Name: _________________________________________

Teacher’s name: ________________________________________

Mathematics IGCSE
March 2025
Mock

2 hours

Instructions:
● Fill in your name at the top of the page
● Answer all questions
● Answer all questions in the space provided
● Calculators allowed

Information:
● The total mark for this paper is 101.
100.
● The marks for each question are shown in brackets
○ Use this as a guide as to how much time you spend on each question

Advice:
● Read each question carefully before you start to answer it
● Try to answer every question
● Check your answers if you have time at the end
 International GCSE Mathematics
Formulae sheet – Higher Tier

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Arithmetic series 1
n Area of trapezium = (a + b)h
Sum to n terms, Sn = [2a + (n – 1)d] 2
2
The quadratic equation a

The solutions of ax2 + bx + c = 0 where

a ¹ 0 are given by: h

"b # b 2 " 4ac

x!
2a b

Trigonometry In any triangle ABC

C a b c
Sine Rule = =
sin A sin B sin C

b a Cosine Rule a2 = b2 + c2 – 2bccos A

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1
Area of triangle = ab sin C
A B 2
c

1 2 Volume of prism
Volume of cone = πr h = area of cross section × length
3
Curved surface area of cone = πrl

l cross
h section

length
r
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Volume of cylinder = πr2h 4 3

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

r
h

v1

21 DD02892A ©2022 Pearson Education Ltd.

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

5 3 3
1 Show that 1 ! 2 " 3
7 16 4
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(Total for Question 1 is 3 marks)

2 The length of a table is measured as 1.4 metres correct to one decimal place.
(a) Write down the upper bound of the length of the table.
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...................................... .. ... .. ... .. ... ... ... ... metres

(1)
(b) Write down the lower bound of the length of the table.

...................................... .. ... .. ... .. ... ... ... ... metres

(1)
(Total for Question 2 is 2 marks)

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 ! p3 "
5
3 (a) Simplify
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................... ... .. .. ... .. ... ... ... ... ... ... .. ... ... ... ...

(1)
(b) Expand and simplify 2n " 4n ! 3# ! n " n $ 4 #
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................... ... .. .. ... .. ... ... ... ... ... ... .. ... ... ... ...

(2)
2x ! 5
(c) Solve " 4#x
3
Show clear algebraic working.
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x= ...................... .. ... .. ... .. ... ... ... ... ... .. ... ... ... ... .

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

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4 Here is a Venn diagram.

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A B

3
9 5 2
7

4 6 8

(a) List the members of the set B

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

(1)
(b) List the members of the set A B

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

(1)
(c) List the members of the set A

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

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(Total for Question 4 is 3 marks)

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35 The diagram shows triangle PQR
P

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Diagram NOT
8.6 cm
accurately drawn

43°
Q x cm R

Work out the value of x

Give your answer correct to one decimal place.

x= ................... ... .. .. ... .. ... ... ... ... ... .. ... ... ... ... .. DO NOT WRITE IN THIS AREA
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(Total for Question 3 is 3 marks)

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56 Cody has a biased 5-sided spinner, numbered 1, 2, 3, 4, 5
The table gives the probabilities that when the spinner is spun it will land on 2 or on

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3 or on 5

Number 1 2 3 4 5

Probability 0.14 0.17 0.21

The probability that the spinner will land on 1 is the same as the probability that the
spinner will land on 4
Cody is going to spin the spinner 400 times.
Work out an estimate for the number of times the spinner will land on 4

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

(Total for Question 5 is 4 marks)

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7 (a) On the grid, draw the straight line with equation
(i) x = 3 (ii) y = 1 (iii) x ! y " 7

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Label each line with its equation.

y
8

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2

O 1 2 3 4 5 6 7 8 x

(3)
(b) Show, by shading on the grid, the region that satisfies all three of the inequalities
x 3 y 1 x y 7

Label the region R

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(1)
(Total for Question 7isis34 marks)

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8 (a) (i) Factorise x 2 ! 5 x " 24

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

(2)
(ii) Hence, solve x 2 ! 5 x " 24 # 0

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

(1)
(b) Solve the inequality 3 y ! 5 " 7 y # 10
Show clear algebraic working.

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

(3)
(Total for Question 8 is
is 6
3 marks)

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 3x ! 2 2 x ! 1
12
9 (a) Solve " #x
5 3
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Show clear algebraic working.

i
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x= ................... ... .. .. ... .. ... ... ... ... ... .. ... ... ... ... ..

(3)
a " bc
(b) Make c the subject of the formula f !
c#d
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.................. ... .. .. ... .. ... ... ... ... ... ... .. ... ... ... ...

(4)
(Total for Question 12isis3 7 marks)

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10 All the students in year 10 and all the students in year 11 named their favourite science
subject from Biology, Chemistry and Physics.

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The pie chart shows information about the results for the year 10 students.
The table shows information about the results for the year 11 students.

science number of
subject students
Biology Chemistry
102° Biology 3x + 6
126°
Chemistry 5x + 8
132°
Physics Physics 7x − 9

Pie chart for year 10 Table for year 11

There are 300 students in year 10

There are 320 students in year 11

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More students in year 10 than in year 11 said Biology was their favourite
science subject.
How many more?

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

(Total for Question 10 is 5 marks)

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 8
11 The diagram shows a trapezium, ABCD
A B
Diagram NOT
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accurately drawn

15 cm

D 14 cm C

DAB and ADC are right angles.

