June 2025 · Paper 2R (4MB1/02R) (Edexcel IGCSE Maths): Exam Questions

Solve the simultaneous equations

x

y

3

4

3

x

y

4

7

2

Show clear algebraic working.

A

B

D

C

The diagram shows quadrilateral ABCD

Construct the locus of all points that are 4 cm from C

A

B

D

C

The diagram shows quadrilateral ABCD

Using ruler and compasses only and showing all your construction lines, construct

the perpendicular bisector of AD

The region R consists of all the points inside the quadrilateral that are less than 4 cm

from C and nearer to A than to D

A

B

D

C

The diagram shows quadrilateral ABCD

Show, by shading, the region R

Label the region R

Diagram NOT

accurately drawn

F

G

E

D

C

B

A

Figure 1

Figure 1 shows part of a regular 20-sided polygon in which AB, BC, CD, DE, EF and

FG are six of the sides.

Find the size, in degrees, of angle ABC

Diagram NOT

accurately drawn

F

G

E

D

C

B

A

Figure 1

Figure 1 shows part of a regular 20-sided polygon in which AB, BC, CD, DE, EF and

FG are six of the sides.

Find the size, in degrees, of angle EGA

Sum of interior angles of a polygon







n

2

4

right angles





Question 3 continued

The nth term of a sequence is given by 2

2

n −

5

Find the difference between the 3rd term and the 7th term of the sequence.

A different sequence is generated.

After the first term the sequence is generated by using the rule

“multiply the previous term by d and then add 2”

The first term of the sequence is 2

x

1

x

The second term of the sequence is 4

9

The third term of the sequence is 20

x

11

Given that 2



x

1

0

The nth term of a sequence is given by 2

2

n −

5

find the value of d

Show all your working.





2

b

b

ac

4

2

ax

bx

c

x

Solutions of

0

are





a

2









Question 4 continued

Question 4 continued

Question 4 continued

A large rental company has cars, vans and minibuses available to rent.

The cost to rent a minibus from the company is found by adding

$1000 rental fee

$400 for each day the minibus is rented

$0.8 per kilometre the minibus travels during the time it is rented

This cost is reduced by n% if the minibus is a hybrid vehicle.

The total cost of hiring 3 minibuses that are hybrid vehicles for 7 days is $10 584

Given that each minibus travels a total distance of 500 kilometres during these 7 days

find the value of n

Show all your working.

The number of cars the company owns is the Highest Common Factor (HCF) of

2

5

3

5

2

5

and 2

×

×

×

×

×

2

3

5

3

5

7

A large rental company has cars, vans and minibuses available to rent.

The cost to rent a minibus from the company is found by adding

$1000 rental fee

$400 for each day the minibus is rented

$0.8 per kilometre the minibus travels during the time it is rented

This cost is reduced by n% if the minibus is a hybrid vehicle.

The total cost of hiring 3 minibuses that are hybrid vehicles for 7 days is $10 584

Given that each minibus travels a total distance of 500 kilometres during these 7 days

Find the number of cars the company owns.

The number of cars that are hybrid vehicles is the least value of N such that

when N is divided by 120 the remainder is 7 and

when N is divided by 504 the remainder is 7

A large rental company has cars, vans and minibuses available to rent.

The cost to rent a minibus from the company is found by adding

$1000 rental fee

$400 for each day the minibus is rented

$0.8 per kilometre the minibus travels during the time it is rented

This cost is reduced by n% if the minibus is a hybrid vehicle.

The total cost of hiring 3 minibuses that are hybrid vehicles for 7 days is $10 584

Given that each minibus travels a total distance of 500 kilometres during these 7 days

Find the number of cars that are hybrid vehicles.

The company owns 200 vans and minibuses in total.

Each van and each minibus is either an electric vehicle or a hybrid vehicle.

The ratio of the number of vans to the number of minibuses is 5 : 3

40% of the vans are hybrid vehicles.

9

25 of the minibuses are hybrid vehicles.

A large rental company has cars, vans and minibuses available to rent.

The cost to rent a minibus from the company is found by adding

$1000 rental fee

$400 for each day the minibus is rented

$0.8 per kilometre the minibus travels during the time it is rented

This cost is reduced by n% if the minibus is a hybrid vehicle.

