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

Anne owns 2400 grams of an alloy made of gold, silver and copper such that

weight of gold : weight of silver : weight of copper = 15 : 3 : 2

Calculate the weight of gold in 2400 grams of the alloy.

Anne sells 2400 grams of the alloy to Geoff at a rate of £29.51 per gram.

Of the money Anne receives, she is charged 10% commission.

Anne owns 2400 grams of an alloy made of gold, silver and copper such that

weight of gold : weight of silver : weight of copper = 15 : 3 : 2

Show that Anne receives £63 700 to 3 significant figures, after she pays commission.

Anne originally paid £56 000 for the alloy.

Anne owns 2400 grams of an alloy made of gold, silver and copper such that

weight of gold : weight of silver : weight of copper = 15 : 3 : 2

Calculate the percentage profit, to 3 significant figures, that Anne makes.

Geoff uses 3600 grams of a different alloy to make n pieces of jewellery.

3

of the pieces he makes are rings each weighing 6 grams.

4

1

of the pieces he makes are bracelets each weighing 24 grams.

6

The remainder of the 3600 grams of alloy is used to make necklaces each weighing

78 grams.

Anne owns 2400 grams of an alloy made of gold, silver and copper such that

weight of gold : weight of silver : weight of copper = 15 : 3 : 2

Find the value of n

Question 1 continued

h mm

a mm

a mm

Figure 1

Figure 1 shows a solid made from an alloy by fixing a small cuboid on the flat top face

of a large cuboid.

The total volume of the solid is V mm³

The base of the large cuboid is a square with sides of length a mm

The height of the large cuboid is h mm

The volume of the small cuboid is U mm³

Given that

a = 73 2. to 1 decimal place

U = 900 to the nearest 10

V = 51860 to 4 significant figures

Anne owns 2400 grams of an alloy made of gold, silver and copper such that

weight of gold : weight of silver : weight of copper = 15 : 3 : 2

calculate the upper bound, to 3 significant figures, of h

Show all your working.

Question 1 continued

Question 1 continued

Akine notices that the rate at which water leaves the hot tap of his bath is different to

the rate at which water leaves the cold tap of his bath.

The rate at which water leaves each tap is constant.

When full, the bath holds 240 litres of water.

It takes 12 minutes to fill the bath using just the cold tap.

It takes 15 minutes to fill the bath using just the hot tap.

Calculate the time taken to fill Akine’s bath with water using both the hot tap and

the cold tap at the same time.

Give your answer in minutes and seconds.

Water leaves the bath at a constant rate of 100 litres per minute.

Akine notices that the rate at which water leaves the hot tap of his bath is different to

the rate at which water leaves the cold tap of his bath.

The rate at which water leaves each tap is constant.

When full, the bath holds 240 litres of water.

It takes 12 minutes to fill the bath using just the cold tap.

It takes 15 minutes to fill the bath using just the hot tap.

Calculate the time taken for the 240 litres of water to leave the bath.

Give your answer in minutes and seconds.

Question 2 continued

Diagram NOT

E

F

accurately drawn

D

G

5 cm

A

B

6 cm

Figure 2

Figure 2 shows a cuboid ABCDEFGH with horizontal base ABGH

AB = 6cm

BG = 5cm

Given that the surface area of the cuboid is 236 cm²

show that the length of BC is 8 cm

Diagram NOT

E

F

accurately drawn

D

G

5 cm

A

B

6 cm

Figure 2

Figure 2 shows a cuboid ABCDEFGH with horizontal base ABGH

AB = 6cm

BG = 5cm

Given that the surface area of the cuboid is 236 cm²

Calculate, in cm to one decimal place, the length of AF

Question 3 continued

A particle P is moving along a straight line.

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

given by

1

4

t ≥0

3

s

t

t

5

4

At time t seconds the acceleration of P is a m/s2

Find the value of a at the instant when P changes direction and starts moving

towards the point O

Show all your working.

Question 4 continued

Figure 3 shows two shapes, A and B

2x cm

Diagram NOT

accurately drawn

A

10 cm

13 cm

B

x cm

10 cm

12 cm

Figure 3

The corners of shape A are all right angles.

Shape B is a right-angled triangle.

The area of shape A is equal to the area of shape B

Find, to 3 significant figures, the value of x





2

b

b

ac

4

2

ax

bx

c

x

Solutions of

0

are





a

2









Question 5 continued

Diagram NOT

accurately drawn

D

C

45°

E

85°

B

A

F

Figure 4

In Figure 4 ABCD is a quadrilateral such that the points A, B, C and D lie on a circle.

EAF is the tangent to the circle at the point A

BD = 22 cm

BC = 17 cm

BDC 45°

ABC 85°

Find the size, to the nearest degree, of the obtuse angle BCD

Diagram NOT

accurately drawn

D

C

45°

E

85°

B

A

F

Figure 4

In Figure 4 ABCD is a quadrilateral such that the points A, B, C and D lie on a circle.

EAF is the tangent to the circle at the point A

BD = 22 cm

BC = 17 cm

BDC 45°

ABC 85°

Find the size, to the nearest degree, of ∠BAD

Diagram NOT

accurately drawn

D

C

45°

E

85°

B

A

F

Figure 4

In Figure 4 ABCD is a quadrilateral such that the points A, B, C and D lie on a circle.

