Maths B

4MB1/02 — June 2021 (Edexcel IGCSE Maths): Past Paper

Exam code:4MB1

12 questions · 100 marks · ≈ 2 hours

Calculator allowed · Answer all questions · Show all your working

Complete reconstruction — all 12 questions · 100/100 marks match the official paper

Guided practice

15 marks

1 mark

(a)

The table gives the area, in km², and the population of each of three countries in 2017

Country	Area (km²)	Population
Greenland	$2.166 \times 10^{6}$	$5.617 \times 10^{4}$
Sri Lanka	$6.561 \times 10^{4}$	$2.144 \times 10^{7}$
China	$9.597 \times 10^{6}$	$1.368 \times 10^{9}$

Write 5.617 × 104 as an ordinary number.

Your answer

2 marks

(b)

Calculate by how many people the population of China in 2017 was greater than the population of Sri Lanka in 2017 Give your answer in standard form.

Your answer

2 marks

(c)

Work out the number of people per km² for Greenland in 2017 Give your answer, to 3 significant figures, in standard form.

Your answer

How did you do?/ 5

25 marks

The curve C has equation y = x³ + ax2 + bx + 8 where a and b are constants. The gradient of C at the point (2, 6) is 9.8 Find the value of a and the value of b. Show clear algebraic working.

Your answer

How did you do?/ 5

36 marks

0 marks

(a)(i)

The principal of a college wishes to introduce three new evening classes. The classes are Cake decorating (C), Needlework (N ) and Photography (P). In a survey, 160 people who attend evening classes at the college were asked which of these new evening classes they would like to attend. Information about the results of the survey is shown in the Venn diagram. The expression in terms of x, where x is a positive integer, in each subset represents the number of people in that subset. E C N 5x +7 8x 2 x² + 9 4x − 1 3x +8 2x2 + 4 x² + 2x − 3 P

Show that 2x2 + 9x − 68 = 0

4 marks

(a)(ii)

Hence find the value of x. One of the people surveyed is selected at random. Given that this person would like to attend Photography …………… , ……………

Your answer

2 marks

(b)

calculate the exact value of the probability that this person would also like to attend Cake decorating but not Needlework.

Your answer

How did you do?/ 6

46 marks

1 mark

(a)

C Diagram NOT accurately drawn B P 5b O 2a A Figure 1 → → In Figure 1, OACB is a quadrilateral in which OA = 2a and OB = 5b →

Find AB in terms of a and b P is the point on OC such that OP : PC = 1 : 4 → Given that BC = 6a + 5b

Your answer

0 marks

(b)(i)

prove that A, P and B are collinear …………… , ……………

Your answer

5 marks

(b)(ii)

find a value of m and a value of n such that AP : PB = m : n

Your answer

How did you do?/ 6

56 marks

Solve the simultaneous equations 2x2 = 11 − 3y 2 4x − y = 5 Show clear algebraic working.

Your answer

How did you do?/ 6

68 marks

2 marks

(a)

The curve $C$ has equation $y = x^2 + 2x + \frac{4}{x} \quad x \ne 0$

Complete the table of values for $C$

$x$	$-4$	$-2$	$-1$	$-0.5$	$0.5$	$1$	$2$	$4$
$y$				$-8.75$		$7$	$10$	$25$

Your answer

1 mark

(b)

On the grid opposite, plot the points from your completed table. The curve has one turning point and this has coordinates (1, 7)

$x$	$-4$	$-2$	$-1$	$-0.5$	$0.5$	$1$	$2$	$4$
$y$				$-8.75$		$7$	$10$	$25$

Your answer

1 mark

(c)

Use your points to draw the graph of y = x² + 2x + x≠0 x

graph — official paper figure (qp.pdf p.13)

Your answer

1 mark

(d)

Using your graph, find an estimate, to one decimal place, for the solution of the equation x² + 2x + =0 x

graph — official paper figure (qp.pdf p.13) (same figure as asset_6_c_graph)

Your answer

3 marks

(e)

By drawing a suitable line on the grid estimate, to one decimal place, the solutions of the equation 4 3 x² + 2x + = 5x + x 2

graph — official paper figure (qp.pdf p.13) (same figure as asset_6_c_graph)

Your answer

How did you do?/ 8

79 marks

2 marks

(a)

Lillian and Graham are co-owners of a small company. Lillian has invested $55 000 in the company. Graham has invested $25 000 in the company. This year Lillian receives 20% of the profit made by the company in 2020 The rest of the profit made by the company in 2020 is shared between Lillian and Graham in the same proportions as the amounts of money they invested in the company.

Show that this year Lillian receives, in total, 75% of the profit made by the company in 2020 In 2020, the company made a profit of $2000 Lillian puts all the money that she receives from the profit made by the company in 2020 in an account that pays interest at a fixed rate of 4.8% per year.

Your answer

2 marks

(b)

Calculate the interest she receives in one year.

Graham goes to a travel agent to change his share of the profit from dollars ($) into pounds (£). The table gives information about the exchange rates that are available.

