cm.
The volume of the cone is 1600 cm3
Work out the value of x.
Give your answer correct to the nearest whole number.
26
*P59762A02628*
`
x = .......................................................
(Total for Question 26 is 6 marks)
TOTAL FOR PAPER IS 100 MARKS
*P59762A02728*
27
BLANK PAGE
28
*P59762A02828*
Please check the examination details below before entering your candidate information
Candidate surname
Pearson Edexcel
International GCSE
Other names
Centre Number
Candidate Number
Wednesday 13 January 2021
Afternoon (Time: 2 hours)
Paper Reference 4MA1/2H
Mathematics A
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
black ink or ball‑point pen.
• Use
Fill
in
boxes at the top of this page with your name,
• centrethe
number and candidate number.
all questions.
• Answer
sufficient working, correct answers may be awarded no marks.
• Without
Answer
the
in the spaces provided
• – there may questions
be more space than you need.
may be used.
• Calculators
must NOT write anything on the formulae page.
• You
Anything you write on the formulae page will gain NO credit.
Information
total mark for this paper is 100.
• The
marks for each question are shown in brackets
• The
– use this as a guide as to how much time to spend on each question.
Advice
each question carefully before you start to answer it.
• Read
• Check your answers if you have time at the end.
Turn over
P66301A
©2021 Pearson Education Ltd.
1/1/1/
*P66301A0128*
International GCSE Mathematics
Formulae sheet – Higher Tier
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a ¹ 0 are given by:
x=
1
(a + b)h
2
Area of trapezium =
h
−b ± b2 − 4ac
2a
b
Trigonometry
In any triangle ABC
C
Sine Rule
a
b
A
Volume of cone =
Cosine Rule a2 = b2 + c2 – 2bccos A
B
c
a
b
c
=
=
sin A sin B sin C
Area of triangle =
1
ab sin C
2
Volume of prism
= area of cross section × length
1 2
πr h
3
Curved surface area of cone = πrl
l
h
cross
section
length
r
Volume of cylinder = πr2h
Curved surface area
of cylinder = 2πrh
Volume of sphere =
4 3
πr
3
Surface area of sphere = 4πr2
r
r
h
2
*P66301A0228*
Answer ALL TWENTY TWO questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1
A train takes 6 hours 39 minutes to travel from New Delhi to Kanpur.
The train travels a distance of 429 km.
Work out the average speed of the train.
Give your answer in km/h correct to one decimal place.
......................................................
km/h
(Total for Question 1 is 3 marks)
*P66301A0328*
3
Turn over
2
Ava writes down five whole numbers.
For these five numbers
the median is 7
the mode is 8
the range is 5
Find a possible value for each of the five numbers that Ava writes down.
.................................................................................
(Total for Question 2 is 3 marks)
4
*P66301A0428*
3
Gladys buys a table for $465 to sell in her shop.
She sells the table for $520
(a) Work out the percentage profit that Gladys makes from the sale of the table.
Give your answer correct to 3 significant figures.
......................................................
(3)
%
Gladys has a sale in her shop.
She decreases all the normal prices by 12%
The normal price of an armchair was $550
(b) Work out the sale price of the armchair.
$. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 3 is 6 marks)
*P66301A0528*
5
Turn over
4
y
7
6
5
4
3
2
1
O
1
2
3
4
5
6
7
x
(a) On the grid, draw and label the straight line with equation
(i)
x = 1.5
(ii)
y=x
(iii)
x+y=6
(3)
(b) Show, by shading on the grid, the region that satisfies all three of the inequalities
x  1.5
yx
x+y6
Label the region R.
(1)
(Total for Question 4 is 4 marks)
6
*P66301A0628*
5
(a) Expand and simplify 4x(2x + 5) – 3x(2x – 3)
......................................................
Given that
(2)
y5 × yn
= y 13
y6
(b) work out the value of n.
n = ......................................................
(2)
(c) (i) Solve the inequality
7t – 8 < 2t + 7
......................................................
(2)
(ii) On the number line below, represent the solution set of the inequality solved in
part (c)(i)
–5
–4
–3
–2
–1
0
1
2
3
4
5
t
(1)
(Total for Question 5 is 7 marks)
*P66301A0728*
7
Turn over
6
(a) Write down the value of y 0
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(b) Work out
9.6 × 10 + 6.4 × 10
3.2 × 1016
141
140
Give your answer in standard form.
......................................................
(3)
(Total for Question 6 is 4 marks)
8
*P66301A0828*
7
There are 5 cocoa pods in a bag.
The mean weight of the 5 cocoa pods is 398 grams.
A sixth cocoa pod is put into the bag.
The mean weight of the 6 cocoa pods is 401 grams.
Work out the weight of the sixth cocoa pod that is put into the bag.
......................................................
grams
(Total for Question 7 is 3 marks)
*P66301A0928*
9
Turn over
8
A, B and C are points on a circle with centre O.
C
O
15 cm
A
8 cm
B
AOC is a diameter of the circle.
AB = 8 cm
BC = 15 cm
Angle ABC = 90°
Work out the total area of the regions shown shaded in the diagram.
Give your answer correct to 3 significant figures.
10
*P66301A01028*
Diagram NOT
accurately drawn
......................................................
cm2
(Total for Question 8 is 5 marks)
9
A = 23 × 32 × 52 × 11
B = 24 × 3 × 54 × 13
Find the lowest common multiple (LCM) of A and B.
Give your answer as a product of powers of prime numbers.
......................................................
(Total for Question 9 is 2 marks)
*P66301A01128*
11
Turn over
10 The people working for a company work in Team A or in Team B.
number of people in Team A : number of people in Team B = 3 : 4
4
of Team A work full time.
5
24% of Team B work full time.
Work out what fraction of the people working for the company work full time.
Give your fraction in its simplest form.
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 10 is 3 marks)
12
*P66301A01228*
 9t 4 w 9 
11 Simplify fully  6 10 
 18t w 
−2
......................................................
(Total for Question 11 is 3 marks)
12 15 people were asked how long, in minutes, they had been waiting for a bus.
Here are the results.
2
3
3
4
5
6
6
8
9
10
11
13
14
15
18
Find the interquartile range of these times.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .
minutes
(Total for Question 12 is 2 marks)
*P66301A01328*
13
Turn over
13 P, Q, R, S and T are points on a circle with centre O.
Q
R
Diagram NOT
accurately drawn
m°
P
124°
O
n°
T
S
QOS is a diameter of the circle.
angle POS = 124°
angle PRS = m°
angle PTS = n°
(a) Find the value of
(i) m
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(ii) n
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(b) Find the size of angle QPO.
. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 13 is 3 marks)
14
*P66301A01428*
°
14 (a) Solve
9a − 7 3a − 7
−
= 4.55
5
4
Show clear algebraic working.
a = ......................................................
(3)
(b) Make c the subject of the formula
p=
ac + 8
3+c
......................................................
(4)
(Total for Question 14 is 7 marks)
*P66301A01528*
15
Turn over
15 A postman records the weight of each parcel that he delivers.
The histogram shows information about the weights of all the parcels that the postman
delivered last Monday. No parcels weighed more than 6 kg.
Frequency
density
0
0
1
2
3
4
5
6
Weight (kg)
63 of the parcels that the postman delivered last Monday each had a weight between
0.5 kg and 2 kg.
(a) Work out the total number of parcels the postman delivered last Monday.
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
The postman picks at random two of the records of the parcels he delivered
last Monday.
(b) Work out an estimate for the probability that each parcel weighed more than 2.25 kg.
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 15 is 6 marks)
16
*P66301A01628*
16 Some students were asked the following question.
“Which of the subjects Russian (R), French (F) and German (G) do you study?”
Of these students
4 study all three of Russian, French and German
10 study Russian and French
13 study French and German
6 study Russian and German
24 study German
11 study none of the three subjects
the number who study Russian only is twice the number who study French only.
Let x be the number of students who study French only.
(a) Show all this information on the Venn diagram, giving the number of students in
each appropriate subset, in terms of x where necessary.
E
F
R
x
G
(3)
Given that the number of students who were asked the question was 80
(b) work out the number of these students that study Russian.
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 16 is 6 marks)
*P66301A01728*
17
Turn over
17 The diagram shows a solid prism ABCDEFGH.
G
B
28 cm
F
C
H
20 cm
Diagram NOT
accurately drawn
E
24 cm
37 cm
A
D
The trapezium ABCD, in which AD is parallel to BC, is a cross section of the prism.
The base ADEH of the prism is a horizontal plane.
ADEH and BCFG are rectangles.
The midpoint of BC is vertically above the midpoint of AD so that BA = CD.
AD = 37 cm
GF = 28 cm
DE = 24 cm
The perpendicular distance between edges AD and BC is 20 cm.
(a) Work out the total surface area of the prism.
......................................................
(4)
18
*P66301A01828*
cm²
(b) Calculate the size of the angle between AF and the plane ADEH.
Give your answer correct to one decimal place.
. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 17 is 7 marks)
*P66301A01928*
19
Turn over
°
18 A rectangle ABCD is to be drawn on a centimetre grid such that
A has coordinates (–4, –2)
B has coordinates (1, 10)
C has coordinates (19, a)
D has coordinates (b, c)
(a) Work out the value of a, the value of b and the value of c.
a = ......................................................
b = ......................................................
c = ......................................................
(4)
20
*P66301A02028*
(b) Calculate the perimeter, in centimetres, of rectangle ABCD.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .
(3)
cm
(Total for Question 18 is 7 marks)
*P66301A02128*
21
Turn over
19 A particle P is moving along a straight line.
The fixed point O lies on this line.
At time t seconds where t  0, the displacement, s metres, of P from O is given by
s = t³ + 5t² – 8t + 10
Find the displacement of P from O when P is instantaneously at rest.
Give your answer in the form
a
where a and b are integers.
b
......................................................
(Total for Question 19 is 5 marks)
22
*P66301A02228*
metres
20
Q B
A P
R
F
Diagram NOT
accurately drawn
C
T
E
D
The diagram shows a shaded region T formed by removing an equilateral triangle PQR
from a regular hexagon ABCDEF.
The points P and Q lie on AB such that AB = 1.5 × PQ
Given that the area of region T is 72 3 cm2
work out the length of PQ.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .
cm
(Total for Question 20 is 4 marks)
*P66301A02328*
23
Turn over
21 Write
25 x 2 − 64
x 2 − 8 x + 15
− ( x − 7)
×
5x + 8
5 x 2 − 13 x − 6
as a single fraction in its simplest form.
Show clear algebraic working.
24
*P66301A02428*
......................................................
(Total for Question 21 is 4 marks)
Turn over for Question 22
*P66301A02528*
25
Turn over
22 The diagram shows a sector OBC of a circle with centre O and radius (6 + x) cm.
A
B
O
50°
6 cm
Diagram NOT
accurately drawn
D
x cm
C
A is the point on OB and D is the point on OC such that OA = OD = 6 cm
Angle BOC = 50°
Given that
the perimeter of sector OBC = 2 × the perimeter of triangle OAD
find the value of x.
Give your answer correct to 3 significant figures.
26
*P66301A02628*
x = ......................................................
(Total for Question 22 is 6 marks)
TOTAL FOR PAPER IS 100 MARKS
*P66301A02728*
27
BLANK PAGE
28
*P66301A02828*
Please check the examination details below before entering your candidate information
Candidate surname
Centre Number
Other names
Candidate Number
Pearson Edexcel International GCSE
Paper
reference
Time 2 hours
Mathematics A
4MA1/2H
 
