June 2026 · Paper 2 (4MB1/02) (Edexcel IGCSE Maths): Exam Questions

A shop sells 1 kg of apples for $a and 1 kg of potatoes for $p

Meg buys 8 kg of apples and 5 kg of potatoes from the shop.

The total cost is $T

Write down a formula for T in terms of a and p

Given that

a

p

4

5

35

a

p

2

15

70

A shop sells 1 kg of apples for $a and 1 kg of potatoes for $p

Meg buys 8 kg of apples and 5 kg of potatoes from the shop.

The total cost is $T

find the total cost of 8 kg of apples and 5 kg of potatoes by first solving these

simultaneous equations.

Show clear algebraic working.

Question 1 continued

ℰ is the universal set and A, B and C are three sets such that

ℰ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

A = {6, 7, 8, 9, 10, 11, 12}

B = {odd numbers}

C = {factors of 30}

(a) List the members of the set $A \cap B$

ℰ is the universal set and A, B and C are three sets such that

ℰ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

A = {6, 7, 8, 9, 10, 11, 12}

B = {odd numbers}

C = {factors of 30}

(b) Find $n\left(\left[A \cup B\right]'\right)$

The set D is such that $D \subset B$ and $D \subset C$

ℰ is the universal set and A, B and C are three sets such that

ℰ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

A = {6, 7, 8, 9, 10, 11, 12}

B = {odd numbers}

C = {factors of 30}

(c) Find the maximum value of $n(D)$

5

3







3

A

B

C

4

6













x

1

2

2

3

A

B

−

Find 5

3

The determinant of BC is 588

Given that x > 0 

5

3







3

A

B

C

4

6













x

1

2

2

3

A

B

−

find the value of x

Determinant of matrix a

b





ad

bc

 







c

d





Question 3 continued

Cone L

30 cm

Cone J

50 cm

K

x cm

Figure 1

A right circular cone J has height 50 cm and base radius x cm

The shaded solid K is formed by removing cone L with height 30 cm

from cone J as shown in Figure 1

E

F

20 cm

H

C

2x cm

A

2x cm

B

Figure 2

Figure 2 shows solid K inside a hollow cuboid ABCDEFGH

= 2 cm and FC = 20 cm

AB

BC

x

=

The base of the cuboid rests on horizontal ground.

The base of K rests on the base of the cuboid.

cm of water is needed to fill the space in the cuboid not

3

Given that exactly 2000

occupied by K

calculate, to one decimal place, the value of x

Show all your working.

Volume of a cone = 1

$\pi$r2h

3 À



Question 4 continued

Question 4 continued

Question 4 continued

E

Diagram NOT

D

F

accurately drawn

5 cm

G

C

H

Figure 3

Figure 3 shows part of a regular 15-sided polygon.

CD, DE, EF, FG and GH are five sides of the polygon.

EFG

Show that

156°

Given that DG = 5cm

E

Diagram NOT

D

F

accurately drawn

5 cm

G

C

H

Figure 3

Figure 3 shows part of a regular 15-sided polygon.

CD, DE, EF, FG and GH are five sides of the polygon.

EFG

find the perimeter, in cm to one decimal place, of the 15-sided polygon.

Show all your working.









Sum of interior angles of polygon





right angles

n

2

4









b

c

a





e

Sine rul

A

B

C





sin

sin

sin

Question 5 continued

A particle P is moving along a straight line.

At time t seconds, the displacement, x metres, of P from a fixed point O on the line is

given by

0

≤≤

3

2

x

t

t

t

10

10

At time t seconds the velocity of P is v m/s

Find the range of values for the acceleration of P, in m/s2, when v > 9 25

.

Show all your working.









2

ax

bx

c

The solutions of

0

where









a

0

are given by:





2

b

b

ac







4

x





a





2

Question 6 continued

Triangle A and triangle B are drawn on the grid opposite.

Triangle A is transformed to triangle C under a reflection in the y-axis.

On the grid, draw and label triangle C

Triangle B is transformed to triangle D under an enlargement with

scale factor −0 5. and centre (0, 4)

Triangle A and triangle B are drawn on the grid opposite.

Triangle A is transformed to triangle C under a reflection in the y-axis.

On the grid, draw and label triangle D

Triangle A and triangle B are drawn on the grid opposite.

Triangle A is transformed to triangle C under a reflection in the y-axis.

Describe fully the single transformation that maps triangle A onto triangle B

Show all your working.

Question 7 continued

y

7

x

−6

Turn over for a spare grid if you need to redraw your triangles.

Question 7 continued

Question 7 continued

Only use this grid if you need to redraw your triangles.

y

7

x

−6

The table below shows information about the time, in minutes, it takes each of

50 teachers to travel to work.

Calculate an estimate, in minutes, for the mean time it takes for these 50 teachers to

travel to work.

Below is some information about how these 50 teachers travel to work.

n teachers walk and travel by bus

21 teachers walk

34 teachers travel by bus

6 teachers do not walk and do not travel by bus

Rosa selects at random 2 teachers from those who walk.

The table below shows information about the time, in minutes, it takes each of

50 teachers to travel to work.

