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

Rory buys and sells jewellery.

Rory buys a necklace for $180

He sells the necklace for $230

Calculate, to 3 significant figures, Rory’s percentage profit.

Rory sells a bracelet for $203

This price represents a 16% profit on his cost price.

Rory buys and sells jewellery.

Rory buys a necklace for $180

He sells the necklace for $230

Calculate the cost price of the bracelet.

Rory travelled by plane from New York to Dubai to buy some jewellery.

The total flight time for the journey was 12 hours 48 minutes.

The average speed for the journey was 860 km/h

Rory buys and sells jewellery.

Rory buys a necklace for $180

He sells the necklace for $230

Calculate the total distance, in kilometres, travelled by the plane.

Rory bought some earrings for a total cost of 91 750 dirhams.

Using the exchange rate,

1 dollar = 3.67 dirhams

Rory buys and sells jewellery.

Rory buys a necklace for $180

He sells the necklace for $230

calculate the total cost of the earrings in dollars.

Question 1 continued

Write 76 000 000 in standard form.

Write $8.3 \times 10^{-4}$ as an ordinary number.

Calculate (3 × 10147)$\div$(6 × 10122)

Give your answer in standard form.

Write 1.6 × 1041 as a product of its prime factors.

Show your working clearly.

Question 2 continued

8 cm

Figure 1

Figure 1 shows a solid right circular cone.

The radius of the base of the cone is 8 cm.

The volume of the cone is 320$\pi$ cm³

The total surface area of the cone is k$\pi$ cm²

Calculate the value of k

Volume of a cone = 1

3 $\pi$r2h

Curved surface area of cone = $\pi$rl

Question 3 continued

Trapeziums P and Q are drawn on the grid opposite.

Describe fully the single transformation that maps trapezium P onto trapezium Q

2

Trapezium P is transformed to trapezium A under the translation

−

3

Trapeziums P and Q are drawn on the grid opposite.

On the grid, draw and label trapezium A

Trapezium P is transformed to trapezium B by a rotation of 90° clockwise about the

point (5, 2)

Trapeziums P and Q are drawn on the grid opposite.

On the grid, draw and label trapezium B

Trapezium C is the image of trapezium Q under the transformation with

matrix M where

1

−

0

2

M =

1

0

2

Trapeziums P and Q are drawn on the grid opposite.

On the grid, draw and label trapezium C

Question 4 continued

y

x

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

Question 4 continued

Question 4 continued

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

y

x

D

8 cm

C

E

F

7 cm

B

5 cm

A

Figure 2

Figure 2 shows right triangular prism ABCDEF

AB = 5 cm DF = 8 cm AF = 7 cm ∠CBA = 90°

Calculate the volume, in cm³ to the nearest whole number, of the triangular prism.

Q

P

20°

12 cm

T

S

R

25 cm

Figure 3

Figure 3 shows a shaded shape made by removing triangle PTQ from rectangle PQRS

QR = 12 cm SR = 25 cm ∠PTQ = 90° ∠TQR = 20°

D

Diagram NOT

accurately drawn

8 cm

C

E

F

7 cm

B

5 cm

A

Figure 2

Figure 2 shows right triangular prism ABCDEF

AB = 5 cm DF = 8 cm AF = 7 cm ∠CBA = 90°

Calculate the perimeter, in cm to the nearest whole number, of the shaded shape.

Question 5 continued

Question 5 continued

Question 5 continued

Ted has two boxes of buttons, Box A and Box B

There are 20 buttons in Box A and 20 buttons in Box B

There are 13 white buttons in Box A

There are 9 white buttons in Box B

Ted takes at random a button from Box A and a button from Box B

Complete the probability tree diagram.

Box A

Box B

white

white

not white

white

not white

not white

Ted has two boxes of buttons, Box A and Box B

There are 20 buttons in Box A and 20 buttons in Box B

There are 13 white buttons in Box A

There are 9 white buttons in Box B

Ted takes at random a button from Box A and a button from Box B

Calculate the probability that Ted takes at least one white button.

Ted also has a bag of buttons.

There are 30 buttons in the bag.

There are x white buttons in the bag.