PAPER 2H
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
black ink or ball-point pen.
• Use
Fill
in
boxes at the top of this page with your name,
• centrethe
number and candidate number.
all questions.
• Answer
sufficient working, correct answers may be awarded no marks.
• Without
Answer
the
in the spaces provided
• – there may questions
be more space than you need.
may be used.
• Calculators
must NOT write anything on the formulae page.
• You
Anything you write on the formulae page will gain NO credit.
Information
total mark for this paper is 100.
• The
marks for each question are shown in brackets
• The
– use this as a guide as to how much time to spend on each question.
Advice
each question carefully before you start to answer it.
• Read
• Check your answers if you have time at the end.
Turn over
P69203A
©2022 Pearson Education Ltd.
L:1/1/1/1/
*P69203A0128*
International GCSE Mathematics
Formulae sheet – Higher Tier
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a ¹ 0 are given by:
h
−b ± b2 − 4ac
2a
x=
b
Trigonometry
In any triangle ABC
C
Sine Rule
a
b
A
a
b
c
=
=
sin A sin B sin C
Cosine Rule a2 = b2 + c2 – 2bccos A
B
c
Volume of cone =
1
(a + b)h
2
Area of trapezium =
Area of triangle =
1
ab sin C
2
Volume of prism
= area of cross section × length
1 2
πr h
3
Curved surface area of cone = πrl
l
h
cross
section
length
r
Volume of cylinder = πr2h
Curved surface area
of cylinder = 2πrh
4 3
πr
3
Volume of sphere =
Surface area of sphere = 4πr2
r
r
h
2
*P69203A0228*

Answer ALL TWENTY SIX questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1
(a) Expand and simplify ( y + 4)(2 − y)
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(b) Factorise fully 15b5c − 35b3c9
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 1 is 4 marks)

*P69203A0328*
3
Turn over
2
Show that 6
3
4
5
÷2 =2
4
7
8
(Total for Question 2 is 3 marks)
4
*P69203A0428*

3
R
Diagram NOT
accurately drawn
C
x cm
16.5 cm
y cm
B
A
4 cm
Q
12 cm
P
Triangle ABC is similar to triangle PQR
AB = 4 cm PQ = 12 cm RQ = 16.5 cm AC = x cm PR = y cm
(a) Calculate the length of BC
.......................................................
(2)
cm
(b) Write down an expression for y in terms of x
y = .......................................................
(1)
(Total for Question 3 is 3 marks)

*P69203A0528*
5
Turn over
4
Each side of a regular octagon has a length of 18 mm, correct to the nearest 0.5 mm
Diagram NOT
accurately drawn
(a) Write down the lower bound of the length of each side of the octagon.
.......................................................
(1)
mm
(b) Write down the upper bound of the length of each side of the octagon.
.......................................................
(1)
mm
(Total for Question 4 is 2 marks)
6
*P69203A0628*

5
The scale diagram shows the position on a map of a house, A
North
Scale: 1 cm represents 200 metres
A
House C is on a bearing of 110° from A
The distance from A to C is 700 m
(a) Mark the position of C on the diagram with a cross (×)
Label your cross C
(3)
(b) Write the scale of the map in the form 1 : n
1 : ............................
(1)
(Total for Question 5 is 4 marks)

*P69203A0728*
7
Turn over
6
A bag contains only pink sweets, white sweets, green sweets and red sweets.
The table gives each of the probabilities that, when a sweet is taken at random from
the bag, the sweet will be green or the sweet will be red.
Sweet
pink
white
Probability
green
red
0.2
0.35
The ratio
number of pink sweets : number of white sweets = 2 : 1
There are 28 red sweets in the bag.
Work out the number of white sweets in the bag.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 6 is 5 marks)
8
*P69203A0828*

7
Find the lowest common multiple (LCM) of 28, 42 and 63
Show your working clearly.
.......................................................
(Total for Question 7 is 3 marks)

*P69203A0928*
9
Turn over
8
The table gives information about the average house price in England in 2018 and
in 2019
Year
2017
Average house price (£)
2018
2019
228 314
231 776
(a) Work out the percentage increase in the average house price from 2018 to 2019
Give your answer correct to one decimal place.
.......................................................
(2)
%
The average house price in 2019 was 7.7% greater than the average house price in 2017
(b) Work out the average house price in 2017
Give your answer correct to 3 significant figures.
£ . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 8 is 5 marks)
10
*P69203A01028*

9
The frequency table gives information about the number of points scored by a player.
Number of points
Frequency
0
13
1
17
2
8
3
x
4
11
The mean number of points scored is 2
Work out the value of x
x = .......................................................
(Total for Question 9 is 4 marks)

*P69203A01128*
11
Turn over
10 Solve the simultaneous equations
3x + 5y = 3.1
6x + 3y = 3.75
Show clear algebraic working.
x = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
y = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 10 is 3 marks)
12
*P69203A01228*

11 The diagram shows a regular 10-sided polygon, ABCDEFGHIJ
Diagram NOT
accurately drawn
A
J
x°
B
y°
I
C
H
D
G
E
F
Show that x = y
(Total for Question 11 is 4 marks)

*P69203A01328*
13
Turn over
12 a = 6 × 1040
Work out the value of a3
Give your answer in standard form.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 12 is 3 marks)
14
*P69203A01428*

13 The shaded region in the diagram is bounded by three lines.
The equation of one of the lines is given.
y
6
4
2
−2
O
x + 2y = 8
2
4
6
8
10 x
−2
Write down three inequalities that define the shaded region.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 13 is 3 marks)

*P69203A01528*
15
Turn over
14 A zip wire is shown as the dashed line AC in the diagram.
A
Diagram NOT
accurately drawn
x
C
2.6 m
B
D
12 m
The zip wire is supported by two vertical posts AB and CD standing on
horizontal ground.
CD = 2.6 m BD = 12 m
The zip wire makes an angle x with the horizontal, as shown in the diagram.
The design of the zip wire requires the angle x to be at least 5°
Work out the least possible height of the post AB
Give your answer correct to 3 significant figures.
.......................................................
m
(Total for Question 14 is 3 marks)
16
*P69203A01628*

15 Diyar recorded the distance, in kilometres, that he cycled each day for 11 days.
Here are his results.
8 10 12 13 5 23 21 7 5 16 14
Find the interquartile range of his results.
.......................................................
km
(Total for Question 15 is 3 marks)

*P69203A01728*
17
Turn over
16 D, E, F and G are points on a circle, centre O
D
42°
G
Diagram NOT
accurately drawn
O
E
F
EOG is a diameter of the circle.
Angle EGD = 42°
Calculate the size of angle DFG
Give a reason for each stage of your working.
Angle DFG = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
°
(Total for Question 16 is 4 marks)
18
*P69203A01828*

17 Show that
12
3+2
can be written in the form a + b where a and b are integers.
(Total for Question 17 is 3 marks)

*P69203A01928*
19
Turn over
18 Prove that when the sum of the squares of any two consecutive odd numbers is divided
by 8, the remainder is always 2
Show clear algebraic working.
(Total for Question 18 is 3 marks)
20
*P69203A02028*

19
Diagram NOT
accurately drawn
S
4 cm
T
Q
3 cm
12 cm
P
R
PTQ is a diameter of a circle.
RTS is a chord of the circle.
TQ = 3 cm ST = 4 cm TR = 12 cm
Calculate the radius of the circle.
.......................................................
cm
(Total for Question 19 is 3 marks)

*P69203A02128*
21
Turn over
20 The histogram gives information about the heights, h cm, of some tomato plants.
Frequency
density
0
50
60
70
80
90
Height (h cm)
There are 12 tomato plants for which 75 < h  85
One of the tomato plants is selected at random.
Find an estimate for the probability that this tomato plant has a height greater than
82.5 cm
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 20 is 4 marks)
22
*P69203A02228*

