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

James bought a car on 1st March 2016

On 1st March 2017, the value of the car was 20% less than the amount that James paid for

the car on 1st March 2016

On 1st March 2018, the value of the car was 10% less than the value of the car on 1st March 2017

On 1st March 2018, the value of the car was £20 340

Calculate the amount, in £, that James paid for the car on 1st March 2016

On 1st March 2019, the value of the car was £19 323

James bought a car on 1st March 2016

On 1st March 2017, the value of the car was 20% less than the amount that James paid for

the car on 1st March 2016

On 1st March 2018, the value of the car was 10% less than the value of the car on 1st March 2017

On 1st March 2018, the value of the car was £20 340

Calculate the percentage decrease in the value of the car from 1st March 2018 to

1st March 2019

Question 1 continued

A mixture for concrete is made up of 105 kg of cement, 252 kg of sand and 273 kg of gravel.

Given that

the mass of cement : the mass of sand : the mass of gravel = 1 : (2x + y) : (x + 2y)

write down two different equations in x and y.

Simplify your equations.

A mixture for concrete is made up of 105 kg of cement, 252 kg of sand and 273 kg of gravel.

Given that

the mass of cement : the mass of sand : the mass of gravel = 1 : (2x + y) : (x + 2y)

Hence solve these two equations for the value of x and for the value of y.

Give each value as a simplified fraction.

Question 2 continued

Find the inverse of the matrix 2

2

5

4

Use your answer to part (a) to find the value of x and the values of y that satisfy

y

x

2

2

0

−

9

2

=

−

x

5

4

2

Inverse of matrix: a

b

d

b

−

1

=

c

d

c

a

−

ad

bc

−

Question 3 continued

Bag B1 and bag B2 each contain soil.

The weight of soil in B1 is 7.5 kg to the nearest 100 g.

The weight of soil in B2 is 5 kg to the nearest 10 g.

Find

the lower bound for the total weight of soil in the two bags,

Bag B1 and bag B2 each contain soil.

The weight of soil in B1 is 7.5 kg to the nearest 100 g.

The weight of soil in B2 is 5 kg to the nearest 10 g.

the upper bound for the difference in the weights of soil in the two bags,

Bag B1 and bag B2 each contain soil.

The weight of soil in B1 is 7.5 kg to the nearest 100 g.

The weight of soil in B2 is 5 kg to the nearest 10 g.

the lower bound, to the nearest 50 g, for the difference in the weights of soil in the two bags.

A large jar is to be filled with sweets.

The jar will be filled using bags of sweets.

The weight of the sweets in each bag of sweets is 220 g to the nearest 5 g.

When the jar is full of sweets, the weight of sweets in the jar is 10 kg to the nearest 0.2 kg.

Bertie has 45 bags of sweets.

Bag B1 and bag B2 each contain soil.

The weight of soil in B1 is 7.5 kg to the nearest 100 g.

The weight of soil in B2 is 5 kg to the nearest 10 g.

Giving your reasons, determine whether Bertie has a sufficient number of bags of

sweets to be sure that he can fill the jar with sweets.

Question 4 continued

Question 4 continued

45

4

3

1

1 2

5 Solve

= 54

9

Show clear algebraic working.

The functions f, g and h are defined as

f : x ↦ x + 3

g : x ↦ x2 - 2x + 3

h : x ↦ 6

x x ≠ 0

1

Find (i) g(–3) (ii) f h −

4

The functions f, g and h are defined as

f : x ↦ x + 3

g : x ↦ x2 - 2x + 3

h : x ↦ 6

x x ≠ 0

1

Express the inverse of the composite function hf in the form (hf)–1 : x ↦ ... and

simplify your answer.

