June 2022 · Paper 2R (4MB1/02R) (Edexcel IGCSE Maths): Exam Questions

The Venn diagram shows information about the numbers of students in a school who study

History (H), Music (M ) and Geography (G).

E

M

H

12

15

14

3

11

6

21

G

32

Find the number of students who study Geography.

The Venn diagram shows information about the numbers of students in a school who study

History (H), Music (M ) and Geography (G).

E

M

H

12

15

14

3

11

6

21

G

32

Find the number of students who study exactly two of the subjects History, Music

and Geography.

The Venn diagram shows information about the numbers of students in a school who study

History (H), Music (M ) and Geography (G).

E

M

H

12

15

14

3

11

6

21

G

32

On the Venn diagram above, shade the region that represents the set H ∩ G¢

Question 1 continued

E is the universal set and A and B are two sets such that

E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A ∩ B = {multiples of 3}

A ∩ B¢ = {2, 4, 8, 10}

(A ∪ B)¢ = {1, 7}

The Venn diagram shows information about the numbers of students in a school who study

History (H), Music (M ) and Geography (G).

E

M

H

12

15

14

3

11

6

21

G

32

Use the information about the sets E, A and B to complete the Venn diagram below.

E

A

B

The Venn diagram shows information about the numbers of students in a school who study

History (H), Music (M ) and Geography (G).

E

M

H

12

15

14

3

11

6

21

G

32

Find n(B)

Diagram NOT

accurately drawn

16‑sided

polygon

B

5 cm

5 cm

A

C

P

Figure 1

Figure 1 shows part of a regular 16‑sided polygon in which PA and AB are two sides.

Figure 1 also shows the isosceles triangle ABC in which AB = CB = 5 cm.

PAC is a straight line.

Calculate the length, in cm to 3 significant figures, of AC.

Sum of interior angles of polygon

n −

(

2

4

)

right angles

Arup collects information about the time delay, in minutes, of some trains. He is going to

draw a pie chart for his results.

The incomplete table below gives some information about his results together with the size,

in degrees, of the angle of each of three sectors in his pie chart.

Complete the table.

Arup collects information about the time delay, in minutes, of some trains. He is going to

draw a pie chart for his results.

The incomplete table below gives some information about his results together with the size,

in degrees, of the angle of each of three sectors in his pie chart.

Calculate an estimate, in minutes to 3 significant figures, for the mean time delay of

these trains.

x

Triangles A, B, C and D are drawn on the grid above.

Describe fully the single transformation that maps

triangle A onto triangle B

x

Triangles A, B, C and D are drawn on the grid above.

Describe fully the single transformation that maps

triangle A onto triangle C

x

Triangles A, B, C and D are drawn on the grid above.

Describe fully the single transformation that maps

triangle A onto triangle D

Triangle E is the image of triangle A under an enlargement with scale factor –2 and

centre of enlargement (4, 0)

x

Triangles A, B, C and D are drawn on the grid above.

Describe fully the single transformation that maps

On the grid, draw and label triangle E

Question 4 continued

Dan is going to play one game of squash and one game of chess against his friend.

The probability that Dan will win the game of squash is 3

5

The probability that Dan will win the game of chess is 1

3

Complete the probability tree diagram.

Squash

Chess

Dan wins

Dan wins

Dan does not win

Dan wins

Dan does not win

Dan does not win

Dan is going to play one game of squash and one game of chess against his friend.

The probability that Dan will win the game of squash is 3

5

The probability that Dan will win the game of chess is 1

3

Find the probability that Dan will win exactly one game.

Given that Dan won exactly one game,

Dan is going to play one game of squash and one game of chess against his friend.

The probability that Dan will win the game of squash is 3

5

The probability that Dan will win the game of chess is 1

3

calculate the probability that he won his game of squash.

Question 5 continued

In 2018, a badminton club had 460 members.

Of these members,

A were younger than 30

B were aged between 30 and 60 inclusive

C were older than 60

Given that A : B : C = 2 : 5 : 3

find the total number of members who were aged 30 or older in 2018

In 2018, the annual membership fee for each member who was older than 60 was $65

The annual membership fee for each other member was $135

Calculate the total amount, in $, that the 460 members paid in annual membership fees in 2018

The annual membership fee for each member who was older than 60 in 2019 was 4% greater than the annual membership fee for each member who was older than 60 in 2018

Calculate the annual membership fee for each member who was older than 60 in 2019

The badminton club buys 12 shuttlecocks for a total cost of $5.10

The club then sells the shuttlecocks to members for $0.50 each.

Calculate the percentage profit, to 3 significant figures, made by the club on each shuttlecock that was sold.

Figure 2 shows a badminton net ABCD and two supports for the net.

The badminton net is shaded in the diagram.

Figure 2 gives information about the dimensions of the badminton net.

Each measurement is given to the nearest cm.

Calculate the upper bound, in cm², of the area of the net ABCD

A particle P is moving along a straight line through the fixed point O

The speed, v m/s, of P at time t seconds is given by

3 for 1 ≤ t ≤ 5

t

2

v

=

2

t

2

27

t

2

3

Complete the table of values for v

=

2

t

2

27

Give your values of v to 2 decimal places.

A particle P is moving along a straight line through the fixed point O

The speed, v m/s, of P at time t seconds is given by

3 for 1 ≤ t ≤ 5

t

2

v

=

2

t

2

27

t

2

3

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

a smooth curve.

