June 2020 · Paper 2R (4MB1/02R) (Edexcel IGCSE Maths): Exam Questions

The manufacturer’s price for a Jinko car is $x

Ben was given a 7% discount on the manufacturer’s price when he bought a Jinko.

Ben paid $23 622 when he bought his Jinko.

Calculate the value of x.

After a year Ben sold his Jinko for $19 880

The manufacturer’s price for a Jinko car is $x

Ben was given a 7% discount on the manufacturer’s price when he bought a Jinko.

Ben paid $23 622 when he bought his Jinko.

Calculate the percentage loss, to 3 significant figures, on the price Ben paid for his Jinko.

During the year that Ben owned the Jinko, he travelled d km in the car.

The average fuel consumption of the car was 10 km per litre.

The average cost of the fuel he used was $1.40 per litre.

Other costs for the car in the year came to $938

The cost per km, including the loss in value, of his Jinko to Ben during the year that he

owned the car was $0.40

The manufacturer’s price for a Jinko car is $x

Ben was given a 7% discount on the manufacturer’s price when he bought a Jinko.

Ben paid $23 622 when he bought his Jinko.

Calculate the value of d.

Question 1 continued

Find the Highest Common Factor (HCF) of 75, 90 and 120

.

Bhu sets the alarm on her phone to sound at 09 10

Her alarm then sounds every 12 minutes.

Dax sets the alarm on his phone to sound at 09 30

His alarm then sounds every 8 minutes.

Bhu’s alarm sounds at 09 10 and Dax’s alarm sounds at 09 30

Find the first time after 09 30 that both alarms will sound at the same time.

Question 2 continued

Solve the equation $3a + 6 = 4 - 5a$

Solve the inequality 3p > 6p + 12

An inequality, in w, is shown on a number line below.

7 w

–3

–2

–1

0

1

2

3

4

5

6

Write down the inequality.

Write down the 3 inequalities that define the shaded region R in Figure 1

y

x

Figure 1

Question 3 continued

A youth club has introduced three new activities

badminton (B), cookery (C) and drama (D).

Each of the 75 members of the youth club is asked to say in which of these activities they

have participated.

Their answers showed that of the 75 members

all have participated in at least one of these activities

27 have participated in badminton and drama

31 have participated in badminton and cookery

23 have participated in cookery and drama

48 have participated in badminton

49 have participated in cookery

40 have participated in drama.

Let x be the number of members of the youth club who have participated in all

three activities.

Using all this information, complete the Venn diagram opposite to show, in terms of x,

the number of elements in each appropriate subset.

A youth club has introduced three new activities

badminton (B), cookery (C) and drama (D).

Each of the 75 members of the youth club is asked to say in which of these activities they

have participated.

Their answers showed that of the 75 members

all have participated in at least one of these activities

27 have participated in badminton and drama

31 have participated in badminton and cookery

23 have participated in cookery and drama

48 have participated in badminton

49 have participated in cookery

40 have participated in drama.

Let x be the number of members of the youth club who have participated in all

three activities.

Find the value of x.

A youth club has introduced three new activities

badminton (B), cookery (C) and drama (D).

Each of the 75 members of the youth club is asked to say in which of these activities they

have participated.

Their answers showed that of the 75 members

all have participated in at least one of these activities

27 have participated in badminton and drama

31 have participated in badminton and cookery

23 have participated in cookery and drama

48 have participated in badminton

49 have participated in cookery

40 have participated in drama.

Let x be the number of members of the youth club who have participated in all

three activities.

Find

n (B ∩ C')









A youth club has introduced three new activities

badminton (B), cookery (C) and drama (D).

Each of the 75 members of the youth club is asked to say in which of these activities they

have participated.

Their answers showed that of the 75 members

all have participated in at least one of these activities

27 have participated in badminton and drama

31 have participated in badminton and cookery

23 have participated in cookery and drama

48 have participated in badminton

49 have participated in cookery

40 have participated in drama.

Let x be the number of members of the youth club who have participated in all

three activities.

find the probability that this member has not participated in any other activity.

Question 4 continued

E

C

D

B

Turn over for a spare Venn diagram if you need to redraw your diagram.

Question 4 continued

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

E

C

D

B

A youth club has introduced three new activities

badminton (B), cookery (C) and drama (D).