21 Part of the graph of y = 2x2 − 4x − 1 is shown on the grid.
y
4
2
−1
O
1
2
3
x
−2
−4
(a) Use the graph to find estimates for the solutions of the equation 2x2 − 4x − 1 = 0
Give your solutions correct to one decimal place.
.......................................................
(2)
(b) By drawing a suitable straight line on the grid, find estimates for the solutions of the
equation x2 − x − 1 = 0
Show your working clearly.
Give your solutions correct to one decimal place.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 21 is 5 marks)

*P69203A02328*
23
Turn over
22 Here is a rectangle.
Diagram NOT
accurately drawn
(2x + 3) cm
(x − 1) cm
Given that the area of the rectangle is less than 75 cm2
find the range of possible values of x
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 22 is 5 marks)
24
*P69203A02428*

23 The diagram shows triangle PQR
Diagram NOT
accurately drawn
R
18°
4.2 cm
P
1.6 cm
Q
PQ = 1.6 cm PR = 4.2 cm Angle PRQ = 18°
Given that angle PQR is obtuse,
work out the area of triangle PQR
Give your answer correct to 3 significant figures.
.......................................................
cm2
(Total for Question 23 is 6 marks)

*P69203A02528*
25
Turn over
24 A particle P moves along a straight line that passes through the fixed point O
The displacement, x metres, of P from O at time t seconds, where t  0 , is given by
x = 4t 3 − 27t + 8
The direction of motion of P reverses when P is at the point A on the line.
The acceleration of P at the instant when P is at A is a m / s2
Find the value of a
a = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 24 is 5 marks)
26
*P69203A02628*

25 The function g is defined as
g : x  5 + 6x − x 2 with domain {x : x  3}
(a) Express the inverse function g−1 in the form g−1 : x  …
g−1 : x  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(4)
(b) State the domain of g−1
.......................................................
(1)
(Total for Question 25 is 5 marks)

*P69203A02728*
27
Turn over
26 An arithmetic series has first term a and common difference d, where d is a
prime number.
The sum of the first n terms of the series is Sn and
Sm = 39
S2m = 320
Find the value of d and the value of m
Show clear algebraic working.
d = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
m = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 26 is 5 marks)
TOTAL FOR PAPER IS 100 MARKS
28
*P69203A02828*

