June 2023 · Paper 2R (4MB1/02R) (Edexcel IGCSE Maths): Exam Questions

On Monday, Tisam buys 600 watermelons in India to sell in the UK.

On Tuesday, Tisam splits 200 of the watermelons each into 8 slices.

She sells each slice for £0.60

She sells all the slices by the end of the day.

Work out how much money Tisam receives from the sale of the watermelon slices

on Tuesday.

On Wednesday, Tisam sells 60% of the remaining watermelons.

She sells them for £1.40 each.

On Monday, Tisam buys 600 watermelons in India to sell in the UK.

On Tuesday, Tisam splits 200 of the watermelons each into 8 slices.

She sells each slice for £0.60

She sells all the slices by the end of the day.

Work out how much money Tisam receives from the sale of the watermelons

on Wednesday.

Tisam gives away for free the watermelons she has left.

Tisam bought the 600 watermelons at a cost of 90 rupees each.

The cost to send the watermelons to the UK was £700

Using an exchange rate of

1 rupee = £0.0097

On Monday, Tisam buys 600 watermelons in India to sell in the UK.

On Tuesday, Tisam splits 200 of the watermelons each into 8 slices.

She sells each slice for £0.60

She sells all the slices by the end of the day.

calculate the percentage profit, to one decimal place, that Tisam makes from the sale

of the watermelons.

Question 1 continued

Question 1 continued

Question 1 continued

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

E = { p, q, r, s, t, u }

A = { p, r, t }

B = { q, r, s }

List the elements of the set A ∩ B'

Given that

n(C) = 3

n(A ∩ C) = 2

n(B ∩ C) = 1

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

E = { p, q, r, s, t, u }

A = { p, r, t }

B = { q, r, s }

list all the possible sets C

Question 2 continued

Solve 4x - 3 ≤ 11

Solve y + 8

≥ 3

2

On the grid opposite, by drawing suitable straight lines and using shading, show the

region R that satisfies the inequalities

4x - 3 ≤ 11

y + 8

≥ 3

2

y ≤ 2x + 1

Label the region R

Question 3 continued

y

x

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

Question 3 continued

Question 3 continued

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

y

x

x = 4.2$\times$10

Write x as an ordinary number.

x = 4.2$\times$10

Calculate xy

Give your answer in standard form.

x = 4.2$\times$10

Calculate x

y

Give your answer in standard form.

x = 4.2$\times$10

Using the values of x and y above, write the following in order of size

x

x y

y

Start with the smallest value.

Question 4 continued

B

Diagram NOT

accurately drawn

8 m

3.5 m

2.5 m

A

D

C

Figure 1

Figure 1 shows a framework of wooden beams, with ADC a straight line.

AB = 8 m BC = 3.5 m BD = 2.5 m ∠ADB = 90°

Calculate, giving your answer to the nearest metre, the length of AC

B

Diagram NOT

accurately drawn

8 m

3.5 m

2.5 m

A

D

C

Figure 1

Figure 1 shows a framework of wooden beams, with ADC a straight line.

AB = 8 m BC = 3.5 m BD = 2.5 m ∠ADB = 90°

Calculate, giving your answer to one decimal place, the size, in degrees,

of ∠BAD

A fourth beam DE is added to the framework.

The point E lies on AB and is such that DE is perpendicular to AB

B

Diagram NOT

accurately drawn

8 m

3.5 m

2.5 m

A

D

C

Figure 1

Figure 1 shows a framework of wooden beams, with ADC a straight line.

AB = 8 m BC = 3.5 m BD = 2.5 m ∠ADB = 90°

Calculate the length, in metres to 3 significant figures, of DE

Question 5 continued

Triangles A and B are shown on the grid opposite.

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

Triangle A is transformed to triangle C under the translation

1





8

Triangles A and B are shown on the grid opposite.

On the grid, draw and label triangle C

Triangle A is transformed to triangle D under the transformation with the

matrix M where

0

1

M =



1

0

Triangles A and B are shown on the grid opposite.

On the grid, draw and label triangle D

Triangle B is transformed to triangle E by a rotation of 180° about the point (0, 1)

Triangles A and B are shown on the grid opposite.

On the grid, draw and label triangle E

Triangles A and B are shown on the grid opposite.

Find the matrix which represents the transformation that maps triangle A onto

triangle E

Question 6 continued

y

x

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

Question 6 continued

Question 6 continued

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

y

x

Diagram NOT

y

accurately drawn

C

B

E

D

A

O

x

Figure 2

8 5

.

15

→ =

→ =

Figure 2 shows a quadrilateral ABCD with AB

 and AC



4 5

.

5

The diagonals AC and BD meet at the point E

→

Find as a column vector BC

The point E has coordinates (6, 4)

Given that AE : AC = 3 : 5

Diagram NOT

y

accurately drawn

C

B

E

D

A

O

x

Figure 2

8 5

.

15

→ =

→ =

Figure 2 shows a quadrilateral ABCD with AB

 and AC



4 5

.

5

The diagonals AC and BD meet at the point E

→

find the coordinates of the point A

Given that ABCD is a kite,

Diagram NOT

y

accurately drawn

C

B

E

D

A

O

x

Figure 2

8 5

.