Each of the 75 members of the youth club is asked to say in which of these activities they

have participated.

Their answers showed that of the 75 members

all have participated in at least one of these activities

27 have participated in badminton and drama

31 have participated in badminton and cookery

23 have participated in cookery and drama

48 have participated in badminton

49 have participated in cookery

40 have participated in drama.

Let x be the number of members of the youth club who have participated in all

three activities.

n

B

C

D







One of the members of the youth club is picked at random.

Given that this member has participated in cooking,

Factorise x2 + 5x − 6

Express as a single fraction in its simplest form

x

x

3

2

2

5

4

The points with coordinates (1, 1), (3, 1) and (4, 3) are the vertices of triangle A.

On the grid opposite, draw and label triangle A.

Triangle B is the image of triangle A under the transformation with matrix M where

M=

2

0





0

2

The points with coordinates (1, 1), (3, 1) and (4, 3) are the vertices of triangle A.

On the grid opposite, draw and label triangle B.

Triangle C is the image of triangle B under a reflection in the line with equation y = 0

The points with coordinates (1, 1), (3, 1) and (4, 3) are the vertices of triangle A.

On the grid opposite, draw and label triangle C.

Triangle A is transformed to triangle C under the transformation with matrix N.

The points with coordinates (1, 1), (3, 1) and (4, 3) are the vertices of triangle A.

Find matrix N.

Triangle D is the image of triangle C under a rotation through 180º about the point (1, 1)

The points with coordinates (1, 1), (3, 1) and (4, 3) are the vertices of triangle A.

On the grid opposite, draw and label triangle D.

The points with coordinates (1, 1), (3, 1) and (4, 3) are the vertices of triangle A.

Describe fully the single transformation that maps triangle D onto triangle A.

Question 6 continued

y

x

Turn over for a spare copy of the 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

8

x

–8

The table gives information about the length of time, in seconds, that each of 28 birds

spent on Ali’s bird table on Monday.

Find the class interval that contains the median length of time that the birds spent on

the bird table on Monday.

The table gives information about the length of time, in seconds, that each of 28 birds

spent on Ali’s bird table on Monday.

Calculate an estimate, in seconds to one decimal place, for the mean length of time

that the birds spent on the bird table on Monday.

The incomplete histogram below gives some information about the length of time, in

seconds, that each of 35 birds spent on Ali’s bird table on Tuesday.

On Tuesday

9 of the birds spent between 5 seconds and 8 seconds on the bird table

6 of the birds spent between 8 seconds and 10 seconds on the bird table

no bird spent longer than 40 seconds on the bird table.

The table gives information about the length of time, in seconds, that each of 28 birds

spent on Ali’s bird table on Monday.

Use this information to complete the histogram.

The table gives information about the length of time, in seconds, that each of 28 birds

spent on Ali’s bird table on Monday.

Find the proportion of birds on Tuesday that spent longer than 15 seconds on the bird table.

Turn over for a spare copy of the histogram if you need to redraw your bar.

Question 7 continued

Question 7 continued

Question 7 continued

Only use this histogram if you need to redraw your bar.

Frequency

density

0

0

10

20

30

40

Length of time (seconds)

Jenny ran a road race.

The distance Jenny ran was 5 km, to the nearest 20 m.

Jenny’s time for the race was 34 minutes, to the nearest minute.

Colin ran a different road race.

The distance Colin ran was 10 km, to the nearest 200 m.

Colin’s time for the race was 1 hour 8 minutes, to the nearest minute.

Colin’s average speed for his race is greater than Jenny’s average speed for her race.

Calculate the upper bound for the difference, in km/h, between Colin’s average speed and

Jenny’s average speed.

Show your working clearly.

Question 8 continued

Figure 2 shows two shapes A and B.

All the lengths are in metres.

P

2x

x

2y

A

6y - 3

B

4y + 4

Q

R

4y

2x + 4

Figure 2

The corners of shape A are all right angles.

The area of shape A is 400 m²

Shape B is triangle PQR.

The perimeter of shape A is equal to the perimeter of shape B.

Show that 4y2 - x2 = 200 and that 2y = 2x + 5

Figure 2 shows two shapes A and B.

All the lengths are in metres.

P

2x

x

2y

A

6y - 3

B

4y + 4

Q

R

4y

2x + 4

Figure 2

The corners of shape A are all right angles.