Write your name here
Surname
Other names
Pearson Edexcel
International GCSE
Centre Number
Candidate Number
Mathematics A
Level 1/2
Paper 2H
Higher Tier
Thursday 7 June 2018 – Morning
Time: 2 hours
Paper Reference
4MA1/2H
You must have:
Total Marks
Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser, calculator. Tracing paper may be used.
Instructions
black ink or ball-point pen.
• Use
Fill in the boxes at the top of this page with your name,
• centre
number and candidate number.
Answer
questions.
• Withoutallsufficient
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
total mark for this paper is 100.
• The
for each question are shown in brackets
• –Theusemarks
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
P54695A
©2018 Pearson Education Ltd.
1/1/1/
*P54695A0124*
International GCSE Mathematics
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a v0 are given by:
x=
1
(a + b)h
2
Area of trapezium =
h
−b ± b2 − 4ac
2a
b
Trigonometry
In any triangle ABC
C
Sine Rule
a
b
c
=
=
sin A sin B sin C
Cosine Rule a2 = b2 + c2 – 2bccos A
Area of triangle =
A
B
c
Volume of cone =
1
ab sin C
2
Volume of prism
= area of cross section ulength
1 2
ʌU h
3
Curved surface area of cone = ʌUO
O
h
DO NOT WRITE IN THIS AREA
a
b
cross
section
length
U
Volume of sphere =
4 3
ʌU
3
Surface area of sphere = 4ʌU2
U
U
h
*P54695A0224*
DO NOT WRITE IN THIS AREA
Volume of cylinder = ʌU2h
Curved surface area
of cylinder = 2ʌUK
2
DO NOT WRITE IN THIS AREA
Formulae sheet – Higher Tier
DO NOT WRITE IN THIS AREA
Answer ALL TWENTY THREE questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1
(a) Make a the subject of the formula M = ac – bd
DO NOT WRITE IN THIS AREA
.......................................................
(2)
(b) Solve the inequality
5x – 4 39
.......................................................
(2)
18e 2 f 3 – 12e 3 f
DO NOT WRITE IN THIS AREA
(c) Factorise fully
.......................................................
(2)
(Total for Question 1 is 6 marks)
*P54695A0324*
3
Turn over
2
Work out the difference between the largest share and the smallest share when 3450 yen
is divided in the ratios 2 : 6 : 7
DO NOT WRITE IN THIS AREA
.......................................................
yen
(Total for Question 2 is 3 marks)
Gopal is paid 20 000 rupees each month.
Jamuna is paid 19 200 rupees each month.
DO NOT WRITE IN THIS AREA
3
Gopal and Jamuna are both given an increase in their monthly pay.
After the increase, they are both paid the same amount each month.
Gopal was given an increase of 8%
Work out the percentage increase that Jamuna was given.
DO NOT WRITE IN THIS AREA
.......................................................
(Total for Question 3 is 4 marks)
4
*P54695A0424*
%
Show that
3
53
5
4
−1 = 1
56
8
7
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
4
(Total for Question 4 is 3 marks)
*P54695A0524*
5
Turn over
5
In the diagram below, P and Q are points on a circle with centre O.
O
DO NOT WRITE IN THIS AREA
P
Diagram NOT
accurately drawn
18q
T
Q
QT is a tangent to the circle.
Angle OPQ = 18q
Work out the size of angle PQT.
Give a reason for each stage of your working.
DO NOT WRITE IN THIS AREA
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .
q
(Total for Question 5 is 3 marks)
DO NOT WRITE IN THIS AREA
6
*P54695A0624*
DO NOT WRITE IN THIS AREA
6
The diagram shows two cylinders, A and B.
Diagram NOT
accurately drawn
0.56 m
A
1.6 m
B
0.6 m
Cylinder A has height 1.6 m and radius 0.56 m.
DO NOT WRITE IN THIS AREA
(a) Work out the curved surface area of cylinder A.
Give your answer in m2 correct to 3 significant figures.
m2
.......................................................
(2)
Cylinder B is mathematically similar to cylinder A.
The height of cylinder B is 0.6 m.
DO NOT WRITE IN THIS AREA
(b) Work out the radius of cylinder B.
.......................................................
m
(2)
(Total for Question 6 is 4 marks)
*P54695A0724*
7
Turn over
7
The students in Class A and in Class B take the same examination.
DO NOT WRITE IN THIS AREA
There are 28 students in Class A and 32 students in Class B.
The mean score for all the students in both classes is 72.6
The mean score for the students in Class A is 75
(a) Work out the mean score for the students in Class B.
(4)
The lowest score in Class A is 39
The range of scores for Class A is 57
The lowest score in Class B is 33
The range of scores for Class B is 60
DO NOT WRITE IN THIS AREA
.......................................................
(b) Find the range of scores for all the students in both classes.
(3)
(Total for Question 7 is 7 marks)
8
*P54695A0824*
DO NOT WRITE IN THIS AREA
.......................................................
8
52q
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Diagram NOT
accurately drawn
12.6 cm
x cm
Work out the value of x.
Give your answer correct to 3 significant figures.
x =. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 8 is 3 marks)
9
Solve the simultaneous equations
x + y = 15
7x – 5y = 3
DO NOT WRITE IN THIS AREA
Show clear algebraic working.
x = .......................................................
y = .......................................................
(Total for Question 9 is 3 marks)
*P54695A0924*
9
Turn over
10
8
= 2n
(a) Find the value of n.
n = .......................................................
(2)
DO NOT WRITE IN THIS AREA
27
(13–6)4 × 135 = 13k
(b) Find the value of k.
(Total for Question 10 is 4 marks)
DO NOT WRITE IN THIS AREA
k = .......................................................
(2)
DO NOT WRITE IN THIS AREA
10
*P54695A01024*
Work out the density of the sphere.
Give your answer correct to 3 significant figures.
.......................................................
g / cm3
(Total for Question 11 is 3 marks)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
11 A solid metal sphere has radius 1.5 cm.
The mass of the sphere is 109.6 grams.
*P54695A01124*
11
Turn over
12
F
D
42q
E
96q
A
DO NOT WRITE IN THIS AREA
50q
Diagram NOT
accurately drawn
C
144q
B
The diagram shows a hexagon ABCDEF.
BC is parallel to ED.
Work out the size of the obtuse angle DEF.
DO NOT WRITE IN THIS AREA
(Total for Question 12 is 5 marks)
12
*P54695A01224*
q
DO NOT WRITE IN THIS AREA
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
13 Felix has 10 cards.
There are 5 red cards, 4 blue cards and 1 green card.
Felix takes at random one of the cards.
He does not replace the card.
Felix then takes at random a second card.
(a) Complete the probability tree diagram.
First card
............................
red
5
10
DO NOT WRITE IN THIS AREA
Second card
............................
blue
............................
4
10
............................
blue
red
blue
............................
green
green
............................
............................
1
10
red
green
red
............................
blue
............................
green
(2)
DO NOT WRITE IN THIS AREA
(b) Work out the probability that Felix takes at least one blue card and no green card.
.......................................................
(3)
(Total for Question 13 is 5 marks)
*P54695A01324*
13
Turn over
14 (a) Complete the table of values for y = x 3 – 2x 2 – 3x + 4
–2
–1
y
–0.5
0
4.875
4
1
1.5
2
3
–1.625
(2)
DO NOT WRITE IN THIS AREA
x
(b) On the grid, draw the graph of y = x 3 – 2x 2 – 3x + 4 for values of x from –2 to 3
y
DO NOT WRITE IN THIS AREA
6
4
2
–2
–1
O
1
2
3
x
DO NOT WRITE IN THIS AREA
–2
–4
–6
(2)
14
*P54695A01424*
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(c) By drawing a suitable straight line on the grid,
find estimates for the solutions of the equation x 3 – 2x 2 – x + 1 = 0
Give your solutions correct to 1 decimal place.
....................................................................
(4)
(Total for Question 14 is 8 marks)
15
e = 8.31 correct to 2 decimal places
f = 0.65 correct to 2 decimal places
DO NOT WRITE IN THIS AREA
Work out the lower bound for the value of e – f
Show your working clearly.
.......................................................
(Total for Question 15 is 2 marks)
*P54695A01524*
15
Turn over
16 R is proportional to t 2
The graph shows the relationship between R and t for 0 - t - 4
DO NOT WRITE IN THIS AREA
R
40
30
20
10
1
2
3
DO NOT WRITE IN THIS AREA
O
4 t
(a) Find a formula for R in terms of t.
(3)
16
*P54695A01624*
DO NOT WRITE IN THIS AREA
.......................................................
8
5x
(b) show that t is inversely proportional to
x for t 0
(2)
(Total for Question 16 is 5 marks)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Given also that R =
*P54695A01724*
17
Turn over
17
y = x 3 – 2x 2 – 15x + 5
dy
dx
dy
= ....................................................................
dx
(2)
DO NOT WRITE IN THIS AREA
(a) Find
C is the curve with equation y = x 3 – 2x 2 – 15x + 5
(b) Work out the range of values of x for which C has a negative gradient.
DO NOT WRITE IN THIS AREA
(4)
(Total for Question 17 is 6 marks)
18
*P54695A01824*
DO NOT WRITE IN THIS AREA
....................................................................
Work out the size of the largest angle of the triangle.
Give your answer correct to 1 decimal place.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
18 A triangle has sides of length 8 cm, 10 cm and 14 cm.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .
q
DO NOT WRITE IN THIS AREA
(Total for Question 18 is 3 marks)
*P54695A01924*
19
Turn over
19 The diagram shows a triangular prism.
DO NOT WRITE IN THIS AREA
E
Diagram NOT
accurately drawn
F
D
C
10 cm
A
8 cm
24 cm
B
AF = 10 cm, AB = 24 cm and BC = 8 cm.
Angle FAB = angle ADC = angle BCD = 90q
DO NOT WRITE IN THIS AREA
Work out the size of the angle between the line BE and the plane ABCD.
Give your answer correct to 1 decimal place.
(Total for Question 19 is 3 marks)
20
*P54695A02024*
q
DO NOT WRITE IN THIS AREA
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
20 The histogram shows information about the birth weights of some babies.
Frequency
density
0
2
3
4
Weight (kg)
5
6 of these babies had a birth weight less than 2.5 kg or greater than 4 kg.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Work out the number of babies who had a birth weight between 2.5 kg and 4 kg.
.......................................................
(Total for Question 20 is 3 marks)
*P54695A02124*
21
Turn over
DO NOT WRITE IN THIS AREA
21 (a) Show that
45 + 20 = 5 5
Show your working clearly.
(2)
p+
q
DO NOT WRITE IN THIS AREA
2
in the form
3 −1
where p and q are integers.
Show your working clearly.
(b) Express
.......................................................
(2)
(c) Express x 2 + 6 2 x – 1 in the form (x + a)2 + b
Show your working clearly.
(2)
(Total for Question 21 is 6 marks)
22
*P54695A02224*
DO NOT WRITE IN THIS AREA
.......................................................
22
Diagram NOT
accurately drawn
DO NOT WRITE IN THIS AREA
D
A
2 cm
7 cm
B
F
5 cm
4 cm
E
C
x cm
O
A, D, B and E are points on a circle, centre O.
AFBC, OEC and OFD are straight lines.
Work out the value of x.
Show your working clearly.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
AF = 7 cm, FB = 4 cm, BC = 5 cm, FD = 2 cm and CE = x cm.
x =. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 22 is 6 marks)
*P54695A02324*
23
Turn over
23 The sum of the first 48 terms of an arithmetic series is 4 times the sum of the first
36 terms of the same series.
DO NOT WRITE IN THIS AREA
Find the sum of the first 30 terms of this series.
DO NOT WRITE IN THIS AREA
(Total for Question 23 is 5 marks)
TOTAL FOR PAPER IS 100 MARKS
24
*P54695A02424*
DO NOT WRITE IN THIS AREA
.......................................................
Please check the examination details below before entering your candidate information
Candidate surname
Pearson Edexcel
International GCSE
Other names
Centre Number