15

→ =

→ =

Figure 2 shows a quadrilateral ABCD with AB

 and AC



4 5

.

5

The diagonals AC and BD meet at the point E

→

find the coordinates of the point D

Question 7 continued

The function f is such that

f : x ↦ 1 - 1

x where x ≠ 0

State a value that cannot be in the range of the function f

The function f is such that

f : x ↦ 1 - 1

x where x ≠ 0

Solve 16 f(x) = x + 8

–1(x)

The function f is such that

f : x ↦ 1 - 1

x where x ≠ 0

Show that ff(x) = f

–1

The function f is such that

f : x ↦ 1 - 1

x where x ≠ 0

State a value that cannot be in the domain of the function f

The function f is such that

f : x ↦ 1 - 1

x where x ≠ 0

Evaluate fff





2

b

b

ac

4

2

ax

bx

c

x

Solutions of

0

are





a

2

Question 8 continued

Question 8 continued

Question 8 continued

The curve C has equation

2 + 24

x - 25 for 0 < x ≤ 5

y = x

Find, to one decimal place, the coordinates of the stationary point of C

The curve C has equation

2 + 24

x - 25 for 0 < x ≤ 5

y = x

Complete the table of values for y

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

The curve C has equation

2 + 24

x - 25 for 0 < x ≤ 5

y = x

On the grid opposite, plot the stationary point and plot the points from your

completed table. Join these to form a smooth curve.

The curve C has equation

2 + 24

x - 25 for 0 < x ≤ 5

y = x

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

of the solutions to the equation

3 + 8x

2 - 49x + 24 = 0

x

within the range 0 < x ≤ 5

Question 9 continued

y

x

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

Question 9 continued

Question 9 continued

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

y

x

Hugo is learning a new game. Each time he plays the game the possible outcomes are

that he may win, draw or lose.

The first time Hugo plays the game the probability that

he wins is 1

4

he draws is 1

12

Show that the probability that Hugo loses the first game is 2

3

The second time Hugo plays the game the probability that

he wins is 3

5

he draws is 1

10

he loses is 3

10

Hugo is learning a new game. Each time he plays the game the possible outcomes are

that he may win, draw or lose.

The first time Hugo plays the game the probability that

he wins is 1

4

he draws is 1

12

Use the information to complete the tree diagram opposite.

Hugo plays the game twice.

Hugo is learning a new game. Each time he plays the game the possible outcomes are

that he may win, draw or lose.

The first time Hugo plays the game the probability that

he wins is 1

4

he draws is 1

12

Find the probability that he draws both of his games.

Hugo scores points each time he plays.

He scores 3 points if he wins, 2 points if he draws and 1 point if he loses.

After 2 games Hugo has 3 points.

Hugo is learning a new game. Each time he plays the game the possible outcomes are

that he may win, draw or lose.

The first time Hugo plays the game the probability that

he wins is 1

4

he draws is 1

12

Find the probability that Hugo lost the first game.

Question 10 continued

First game

Second game

win

draw

win

lose

win

draw

draw

lose

win

lose

draw

lose

Turn over for a spare copy of the tree diagram.

Question 10 continued

Question 10 continued

Only use this diagram if you need to redraw your tree diagram.

First game

Second game

win

draw

win

lose

win

draw

draw

lose

win

lose

draw

lose

Diagram NOT

C

accurately drawn

x cm

3 5 cm

15°

A

B

4 3 cm

Figure 3

Figure 3 shows triangle ABC

AB = 4 3 cm BC = 3 5 cm AC = x cm ∠BAC = 15°

6

2

Given that the exact value of cos 15° =

4

show that x is a solution of the equation

x + 3 = 0

2 - 6 2

x

2 6

2 = 21 + 12 3

Diagram NOT

C

accurately drawn

x cm

3 5 cm

15°

A

B

4 3 cm

Figure 3

Figure 3 shows triangle ABC

AB = 4 3 cm BC = 3 5 cm AC = x cm ∠BAC = 15°

6

2

Given that the exact value of cos 15° =

4

Write the equation given in part (a) in the form (x - k)

where k is a constant that should be stated as a simplified surd.

= 21 + 12 3

2

Diagram NOT

C

accurately drawn

x cm

3 5 cm

15°

A

B

4 3 cm

Figure 3

Figure 3 shows triangle ABC

AB = 4 3 cm BC = 3 5 cm AC = x cm ∠BAC = 15°

6

2

Given that the exact value of cos 15° =

4

Show that 3

2 3

Given that ∠ABC is obtuse

Diagram NOT

C

accurately drawn

x cm

3 5 cm

15°

A

B

4 3 cm

Figure 3

Figure 3 shows triangle ABC

AB = 4 3 cm BC = 3 5 cm AC = x cm ∠BAC = 15°

6

2

Given that the exact value of cos 15° =

4

use parts (b) and (c) to find the exact value of x

Give your answer in the form a + b

2 + c 3 +

d where a, b, c and d

are integers.





2

2

2

Cosine rule: a

b

c

bc

A

2

cos

Question 11 continued

Question 11 continued

Question 11 continued

Question 11 continued