June 2021 · Paper 2 (4MB1/02) (Edexcel IGCSE Maths): Exam Questions

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

Write 5.617$\times$104 as an ordinary number.

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

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.

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

Work out the number of people per km² for Greenland in 2017

Give your answer, to 3 significant figures, in standard form.

Question 1 continued

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.

Question 2 continued

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

N

C

x +

5

7

8x

x2 + 9

2

4x − 1

x +

3

8

2x2 + 4

2

x2 + 2x − 3

P

0

Show that 2x2 + 9x − 68 = 0

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

N

C

x +

5

7

8x

x2 + 9

2

4x − 1

x +

3

8

2x2 + 4

2

x2 + 2x − 3

P

0

Hence find the value of x.

One of the people surveyed is selected at random.

Given that this person would like to attend Photography,

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

N

C

x +

5

7

8x

x2 + 9

2

4x − 1

x +

3

8

2x2 + 4

2

x2 + 2x − 3

P

0

calculate the exact value of the probability that this person would also like to attend

Cake decorating but not Needlework.

Question 3 continued

C

Diagram NOT

accurately drawn

B

P

5b

O

2a

A

Figure 1

→

→

= 2a and OB

= 5b

In Figure 1, OACB is a quadrilateral in which OA

→

in terms of a and b

Find AB

P is the point on OC such that OP : PC = 1 : 4

→

= 6a + 5b

Given that BC

C

Diagram NOT

accurately drawn

B

P

5b

O

2a

A

Figure 1

→

→

= 2a and OB

= 5b

In Figure 1, OACB is a quadrilateral in which OA

→

in terms of a and b

prove that A, P and B are collinear,

C

Diagram NOT

accurately drawn

B

P

5b

O

2a

A

Figure 1

→

→

= 2a and OB

= 5b

In Figure 1, OACB is a quadrilateral in which OA

→

in terms of a and b

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

Solve the simultaneous equations

2x2 = 11 − 3y 2

4x − y = 5

Show clear algebraic working.

Question 5 continued

The curve C has equation

y = x2 + 2x + 4

x ≠ 0

x

Complete the table of values for C

The curve C has equation

y = x2 + 2x + 4

x ≠ 0

x

On the grid opposite, plot the points from your completed table.

The curve has one turning point and this has coordinates (1, 7)

The curve C has equation

y = x2 + 2x + 4

x ≠ 0

x

Use your points to draw the graph of y = x2 + 2x + 4

x ≠ 0

x

The curve C has equation

y = x2 + 2x + 4

x ≠ 0

x

Using your graph, find an estimate, to one decimal place, for the solution of the

equation

x2 + 2x + 4

= 0

x

The curve C has equation

y = x2 + 2x + 4

x ≠ 0

x

By drawing a suitable line on the grid estimate, to one decimal place, the solutions of

the equation

x2 + 2x + 4

x = 5x + 3

2

Question 6 continued

y

5 x

−5

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

Question 6 continued

.............................................................................................................................................................................................................................................……

Question 6 continued

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

y

5 x

−5

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.

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.

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

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.

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)

Calculate the value of x.

Question 7 continued

There are 45 young people in a youth club.

The table below gives information about the heights of these young people.

Find the class interval that contains the median.

There are 45 young people in a youth club.

The table below gives information about the heights of these young people.

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.

There are 45 young people in a youth club.

The table below gives information about the heights of these young people.

Complete the probability tree diagram.

Given that, for these young people, hair colour is independent of height

There are 45 young people in a youth club.

The table below gives information about the heights of these young people.

calculate the probability that the young person selected has fair hair and a height of

more than 160 cm.

Question 8 continued

Eye colour

Hair colour

fair

4

9

blue

1

not fair

3

fair

3

5

not blue

not fair

Question 8 continued

Question 8 continued

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.

7



Triangle B is transformed to triangle C under the translation



3

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 C.

Triangle C is transformed to triangle D under the transformation with matrix M where

2

0



M =



0

2

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 D.

The grid opposite shows triangle A.

Triangle A is transformed to triangle B by a reflection in the line with equation x = 1

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

Question 9 continued

y

x

−8

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

8

x

Diagram NOT

F

accurately drawn

D

C

E

51°

108°

O

B

A

Figure 2

Figure 2 shows the circle ABCDE with centre O.

The chords AE and BD intersect outside the circle at the point F.

Ð BCD = 108° Ð ADB = 51°

Giving your reasons, show that Ð OBD = 18°

Given that AE = 4.9 cm, EF = 3.5 cm and DF = 3.0 cm,

Diagram NOT

F

accurately drawn

D

C

E

51°

108°

O

B

A

Figure 2

Figure 2 shows the circle ABCDE with centre O.

The chords AE and BD intersect outside the circle at the point F.

Ð BCD = 108° Ð ADB = 51°

calculate the area, in cm² to 3 significant figures, of  ABF.

a

b

c



Sine Rule



A

B

C

sin

sin

sin



= 1



ab

C

sin

Area of triangle





2

Question 10 continued

Question 10 continued

Question 10 continued

E

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.

Ð ACB = 35° CB = 8 cm CD = 24 cm

Calculate the total surface area, in cm² to 3 significant figures, of the prism.

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 ) $\pi$ cm²

Given that r = 3 3 + 2

E

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.

Ð ACB = 35° CB = 8 cm CD = 24 cm

find the exact value of h.

Show your working clearly and give your answer in the form a 27 where a is an integer.

Question 11 continued

1

ab

C

=

Area of triangle

sin

2

$\pi$rh

=

Curved surface area of cylinder

2

Question 11 continued

Question 11 continued

The function f is defined by

7

x

f ( )

4

x

3

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

The function f is defined by

7

x

f ( )

4

x

3

Find f (−1)

The function g is defined as

g : x ↦ 2x2 + 4x − 1 where x ≥ −1

Given that fg–1(x) = 1.2

The function f is defined by

7

x

f ( )

4

x

3

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

The function f is defined by

7

x

f ( )

4

x

3

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

The function f is defined by

7

x

f ( )

4

x

3

Find the domain of m−1

Question 12 continued

Question 12 continued

Question 12 continued

Question 12 continued