January 2022 · Paper 2 (4MB1/02) (Edexcel IGCSE Maths): Exam Questions

Write 248 000 000 in standard form.

–4 as an ordinary number.

Write 2.56 × 10

Calculate, giving your answer in standard form

×

−

×

2 5

.

10

1 3

.

10

60

59

×

−

1 5

10

.

48

The ages, in years, of 7 friends are

9

8

7

6

10

7

a

The mean age of the 7 friends is 8 years.

Work out the value of a

The ages, in years, of 7 friends are

9

8

7

6

10

7

a

The mean age of the 7 friends is 8 years.

Find the median age of the 7 friends.

There are 34 passengers on a bus.

The mean age of these passengers is 49 years.

11 of these passengers are pensioners.

The mean age of these pensioners is 72 years.

The ages, in years, of 7 friends are

9

8

7

6

10

7

a

The mean age of the 7 friends is 8 years.

Calculate the mean age, in years, of the passengers on the bus who are not pensioners.

Triangles A and D are drawn on the grid below.

Triangle B is the image of triangle A under a reflection in the line with equation y = –x

On the grid below, draw and label triangle B.

Triangle A is transformed to triangle C under the translation −

9

−

2

Triangles A and D are drawn on the grid below.

Triangle B is the image of triangle A under a reflection in the line with equation y = –x

On the grid, draw and label triangle C.

Triangles A and D are drawn on the grid below.

Triangle B is the image of triangle A under a reflection in the line with equation y = –x

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

y

x

–10

A spare grid is on the next page if you need to redraw your triangles.

Question 3 continued

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

y

x

A curve C has equation x

A straight line l has equation 4y + 3x = 40

Show that the line l intersects the curve C only once.

Show clear algebraic working.

Question 4 continued

B

E

A

Diagram NOT

accurately drawn

D

C

O

Figure 1

Figure 1 shows triangle OAB

→ = a and OB

→ = b

Given that OA

→ in terms of a and b

find AB

The point C lies on OA such that OC : OA = 1 : 3

→ = 2

→

The point D lies on OB such that OD

5 OB

Given that the point E is such that ABE and CDE are straight lines,

→

B

E

A

Diagram NOT

accurately drawn

D

C

O

Figure 1

Figure 1 shows triangle OAB

→ = a and OB

→ = b

Given that OA

→ in terms of a and b

find and simplify an expression, in terms of a and b, for AE

Question 5 continued

x

−

−

−

4

14

2

3

A =

BA =

x

−

1

4

2

Given that the determinant of B is 10

find B

Show your working clearly.

a

b

Determinant of matrix

ad

bc

=

−

c

d

a

b

d

b

−

1

Inverse of matrix

=

c

a

c

d

−

ad

bc

−

Question 6 continued

B

F

C

86°

O

38°

D

A

G

E

Figure 2

In Figure 2, ABCDG is a circle, centre O

EDF is the tangent to the circle at the point D

∠ABC = 86°

∠CDF = 38°

The length of the arc AGD is 0.8$\pi$ cm.

Giving reasons, show that the radius of the circle is 1.5 cm.

2 to 2 decimal places, of the circle ABCDG

B

F

C

86°

O

38°

D

A

G

E

Figure 2

In Figure 2, ABCDG is a circle, centre O

EDF is the tangent to the circle at the point D

∠ABC = 86°

∠CDF = 38°

The length of the arc AGD is 0.8$\pi$ cm.

Calculate the area, in cm

Question 7 continued

Question 7 continued

Question 7 continued

All 66 students in a drama group take part in at least one of the four activities given below.

acting (A) dancing (D) singing (S) stage management (M)

Of these 66 students

11 take part in acting, dancing and singing

17 take part in acting and singing

14 take part in dancing and singing

16 take part in acting and dancing

33 take part in singing

37 take part in acting

29 take part in dancing

Any student who takes part in stage management does not take part in acting, dancing

or singing.

Show all this information on the Venn diagram, giving the number of students in

each subset.

E

D

A

S

All 66 students in a drama group take part in at least one of the four activities given below.

acting (A) dancing (D) singing (S) stage management (M)

Of these 66 students

11 take part in acting, dancing and singing

17 take part in acting and singing

14 take part in dancing and singing

16 take part in acting and dancing

33 take part in singing

37 take part in acting

29 take part in dancing

Any student who takes part in stage management does not take part in acting, dancing

or singing.

Find

n(M)

All 66 students in a drama group take part in at least one of the four activities given below.

acting (A) dancing (D) singing (S) stage management (M)

Of these 66 students

11 take part in acting, dancing and singing

17 take part in acting and singing

14 take part in dancing and singing

16 take part in acting and dancing

33 take part in singing

37 take part in acting

29 take part in dancing

Any student who takes part in stage management does not take part in acting, dancing

or singing.

n([A ∩ D¢] ∪ S)

All 66 students in a drama group take part in at least one of the four activities given below.

acting (A) dancing (D) singing (S) stage management (M)

Of these 66 students

11 take part in acting, dancing and singing

17 take part in acting and singing

14 take part in dancing and singing

16 take part in acting and dancing

33 take part in singing

37 take part in acting

29 take part in dancing

Any student who takes part in stage management does not take part in acting, dancing

or singing.

n([A ∩ D ∩ S¢]¢)

One of the students in the drama group is selected at random.

