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

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

Write 3 3

as an ordinary number.

. ×

106

Elter Water is another lake and has a volume of 500 000 m³

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

Write 500 000 in standard form.

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

Calculate the difference, in standard form, between Windermere’s surface area and

Wastwater’s surface area.

volume of water in Thirlmere

Volume of water in Windermere

k

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

Work out the value of k

The area of circle C is equal to the surface area of Ullswater.

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

Find, in metres to 2 significant figures, the radius of C

106 where n is an integer.

x

n

4

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

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

Question 1 continued

B

Diagram NOT

accurately drawn

A

C

D

Figure 1

Figure 1 shows a kite ABCD where AB = BC

AB



x

y

cm

6

2

10



BC

x

y

cm

3

1



AD

x

y

cm

2

9

14



CD

x

y

cm

5

5

9

Calculate the length, in cm, of the perimeter of the kite.

Question 2 continued

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) $A \cap B$

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

(b) $A' \cap B$

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

(c) $(A \cup B)'$

x

x

10

3

3

3

1

Given that y

x

=

3

show that y

y

3

10

0

2

x

x

10

3

3

3

1

Given that y

x

=

3

Solve the equation y

y

3

10

0

2

1

1

x

x

10

3

3

3

1

Given that y

x

=

3

Hence find the solutions to x

x

10

3

3

3





b

b

ac

4

2

ax

bx

c

x

Solutions of

0

are

2





a

2









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.

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

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

Show your working clearly.

Question 5 continued

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

Write down the class interval that contains the median time.

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

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.

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

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.

Frequency

density

0

3

4

5

11

0

1

2

6

7

8

9

10

12

13

14

15

Time in minutes

There were 15 customers who spent between 5 and 10 minutes in the queue.

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

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

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)

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

Draw and label triangle C

The area of triangle A is x cm²

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

Find, in terms of x, the area in cm², of triangle C

y

1

M = 3

2



 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

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

draw and label triangle D

Show your working clearly.

Determinant of matrix a

b





ad

bc

 







c

d





Question 7 continued

y

x

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

Question 7 continued

Question 7 continued

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

y

x

Complete the table of values for y

x

x

4

4

2

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

form a smooth curve.

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

≤

≤

in the range −2

for the solutions of the equation x

x

x

x

5

4

4

2

1

2

By drawing a suitable straight line on your grid, find an estimate to the nearest

4 at the point

whole number, of the gradient of the curve y

x

x

4

2

where x 1

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

O

Diagram NOT

accurately drawn

C

E

B

D

A

Figure 2

→ = 4a and OB

→ = 3b

Figure 2 shows triangle OAB with OA

→ = 2b

The point C lies on OB such that OC

The point D is the midpoint of AB

The point E lies on AC such that OED is a straight line.

Find, in terms of a and b, simplifying your answer where possible,

→ (ii) AB

→ (iii) OD

→

CA

Given that CE

λ

O

C

E

B

D

A

Figure 2

→ = 4a and OB

→ = 3b

Figure 2 shows triangle OAB with OA

→ = 2b

The point C lies on OB such that OC

The point D is the midpoint of AB

The point E lies on AC such that OED is a straight line.

use a vector method to find the value of λ

→ = μOD

→ where μ 1 and AP

→ is parallel to OB

→

The point P is such that OP

Given that the area of triangle OCE is 8 cm²

O

C

E

B

D

A

Figure 2

→ = 4a and OB

→ = 3b

Figure 2 shows triangle OAB with OA

→ = 2b

The point C lies on OB such that OC

The point D is the midpoint of AB

The point E lies on AC such that OED is a straight line.

find the area, in cm², of triangle APE

Question 9 continued

Question 9 continued

Question 9 continued

Diagram NOT

E

accurately drawn

F

D

A

H

4 m

2.4 m

G

1.5 m

B

C

3 m

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

90

Calculate the volume, in m³, of the prism.

Diagram NOT

E

accurately drawn

F

D

A

H

4 m

2.4 m

G

1.5 m

B

C

3 m

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

90

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

Diagram NOT

E

accurately drawn

F

D

A

H

4 m

2.4 m

G

1.5 m

B

C

3 m

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

90

Calculate the length, in metres to 3 significant figures, of AH

The point P lies on the line GH such that GP = 2

GH

3

The point Q lies on the line BC such that BQ = 2

BC

3

Diagram NOT

E

accurately drawn

F

D

A

H

4 m

2.4 m

G

1.5 m

B

C

3 m

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

90

Calculate, in degrees to one decimal place, ∠APQ

1



Area of trapezium

a

b h

2 (

)





Question 10 continued

Question 10 continued

Question 10 continued

The function f is defined as f : x

x

x

↦2

3

Find f(−2)

x

The function f is defined as f : x

x

x

↦2

3

Find the value of x such that df

( )

= 0

x

d

x

7

The function g is defined as g : x

↦4

x

3

The function f is defined as f : x

x

x

↦2

3

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

The function f is defined as f : x

x

x

↦2

3

Find fg

The function h is such that

x

3

4

x > 1

gh(x)

x

1

The function f is defined as f : x

x

x

↦2

3

Find h(x) in its simplest form.

Show clear algebraic working.

Question 11 continued

Question 11 continued

Question 11 continued