Maths B

4MB1/02 — November 2023 (Edexcel IGCSE Maths): Past Paper

Exam code:4MB1

11 questions · 100 marks · ≈ 2 hours

Calculator allowed · Answer all questions · Show all your working

Complete reconstruction — all 11 questions · 100/100 marks match the official paper

Guided practice

111 marks

1 mark

(a)

The table shows information about 5 lakes in the Lake District.

Name	Surface area (m²)	Volume (m³)
Windermere	$1.5 \times 10^{7}$	$3.1 \times 10^{8}$
Ullswater	$8.9 \times 10^{6}$	$2.2 \times 10^{8}$
Thirlmere	$3.3 \times 10^{6}$	$5.0 \times 10^{7}$
Wastwater	$2.9 \times 10^{6}$	$1.1 \times 10^{8}$
Ennerdale Water	$3.0 \times 10^{6}$	$5.4 \times 10^{7}$

Write 3.3 × 106 as an ordinary number. Elter Water is another lake and has a volume of 500 000

…………… m³

Your answer

1 mark

(b)

Write 500 000 in standard form.

Your answer

2 marks

(c)

Calculate the difference, in standard form, between Windermere’s surface area and Wastwater’s surface area. Volume of water in Windermere k volume of water in Thirlmere

Your answer

2 marks

(d)

Work out the value of k The area of circle C is equal to the surface area of Ullswater.

Your answer

2 marks

(e)

Find, in metres to 2 significant figures, the radius of C x 4 106 n where n is an integer.

Your answer

3 marks

(f)

Find, in standard form, an expression for x 2 in terms of n

Your answer

How did you do?/ 11

26 marks

y 10 cm BC 3 x y 1 cm AD 2 x 9 y 14 cm CD 5 x 5 y 9 cm Calculate the length, in cm, of the perimeter of the kite.

Your answer

How did you do?/ 6

34 marks

1 mark

(a)

E is the universal set and A and B are two other sets. E 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 A 7, 8, 9, 10, 11, 12, 13, 14, 15 B 12, 13, 14, 15, 16, 17, 18, 19, 20 List the members of the set

A ∩ B

Your answer

1 mark

(b)

A B

Your answer

2 marks

(c)

A B

Your answer

How did you do?/ 4

46 marks

2 marks

(a)

x 3 10 x 3 Given that y = x³

show that y 2 3 y

Your answer

2 marks

(b)(i)

Solve the equation y 2 3 y 1 1

Your answer

2 marks

(b)(ii)

Hence find the solutions to x³ 10 x 3

Your answer

How did you do?/ 6

57 marks

4 marks

(a)

A solid square-based cuboid is made of steel. The mass of the cuboid is 1500 grams, to the nearest 50 grams. The length of the side of the square base of the cuboid is 12 cm, to 2 significant figures. The density of the steel is 7.98 g/cm³, to 3 significant figures. Given that Mass Density = Volume

show that the lower bound of the height of the cuboid is 1.2 cm to one decimal place. Show your working clearly. Another solid square-based cuboid is made of wood. The length of the side of the square base of this cuboid is 13 cm, to 2 significant figures. The height of the cuboid is 2.4 cm, to one decimal place.

Your answer

3 marks

(b)

Find, in cm² to one decimal place, the lower bound of the surface area of the cuboid. Show your working clearly.

Your answer

How did you do?/ 7

69 marks

1 mark

(a)

The table gives information about the time, in minutes, spent in a supermarket by 65 customers.

Time ( $t$ minutes)	Frequency
$0 < t \le 15$	15
$15 < t \le 25$	21
$25 < t \le 30$	20
$30 < t \le 40$	8
$40 < t \le 60$	1

Write down the class interval that contains the median time.

Your answer

4 marks

(b)

Calculate an estimate for the mean time spent by these 65 customers in the supermarket. Give your answer to one decimal place. One of the 65 customers is chosen at random.

Your answer

1 mark

(c)

Calculate the probability that the customer spent more than 30 minutes in the supermarket. The histogram below shows information about the time, in minutes, spent in the checkout queue for each of these 65 customers. histogram — official paper figure (qp.pdf p.10) There were 15 customers who spent between 5 and 10 minutes in the queue.

Your answer

3 marks

(d)

Calculate the number of these 65 customers who spent more than 3 minutes in the queue.

