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

red

72°

A bag contains red bricks, yellow bricks and green bricks only.

The incomplete table and an incomplete pie chart give information about the colours of

the bricks in the bag.

Find the number of red bricks.

A box contains 9 red bricks and 6 green bricks only.

Asha takes a brick from the bag and a brick from the box.

red

72°

A bag contains red bricks, yellow bricks and green bricks only.

The incomplete table and an incomplete pie chart give information about the colours of

the bricks in the bag.

Complete the tree diagram opposite.

red

72°

A bag contains red bricks, yellow bricks and green bricks only.

The incomplete table and an incomplete pie chart give information about the colours of

the bricks in the bag.

Calculate the probability that exactly one of the bricks is green.

Question 1 continued

Bag

Box

6

green

15

green

50

130

not green

green

not green

not green

A farmer grows 300 pumpkins.

The pumpkins are small or medium or giant.

It cost the farmer $1.25 to grow each small pumpkin.

He sells each small pumpkin for $1.30

Calculate the percentage profit the farmer makes on each small pumpkin he sells.

The farmer sells each medium pumpkin for 20% more than he sells each small pumpkin.

A farmer grows 300 pumpkins.

The pumpkins are small or medium or giant.

It cost the farmer $1.25 to grow each small pumpkin.

He sells each small pumpkin for $1.30

Calculate the price, in $, that the farmer sells each medium pumpkin for.

Of the 300 pumpkins, 28% are small.

A farmer grows 300 pumpkins.

The pumpkins are small or medium or giant.

It cost the farmer $1.25 to grow each small pumpkin.

He sells each small pumpkin for $1.30

Calculate the number of small pumpkins the farmer grows.

The remaining pumpkins are medium or giant.

The ratio of medium pumpkins to giant pumpkins is 3 : 5

A farmer grows 300 pumpkins.

The pumpkins are small or medium or giant.

It cost the farmer $1.25 to grow each small pumpkin.

He sells each small pumpkin for $1.30

Calculate the number of giant pumpkins the farmer grows.

The farmer sells all of his giant pumpkins for the same price.

The farmer’s profit from giant pumpkins is

30% of the selling price of the first 50 giant pumpkins sold,

60% of the selling price of the next 40 giant pumpkins sold,

90% of the selling price of the remaining giant pumpkins sold.

A farmer grows 300 pumpkins.

The pumpkins are small or medium or giant.

It cost the farmer $1.25 to grow each small pumpkin.

He sells each small pumpkin for $1.30

Calculate the percentage of the total selling price of the giant pumpkins that is the

farmer’s profit from giant pumpkins.

Give your answer to the nearest whole number.

Question 2 continued

The table below shows information about the prices of secondhand cars for sale at

a garage.

Calculate an estimate, in dollars, for the mean price of a secondhand car at this garage.

Question 3 continued

Each interior angle of a regular polygon is 172°

Calculate the number of sides of the polygon.

The length of each side of the regular polygon is 5.2 cm to 2 significant figures.

Each interior angle of a regular polygon is 172°

Calculate, in cm² to 3 significant figures, the upper bound of the area of the polygon.

Sum of interior angles of polygon

n

2

4

right angles

Question 4 continued

Part of the curve C with equation y

is drawn on the grid.

x

x

2

2

2

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

for the solutions of the equation

1

1

x

x

1

0

1

2

2

The equation of curve D is given by

y

x

x

x

3

3

2

Part of the curve C with equation y

is drawn on the grid.

x

x

2

2

2

Complete the table of values for y

x

x

x

3 , giving your values to 2 decimal

3

2

places where necessary.

Part of the curve C with equation y

is drawn on the grid.

x

x

2

2

2

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

form a smooth curve.

≤

≤

x

Curve C and curve D intersect twice in the range −2

2

Part of the curve C with equation y

is drawn on the grid.

x

x

2

2

2

Write down the coordinates, to one decimal place, of these 2 points of

intersection.

Part of the curve C with equation y

is drawn on the grid.

x

x

2

2

2

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

intersection.

Give your answer in the form y = mx + c where the values of m and c are given

to one decimal place.

Show your working clearly.

Question 5 continued

y

x

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

Question 5 continued

Question 5 continued

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

y

x

The Venn diagram shows information about the numbers of students who play Rugby (R),

Basketball (B) or Hockey (H).

The number of students who do not play Basketball is 35

Use this information to complete the Venn diagram.