Ted takes at random a button from Box A, a button from Box B and a button from

the bag.

The probability that of the 3 buttons Ted has, 2 of the buttons are white is 337

1000

Ted has two boxes of buttons, Box A and Box B

There are 20 buttons in Box A and 20 buttons in Box B

There are 13 white buttons in Box A

There are 9 white buttons in Box B

Ted takes at random a button from Box A and a button from Box B

Work out the value of x

Show clear algebraic working.

Question 6 continued

Question 6 continued

Question 6 continued

The function g is defined as

10

g : x ↦

x −

2

3

Find the value of x that must be excluded from the domain of g

The function g is defined as

10

g : x ↦

x −

2

3

Solve g(x) = 5

The function f is defined as

f : x ↦ 3x2 + 9x - 7 for x > – 3

2

1

The function g is defined as

10

g : x ↦

x −

2

3

Find f −

2

The function g is defined as

10

g : x ↦

x −

2

3

Express the inverse function f –1 in the form f –1 : x ↦ ...

2

b

b

ac

= −±

−

4

2

ax

bx

c

x

=

Solutions of

0 are

a

2

Question 7 continued

The equation of a curve is y = 1

2 x3 - 5x - 3

Complete the table of values for y = 1

2 x3 - 5x - 3

The equation of a curve is y = 1

2 x3 - 5x - 3

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

form a smooth curve.

The equation of a curve is y = 1

2 x3 - 5x - 3

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

place, of the solutions to the equation

1

2 x3 - 5x - 3 = 1 - 1

2 x in the interval –4 ≤ x ≤ 4

Question 8 continued

y

x

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

Question 8 continued

Question 8 continued

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

y

x

Solve the inequality 5y - 7 > 2y - 13

Hence, represent on the number line at the top of the next page, the values of y

for which 5y - 7 > 2y - 13

Solve the inequality 4x2 + 4x - 35 < 0

Hence find the values of x for which

5x - 7 > 2x - 13 and 4x2 + 4x - 35 < 0

2

b

b

ac

= −±

−

4

2

ax

bx

c

x

=

Solutions of

0 are

a

2

Question 9 continued

–5

–4

–3

–2

–1

0

1

2

3

4

5

Express

in the form

5

Show your working clearly.

27

x

×

=

Given that

3

3

4

81

3

find the value of x, giving your answer as a fraction in its simplest form.

Show your working clearly.

Question 10 continued

A curve C and a straight line L are drawn on a grid.

C has equation y = 5x2 - 16x - 5

L has equation y + 5x = 7

Find the coordinates of the points of intersection of C and L

Show clear algebraic working.

P is the point on the curve with equation y = 5x2 - 16x - 5 with x coordinate 2

The line Q is the tangent to the curve at the point P

The line Q crosses the x‑axis at the point X and the y‑axis at the point Y

The point M lies on Q and is such that XM = MY

A curve C and a straight line L are drawn on a grid.

C has equation y = 5x2 - 16x - 5

L has equation y + 5x = 7

Calculate the coordinates of the point M

Give your coordinates as exact values.

2

b

b

ac

= −±

−

4

2

ax

bx

c

x

=

Solutions of

0 are

a

2

Question 11 continued

Diagram NOT

C

accurately drawn

B

D

E

A

F

Figure 4

Figure 4 shows a regular hexagon ABCDEF

Given that the area of hexagon ABCDEF = 150 3 cm²

find the perimeter, in cm, of the hexagon.

Diagram NOT

L

K

accurately drawn

C

B

D

J

E

I

A

F

H

G

Figure 5

Figure 5 shows a shape AGHIJKLBCDEF made from a regular octagon GHIJKLBA

and the regular hexagon ABCDEF from part (a).

Diagram NOT

C

accurately drawn

B

D

E

A

F

Figure 4

Figure 4 shows a regular hexagon ABCDEF

Given that the area of hexagon ABCDEF = 150 3 cm²

Work out the length, in cm to one decimal place, of the straight line KF

Area of triangle = 1

2 ab

C

sin

Sum of interior angles of polygon is (2n - 4) right angles

Question 12 continued

Question 12 continued