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

A car travels at an average speed of 60 km/h for 2 hours.

It then travels at an average speed of x km/h for 3 hours.

The car travels at an average speed of 64.2 km/h for the whole journey.

Calculate the value of x

B

D

8 cm

3 cm

A

E

C

Figure 1

Figure 1 shows triangle ABC

The point D lies on AB and the point E lies on AC such that DE and BC are parallel.

DEA

BCA

90

AD = 8 cm DE = 3cm AE : EC = 1 : 2

Calculate the area, in cm² to 2 significant figures, of the region BCED shown shaded in

the diagram.

Area of trapezium = 1



2 a

b h





Diagram NOT

(3x + 5) m

B

C

accurately drawn

A

D

(3x + 2) m

(3x + 2) m

F

E

(3x + 21) m

Figure 2

Figure 2 shows a hexagon ABCDEF in which

BC = (3x + 5) metres AF = DE = (3x + 2) metres FE = (3x + 21) metres

BC is parallel to FE and AB = DC

The perpendicular distance between BC and FE is (3x + 17) metres.

The perimeter of the hexagon ABCDEF is 172 metres.

Calculate the value of x

Question 3 continued

B

3.8 cm

O

70°

A

C

Figure 3

Figure 3 shows a circle centre O and radius 3.8 cm

The points A and B lie on the circle.

The point C is such that AC and BC are tangents to the circle and ∠ACB = 70°

The region inside the quadrilateral OACB but outside the circle is shown shaded in Figure 3

Calculate the area, in cm² to 3 significant figures, of the shaded region.

Question 4 continued

Solve the simultaneous equations

x

y

5

7

x

xy

3

13

2

Show clear algebraic working.

Question 5 continued

Diagram NOT

accurately drawn

D

C

B

A

4a

5b

O

Figure 4

Figure 4 shows triangle OAB

= 3

The point C lies on AB such that AC

AB

5

→ = 4a and OB

→ = 5b

Given that OA

→ in terms of a and b

find an expression for OC

Give your answer in its simplest form.

The point D is such that OCD is a straight line.

Given that BD is parallel to OA

→ in terms of a and b

Diagram NOT

accurately drawn

D

C

B

A

4a

5b

O

Figure 4

Figure 4 shows triangle OAB

= 3

The point C lies on AB such that AC

AB

5

→ = 4a and OB

→ = 5b

Given that OA

→ in terms of a and b

use a vector method to find an expression for OD

Give your answer in its simplest form.

Question 6 continued

ℰ = {odd numbers between 0 and 30}

A = {multiples of 3}

B = {prime numbers}

C = {factors of 30}

Complete the Venn diagram for this information showing the position of each of the

numbers in the universal set.

ℰ

A

B

C





A

C

B

ℰ = {odd numbers between 0 and 30}

A = {multiples of 3}

B = {prime numbers}

C = {factors of 30}

Find

n







B

C

A

ℰ = {odd numbers between 0 and 30}

A = {multiples of 3}

B = {prime numbers}

C = {factors of 30}

n

A number is chosen at random from the universal set, ℰ

ℰ = {odd numbers between 0 and 30}

A = {multiples of 3}

B = {prime numbers}

C = {factors of 30}

Write down the probability that the number is in the set C

A

Given that the number chosen from ℰ is a multiple of 3

ℰ = {odd numbers between 0 and 30}

A = {multiples of 3}

B = {prime numbers}

C = {factors of 30}

find the probability that the number is also a factor of 30

Question 7 continued

Aanshi makes granola.

She uses nuts, dried raspberries and oats in the ratios 2 : 3 : 7 by weight.

Aanshi uses 80 grams of nuts.

Work out the weight, in grams, of oats she uses to make the granola.

Nuts cost $26 for 500 grams.

Aanshi makes granola.

She uses nuts, dried raspberries and oats in the ratios 2 : 3 : 7 by weight.

Aanshi uses 80 grams of nuts.

Work out the cost of the nuts used to make 270 grams of the granola.

Aanshi is going to buy 500 grams of dried raspberries from one of the following online

supermarkets.

Using an exchange rate of

$1 = £0.71

Aanshi makes granola.

She uses nuts, dried raspberries and oats in the ratios 2 : 3 : 7 by weight.