Given that this student takes part in dancing,

All 66 students in a drama group take part in at least one of the four activities given below.

acting (A) dancing (D) singing (S) stage management (M)

Of these 66 students

11 take part in acting, dancing and singing

17 take part in acting and singing

14 take part in dancing and singing

16 take part in acting and dancing

33 take part in singing

37 take part in acting

29 take part in dancing

Any student who takes part in stage management does not take part in acting, dancing

or singing.

find the probability that this student also takes part in

stage management,

All 66 students in a drama group take part in at least one of the four activities given below.

acting (A) dancing (D) singing (S) stage management (M)

Of these 66 students

11 take part in acting, dancing and singing

17 take part in acting and singing

14 take part in dancing and singing

16 take part in acting and dancing

33 take part in singing

37 take part in acting

29 take part in dancing

Any student who takes part in stage management does not take part in acting, dancing

or singing.

singing.

Question 8 continued

T

Diagram NOT

accurately drawn

30 m

C

B

A

Figure 3

Figure 3 shows three points A, B and C on horizontal ground.

A vertical mast BT of height 30 m is at point B.

The angle of elevation of T from A is 32°

The angle of elevation of T from C is 25°

The bearing of A from B is 195°

The bearing of C from B is 280°

Calculate the bearing, in degrees to the nearest degree, of C from A.

a

b

c

Sine rule:

=

=

A

B

C

sin

sin

sin

Cosine rule: a

2

2

2

b

c

bc

A

=

−

2

cos

Question 9 continued

Question 9 continued

Question 9 continued

The production costs of building a Kimo boat are

$L for labour

$M for materials

$H for overheads

In 2020, the total of the production costs for a Kimo boat was $120 000 where

L : M : H = 5 : 3 : 2

Calculate the value of H in 2020

The production costs were different in 2021 from what they were in 2020

The labour costs had increased by 10%

The cost of materials had increased by 5%

The overheads had decreased by 4%

The production costs of building a Kimo boat are

$L for labour

$M for materials

$H for overheads

In 2020, the total of the production costs for a Kimo boat was $120 000 where

L : M : H = 5 : 3 : 2

Calculate the percentage increase, from 2020 to 2021, in the total of the production

costs of building a Kimo boat.

Gordon bought a Kimo boat and sold it a year later for $360 000, making a loss of 25% on

the price for which he bought the boat.

The production costs of building a Kimo boat are

$L for labour

$M for materials

$H for overheads

In 2020, the total of the production costs for a Kimo boat was $120 000 where

L : M : H = 5 : 3 : 2

Calculate the price for which Gordon bought the boat.

Gordon sold the boat to a friend living in Hungary. Gordon’s friend paid Gordon the

$360 000 in Hungarian forints.

Using exchange rates of

£1 = $1.35 £1 = 388.50 Hungarian forints

The production costs of building a Kimo boat are

$L for labour

$M for materials

$H for overheads

In 2020, the total of the production costs for a Kimo boat was $120 000 where

L : M : H = 5 : 3 : 2

change $360 000 to Hungarian forints.

Question 10 continued

Question 10 continued

Question 10 continued

On the grid on the opposite page, draw the straight line with equation

–3 ≤ x ≤ 4

4y - 3x = 6

3y + 2x = 15

Using your straight lines, find an estimate, to one decimal place, of the solution of

the simultaneous equations

4y - 3x = 6

3y + 2x = 15

x

x

−

Hence, or otherwise, solve the inequality 6

3

15

2

<

4

3

2 - 2x - 1

Complete the table of values for y = x

On the same grid on the opposite page, plot the points from your completed table and

join them to form a smooth curve.

Using part (a) and part (e), find an estimate, to one decimal place, for the range of

values of x for which

11

5

x

x

−

2

−

< 0

4

2

Show your working clearly.

Question 11 continued

y

x

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.

y

7

x

–2

The function g is defined for all values of x by

2

g : x ↦ 5 - x

Find g(–4)

The function g is defined for all values of x by

2

g : x ↦ 5 - x

Write down the range of the function g

The function f is defined as

4

x ≠ 11

f : x ↦

x −

2

2

11

The function g is defined for all values of x by

2

g : x ↦ 5 - x

Find fg

–1 in the form f

–1 : x ↦ ...

The function g is defined for all values of x by

2

g : x ↦ 5 - x

Express the inverse function f

–1

The function g is defined for all values of x by

2

g : x ↦ 5 - x

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

The function g is defined for all values of x by

2

g : x ↦ 5 - x

Express ff(x) in terms of x giving your answer as a single fraction in its simplest form.

The function h is defined for all values of x by

h : x ↦ x(x + 1)

The function m is defined for all values of x by

m : x ↦ ax + b

where a and b are constants such that a > 0 and b > 0

Given that hm(x) = 3(x + 1)(3x + 2) for all values of x

The function g is defined for all values of x by

2

g : x ↦ 5 - x

find the value of a and the value of b

Question 12 continued

Question 12 continued