The total cost of hiring 3 minibuses that are hybrid vehicles for 7 days is $10 584

Given that each minibus travels a total distance of 500 kilometres during these 7 days

Express the total number of vans and minibuses which are hybrid vehicles as a

percentage of the total number of vans and minibuses.

Show your working clearly.

Question 5 continued

Question 5 continued

Question 5 continued

A group of 90 students were asked if they own any of a dog (D), a cat (C) or a horse (H)

Of these 90 students

4 own all three

14 own a dog and a cat

7 own a cat and a horse

26 own a dog only

2 own a horse only

6 own none of these animals

Let x be the number of these students who own a cat only.

Show all this information on the Venn diagram, giving the number of students in

each appropriate subset, in terms of x where necessary.

E

C

D

H

The number of these students who own a cat is 37 more than the number of these

students who own a horse.

A group of 90 students were asked if they own any of a dog (D), a cat (C) or a horse (H)

Of these 90 students

4 own all three

14 own a dog and a cat

7 own a cat and a horse

26 own a dog only

2 own a horse only

6 own none of these animals

Let x be the number of these students who own a cat only.

Find the value of x

A group of 90 students were asked if they own any of a dog (D), a cat (C) or a horse (H)

Of these 90 students

4 own all three

14 own a dog and a cat

7 own a cat and a horse

26 own a dog only

2 own a horse only

6 own none of these animals

Let x be the number of these students who own a cat only.

Find n D

H





A group of 90 students were asked if they own any of a dog (D), a cat (C) or a horse (H)

Of these 90 students

4 own all three

14 own a dog and a cat

7 own a cat and a horse

26 own a dog only

2 own a horse only

6 own none of these animals

Let x be the number of these students who own a cat only.

Find n

C

D





Question 6 continued

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

Triangle A is transformed to triangle C under the translation

4





7

On the grid, draw and label triangle C

Triangle A is transformed to triangle D under a reflection in the line with

equation x = 4

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

Triangle A is transformed to triangle C under the translation

4





7

On the grid, draw and label triangle D

Triangle B is the image of triangle A under an enlargement with centre the origin and

5 followed by a clockwise rotation of θ° about the origin.

scale factor

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

Triangle A is transformed to triangle C under the translation

4





7

Calculate the value, to 4 significant figures, of θ

Show your working.

Question 7 continued

y

x

−7

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

x

−7

Table 1 gives information about the probability that a biased red six-sided dice will land

on each of the numbers 1, 2, 5, 7, 9, 11

Table 1

Calvin rolls the red dice once.

Calculate the probability that the red dice lands on

either the number 2 or the number 5

Table 1 gives information about the probability that a biased red six-sided dice will land

on each of the numbers 1, 2, 5, 7, 9, 11

Table 1

Calvin rolls the red dice once.

an odd number

Table 1 gives information about the probability that a biased red six-sided dice will land

on each of the numbers 1, 2, 5, 7, 9, 11

Table 1

Calvin rolls the red dice once.

a number less than 8

Pabel rolls the red dice twice.

Table 1 gives information about the probability that a biased red six-sided dice will land

on each of the numbers 1, 2, 5, 7, 9, 11

Table 1

Calvin rolls the red dice once.

Calculate the probability that the red dice lands on the numbers 2 and 5

Tai rolls the red dice 80 times.

Table 1 gives information about the probability that a biased red six-sided dice will land

on each of the numbers 1, 2, 5, 7, 9, 11

Table 1

Calvin rolls the red dice once.

Calculate the expected number of times the red dice lands on a number less than 5

A biased blue six-sided dice has faces numbered 2, 4, 6, 8, 10, 12

The probability that the blue dice lands on the number 2 is 0.24

The probability that the blue dice lands on the number 4 is 0.12

In a game Tai rolls the red dice once and the blue dice once.

The number that the red dice lands on is added to the number that the blue dice lands on

to give his score in the game.

Given that his score is less than 6

Table 1 gives information about the probability that a biased red six-sided dice will land

on each of the numbers 1, 2, 5, 7, 9, 11

Table 1

Calvin rolls the red dice once.

find the probability that the red dice lands on the number 2

Question 8 continued

Question 8 continued

Question 8 continued

E

F

D

C

G

H

A

B

Figure 2

Figure 2 shows a solid made by joining a half cylinder to a prism.