Aanshi uses 80 grams of nuts.

compare the cost, including postage, of 500 g of dried raspberries bought from the

US supermarket with the cost of 500 g of dried raspberries bought from the UK

supermarket.

State which supermarket is the cheaper when buying 500 g of dried raspberries.

Show your working clearly.

Question 8 continued

Question 8 continued

Question 8 continued

J

G

5 cm

13 cm

K

I

20 cm

F

H

12 cm

Figure 5

Figure 5 shows a solid right-angled triangular prism FGHIJK in which

FG = 13 cm FH = 12 cm IJ = 5 cm HI = 20 cm

The faces FHIK and GHIJ of the prism are rectangles.

Calculate the total surface area, in cm², of the prism FGHIJK

J

Diagram NOT

accurately drawn

G

5 cm

13 cm

K

I

20 cm

F

H

12 cm

Figure 5

Figure 5 shows a solid right-angled triangular prism FGHIJK in which

FG = 13 cm FH = 12 cm IJ = 5 cm HI = 20 cm

The faces FHIK and GHIJ of the prism are rectangles.

Calculate the size, in degrees to one decimal place, of ∠FJI

A company makes door wedges the same size and shape as the triangular prism FGHIJK

The company packs the door wedges into boxes that are in the shape of a cube of

side 60 cm.

J

Diagram NOT

accurately drawn

G

5 cm

13 cm

K

I

20 cm

F

H

12 cm

Figure 5

Figure 5 shows a solid right-angled triangular prism FGHIJK in which

FG = 13 cm FH = 12 cm IJ = 5 cm HI = 20 cm

The faces FHIK and GHIJ of the prism are rectangles.

Calculate the maximum number of door wedges that can fit into the box.

Question 9 continued

Question 9 continued

Question 9 continued

A box contains 8 green counters and 2 white counters only.

Peter takes at random 2 counters from the box.

Calculate the probability that Peter will take 1 green counter and 1 white counter.

A bag contains 28 blue beads and n red beads only.

Naasir selects a bead from the bag at random.

A box contains 8 green counters and 2 white counters only.

Peter takes at random 2 counters from the box.

Explain why the probability of the bead being red cannot be 6

11

Naasir keeps the first bead and selects a second bead at random from the bag.

The probability of both beads being different colours is 1

2

Given that there are fewer blue beads than red beads,

A box contains 8 green counters and 2 white counters only.

Peter takes at random 2 counters from the box.

calculate the probability that both beads are blue.

Show clear algebraic working.

Question 10 continued

Question 10 continued

Question 10 continued

The equation of a curve C is y

where k is a constant.

1

x

x

2

A minimum point on C occurs when x = –1.5

Show that the value of k is 12

12

9

The equation of a curve C is y

where k is a constant.

1

x

x

2

A minimum point on C occurs when x = –1.5

Complete the table of values for y

1

x

x

2

Give your values of y to 2 decimal places.

The equation of a curve C is y

where k is a constant.

1

x

x

2

A minimum point on C occurs when x = –1.5

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

completed table.

The equation of a curve C is y

where k is a constant.

1

x

x

2

A minimum point on C occurs when x = –1.5

Join all the points to form a smooth curve.

The equation of a curve C is y

where k is a constant.

1

x

x

2

A minimum point on C occurs when x = –1.5

By drawing a suitable straight line on the grid, find the range of values, to one

x

decimal place, of x in −

≤

≤

. , for which

6

0 8

−

12

9

1

x

≤

1

2

x

x

2

2

Question 11 continued

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

Question 11 continued

Question 11 continued

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

(Total Question 11 is 13 marks)

12 The functions f and g are such that

where x > 1

The functions f and g are such that

f : x ↦ 2x2 − 4x + 1 where x > 1

g : x ↦ 20/(5 + x)

State the value of x that must be excluded from any domain of g

Find the value of k such that g(k) = 8

Find fg(−3)

Find the inverse of the function f in the form f −1 : x ↦ ...

Simplify your answer.

The function h is defined for all values of x as

h : x ↦ (ax + b)/3

where a and b are constants.

Given that

h(2) = 4 and f −1h(1.7) = 2.5

find the value of a and the value of b

Show clear algebraic working.