Candidate Number
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
black ink or ball-point pen.
• Use
Fill in the boxes at the top of this page with your name,
• centre
number and candidate number.
Answer
questions.
• Withoutallsufficient
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
total mark for this paper is 100.
• The
for each question are shown in brackets
• –Theusemarks
this as a guide as to how much time to spend on each question.
Advice
each question carefully before you start to answer it.
• Read
• Check your answers if you have time at the end.
Turn over
P58371A
©2019 Pearson Education Ltd.
1/1/1/
*P58371A0128*
International GCSE Mathematics
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a v0 are given by:
x=
1
(a + b)h
2
Area of trapezium =
h
−b ± b2 − 4ac
2a
b
Trigonometry
In any triangle ABC
C
Sine Rule
a
b
c
=
=
sin A sin B sin C
Cosine Rule a2 = b2 + c2 – 2bccos A
Area of triangle =
A
B
c
Volume of cone =
1
ab sin C
2
Volume of prism
= area of cross section ulength
1 2
ʌU h
3
Curved surface area of cone = ʌUO
O
h
DO NOT WRITE IN THIS AREA
a
b
cross
section
length
U
Volume of sphere =
4 3
ʌU
3
Surface area of sphere = 4ʌU2
U
U
h
*P58371A0228*
DO NOT WRITE IN THIS AREA
Volume of cylinder = ʌU2h
Curved surface area
of cylinder = 2ʌUK
2
DO NOT WRITE IN THIS AREA
Formulae sheet – Higher Tier
DO NOT WRITE IN THIS AREA
Answer ALL TWENTY FOUR questions.
Write your answers in the spaces provided.
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
DO NOT WRITE IN THIS AREA
Work out an estimate for the mean height of the sunflowers.
.......................................................
cm
DO NOT WRITE IN THIS AREA
(Total for Question 1 is 4 marks)
*P58371A0328*
3
Turn over
2
Use ruler and compasses to construct the perpendicular bisector of the line DE.
You must show all your construction lines.
DO NOT WRITE IN THIS AREA
D
E
DO NOT WRITE IN THIS AREA
(Total for Question 2 is 2 marks)
DO NOT WRITE IN THIS AREA
4
*P58371A0428*
DO NOT WRITE IN THIS AREA
3
E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {2, 3, 5, 7}
B = {4, 6, 8, 10}
(a) Explain why A ˆB = ‡
. . . . . . . . . . . .................................................... ....................................... . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . .................................................... ....................................... . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . .................................................... ....................................... . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
x  E and x  A ‰ B
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(b) Write down the two possible values of x.
.............................
, .............................
(1)
Set C is such that
A ‰ B ‰ C =E
A ˆC = {2}
B ˆC ‫`^ މ‬
(c) List all the members of set C.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 3 is 4 marks)
*P58371A0528*
5
Turn over
4
A cylinder has diameter 14 cm and height 20 cm.
DO NOT WRITE IN THIS AREA
Work out the volume of the cylinder.
Give your answer correct to 3 significant figures.
(Total for Question 4 is 2 marks)
cm3
DO NOT WRITE IN THIS AREA
.......................................................
DO NOT WRITE IN THIS AREA
6
*P58371A0628*
Josh buys and sells books for a living.
He buys 120 books for £4 each.
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.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
5
.......................................................
%
(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.
DO NOT WRITE IN THIS AREA
(b) Find the value of the book on the 1st May 2018
£. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 5 is 8 marks)
*P58371A0728*
7
Turn over
6
ABC and DEF are similar triangles.
Diagram NOT
accurately drawn
B
19.5 cm
6 cm
A
DO NOT WRITE IN THIS AREA
E
15 cm
C
4.2 cm
D
F
.......................................................
cm
DO NOT WRITE IN THIS AREA
(a) Work out the length of DF.
(2)
(b) Work out the length of BC.
(2)
(Total for Question 6 is 4 marks)
8
*P58371A0828*
cm
DO NOT WRITE IN THIS AREA
.......................................................
30 students in a class sat a Mathematics test.
The mean mark in the test for the 30 students was 26.8
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.
.......................................................
(Total for Question 7 is 3 marks)
8
Change a speed of x kilometres per hour into a speed in metres per second.
Simplify your answer.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
7
.......................................................
m/s
(Total for Question 8 is 3 marks)
*P58371A0928*
9
Turn over
9
Solve the simultaneous equations
3x – y =
DO NOT WRITE IN THIS AREA
x + 2y í
16
Show clear algebraic working.
y =. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 9 is 3 marks)
DO NOT WRITE IN THIS AREA
x =. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
10
*P58371A01028*
DO NOT WRITE IN THIS AREA
10 The straight line LKDVJUDGLHQWDQGSDVVHVWKURXJKWKHSRLQWZLWKFRRUGLQDWHV í
(a) Write down an equation for L.
.......................................................
(2)
(b)
y
5
DO NOT WRITE IN THIS AREA
4
3
R
2
1
–2
–1 O
1
2
3
4 x
–1
–2
–3
The region R, shown shaded in the diagram, is bounded by four straight lines.
DO NOT WRITE IN THIS AREA
Write down the inequalities that define R.
. . . . . . . . . . . .................................................... ....................................... . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 10 is 4 marks)
*P58371A01128*
11
Turn over
11 The table gives the average crowd attendance per match for each of five football clubs
for one season.
DO NOT WRITE IN THIS AREA
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)
“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.
. . . . . . . . . . . .................................................... ....................................... . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
Antonio says,
. . . . . . . . . . . .................................................... ....................................... . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . .................................................... ....................................... . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(c) Work out the overall percentage change in the cost of a ticket to watch Seapron
United during last season.
.......................................................
(2)
(Total for Question 11 is 6 marks)
12
*P58371A01228*
%
DO NOT WRITE IN THIS AREA
During last season the cost of a ticket to watch Seapron United increased by 15% and
then decreased by 8%
B
21.2 cm
C
Diagram NOT
accurately drawn
16.7 cm
43°
A
D
Calculate the perimeter of the trapezium.
Give your answer correct to 3 significant figures.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
12 ABCD is a trapezium.
.......................................................
cm
(Total for Question 12 is 4 marks)
*P58371A01328*
13
Turn over
13 The table gives information about the times taken, in minutes, for 80 taxi journeys.
Frequency
0t- 5
7
5 t - 10
10
10 t - 15
12
15 t - 20
19
20 t - 25
18
25 t - 30
14
DO NOT WRITE IN THIS AREA
Time taken (t minutes)
(a) Complete the cumulative frequency table.
Time taken (t minutes)
Cumulative frequency
0t- 5
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.
DO NOT WRITE IN THIS AREA
0 t - 10
DO NOT WRITE IN THIS AREA
14
*P58371A01428*
DO NOT WRITE IN THIS AREA
80
70
60
50
DO NOT WRITE IN THIS AREA
Cumulative
40
frequency
30
20
10
0
0
5
10
15
20
25
30
Time taken (minutes)
DO NOT WRITE IN THIS AREA
(2)
(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 13 is 6 marks)
*P58371A01528*
15
Turn over
14 Here are two vectors.
→ ⎛ 1⎞
CB = ⎜ ⎟
⎝ 3⎠
DO NOT WRITE IN THIS AREA
→ ⎛ 6⎞
AB = ⎜ ⎟
⎝ −9⎠
→
Find the magnitude of AC .
(Total for Question 14 is 3 marks)
15 Make x the subject of the formula y =
3x − 2
x +1
DO NOT WRITE IN THIS AREA
.......................................................
DO NOT WRITE IN THIS AREA
.......................................................
(Total for Question 15 is 4 marks)
16
*P58371A01628*
4+ 8
can be written in the form a + b 2, where a and b are integers.
2 −1
Show each stage of your working clearly and give the value of a and the value of b.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
16 Show that
(Total for Question 16 is 3 marks)
*P58371A01728*
17
Turn over
17 y is directly proportional to the cube of x
y = 20 h when x = h (h ≠ 0)
DO NOT WRITE IN THIS AREA
(a) Find a formula for y in terms of x and h
y =. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
DO NOT WRITE IN THIS AREA
(b) Find x in terms of h when y = 67.5 h
Give your answer in its simplest form.
(Total for Question 17 is 5 marks)
18
*P58371A01828*
DO NOT WRITE IN THIS AREA
x =. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
18 The diagram shows a solid cuboid.
DO NOT WRITE IN THIS AREA
Diagram NOT
accurately drawn
(12 – 3x) cm
x cm
x cm
The total surface area of the cuboid is A cm2
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Find the maximum value of A.
.......................................................
(Total for Question 18 is 5 marks)
*P58371A01928*
19
Turn over
19 ABCD is a quadrilateral.
Diagram NOT
accurately drawn
39°
B
26 cm
D
95°
DO NOT WRITE IN THIS AREA
A
47°
C
Calculate the area of the quadrilateral ABCD.
Show your working clearly.
Give your answer correct to 3 significant figures.
DO NOT WRITE IN THIS AREA
The area of triangle ACD is 250 cm2
DO NOT WRITE IN THIS AREA
20
*P58371A02028*
DO NOT WRITE IN THIS AREA
cm2
(Total for Question 19 is 6 marks)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
.......................................................
*P58371A02128*
21
Turn over
20 The equation of the line L is y íx
The equation of the curve C is x2íxy + 2y2 = 0
DO NOT WRITE IN THIS AREA
L and C intersect at two points.
Find the coordinates of these two points.
Show clear algebraic working.
DO NOT WRITE IN THIS AREA
(Total for Question 20 is 5 marks)
22
*P58371A02228*
DO NOT WRITE IN THIS AREA
(..... . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ) and (. . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
21 The diagram shows cuboid ABCDEFGH.
DO NOT WRITE IN THIS AREA
E
F
Diagram NOT
accurately drawn
H
G
C
D
A
B
For this cuboid
Calculate the size of the angle between AF and the plane ABCD.
Give your answer correct to one decimal place.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
the length of AB : the length of BC : the length of CF = 4 : 2 : 3
.......................................................
°
(Total for Question 21 is 3 marks)
*P58371A02328*
23
Turn over
22 Simplify fully
DO NOT WRITE IN THIS AREA
6 x 3 + 13 x 2 − 5 x
4 x 2 − 25
(Total for Question 22 is 3 marks)
DO NOT WRITE IN THIS AREA
.......................................................
DO NOT WRITE IN THIS AREA
24
*P58371A02428*
Boris takes at random 2 sweets from the bag.
The probability that Boris takes exactly 1 red sweet from the bag is
Originally there were 3 red sweets in the bag.
12
35
Work out how many green sweets there were originally in the bag.
Show your working clearly.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
23 Boris has a bag that only contains red sweets and green sweets.
.......................................................
(Total for Question 23 is 5 marks)
*P58371A02528*
25
Turn over
24 The function f is such that f (x) = 3x – 2
.......................................................
(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) = ...
DO NOT WRITE IN THIS AREA
(a) Find f (5)
DO NOT WRITE IN THIS AREA
(Total for Question 24 is 5 marks)
TOTAL FOR PAPER IS 100 MARKS
26
*P58371A02628*