The functions f, g and h are defined as

f : x ↦ x + 3

g : x ↦ x2 - 2x + 3

h : x ↦ 6

x x ≠ 0

1

State the value of x that must be excluded from any domain of (hf)–1

The functions f, g and h are defined as

f : x ↦ x + 3

g : x ↦ x2 - 2x + 3

h : x ↦ 6

x x ≠ 0

1

Find the two values of x for which hgf(x) = 2

Question 6 continued

Write down all the multiples of 3 lying between 1 and 20

Ahmed and Hani play a game with 20 numbered balls.

The 20 balls are numbered from 1 to 20

1

2

3

20

...

The balls are put in a bag.

Ahmed takes at random a ball from the bag, makes a note of its number and puts the ball

back into the bag.

If the number of the ball is a multiple of 5, Ahmed wins the game.

If Ahmed does not win the game, Hani takes at random a ball from the bag, makes a note

of its number and puts the ball back into the bag.

If the number of the ball is a multiple of 3, Hani wins the game.

If Hani does not win the game, Ahmed takes at random a ball from the bag, makes a note

of its number and puts the ball back into the bag.

If the number of the ball is a multiple of 6, Ahmed wins the game.

If Ahmed does not win the game, Hani takes at random a ball from the bag, makes a note

of its number and puts the ball back into the bag.

If the number of the ball is a multiple of 4, Hani wins the game.

If Hani does not win the game, the game stops and the result is a draw.

The incomplete probability tree diagram for the game is shown below.

Complete the probability tree diagram for Ahmed and Hani’s game.

Determine which player, Ahmed or Hani, is more likely to win the game.

Give a reason for your answer.

Ahmed

wins

Hani

wins

Ahmed

Ahmed

does not

wins

win

Hani

Hani

does not

wins

win

Ahmed

does not

win

Hani

does not

win

Question 7 continued

Diagram NOT

A

accurately drawn

100 cm

E

D

30 cm

70°

B

C

M

Figure 1

Figure 1 shows triangle ABC in which AB = 100 cm, AC = 30 cm and ∠ACB = 70°

Calculate, to 3 significant figures,

the size, in degrees, of ∠ABC,

Diagram NOT

A

accurately drawn

100 cm

E

D

30 cm

70°

B

C

M

Figure 1

Figure 1 shows triangle ABC in which AB = 100 cm, AC = 30 cm and ∠ACB = 70°

Calculate, to 3 significant figures,

the length, in cm, of BC.

As shown in Figure 1, the point E lies on AB and the point D lies on AC such that ED

and BC are parallel and AD : DC = 1 : 2

Diagram NOT

A

accurately drawn

100 cm

E

D

30 cm

70°

B

C

M

Figure 1

Figure 1 shows triangle ABC in which AB = 100 cm, AC = 30 cm and ∠ACB = 70°

Calculate, to 3 significant figures,

Write down the length, in cm, of DC.

The midpoint of BC is the point M.

Diagram NOT

A

accurately drawn

100 cm

E

D

30 cm

70°

B

C

M

Figure 1

Figure 1 shows triangle ABC in which AB = 100 cm, AC = 30 cm and ∠ACB = 70°

Calculate, to 3 significant figures,

Calculate the area, in cm² to 3 significant figures, of triangle DCM.

ABC

Given that area

DCM = k,

area

Diagram NOT

A

accurately drawn

100 cm

E

D

30 cm

70°

B

C

M

Figure 1

Figure 1 shows triangle ABC in which AB = 100 cm, AC = 30 cm and ∠ACB = 70°

Calculate, to 3 significant figures,

find the value of k without working out the area of triangle ABC.

a

b

c

Sine rule

=

=

A

B

C

sin

sin

sin

Cosine rule a

2

2

2

b

c

bc

A

=

−

2

cos

Area of triangle = 1

2 ab

C

sin

Question 8 continued

Question 8 continued

Question 8 continued

The triangle A has vertices with coordinates (–5, 2), (–11, 0) and (–7, 6).

On the grid, draw and label triangle A.