EAF is the tangent to the circle at the point A

BD = 22 cm

BC = 17 cm

BDC 45°

ABC 85°

Find the size, to the nearest degree, of ∠BAF

Give a reason for each stage of your working.

a

b

c



Sine rule :



A

B

C

sin

sin

sin

Question 6 continued

Given that 3

3

=

27

show that 3

a

b

4

3

1

a

Given that 4

b

82

Given that 3

3

=

27

show that 2

a

b

3

6

Given that 3

3

=

27

Solve the simultaneous equations

x

y

3

4

3

x

y

2

3

6

Show clear algebraic working.

Given that 3

3

=

27

Hence write down the value of a and the value of b that satisfy

b

2

9

1

a

and 4

a

3

=

3

b

82

27

Question 7 continued

A bag contains only red counters, blue counters and green counters.

The bag contains 15 counters.

There are 5 red counters and 3 blue counters.

A counter is taken at random from the bag.

Show that the probability of this counter being green is 7

15

A second counter is taken at random from the same bag without replacing the

first counter.

A bag contains only red counters, blue counters and green counters.

The bag contains 15 counters.

There are 5 red counters and 3 blue counters.

A counter is taken at random from the bag.

Complete the tree diagram on the opposite page.

A bag contains only red counters, blue counters and green counters.

The bag contains 15 counters.

There are 5 red counters and 3 blue counters.

A counter is taken at random from the bag.

Calculate the probability that at least one of the two counters taken is green.

Question 8 continued

first counter

second counter

Red

Blue

Red

5

Green

15

Red

3

15

Blue

Blue

Green

Red

Green

Blue

Green

Diagram NOT

accurately drawn

C

M

B

N

A

E

D

Figure 5

Figure 5 shows a quadrilateral ABCD such that

= 7a

= 5b

4

2

M is the midpoint of BC and N is the midpoint of CD

Find, as a simplified expression in terms of a and b

MC

Diagram NOT

accurately drawn

C

M

B

N

A

E

D

Figure 5

Figure 5 shows a quadrilateral ABCD such that

= 7a

a

b

= 5b

4

2

M is the midpoint of BC and N is the midpoint of CD

CD

Diagram NOT

accurately drawn

C

M

B

N

A

E

D

Figure 5

Figure 5 shows a quadrilateral ABCD such that

= 7a

a

b

= 5b

4

2

M is the midpoint of BC and N is the midpoint of CD

MN

The point E is such that MNE and ADE are straight lines.

Diagram NOT

accurately drawn

C

M

B

N

A

E

D

Figure 5

Figure 5 shows a quadrilateral ABCD such that

= 7a

a

b

= 5b

4

2

M is the midpoint of BC and N is the midpoint of CD

Using a vector method, find BE as a simplified expression in terms of a and b

Question 9 continued

Triangles A and B are drawn on the grid opposite.

, 2

and 2

Triangle C has vertices at coordinates 1

,

,

,

1

1

3

On the grid, draw and label triangle C

2



Triangle A is transformed to triangle D under the translation



2

Triangles A and B are drawn on the grid opposite.

, 2

and 2

Triangle C has vertices at coordinates 1

,

,

,

1

1

3

On the grid, draw and label triangle D

Triangle B is transformed to triangle E by a rotation of 90° anticlockwise about the

point 1 0

,

Triangles A and B are drawn on the grid opposite.

, 2

and 2

Triangle C has vertices at coordinates 1

,

,

,

1

1

3

On the grid, draw and label triangle E

Triangles A and B are drawn on the grid opposite.

, 2

and 2

Triangle C has vertices at coordinates 1

,

,

,

1

1

3

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

Triangle C is transformed to triangle F by an enlargement with scale factor −2

and centre of enlargement 0

,

2

Triangles A and B are drawn on the grid opposite.

, 2

and 2

Triangle C has vertices at coordinates 1

,

,

,

1

1

3

On the grid, draw and label triangle F

Question 10 continued

y

7

x

−7

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

Question 10 continued

Question 10 continued

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

y

7

x

−7

The functions f and h are defined as

2

f : x

x

x

x

↦4

4

15

1

x

2

h : x

x

0

↦

x

1

Find f 2

The functions f and h are defined as

2

f : x

x

x

x

↦4

4

15

1

x

2

h : x

x

0

↦

x

1

Solve the equation f x 0

The functions f and h are defined as

2

f : x

x

x

x

↦4

4

15

1

x

2

h : x

x

0

↦

x

1

Express hh x in the form ax

b

where a, b, c and d are integers.

cx

d

The functions f and h are defined as

2

f : x

x

x

x

↦4

4

15

1

x

2

h : x

x

0

↦

x

1

Find the inverse of the function f

Give your answer in the form f −1 : x ↦…

The functions f and h are defined as

2

f : x

x

x

x

↦4

4

15

1

x

2

h : x

x

0

↦

x

1

Find the domain of f −1





2

b

b

ac

4

2

ax

bx

c

x

Solutions of

0

are





a

2









Question 11 continued

Question 11 continued

Question 11 continued

Complete the following table of values for y

2

x

5

10

2

x

2

Give values to 2 decimal places.

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

form a smooth curve.

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

solutions to the equation

1

≤

≤

in the interval 0 2

x

2

x

x

.

1 6

.

5

9

13

0

2

x

2

Question 12 continued

y

8

6

4

2

0

−2

−4

−6

−8

−10

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

Question 12 continued

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

y

8

6

4

2

0

−2

−4

−6

−8

−10