DO NOT WRITE IN THIS AREA
g–1(x) = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(4)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
BLANK PAGE
*P58371A02728*
27
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
*P58371A02828*
28
DO NOT WRITE IN THIS AREA
BLANK PAGE
Please check the examination details below before entering your candidate information
Candidate surname
Pearson Edexcel
International GCSE
Time 2 hours
Other names
Centre Number
Candidate Number
Paper
reference
4MA1/2H
Mathematics A
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
black ink or ball‑point pen.
• Use
Fill in the boxes at the top of this page with your name,
• centre
number and candidate number.
Answer
questions.
• Withoutallsufficient
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
total mark for this paper is 100.
• The
The
for each question are shown in brackets
• – usemarks
this as a guide as to how much time to spend on each question.
Advice
each question carefully before you start to answer it.
• Read
Check
your answers if you have time at the end.
• Good luck
with your examination.
•
Turn over
P65918A
©2021 Pearson Education Ltd.
1/1/1/1/1/
*P65918A0128*
International GCSE Mathematics
Formulae sheet – Higher Tier
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a ¹ 0 are given by:
x=
1
(a + b)h
2
Area of trapezium =
h
−b ± b2 − 4ac
2a
b
Trigonometry
In any triangle ABC
C
Sine Rule
a
b
A
Volume of cone =
Cosine Rule a2 = b2 + c2 – 2bccos A
B
c
a
b
c
=
=
sin A sin B sin C
Area of triangle =
1
ab sin C
2
Volume of prism
= area of cross section × length
1 2
πr h
3
Curved surface area of cone = πrl
l
h
cross
section
length
r
Volume of cylinder = πr2h
Curved surface area
of cylinder = 2πrh
Volume of sphere =
4 3
πr
3
Surface area of sphere = 4πr2
r
r
h
2
*P65918A0228*
Answer ALL TWENTY THREE questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1
Write 600 as a product of powers of its prime factors.
Show your working clearly.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 1 is 3 marks)
*P65918A0328*
3
Turn over
2
Show that 2
4
1
2
÷1 =2
7
8
7
(Total for Question 2 is 3 marks)
3
The bearing of Paris from London is 149°
Work out the bearing of London from Paris.
.......................................................
(Total for Question 3 is 2 marks)
4
*P65918A0428*
°
4
E = {letters of the alphabet}
B = {b, r, a, z, i, l}
I = {i, r, e, l, a, n, d}
(a) List the members of the set
(i) B ∪ I
.............................................................................................................
(ii) B ∩ I ʹ
.............................................................................................................
(2)
K = {k, e, n, y, a}
Cody writes down the statement B ∩ K = ∅
Cody’s statement is wrong.
(b) Explain why.
............................ ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
............................ ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 4 is 3 marks)
*P65918A0528*
5
Turn over
5
E
Diagram NOT
accurately drawn
44°
B
A
G
F
C
D
H
I
J
ABCD and FGHI are parallel straight lines.
EBGJ and ECH are straight lines.
BE = CE
Angle BEC = 44°
Work out the size of angle JGH.
Give a reason for each stage of your working.
.......................................................
(Total for Question 5 is 5 marks)
6
*P65918A0628*
°
6
Mariana sells bags of bird food.
The bags that Mariana sold last week each contained 12 kg of seeds.
The bags that she is going to sell next week will each contain a mixture of nuts and seeds
where for each bag
weight of nuts : weight of seeds = 4 : 5
The total weight of the nuts and the seeds in each bag will be 19.35 kg
The weight of seeds in each bag that Mariana sells next week will be less than the weight
of seeds in each bag that Mariana sold last week.
Work out this decrease as a percentage of the weight of seeds in each bag that Mariana
sold last week.
Give your answer correct to one decimal place.
. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .
%
(Total for Question 6 is 4 marks)
*P65918A0728*
7
Turn over
7
Here is a right-angled triangle.
Diagram NOT
accurately drawn
6.5 cm
x cm
42°
Work out the value of x.
Give your answer correct to one decimal place.
x = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 7 is 3 marks)
8
*P65918A0828*
8
Solve the simultaneous equations
5a + 2c = 10
2a – 4c = 7
Show clear algebraic working.
a = .......................................................
c = .......................................................
(Total for Question 8 is 3 marks)
9
(i) Factorise x2 + 2x – 24
.......................................................
(2)
(ii) Hence solve x2 + 2x – 24 = 0
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 9 is 3 marks)
*P65918A0928*
9
Turn over
10 Here is a triangular prism.
11.2 cm
7.4 cm
Diagram NOT
accurately drawn
15 cm
Work out the volume of the prism.
Give your answer correct to 3 significant figures.
.......................................................
(Total for Question 10 is 5 marks)
10
*P65918A01028*
cm3
11 Chengbo sold a house for 180 000 yuan.
The amount for which he sold the house is 24% more than the amount he paid for the house.
(a) Work out how much Chengbo paid for the house.
Give your answer correct to 3 significant figures.
.......................................................
yuan
.......................................................
yuan
(3)
Zhi bought a house on 1st January 2017
When she bought the house, its value was 120 000 yuan.
The value of the house increased by 1.8% per year.
(b) Work out the value of Zhi’s house on 1st January 2020
Give your answer correct to 3 significant figures.
(3)
(Total for Question 11 is 6 marks)
*P65918A01128*
11
Turn over
12 The cumulative frequency table gives information about the distance, in kilometres, that
each of 80 workers travel from home to work at Office A.
Distance travelled (d km)
Cumulative frequency
0<d„ 5
17
0 < d „ 10
32
0 < d „ 15
57
0 < d „ 20
70
0 < d „ 25
76
0 < d „ 30
80
(a) On the grid below, draw a cumulative frequency graph for the information in the table.
80
70
60
50
Cumulative
40
frequency
30
20
10
0
12
0
5
10
15
20
Distance travelled (km)
*P65918A01228*
25
30
(2)
(b) Use your graph to find an estimate for the median distance travelled.
.......................................................
(1)
km
(c) Use your graph to find an estimate for the interquartile range of the distances travelled.
.......................................................
(2)
km
For Office B, the median distance workers travel from home to work is 15 km and the
interquartile range is 5 km.
(d) Use the information above to compare the distances that workers at Office A and
workers at Office B travel from home to work.
Write down two comparisons.
1.. ..................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
............................ ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
............................ ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.. ..................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
............................ ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
............................ ............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 12 is 7 marks)
*P65918A01328*
13
Turn over
13 Emilie takes part in two races.
The probability that she wins the first race is 0.7
The probability that she wins the second race is 0.4
The outcomes of the two races are independent.
(a) Complete the probability tree diagram.
First race
Second race
Emilie wins
0.4
Emilie wins
0.7
....................
Emilie does
not win
Emilie wins
....................
....................
Emilie does
not win
....................
Emilie does
not win
(2)
(b) Work out the probability that Emilie wins exactly one of the two races.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
14
*P65918A01428*
Emilie is going to take part in a third race.
If she wins both of the first two races, the probability that she will win the third race is 0.6
If she wins exactly one of the first two races, the probability that she will win the third race is 0.3
(c) Work out the probability that Emilie will win exactly two of the three races.
.......................................................
(3)
(Total for Question 13 is 8 marks)
*P65918A01528*
15
Turn over
−
1
 9x4  2
14 Simplify fully 
 16 y10 
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 14 is 3 marks)
15 (a) Complete the table of values for y =
x
0.25
y
16.25
0.5
1 2
( x + 4)
x
1
2
4
8
8.5
(2)
16
*P65918A01628*
(b) On the grid, draw the graph of y =
1 2
( x + 4) for 0.25  x  8
x
y
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
O
1
2
3
4
5
6
8 x
7
(2)
(Total for Question 15 is 4 marks)
*P65918A01728*
17
Turn over
16 A is inversely proportional to the square of r
A = 5 when r = 0.3
(a) Find a formula for A in terms of r
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(b) Find the value of A when r = 7.5A
A = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 16 is 6 marks)
18
*P65918A01828*
17 The straight line L passes through the points (4, −1) and (6, 4)
The straight line M is perpendicular to L and intersects the y-axis at the point (0, 8)
Find the coordinates of the point where M intersects the x-axis.
(. . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
(Total for Question 17 is 4 marks)
*P65918A01928*
19
Turn over
18
A
B
8 cm
Diagram NOT
accurately drawn
98°
7.5 cm
35°
C
D
ABCD is a quadrilateral where A, B, C and D are points on a circle.
AB = 8 cm
BC = 7.5 cm
Angle ABC = 98°
Angle ACD = 35°
Work out the perimeter of quadrilateral ABCD.
Give your answer correct to one decimal place.
20
*P65918A02028*
.......................................................
cm
(Total for Question 18 is 6 marks)
*P65918A02128*
21
Turn over
19 Solve the simultaneous equations
y = 3 – 2x
x + y2 = 18
2
Show clear algebraic working.
...........................................................................................................
(Total for Question 19 is 5 marks)
22
*P65918A02228*
20 Mathematically similar wooden blocks are made in a workshop.
There are small blocks and there are large blocks.
The volume of each small block is 300 cm3
Given that
the surface area of each small block : the surface area of each large block = 25 : 36
work out the volume of each large block.
.......................................................
cm3
(Total for Question 20 is 3 marks)
*P65918A02328*
23
Turn over
16
21 The point A is the only stationary point on the curve with equation y = kx 2 +
x
where k is a constant.
2 
Given that the coordinates of A are  , a
3 
find the value of a.
Show your working clearly.
a = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 21 is 5 marks)
24
*P65918A02428*
22 The curve S has equation y = f(x) where f(x) = x2
The curve T has equation y = g(x) where g(x) = 2x2 – 12x + 13
By writing g(x) in the form a(x – b)2 – c, where a, b and c are constants,
describe fully a series of transformations that map the curve S onto the curve T.
................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . ............................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . ............................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 22 is 4 marks)
*P65918A02528*
25
Turn over
23 Pippa has a box containing N pens.
There are only black pens and red pens in the box.
The number of black pens in the box is 3 more than the number of red pens.
Pippa is going to take at random 2 pens from the box.
The probability that she will take a black pen followed by a red pen is
Find the possible values of N.
Show clear algebraic working.
26
9
35
*P65918A02628*
.......................................................
(Total for Question 23 is 5 marks)