E

R

B

6

10

3

4

6

12

0

H

The Venn diagram shows information about the numbers of students who play Rugby (R),

Basketball (B) or Hockey (H).

The number of students who do not play Basketball is 35

Find

n H

B

The Venn diagram shows information about the numbers of students who play Rugby (R),

Basketball (B) or Hockey (H).

The number of students who do not play Basketball is 35

n H

B







R

B

H

The Venn diagram shows information about the numbers of students who play Rugby (R),

Basketball (B) or Hockey (H).

The number of students who do not play Basketball is 35

n

One of the students is selected at random.

Given that this student plays Hockey,

The Venn diagram shows information about the numbers of students who play Rugby (R),

Basketball (B) or Hockey (H).

The number of students who do not play Basketball is 35

calculate the probability that they also play Rugby.

Give your answer in the form m

n where m and n are integers.

Question 6 continued

The functions f, g and h are defined as

f : x

x

x

−

2

2

↦

2

g : x

x

1

0

x

x

↦5

4

h : x

x

3

x

3

Find f (−3)

The functions f, g and h are defined as

f : x

x

x

−

2

2

↦

2

g : x

x

1

0

x

x

↦5

4

h : x

x

3

x

3

Find the inverse function h1, giving your answer in the form h−1 :

x ↦

...

The functions f, g and h are defined as

f : x

x

x

−

2

2

↦

2

g : x

x

1

0

x

x

↦5

4

h : x

x

3

x

3

Solve fg(x) = x

−

1

54

Question 7 continued

A

Diagram NOT

B

accurately drawn

O

C

Figure 1

Figure 1 shows three points A, B and C on a circle with centre O where AOC is a

diameter of the circle.

The length of AB is 2 cm less than the length of BC

≤5

Given that AC

BC

4

calculate the range of possible values for the length, in cm to one decimal place, of BC

Question 8 continued

where a and b are integers.

x

x

ax

x

b

f ( )

3

20

3

2

(x + 4) is a factor of f(x)

(x − 2) is a factor of f(x)

Use the factor theorem to find the value of a and the value of b

is 3

x

x

x

One solution of the equation 8

18

5

6

0

3

2

2

where a and b are integers.

x

x

ax

x

b

f ( )

3

20

3

2

(x + 4) is a factor of f(x)

(x − 2) is a factor of f(x)

Without using a calculator and showing all your working, find the other 2 solutions

of the equation.

Give your answers in exact form.

Question 9 continued

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

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

Triangle A is transformed to triangle C under an enlargement with scale factor 3 and

centre of enlargement (6, −2)

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

On the grid, draw and label triangle C

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

equation y = −3

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

On the grid, draw and label triangle D

Triangle B is transformed to triangle E under the transformation with matrix P where

k

1



P =



k

3

0

Triangle E is transformed to triangle F under the transformation with matrix Q where

k

1



Q =



2

k

k

1

Triangle F is the image of triangle B under the matrix N

Given that the determinant of N is 2

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

find the coordinates of the vertices of triangle F

Determinant of matrix a

b





ad

bc

 







c

d





Question 10 continued

y

5

x

−4

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

5

x

−4

Differentiate 4

t

t

10

6 2

A rocket moves vertically so that at time t seconds, the velocity, v m/s is given by

v

t

t

4

10

6 2

Find the time, in seconds, when the rocket stops accelerating vertically.

The vertical displacement, d metres, of the rocket at time t seconds, is given by

3 t ≥ 0

d

t

t

t

4

5

2

2

The rocket is launched from a height of k metres above horizontal ground.

The height, in metres, above ground when the rocket is first instantaneously at rest is

20 metres.

Find the value of k

Question 11 continued

O

Diagram NOT

accurately drawn

M

N

A

C

B

Figure 2

→ = 3a and OB

→ = 15b

Figure 2 shows the triangle OAB in which OA

→ = 1

→

C is the point on AB such that AC

3 AB

→ = 3

→

4 OC

N is the point on OC such that ON

→ in terms of a and b

Find and simplify an expression for BN

M is the point on OA such that B, N and M are collinear.

O

Diagram NOT

accurately drawn

M

N

A

C

B

Figure 2

→ = 3a and OB

→ = 15b

Figure 2 shows the triangle OAB in which OA

→ = 1

→

C is the point on AB such that AC

3 AB

→ = 3

→

4 OC

N is the point on OC such that ON

→ in terms of a and b

Find the ratio OM : MA

Show your working clearly.

Question 12 continued

Question 12 continued