Exchange rate
1 euro = $1.20
1 euro = £x
$1 = £0.76

Graham has to decide whether to change his dollars into euros and then change the euros into pounds or change his dollars straight into pounds. He calculates that if he chooses to do (i) he will receive £20 more than if he chooses to do (ii)

Your answer

5 marks

(c)

Calculate the value of x.

Your answer

How did you do?/ 9

89 marks

1 mark

(a)

There are 45 young people in a youth club. The table below gives information about the heights of these young people. Height (h cm) Frequency 140 < h ≤ 150 5 150 < h ≤ 155 8 155 < h ≤ 160 11 160 < h ≤ 165 6 165 < h ≤ 170 12 170 < h ≤ 190 3

Find the class interval that contains the median.

Your answer

4 marks

(b)

Calculate an estimate of the mean height, in cm to one decimal place, of these young people. One of the young people is selected at random. The incomplete probability tree diagram on the opposite page gives information about the eye colour and the hair colour of this young person.

figure — official paper figure (qp.pdf p.20)

Your answer

1 mark

(c)

Complete the probability tree diagram. Given that, for these young people, hair colour is independent of height

figure — official paper figure (qp.pdf p.20)

Your answer

3 marks

(d)

calculate the probability that the young person selected has fair hair and a height of more than 160 cm. Eye colour Hair colour 4 fair blue not fair 3 fair not blue not fair

Your answer

How did you do?/ 9

910 marks

2 marks

(a)

The grid opposite shows triangle A. Triangle A is transformed to triangle B by a reflection in the line with equation x = 1

On the grid, draw and label triangle B. Triangle B is transformed to triangle C under the translation

grid — official paper figure (qp.pdf p.25)

Your answer

2 marks

(b)

On the grid, draw and label triangle C. Triangle C is transformed to triangle D under the transformation with matrix M where 2 0 M= 0 2

grid — official paper figure (qp.pdf p.25) (same figure as asset_9_a_grid)

Your answer

3 marks

(c)

On the grid, draw and label triangle D.

grid — official paper figure (qp.pdf p.25) (same figure as asset_9_a_grid)

Your answer

3 marks

(d)

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

grid — official paper figure (qp.pdf p.25) (same figure as asset_9_a_grid)

Your answer

How did you do?/ 10

1010 marks

5 marks

(a)

F Diagram NOT accurately drawn D C E 51° 108° O A B Figure 2 Figure 2 shows the circle ABCDE with centre O. The chords AE and BD intersect outside the circle at the point F. ∠ BCD = 108° ∠ ADB = 51°

Giving your reasons, show that ∠ OBD = 18° Given that AE = 4.9 cm, EF = 3.5 cm and DF = 3.0 cm …………… , ……………

Your answer

5 marks

(b)

calculate the area, in cm² to 3 significant figures, of △ ABF. a b c Sine Rule sin A sin B sin C Area of triangle = 1 ab sin C

Your answer

How did you do?/ 10

1111 marks

5 marks

(a)

E Diagram NOT accurately drawn F D A 24 cm 35° B C 8 cm Figure 3 Figure 3 shows a solid right triangular prism ABCDEF. A cross section ABC of the prism is an isosceles triangle in which AB = AC. ∠ ACB = 35° CB = 8 cm CD = 24 cm

Calculate the total surface area, in cm² to 3 significant figures, of the prism. Diagram NOT accurately drawn h cm r cm Figure 4 Figure 4 shows a solid right circular cylinder with radius r cm and length h cm. The total surface area of the cylinder is (224 + 60 3 ) π cm² Given that r = 3 3 + 2

diagram — official paper figure (qp.pdf p.32)

Your answer

6 marks

(b)

find the exact value of h. Show your working clearly and give your answer in the form a 27 where a is an integer. ⎡ 1 ⎤ ⎢ Area of triangle = 2 ab sin C ⎥ ⎢ ⎥ ⎣Curved surface area of cylinder = 2πrh ⎦

Your answer

How did you do?/ 11

1215 marks

1 mark

(a)

The function f is defined by f ( x) 4 x

Write down the value of x that must be excluded from any domain of function f

Your answer

1 mark

(b)

Find f (−1) The function g is defined as g : x ↦ 2x2 + 4x − 1 where x ≥ −1 Given that fg–1(x) = 1.2

Your answer

7 marks

(c)

find the value of x The function h is defined as h : x ↦ x + 2 for all values of x ≥ −3 Given that the function m is such that m(x) = gh(x) + 3

Your answer

4 marks

(d)

express m(x) in the form a (x + b)² where a and b are integers.

Your answer

2 marks

(e)

Find the domain of m−1

Your answer

How did you do?/ 15

Country

Area (km²)

Population

Greenland

2.166 \times 10^{6}

5.617 \times 10^{4}

Sri Lanka

6.561 \times 10^{4}

2.144 \times 10^{7}

China

9.597 \times 10^{6}

1.368 \times 10^{9}

x

-4

-2

-1

-0.5

0.5

1

2

4

y

-8.75

7

10

25

x

-4

-2

-1

-0.5

0.5

1

2

4

y

-8.75

7

10

25

Exchange rate

1 euro = $1.20

1 euro = £x

$1 = £0.76