TOTAL FOR PAPER IS 100 MARKS
*P65918A02728*
27
BLANK PAGE
28
*P65918A02828*
Please check the examination details below before entering your candidate information
Candidate surname
Pearson Edexcel
International GCSE
Other names
Centre Number
Candidate Number
Thursday 4 June 2020
Morning (Time: 2 hours)
Paper Reference 4MA1/2H
Mathematics A
Paper 2H
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
black ink or ball-point pen.
• Use
Fill in the boxes at the top of this page with your name,
• centre
number and candidate number.
Answer
questions.
• Withoutallsufficient
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
total mark for this paper is 100.
• The
marks for each question are shown in brackets
• The
– 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
P62657A
©2020 Pearson Education Ltd.
1/1/1/1/
*P62657A0124*
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a ¹ 0 are given by:
h
−b ± b2 − 4ac
2a
b
Trigonometry
In any triangle ABC
Sine Rule
B
c
Volume of cone =
Area of triangle =
1
ab sin C
2
Volume of prism
= area of cross section × length
1 2
πr h
3
Curved surface area of cone = πrl
l
h
cross
section
length
r
Volume of cylinder = πr2h
Curved surface area
of cylinder = 2πrh
Volume of sphere =
4 3
πr
3
Surface area of sphere = 4πr2
r
r
h
2
DO NOT WRITE IN THIS AREA
A
Cosine Rule a2 = b2 + c2 – 2bccos A
DO NOT WRITE IN THIS AREA
a
b
a
b
c
=
=
sin A sin B sin C
DO NOT WRITE IN THIS AREA
C
DO NOT WRITE IN THIS AREA
x=
1
(a + b)h
2
Area of trapezium =
DO NOT WRITE IN THIS AREA
Formulae sheet – Higher Tier
DO NOT WRITE IN THIS AREA
International GCSE Mathematics
*P62657A0224*
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Answer ALL TWENTY ONE questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1
(a) Simplify g6 × g4
.......................................................
(1)
(b) Simplify k10 ÷ k3
.......................................................
(1)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(c) Simplify (3cd 4)2
.......................................................
(2)
(d) Solve the inequality 4x + 7 > 2
.......................................................
(2)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(Total for Question 1 is 6 marks)
*P62657A0324*
3
Turn over
Frequency
20 < L  30
6
30 < L  40
26
40 < L  50
31
50 < L  60
40
60 < L  70
17
DO NOT WRITE IN THIS AREA
Length of time (L minutes)
DO NOT WRITE IN THIS AREA
The table shows information about the lengths of time, in minutes, 120 customers spent
in a supermarket.
(a) Write down the modal class.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(4)
(Total for Question 2 is 5 marks)
4
*P62657A0424*
minutes
DO NOT WRITE IN THIS AREA
.......................................................
DO NOT WRITE IN THIS AREA
(b) Work out an estimate for the mean length of time spent by the 120 customers in the
supermarket.
DO NOT WRITE IN THIS AREA
(1)
DO NOT WRITE IN THIS AREA
2
3
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
E
C
Diagram NOT
accurately drawn
F
D
58°
B
A
The diagram shows a parallelogram ABCD and an isosceles triangle DEF in which DE = DF
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
CDF and ADE are straight lines.
Angle BCD = 58°
Work out the size of angle DEF.
Give a reason for each stage of your working.
.......................................................
°
(Total for Question 3 is 5 marks)
*P62657A0524*
5
Turn over
Work out how much money Andreas has left from his share of the money when he has
bought the video game.
6
*P62657A0624*
DO NOT WRITE IN THIS AREA
(Total for Question 4 is 4 marks)
DO NOT WRITE IN THIS AREA
£. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
Andreas buys a video game for £48.50 with some of his share of the money.
DO NOT WRITE IN THIS AREA
The total amount of money that Isla and Paulo receive is £76 more than the amount of
money that Andreas receives.
DO NOT WRITE IN THIS AREA
Andreas, Isla and Paulo share some money in the ratios 3 : 2 : 5
DO NOT WRITE IN THIS AREA
4
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
5
Himari’s annual salary is 3 130 000 Japanese Yen (JPY).
She gets a salary increase of 4%
(a) Work out Himari’s salary after this increase.
.......................................................
JPY
.......................................................
JPY
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(3)
Kaito bought a car.
The value of the car when Kaito bought it was 750 000 JPY.
At the end of each year, the value of his car had depreciated by 15%
(b) Work out the value of Kaito’s car at the end of 3 years.
Give your answer correct to the nearest JPY.
(3)
(Total for Question 5 is 6 marks)
*P62657A0724*
7
Turn over
5
DO NOT WRITE IN THIS AREA
y
6
L
4
3
2
DO NOT WRITE IN THIS AREA
The line L is shown on the grid.
1
–3
–2
–1 O
1
2
3 x
–4
–5
–6
Find an equation for L.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 6 is 2 marks)
8
*P62657A0824*
DO NOT WRITE IN THIS AREA
–3
DO NOT WRITE IN THIS AREA
–2
DO NOT WRITE IN THIS AREA
–1
DO NOT WRITE IN THIS AREA
6
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
7
The diagram shows a right-angled triangle.
Diagram NOT
accurately drawn
3.4 cm
x°
4.7 cm
Calculate the value of x.
Give your answer correct to one decimal place.
x = .......................................................
(Total for Question 7 is 3 marks)
*P62657A0924*
9
Turn over
DO NOT WRITE IN THIS AREA
Diagram NOT
accurately drawn
8.5 cm
8.5 cm
DO NOT WRITE IN THIS AREA
The diagram shows an isosceles triangle.
8 cm
10
*P62657A01024*
DO NOT WRITE IN THIS AREA
(Total for Question 8 is 4 marks)
cm2
DO NOT WRITE IN THIS AREA
.......................................................
DO NOT WRITE IN THIS AREA
Work out the area of the triangle.
DO NOT WRITE IN THIS AREA
8
The diagram shows a solid cylinder with radius 3 m.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
9
3m
Diagram NOT
accurately drawn
The volume of the cylinder is 72π m3
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Calculate the total surface area of the cylinder.
Give your answer correct to 3 significant figures.
.......................................................
m2
(Total for Question 9 is 5 marks)
*P62657A01124*
11
Turn over
Frequency
0 < L  10
10
10 < L  20
16
20 < L  30
44
30 < L  40
29
40 < L  50
15
50 < L  60
6
DO NOT WRITE IN THIS AREA
Number of minutes late (L)
DO NOT WRITE IN THIS AREA
10 The table shows information about the number of minutes each of 120 buses was late last Monday.
(a) Complete the cumulative frequency table below.
0 < L  30
0 < L  40
0 < L  50
0 < L  60
(1)
12
*P62657A01224*
DO NOT WRITE IN THIS AREA
0 < L  20
DO NOT WRITE IN THIS AREA
0 < L  10
DO NOT WRITE IN THIS AREA
Cumulative
frequency
DO NOT WRITE IN THIS AREA
Number of minutes late (L)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(b) On the grid, draw a cumulative frequency graph for your table.
120
100
80
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Cumulative
frequency
60
40
20
0
0
10
20
30
40
50
60
Number of minutes late
(2)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(c) Use your graph to find an estimate for the interquartile range.
.......................................................
(2)
minutes
(d) Use your graph to find an estimate for the number of buses that were more than
48 minutes late last Monday.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 10 is 7 marks)
*P62657A01324*
13
Turn over
2
 y
(b) Express  
 2
(2)
−4
in the form ay n where a and n are integers.
DO NOT WRITE IN THIS AREA
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
11 (a) Simplify fully (8e15) 3
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 11 is 8 marks)
14
*P62657A01424*
DO NOT WRITE IN THIS AREA
x = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(4)
DO NOT WRITE IN THIS AREA
Show clear algebraic working.
DO NOT WRITE IN THIS AREA
4 x − 2 5 − 3x
−
=6
3
4
DO NOT WRITE IN THIS AREA
(c) Solve
3x
= 81
93 x
find the value of x.
Show clear algebraic working.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
12 Given that
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
x = .......................................................
(Total for Question 12 is 3 marks)
. . 15
13 Use algebra to show that 0.681 =
22
(Total for Question 13 is 2 marks)
*P62657A01524*
15
Turn over
........................................................
(1)
(b) List the members of the set (A ∪ B)ʹ
DO NOT WRITE IN THIS AREA
(a) Write down n(A)
DO NOT WRITE IN THIS AREA
14 E = {integers x such that 10  x  25}
A = {x : x < 18}
B = {x : 13  x < 22}
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C ⊂ A, C ⊂ B and n(C) = 5
DO NOT WRITE IN THIS AREA
(2)
DO NOT WRITE IN THIS AREA
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
(c) List the members of the set Aʹ ∩ B
DO NOT WRITE IN THIS AREA
(2)
(d) List the members of the set C
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 14 is 6 marks)
16
*P62657A01624*
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
15 Make x the subject of y =
5 − 2x
x+3
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 15 is 4 marks)
*P62657A01724*
17
Turn over
18
*P62657A01824*
DO NOT WRITE IN THIS AREA
(Total for Question 16 is 5 marks)
DO NOT WRITE IN THIS AREA
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
Show clear algebraic working.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
3xy – y 2 = 8
x – 2y = 1
DO NOT WRITE IN THIS AREA
16 Solve the simultaneous equations
17 The diagram shows a rectangle.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(2x – 4) cm
Diagram NOT
accurately drawn
(3x + 2) cm
The area of the rectangle is A cm2
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
Given that A < 3x + 27
find the range of possible values for x.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 17 is 5 marks)
*P62657A01924*
19
Turn over
F
H
4 cm
A
DO NOT WRITE IN THIS AREA
E
Diagram NOT
accurately drawn
G
C
D
5 cm
DO NOT WRITE IN THIS AREA
18 The diagram shows cuboid ABCDEFGH.
B
(Total for Question 18 is 5 marks)
20
*P62657A02024*
cm3
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
.......................................................
DO NOT WRITE IN THIS AREA
Calculate the volume of the cuboid.
Give your answer correct to 3 significant figures.
DO NOT WRITE IN THIS AREA
AB = 5 cm
AH = 4 cm
The size of the angle between CH and the plane ABCD is 35°
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
19 OAB is a triangle.
→
→
OA = a
OB = b
The point C lies on OA such that OC : CA = 1 : 2
The point D lies on OB such that OD : DB = 1 : 2
Using a vector method, prove that ABDC is a trapezium.
(Total for Question 19 is 3 marks)
*P62657A02124*
21
Turn over
Finty takes at random 2 counters from the bag.
The probability that Finty takes 2 blue counters from the bag is
Work out the value of X.
Show clear algebraic working.
3
8
22
*P62657A02224*
DO NOT WRITE IN THIS AREA
(Total for Question 20 is 5 marks)
DO NOT WRITE IN THIS AREA
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DO NOT WRITE IN THIS AREA
There are 4 more blue counters than red counters in the bag.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
There are only red counters and blue counters in the bag.
DO NOT WRITE IN THIS AREA
20 A bag contains X counters.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
21 The function f is such that f(x) = 5 + 6x – x2 for x  3
(a) Express 5 + 6x – x2 in the form p – (x – q)2 where p and q are constants.
.......................................................
(2)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(b) Using your answer to part (a), find the range of values of x for which f –1(x) is positive.
.......................................................
(5)
(Total for Question 21 is 7 marks)
TOTAL FOR PAPER IS 100 MARKS