Your answer

How did you do?/ 9

711 marks

2 marks

(a)

On the grid opposite, triangle B is the image of triangle A under a single transformation.

Describe fully the single transformation. Triangle B is transformed to triangle C by an enlargement with scale factor 2 centre (2, 7)

Your answer

3 marks

(b)

Draw and label triangle C The area of triangle A is x

…………… cm²

Your answer

1 mark

(c)

Find, in terms of x, the area in cm², of triangle C 3 2 y 1 M= N = 5 4 2 2 Triangle B is transformed to triangle D under the transformation with matrix N Given that the determinant of M is equal to the determinant of N

Your answer

5 marks

(d)

draw and label triangle D. Show your working clearly.

[Determinant of matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad-bc$ ]

figure — official paper figure (qp.pdf p.12)

Your answer

How did you do?/ 11

89 marks

2 marks

(a)

Complete the table of values for y x 2 4 x x −2 −1 0 1 2 3 4 5 y 8 −4 −7 −7 −4

figure — official paper figure (qp.pdf p.3)

Your answer

2 marks

(b)

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

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Use the text description to work through it.

Your answer

3 marks

(c)

By drawing a suitable straight line on your grid, find estimates to one decimal place, for the solutions of the equation x 2 4 x 4 2 x 1 in the range −2 ≤ x ≤ 5

figure — official paper figure (qp.pdf p.16)

Your answer

2 marks

(d)

By drawing a suitable straight line on your grid, find an estimate to the nearest whole number, of the gradient of the curve $y = x^2 - 4x - 4$ at the point where $x = -1$ .

grid — official paper figure (qp.pdf p.17)

Your answer

How did you do?/ 9

912 marks

4 marks

(a)(i)

O Diagram NOT accurately drawn C E B D A Figure 2 → → Figure 2 shows triangle OAB with OA = 4a and OB = 3b → The point C lies on OB such that OC = 2b The point D is the midpoint of AB The point E lies on AC such that OED is a straight line.

CA (ii) AB (iii) OD Given that CE λCA

Your answer

4 marks

(b)

use a vector method to find the value of λ → → → → The point P is such that OP = μOD where μ 1 and AP is parallel to OB Given that the area of triangle OCE is 8

…………… cm²

Your answer

4 marks

(c)

find the area, in cm², of triangle APE

Your answer

How did you do?/ 12

1011 marks

2 marks

(a)

E Diagram NOT accurately drawn F A D H 4m G 1.5 m 2.4 m B 3m C Figure 3 Figure 3 shows a solid right prism ABCDEFGH The base of the prism, ABCD, is a rectangle and is horizontal. Trapezium BCHG is a cross section of the prism. AB = 4 m BC = 3 m CH = 2.4 m GB = 1.5 m GBC BCH ABG DCH

Calculate the volume, in m³, of the prism.

Your answer

3 marks

(b)

Calculate the angle of depression, in degrees to one decimal place, of G from E

Your answer

2 marks

(c)

Calculate the length, in metres to 3 significant figures, of AH The point P lies on the line GH such that GP = GH The point Q lies on the line BC such that BQ = BC

Your answer

4 marks

(d)

Calculate, in degrees to one decimal place, ∠APQ Area of trapezium ( a b) h

Your answer

How did you do?/ 11

1114 marks

1 mark

(a)

The function f is defined as f : x ↦ 2 x 2 + 3 x

Find f(−2) df ( x)

Your answer

3 marks

(b)

Find the value of x such that =0 dx x The function g is defined as g : x ↦ 4 x

Your answer

1 mark

(c)

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

Your answer

2 marks

(d)

Find fg(5) The function h is such that 3x gh(x) x > 1 x

Your answer

7 marks

(e)

Find h(x) in its simplest form. Show clear algebraic working.

Your answer

How did you do?/ 14

Name

Surface area (m²)

Volume (m³)

Windermere

1.5 \times 10^{7}

3.1 \times 10^{8}

Ullswater

8.9 \times 10^{6}

2.2 \times 10^{8}

Thirlmere

3.3 \times 10^{6}

5.0 \times 10^{7}

Wastwater

2.9 \times 10^{6}

1.1 \times 10^{8}

Ennerdale Water

3.0 \times 10^{6}

5.4 \times 10^{7}

Time (

t

minutes)

Frequency

0 < t \le 15

15 < t \le 25

25 < t \le 30

30 < t \le 40

40 < t \le 60