AD = 15 cm DC = 14 cm
The area of the trapezium is 360 cm²
Work out the perimeter of the trapezium.
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............................. ... ... . ... ... .. ... ... ... ... ... ... cm
(Total for Question 8 is 6 marks)
of

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12 ABC is a right-angled triangle.
D is a point on BC

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A Diagram NOT
accurately drawn

47°

24°
B D C

AB = 4250 m angle BAD ! 47" angle BCA ! 24"

Work out the length of DC
Give your answer correct to the nearest integer.

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.......................... ... ... . ... ... ... .. ... ... ... ... ... .. .. m
(Total for Question 12 is 4 marks)

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 13 The probability that Thomas gets to work early on Saturday is 0.7
If Thomas gets to work early on Saturday, the probability that he will get to work early
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on Sunday is 0.9
If Thomas does not get to work early on Saturday, the probability that he will get to
work early on Sunday is 0.6
(a) Use this information to complete the probability tree diagram.

Saturday Sunday

early

early

0.7 not
early
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early

not
early

not
early
(2)
(b) Work out the probability that Thomas gets to work early on both Saturday
and Sunday.
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.................... ... .. .. ... .. ... ... ... ... ... ... .. ... ... ... ...

(2)
(Total for Question 13 is 4 marks)

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22
14 The diagram shows a cuboid ABCDEFGH with horizontal base ADEH

Diagram NOT

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G accurately drawn
F

H E
B C

M 20 cm
8 cm

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A 12 cm D

AB = 8 cm AD = 12 cm DE = 20 cm
M is the midpoint of the base ADEH and P is the midpoint of the edge CF
Work out the size of angle BMP
Give your answer correct to one decimal place.

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

(Total for Question 22 is 6 marks)

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Turn over for Question 23

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14 B is inversely proportional to the square of d
B = 0.25 when d = 12

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Find a formula for B in terms of d

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

(Total for Question 14 is 3 marks)

15 Write 3 x " 2 x ! 1# " 5 x $ 4 # in the form ax3 bx 2 cx where a, b and c are integers.

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

(Total for Question 15 is 3 marks)

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 16 OAPB is a sector of a circle, centre O
A
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Diagram NOT
accurately drawn

P 50° O

Angle AOB ! 50"

Area of triangle OAB = 120 cm 2
Work out the area of the sector OAPB
Give your answer correct to 3 significant figures.
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.................................. .. ... .. .. ... ... ... ... ... .. ... . cm2

(Total for Question 16 is 4 marks)
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17 (a) Express 675 in the form n 27 where n is a positive integer.

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

(1)

5 2
(b) Show that can be written in the form a b 2 where a and b
2 1
are integers.

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(3)
(Total for Question 17 is 4 marks)
or
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 18 The histogram shows information about the times some students took to complete
a puzzle.
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3
Frequency
density

2
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0
0 10 20 30 40 50 60 70
Time (minutes)

Work out an estimate for the fraction of these students who took between 20 minutes
and 60 minutes to complete the puzzle.
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...................... .. ... .. ... .. ... ... ... ... ... .. ... ... ... ... .

(Total for Questionour

18 is 4 marks)

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 32 n ! 3
14
19 Given that # 33 $ 31 " 2 n
34

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find the value of n
Show your working clearly.

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n= ................... ... .. .. ... .. ... ... ... ... ... .. ... ... ... ... ..

(Total for Question To

14 is 3 marks)
! ! 42
20 Use algebra to show that 0.7 63 "
15
55

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(Total for QuestionTed

15 is 2 marks)

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 x2 " y 2
21 T !
w

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x = 28.4 correct to 1 decimal place.
y = 17 correct to 2 significant figures.
w = 90 correct to the nearest 5
Calculate the upper bound for the value of T
Give your answer correct to 3 significant figures.
Show your working clearly.

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

(Total for QuestionMd

21 is 3 marks)

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 22 The straight line L is perpendicular to the straight line with equation 2 x ! y " 9
18
and passes through the point with coordinates (8, 11)
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Find an equation for L

Give your answer in the form y ! mx " c
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................... ... .. .. ... .. ... ... ... ... ... .. ... ... ... ... ..

(Total for Questionmad

18 is 4 marks)

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 21
23 The Venn diagram shows information about the numbers of items in
set A, set B and set C, where x is an integer.
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E
A B

x+2
3x 4x
x
x+7 2x

5x 3x + 2

C
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Given that n( A ! B)" # 26

find n( A! " C )
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n( A! " C ) # ................... ... .. .. ... .. ... ... ... ... ... .. ... ... ... ... ..

(Total for QuestionMd

21 is 4 marks)

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 16 x 2 ! 36 2 x2 # 7 x # 6
23
24 Show that " 2 ! (7 # 8 x ) $ n
x!7 x ! 5 x ! 14
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where n is an integer to be found.

Show clear algebraic working.
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(Total for Questionodd

23 is 4 marks)

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25 The diagram shows an equilateral triangle ABC and a circle with centre O

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C
Diagram NOT
accurately drawn

x cm

A B

AB, BC and CA are tangents to the circle.

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The radius of the circle is x cm
The total area, in cm2, of the regions shown shaded in the diagram is nx²
Find the value of n
Give your answer correct to 3 significant figures.

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n= ................... ... .. .. ... .. ... ... ... ... ... .. ... ... ... ... ..

(Total for Question 25 is 5 marks)

TOTAL FOR PAPER IS 100 MARKS

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 21
26 There are 25 counters in a bag such that

6 counters are blue

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x counters are orange, where x > 9

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

(Total for QuestionNo

21 is 5 marks)

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