The area of shape A is 400 m²

Shape B is triangle PQR.

The perimeter of shape A is equal to the perimeter of shape B.

Find the value of x and the value of y.

Show clear algebraic working.

Question 9 continued

Question 9 continued

Question 9 continued

f(x) = 3x3 - 7x2 + 5x - 1

Use the factor theorem to show that (3x - 1) is a factor of f(x).

f(x) = 3x3 - 7x2 + 5x - 1

Hence solve the equation f(x) = 0

Show clear algebraic working.

The curve C has equation y = f(x)

f(x) = 3x3 - 7x2 + 5x - 1

Find the exact coordinates of the turning points on C.

The curve C crosses the y-axis at the point P.

f(x) = 3x3 - 7x2 + 5x - 1

Find the gradient of C at P.

f(x) = 3x3 - 7x2 + 5x - 1

Hence find an equation of the tangent to C at P.

Question 10 continued

Question 10 continued

Question 10 continued

Cone B

Cone A

F

30 cm

Figure 3

A right circular cone, A, has height 100 cm and base radius 30 cm.

The shaded solid, F, is formed by removing the right circular cone, B, of height 20 cm

from the top of A, as shown in Figure 3

The volume of F is k $\pi$ cm³ where k is an integer.

Find the value of k.

Diagram NOT

20 cm

accurately drawn

102 cm

Figure 4

Figure 4 shows a solid circular cylinder.

The cylinder has a radius of 20 cm, a height of 102 cm and a volume of V cm³

Cone B

Cone A

F

30 cm

Figure 3

A right circular cone, A, has height 100 cm and base radius 30 cm.

The shaded solid, F, is formed by removing the right circular cone, B, of height 20 cm

from the top of A, as shown in Figure 3

The volume of F is k $\pi$ cm³ where k is an integer.

Calculate the value of V.

Give your answer in terms of $\pi$.

2

$\pi$r h

Volume of a cylinder



1



2

$\pi$r h

Volume of a cone = 3







Question 11 continued

Question 11 continues on the next page.

Question 11 continued

Figure 5 below shows a door stop made from a hollow hemisphere and a hollow right

circular cone.

108 cm

30 cm

h cm

Figure 5

The radius of the base of the cone and the radius of the hemisphere are both 30 cm.

The centre of the base of the cone coincides with the centre of the hemisphere.

The height of the cone is 108 cm.

The door stop rests on horizontal ground with the cone on top of the hemisphere and the

axis of symmetry of the door stop vertical.

The door stop contains sand to a height of h cm.

Given that the volume of sand in the door stop is V cm³, where V cm³ is the volume of the

cylinder in Figure 4

Cone B

Cone A

F

30 cm

Figure 3

A right circular cone, A, has height 100 cm and base radius 30 cm.

The shaded solid, F, is formed by removing the right circular cone, B, of height 20 cm

from the top of A, as shown in Figure 3

The volume of F is k $\pi$ cm³ where k is an integer.

calculate the value of h.

4

3

3 $\pi$r

Volume of a sphere







Question 11 continued

A

Diagram NOT

accurately drawn

B

C

F

E

O

Figure 6

Figure 6 shows triangle OAB.

The point E lies on OB such that OE : OB = 1 : 2

→ = 1

→

5 OA

The point F lies on OA such that OF

→= a and OB

→= b

Given that OA

→ in terms of a and b

find FE

The point C is such that ABC is a straight line and AB = BC.

A

Diagram NOT

accurately drawn

B

C

F

E

O

Figure 6

Figure 6 shows triangle OAB.

The point E lies on OB such that OE : OB = 1 : 2

→ = 1

→

5 OA

The point F lies on OA such that OF

→= a and OB

→= b

Given that OA

→ in terms of a and b

Show that F, E and C are not collinear.

Given that ABG and FEG are straight lines,

→ in terms of a and b

A

Diagram NOT

accurately drawn

B

C

F

E

O

Figure 6

Figure 6 shows triangle OAB.

The point E lies on OB such that OE : OB = 1 : 2

→ = 1

→

5 OA

The point F lies on OA such that OF

→= a and OB

→= b

Given that OA

→ in terms of a and b

find OG

Question 12 continued

Question 12 continued