The plane face of the half cylinder coincides with the top face of the prism.

The rectangular base ABGH of the solid is horizontal.

The cross section ABCD of the prism is a trapezium such that AB is parallel to DC

AB = 26 cm

BG = 20 cm

DC = 10 cm

AD

BC

=

= 17 cm

The perpendicular height of the trapezium ABCD is 15 cm

Calculate, in cm² to 2 significant figures, the total surface area of the solid.

Show all your working.

O is the midpoint of EF

N is the point on the edge of the half cylinder vertically above O

Diagram NOT

accurately drawn

E

F

D

C

G

H

A

B

Figure 2

Figure 2 shows a solid made by joining a half cylinder to a prism.

The plane face of the half cylinder coincides with the top face of the prism.

The rectangular base ABGH of the solid is horizontal.

The cross section ABCD of the prism is a trapezium such that AB is parallel to DC

AB = 26 cm

BG = 20 cm

DC = 10 cm

AD

BC

=

= 17 cm

The perpendicular height of the trapezium ABCD is 15 cm

Calculate the size, in degrees to 3 significant figures, of ∠AON

Area of trapezium = 1



a

b h

2 (

)



Question 9 continued

Question 9 continued

Question 9 continued

Diagram NOT

B

accurately drawn

N

C

O

A

M

Figure 3

= 5b

= 10a and

Figure 3 shows triangle OAB where

M is the midpoint of OA

The point N lies on the line AB such that AN = 2

AB

5

in terms of a and b

Find an expression for

Give your answer in its simplest form.

= 3 4

The point C lies on BM such that BC BM

:

:

2

The area of triangle OBM = 45

cm

Given that a

b

= 2 cm 

=

Diagram NOT

B

accurately drawn

N

C

O

A

M

Figure 3

= 5b

= 10a and

Figure 3 shows triangle OAB where

M is the midpoint of OA

The point N lies on the line AB such that AN = 2

AB

5

in terms of a and b

find the length, in cm to 3 significant figures, of OC

a

b

c



Sine Rule





A

B

c

sin

sin

sin





Cosine Rule

2

2

2

a

b

c

bc

A

2

cos









1

Area of triangle

ab

C

sin





2





Question 10 continued

Question 10 continued

Question 10 continued

The curve C has equation f x

3

2

x

x

x

2

5

2

2 is a factor of f x

Use the factor theorem to show that x

The curve C has equation f x

3

2

x

x

x

2

5

2

2 is a factor of f x

Hence find the x coordinate of each point where curve C crosses the x-axis.

Show clear algebraic working.

The curve C has two turning points.

2



The x coordinates of the turning points are such that 6

x

x

2

5

0

The curve C has equation f x

3

2

x

x

x

2

5

2

2 is a factor of f x

Find the coordinates, to 2 decimal places, of these two turning points.

Show your working clearly.

f

The curve C has equation f x

3

2

x

x

x

2

5

2

2 is a factor of f x

Complete the table of values for y

x

The curve C has equation f x

3

2

x

5

2 is a factor of f x

On the grid opposite, plot the points where curve C crosses the x-axis,

the two turning points and all the points from your completed table.

Join all the points to form a smooth curve.

The curve C has equation f x

3

2

x

x

x

2

5

2

2 is a factor of f x

By drawing a suitable line on the grid, find estimates to one decimal place, of the

≤

≤

in the interval −1 5

solutions to the equation 2

x

3

2

x

x

x

.

2 25

.

3

1

0

The curve C has equation f x

3

2

x

x

x

2

5

2

2 is a factor of f x

By drawing a suitable line (at least 3 cm long) on the grid, find the gradient of

curve C at the point where x = 1 5.





2

b

b

ac

4

2

ax

bx

c

x

Solutions of

0

are





a

2









Question 11 continued

y

5

x

Turn over to page 37 for a spare grid if you need to redraw your graph.

Question 11 continued

Question 11 continued

Question 11 continued

Question 11 continued

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

y

5

x

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

3 where k is a constant.

x

k

t

t

(

48

)

When t = 2, the particle P is at the point A on the line.

P is instantaneously at rest at the point B on the line.

Given that AB = 5 metres

calculate the distance, in metres, of P from O when t = 2

Show all your working.

Question 12 continued

Question 12 continued