A particle P is moving along a straight line through the fixed point O

The speed, v m/s, of P at time t seconds is given by

3 for 1 ≤ t ≤ 5

t

2

v

=

2

t

2

27

t

2

3

Using your curve, find an estimate, to one decimal place, for the speed of P when t = 1.75

2

The acceleration of P at time t seconds where 1 ≤ t ≤ 5 is a m/s

A particle P is moving along a straight line through the fixed point O

The speed, v m/s, of P at time t seconds is given by

3 for 1 ≤ t ≤ 5

t

2

v

=

2

t

2

27

t

2

3

Find an expression for a in terms of t

A particle P is moving along a straight line through the fixed point O

The speed, v m/s, of P at time t seconds is given by

3 for 1 ≤ t ≤ 5

t

2

v

=

2

t

2

27

t

2

3

Using your answer to part (d), find the value of t when P has its minimum speed in

the time interval 1 ≤ t ≤ 5

Show clear algebraic working.

Question 7 continued

v

6

5

4

3

2

1

0

t

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

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

Question 7 continued

Question 7 continued

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

v

6

5

4

3

2

1

0

t

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

The equation of the straight line L is y = 2 - 3x

Find the exact coordinates of the points where L crosses the coordinate axes.

The functions f and g are defined as

f : x ↦ 2 - 3x

x

g : x ↦ 3

x x ≠ 1

−

2

1

2

The equation of the straight line L is y = 2 - 3x

Find g(–2)

The equation of the straight line L is y = 2 - 3x

Find the values of x for which ff(x) + g(x) = 0

Show your working clearly and give your answer in the form

a

b

±

c

where a, b and c are integers.

–1 : x ↦ ...

The equation of the straight line L is y = 2 - 3x

Express the inverse of the composite function fg in the form (fg)

b

b

ac

= −

±

−

2

4

ax

bx

c

x

=

2

Solutions of

0 are

a

2

Question 8 continued

Question 8 continued

Question 8 continued

C

Diagram NOT

accurately drawn

D

E

A

O

B

Figure 3

Figure 3 shows three points A, B and C on a circle with centre O where AOB is a diameter

of the circle.

D is the point on AC such that AD : DC = 3 : 2

→ = a and AD

→ = b

Given that OA

find, in terms of a or b or a and b where appropriate, a simplified expression for

→

→

→

C

Diagram NOT

accurately drawn

D

E

A

O

B

Figure 3

Figure 3 shows three points A, B and C on a circle with centre O where AOB is a diameter

of the circle.

D is the point on AC such that AD : DC = 3 : 2

→ = a and AD

→ = b

Given that OA

CO

C

Diagram NOT

accurately drawn

D

E

A

O

B

Figure 3

Figure 3 shows three points A, B and C on a circle with centre O where AOB is a diameter

of the circle.

D is the point on AC such that AD : DC = 3 : 2

→ = a and AD

→ = b

Given that OA

DB

C

Diagram NOT

accurately drawn

D

E

A

O

B

Figure 3

Figure 3 shows three points A, B and C on a circle with centre O where AOB is a diameter

of the circle.

D is the point on AC such that AD : DC = 3 : 2

→ = a and AD

→ = b

Given that OA

AC

E is the point such that CEO and DEB are straight lines.

→ + DE

→ and AC

→ + CE

→

By considering both AD

→ in terms of a and b

C

Diagram NOT

accurately drawn

D

E

A

O

B

Figure 3

Figure 3 shows three points A, B and C on a circle with centre O where AOB is a diameter

of the circle.

D is the point on AC such that AD : DC = 3 : 2

→ = a and AD

→ = b

Given that OA

find a simplified expression for AE

Given that ½a½ = 7 cm and ½b½ = 6 cm,

2, of ΔABC

calculate the exact area, in cm

A

B

=

=

k

k

k

−

3

3

1

The determinant of matrix A is equal to the determinant of matrix B

Show that k is a root of the equation

3 + 5k

2 - 28k - 15 = 0

2k

3 + 5k

2 - 28k - 15

Given that f(k) = 2k

A

B

=

=

k

k

k

−

3

3

1

The determinant of matrix A is equal to the determinant of matrix B

use the factor theorem to show that (k + 5) is a factor of f(k)

A

B

=

=

k

k

k

−

3

3

1

The determinant of matrix A is equal to the determinant of matrix B

Hence, factorise completely f(k)

The transformation with matrix C, where C is a 2 × 2 matrix, is equivalent to the

transformation with matrix A followed by the transformation with matrix B

Given that k is positive,

A

B

=

=

k

k

k

−

3

3

1

The determinant of matrix A is equal to the determinant of matrix B

find matrix C

Determinant of matrix a

b

ad

bc

=

−

c

d

Question 10 continued

Question 10 continued

Question 10 continued

G

Diagram NOT

accurately drawn

C

D

(4x - 8) cm

A

B

θ°

E

F

(2x + 3) cm

(4x + 2) cm

Figure 4

Figure 4 shows a rectangle ABCD and an isosceles triangle EFG with EG = FG

AB = (2x + 3) cm BC = (4x - 8) cm EF = (4x + 2) cm

∠FEG = θ° where tan θ° = 1

2

2

The perimeter of the rectangle is P cm and the area of the triangle is T cm

Given that P ≥ T

find the range of possible values of x

Show your working clearly.

Question 11 continued

Question 11 continued