*P62657A02324*
23
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
*P62657A02424*
24
DO NOT WRITE IN THIS AREA
BLANK PAGE
Please check the examination details below before entering your candidate information
Candidate surname
Pearson Edexcel
International GCSE
Time 2 hours
Other names
Centre Number
Candidate Number
Paper
reference
4MA1/2H
Mathematics A
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
black ink or ball-point pen.
• Use
in the boxes at the top of this page with your name,
• Fill
centre number and candidate number.
all questions.
• Answer
sufficient working, correct answers may be awarded no marks.
• Without
the questions in the spaces provided
• Answer
– there may be more space than you need.
may be used.
• Calculators
must NOT write anything on the formulae page.
• You
Anything you write on the formulae page will gain NO credit.
Information
total mark for this paper is 100.
• The
The
for each question are shown in brackets
• – usemarks
this as a guide as to how much time to spend on each question.
Advice
each question carefully before you start to answer it.
• Read
Check
your answers if you have time at the end.
• Good luck
with your examination.
•
Turn over
P65919RA
©2021 Pearson Education Ltd.
1/1/1/1/1/1
*P65919RA0128*
International GCSE Mathematics
Formulae sheet – Higher Tier
Arithmetic series
n
Sum to n terms, Sn =
[2a + (n – 1)d]
2
a
The quadratic equation
The solutions of ax2 + bx + c = 0 where
a ¹ 0 are given by:
x=
1
(a + b)h
2
Area of trapezium =
h
-b ± b2 - 4ac
2a
b
Trigonometry
In any triangle ABC
C
Sine Rule
a
b
A
Volume of cone =
Cosine Rule a2 = b2 + c2 – 2bccos A
B
c
a
b
c
=
=
sin A sin B sin C
Area of triangle =
1
ab sin C
2
Volume of prism
= area of cross section × length
1 2
πr h
3
Curved surface area of cone = πrl
l
h
cross
section
length
r
Volume of cylinder = πr2h
Curved surface area
of cylinder = 2πrh
Volume of sphere =
4 3
πr
3
Surface area of sphere = 4πr2
r
r
h
2
*P65919RA0228*
Answer ALL TWENTY TWO questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1
(a) Write down the value of m, given that 34 ´ 35 = 3m
m = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(b) Write down the value of n, given that (53)7 = 5n
n = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
78 7 2
76
(c) Find the value of p, given that
p
7
p = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 1 is 4 marks)
*P65919RA0328*
3
Turn over
2
Here are two rectangles, rectangle A and rectangle B.
rectangle A
rectangle B
Diagram NOT
accurately drawn
(2x – 1) cm
(5 – x) cm
4 cm
5 cm
The area of rectangle B is twice the area of rectangle A.
Work out the value of x.
Show your working clearly.
x = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 2 is 4 marks)
4
*P65919RA0428*
3
The table gives information about the amounts of money, in euros, that 70 of Anjali’s
friends spent last Saturday.
Money spent (S euros)
Frequency
0<S 8
6
8 < S  16
14
16 < S  24
19
24 < S  32
25
32 < S  40
6
One of Anjali’s 70 friends is going to be chosen at random.
(a) Find the probability that this friend spent more than 24 euros last Saturday.
.......................................................
(1)
(b) Work out an estimate for the mean amount of money spent by Anjali’s friends last Saturday.
Give your answer correct to 2 decimal places.
.......................................................
(4)
euros
(Total for Question 3 is 5 marks)
*P65919RA0528*
5
Turn over
4
ABC and DEF are similar triangles.
B
E
Diagram NOT
accurately drawn
36 cm
A
C
45 cm
D
20 cm
F
(a) Work out the length of AB.
.......................................................
cm
.......................................................
cm
(2)
Given that BC = 54 cm,
(b) work out the length of EF.
(2)
(Total for Question 4 is 4 marks)
6
*P65919RA0628*
5
The diagram shows a regular octagon ABCDHIJK and a pentagon DEFGH.
E
C
B
Diagram NOT
accurately drawn
102°
D
112°
96°
F
A
H
x
G
K
J
I
Angle GHD = angle FGH.
Work out the size of the angle marked x.
Show your working clearly.
.......................................................
(Total for Question 5 is 5 marks)
*P65919RA0728*
7
Turn over
°
6
Victor buys 12 bottles of apple juice for a total cost of $21
Victor sells all 12 bottles at $2.45 each bottle.
Work out Victor’s percentage profit.
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 6 is 3 marks)
8
*P65919RA0828*
%
7
Ali and Badia each have 25 000 dollars to invest.
Cyclone Bank
Tornado Bank
Invest 25 000 dollars
4.5% compound interest per year
for 3 years
Invest 25 000 dollars
Receive 1150 dollars interest each year
for 3 years
Ali invests in the Cyclone Bank for 3 years.
Badia invests in the Tornado Bank for 3 years.
By the end of the 3 years, Ali will have received more interest than Badia.
How much more?
Show your working clearly.
Give your answer correct to the nearest dollar.
.......................................................
dollars
(Total for Question 7 is 4 marks)
*P65919RA0928*
9
Turn over
8
(a) Simplify (3x2y)0
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(b) (i) Factorise x2 – 5x – 36
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(ii) Hence solve x2 – 5x – 36 = 0
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 8 is 4 marks)
10
*P65919RA01028*
9
A rainwater tank contains 2.4 ´ 107 raindrops.
The rainwater tank also contains 1.75 ´ 106 bacteria.
(a) Work out the number of bacteria per raindrop in the tank.
Give your answer in standard form correct to 2 significant figures.
. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
A drop of rainwater contains 5.01 ´ 1021 atoms.
In a drop of rainwater the number of atoms is 3 times the number of molecules.
(b) Work out the number of molecules in the rainwater tank.
Give your answer in standard form correct to one significant figure.
molecules
(2)
.......................................................
(Total for Question 9 is 5 marks)
*P65919RA01128*
11
Turn over
10 ABC is an isosceles triangle with BA = BC.
B
Diagram NOT
accurately drawn
A
38°
C
N
9.3 cm
N is the point on AC such that AN = 9.3 cm and BN is perpendicular to AC.
Work out the perimeter of triangle ABC.
Give your answer correct to 3 significant figures.
.......................................................
(Total for Question 10 is 4 marks)
12
*P65919RA01228*
cm
11
E
Diagram NOT
accurately drawn
O
F
D
A
B
48°
C
B, D, E and F are points on a circle, centre O.
ABC is a tangent to the circle.
ODC is a straight line.
BOE is a diameter of the circle.
Angle BCD = 48°
Find the size of angle DFE.
.......................................................
(Total for Question 11 is 3 marks)
*P65919RA01328*
13
Turn over
°
2
12 (a) Simplify (64p9q12) 3
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
2
4
9
+
3 x 5 x 10 x
Give your answer in its simplest form.
(b) Write as a single fraction . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
14
*P65919RA01428*
(c) Expand and simplify 4x(x – 5)(2x + 3)
Show your working clearly.
..................................................................................
(3)
(Total for Question 12 is 7 marks)
*P65919RA01528*
15
Turn over
13
y
4
y = 2x + 2
2
–4
–2
O
2
4
x
R
–2
–4
The region R, shown shaded in the diagram, is bounded by three straight lines.
Write down the three inequalities that define R.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 13 is 3 marks)
16
*P65919RA01628*
14 Manuel collected information about the flights that arrived late at an airport last month.
The table gives information about the number of minutes that these flights were late.
Minutes late (L minutes)
Frequency
0 < L  10
8
10 < L  15
13
15 < L  25
19
25 < L  40
24
40 < L  60
6
(a) On the grid, draw a histogram for this information.
3
Frequency
density
2
1
0
0
10
20
30
40
50
60
Number of minutes late
(3)
Manuel selected at random a flight that was late by 25 minutes or less from his results.
(b) Work out an estimate for the probability that this flight was late by 5 minutes or less.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 14 is 5 marks)
*P65919RA01728*
17
Turn over
15 The functions f and g are such that
f ( x) = 2 x - 3
x
g( x) =
3x + 1
(a) State the value of x that cannot be included in any domain of g
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(b) Find gf(x)
Simplify your answer.
gf(x) = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(c) Express the inverse function g−1 in the form g−1(x) = ...
g−1(x) = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 15 is 6 marks)
18
*P65919RA01828*
16 A box contains 15 counters.
There are 4 red counters, 5 green counters and the rest are yellow counters.
Niklas takes at random a counter from the box and writes down the colour of his counter.
He then puts the counter back into the box.
Sasha then takes at random a counter from the box and writes down the colour of her counter.
Work out the probability that the counters taken by Niklas and Sasha both have the same colour.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 16 is 3 marks)
*P65919RA01928*
19
Turn over
8
in the form a + b where a and b are integers.
5 -1
Show each stage of your working clearly.
17 Express
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 17 is 3 marks)
20
*P65919RA02028*
18 Here is a quadrilateral ABCD.
B
12 cm
60°
Diagram NOT
accurately drawn
C
9 cm
84°
7 cm
D
A
Calculate the area of quadrilateral ABCD.
Give your answer correct to 3 significant figures.
Show your working clearly.
.......................................................
cm2
(Total for Question 18 is 5 marks)
*P65919RA02128*
21
Turn over
19 The straight line L has equation x – y = 3
The curve C has equation 3x2 – y2 + xy = 9
L and C intersect at the points P and Q.
Find the coordinates of the midpoint of PQ.
Show clear algebraic working.
(. . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
(Total for Question 19 is 6 marks)
22
*P65919RA02228*
20 Here are the first four terms of an arithmetic series.
k
3k
4
k
2
k
4
Given that the 15th term of the series is (90 + 2k),
calculate the sum of the first 30 terms of the series.
. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 20 is 5 marks)
*P65919RA02328*
23
Turn over
21 The curve C has equation y = f(x) where f(x) = 9 – 3(x + 2)2
The point A is the maximum point on C.
(a) Write down the coordinates of A.
4
The curve C is transformed to the curve S by a translation of 0
(b) Find an equation for the curve S.
(. . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . )
(1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
The curve C is transformed to the curve T.
The curve T has equation y = 3(x + 2)2 – 9
(c) Describe fully the transformation that maps curve C onto curve T.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
24
*P65919RA02428*
The graph of y = acos (x – b)° + c for −180  x  360 is drawn on the grid below.
y
6
5
4
3
2
1
–180
–90
O
–1
90
180
270
360 x
(d) Find the value of a, the value of b and the value of c.
a = .......................................................
b = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
c = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 21 is 6 marks)
*P65919RA02528*
25
Turn over
22 The diagram shows a sphere of diameter x cm and a pyramid ABCDE with a horizontal
rectangular base BCDE.
A
Diagram NOT
accurately drawn
5x cm
x cm
E
D
2x cm
O
B
x cm
C
The vertex A of the pyramid is vertically above the centre O of the base so that
AB = AC = AD = AE.
BC = x cm, CD = 2x cm and AO = 5x cm.
The volume of the sphere is 288π cm3
Calculate the total surface area of the pyramid.
Give your answer correct to the nearest cm2
26
*P65919RA02628*
.......................................................
cm2
(Total for Question 22 is 6 marks)
TOTAL FOR PAPER IS 100 MARKS
*P65919RA02728*
27
Turn over
BLANK PAGE
28
*P65919RA02828*