Find the probability that exactly one of these 2 teachers also travels by bus.

Question 8 continued

Question 8 continued

Question 8 continued

Each year Umera goes on a skiing holiday in France.

In 2023, the cost of her flights was $250

In 2024, the cost of her flights is $315

Calculate the percentage increase in the cost of her flights from 2023 to 2024

The plane takes 2 hours 54 minutes to fly to France at an average speed of 640 km/h

Each year Umera goes on a skiing holiday in France.

In 2023, the cost of her flights was $250

In 2024, the cost of her flights is $315

Calculate the total distance, in kilometres, the plane travels to France.

The cost to hire skis is 680 euros.

The cost to buy a lift pass is 200 euros.

The exchange rate is $1 = x euros

Umera pays $612 to hire the skis.

Each year Umera goes on a skiing holiday in France.

In 2023, the cost of her flights was $250

In 2024, the cost of her flights is $315

Using the same exchange rate, calculate in $, the cost to buy a lift pass.

Umera stays in a hotel while on holiday.

She makes 3 separate payments to cover the total cost of staying in the hotel.

The 1st payment is 560 euros.

The 2nd payment is 2

of the total cost.

5

The 3rd payment is 28% of the total cost.

Each year Umera goes on a skiing holiday in France.

In 2023, the cost of her flights was $250

In 2024, the cost of her flights is $315

Calculate, in euros, 28% of the total cost.

Question 9 continued

Question 9 continued

Question 9 continued

Part of the curve C with equation y

2

x

x

By drawing a suitable straight line on the grid, find estimates,

to one decimal place, of the solutions to the equation

2

x

x

x

12

3

0 5.

1

9

The equation of curve D is

3

y

x

x

6

2

2

1

9

Part of the curve C with equation y

2

x

x

Complete the table of values for

3

y

x

x

6

2

2

Give your values of y to one decimal place where appropriate.

Part of the curve C with equation y

2

x

x

On the grid, plot the points from your completed table and join them to form a

smooth curve.

≤

≤

Curve C and curve D intersect twice in the range −3 5

x

.

3 5

.

Part of the curve C with equation y

2

x

x

Write down the coordinates of these 2 points of intersection.

Part of the curve C with equation y

2

x

x

Work out the equation of the line that passes through these 2 points

of intersection.

Give your answer in the form y

mx

c

Show all your working.

Question 10 continued

y

x

Turn over for a spare grid if you need to redraw your graph.

Question 10 continued

Question 10 continued

Only use this grid if you need to redraw your graph.

y

x

The three functions f, g and h are defined as

x

↦5

2

f : x

x

2

3

x > 0

2

g : x

x

−

2

↦

3

2

h : x

x

x

x

↦10

29

5

6

State the value of x that must be excluded from any domain of f

The three functions f, g and h are defined as

x

↦5

2

f : x

x

2

3

x > 0

2

g : x

x

−

2

↦

3

2

h : x

x

x

x

↦10

29

5

6

Write down the range of g

The three functions f, g and h are defined as

x

↦5

2

f : x

x

2

3

x > 0

2

g : x

x

−

2

↦

3

2

h : x

x

x

x

↦10

29

5

6

Find g(

−3

)

The three functions f, g and h are defined as

x

↦5

2

f : x

x

2

3

x > 0

2

g : x

x

−

2

↦

3

2

h : x

x

x

x

↦10

29

5

6

Find hf

is a factor of h( )

The three functions f, g and h are defined as

x

↦5

2

f : x

x

2

3

x > 0

2

g : x

x

−

2

↦

3

2

h : x

x

x

x

↦10

29

5

6

Use the factor theorem to show that 5

x

x

2

The three functions f, g and h are defined as

x

↦5

2

f : x

x

2

3

x > 0

2

g : x

x

−

2

↦

3

2

h : x

x

x

x

↦10

29

5

6

Hence solve the equation h( )

x = 0

Show clear algebraic working.









2

ax

bx

c

The solutions of

0

where









a

0

are given by:





2

b

b

ac







4

x





a





2

Question 11 continued

Question 11 continued

Question 11 continued

A

Diagram NOT

accurately drawn

M

B

O

N

P

Figure 4

Figure 4 shows triangle OAB

3b 

3a and

Given that

in terms of a and b

find an expression for

The point M lies on OA such that OM MA

= 2 1

:

:

2

5

The point N lies on OB such that

The point P is such that ONPB is a straight line and AP is parallel to MN

a

b

The point Q is such that

12

9

A

Diagram NOT

accurately drawn

M

B

O

N

P

Figure 4

Figure 4 shows triangle OAB

3b 

3a and

Given that

in terms of a and b

Show that A, P and Q are collinear.

The point R is such that NMR and BAR are straight lines.

in terms of a and b

A

Diagram NOT

accurately drawn

M

B

O

N

P

Figure 4

Figure 4 shows triangle OAB

3b 

3a and

Given that

in terms of a and b

Find an expression for

Give your answer in its simplest form.

Show all your working.

Question 12 continued

Question 12 continued

Question 12 continued