Triangle B is the image of triangle A under the enlargement with centre (1, 4) and

scale factor −1

2

The triangle A has vertices with coordinates (–5, 2), (–11, 0) and (–7, 6).

On the grid, draw and label triangle B.

Triangle C is the image of triangle B under a rotation of 180° about the point (3, 1).

The triangle A has vertices with coordinates (–5, 2), (–11, 0) and (–7, 6).

On the grid, draw and label triangle C.

The triangle A has vertices with coordinates (–5, 2), (–11, 0) and (–7, 6).

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

Question 9 continued

y

x

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

Question 9 continued

Question 9 continued

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

y

x

1

2 a

C

B

Diagram NOT

accurately drawn

M

N

D

A

O

a

Figure 2

Figure 2 shows trapezium ABCD in which the point O is the midpoint of AD and the

point M is the midpoint of CD.

→ = a, CB

→ = 1

→ = b,

2 a and OB

Given that OA

find, in terms of a and b, simplifying your answers where possible,

→ (ii) AC

→ (iii) CD

→ (iv) AM

→

1

2 a

C

B

Diagram NOT

accurately drawn

M

N

D

A

O

Figure 2

Figure 2 shows trapezium ABCD in which the point O is the midpoint of AD and the

point M is the midpoint of CD.

→ = a, CB

→ = 1

→ = b,

2 a and OB

Given that OA

AB

→ = λAM

→ and ON

→ = μOB

→, where λ and μ

The lines OB and AM intersect at N so that AN

are positive constants.

→

Find and simplify an expression in terms of a, b and λ for ON

1

2 a

C

B

Diagram NOT

accurately drawn

M

N

D

A

O

a

Figure 2

Figure 2 shows trapezium ABCD in which the point O is the midpoint of AD and the

point M is the midpoint of CD.

→ = a, CB

→ = 1

→ = b,

2 a and OB

Given that OA

Hence find the value of λ and the value of μ

The area of triangle OAB is 14 square units.

1

2 a

C

B

Diagram NOT

accurately drawn

M

N

D

A

O

a

Figure 2

Figure 2 shows trapezium ABCD in which the point O is the midpoint of AD and the

point M is the midpoint of CD.

→ = a, CB

→ = 1

→ = b,

2 a and OB

Given that OA

Find the area of triangle BNA.

Question 10 continued

Question 10 continued

Question 10 continued

Part of the curve with equation y = x2 - 5x + 3 is drawn on the grid.

The equation of another curve is y = – x

x

x

6

3

3

2

−

6

5

2

Complete the table of values for y = – x

x

x

6

3

3

2

−

6

5

2

Give your values of y to 2 decimal places.

Part of the curve with equation y = x2 - 5x + 3 is drawn on the grid.

The equation of another curve is y = – x

x

x

6

3

3

2

−

6

5

2

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

a smooth curve.

Part of the curve with equation y = x2 - 5x + 3 is drawn on the grid.

The equation of another curve is y = – x

x

x

6

3

3

2

−

6

5

2

Use the two curves on the grid to find an estimate, to 2 decimal places, of the range

of positive values of x for which x

x

x

7

3

2

−

−

• 3 < 0

6

5

2

Show your working clearly.

For positive values of x, the two curves on the grid intersect at the points P and Q.

Part of the curve with equation y = x2 - 5x + 3 is drawn on the grid.

The equation of another curve is y = – x

x

x

6

3

3

2

−

6

5

2

Find an estimate, to 1 decimal place, of the gradient of the straight line through P and Q.

The equation of the straight line through P and Q has the form y = ax + b

Part of the curve with equation y = x2 - 5x + 3 is drawn on the grid.

The equation of another curve is y = – x

x

x

6

3

3

2

−

6

5

2

Find, to 1 decimal place, the value of b.

Question 11 continued

y

3.5

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

Question 11 continued

Question 11 continued

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

y

3.5

Question 11 continued