November 2024 · Paper 2 (4MB1/02) (Edexcel IGCSE Maths): Exam Questions

Solve the simultaneous equations

x

y

3

5

7 5

.

x

y

7

6

3 9

.

Show clear algebraic working.

The line L with equation y

2 is drawn on the grid opposite.

2

x

On the grid opposite, draw the graph with equation x

4

y

for values of x from −4 to 6

The line L with equation y

2 is drawn on the grid opposite.

2

x

On the grid opposite, draw the graph with equation 3

3

y

x

for values of x from −4 to 6

The line L with equation y

2 is drawn on the grid opposite.

2

x

Show, by shading on the grid opposite, the region R defined by all of

the inequalities

≤

3

3

y

x

≥−

≤4

2

2

y

x

−

x

y

−

Label the region R

The point P with coordinates (x, y) lies in the region R

Given that y is an integer and P lies on the line with equation x = 1

The line L with equation y

2 is drawn on the grid opposite.

2

x

write down all the possible y coordinates of the point P

Question 2 continued

y

6

x

−4

E = {2, 3, 4, 5, 6, 7, 8, 9, 10}

P = {prime numbers}

E = {even numbers}

F = {factors of 36}

Write down all the elements of

′

E

E = {2, 3, 4, 5, 6, 7, 8, 9, 10}

P = {prime numbers}

E = {even numbers}

F = {factors of 36}

P

F

E = {2, 3, 4, 5, 6, 7, 8, 9, 10}

P = {prime numbers}

E = {even numbers}

F = {factors of 36}

E

F

∪

70 children were asked which flavours of ice cream they like from chocolate (C),

vanilla (V) and strawberry (S).

5 children like chocolate and vanilla and strawberry

15 like strawberry only

12 like chocolate only

8 like none of the flavours

6 like strawberry and vanilla

11 like chocolate and vanilla

21 like strawberry

35 like vanilla

E = {2, 3, 4, 5, 6, 7, 8, 9, 10}

P = {prime numbers}

E = {even numbers}

F = {factors of 36}

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

students in each appropriate subset.

E = {2, 3, 4, 5, 6, 7, 8, 9, 10}

P = {prime numbers}

E = {even numbers}

F = {factors of 36}

Find

n( )

C

E = {2, 3, 4, 5, 6, 7, 8, 9, 10}

P = {prime numbers}

E = {even numbers}

F = {factors of 36}

n C

V

S

One of the 70 children is chosen at random.

Given that this child likes vanilla

E = {2, 3, 4, 5, 6, 7, 8, 9, 10}

P = {prime numbers}

E = {even numbers}

F = {factors of 36}

find the probability that this child also likes chocolate.

Question 3 continued

E

C

V

S

Question 3 continued

Question 3 continued

D

Diagram NOT

accurately drawn

E

F

C

B

A

O

Figure 1

Figure 1 shows 3 sectors, OAF, OBE and OCD

The three sectors have the same centre O

OABC and OFED are straight lines.

80 and OD = 6 6. cm

DOC

Calculate the length, in cm to 3 significant figures, of the arc CD

The area of the shaded region ABEF is 5

12 of the area of sector OCD

D

E

F

C

B

A

O

Figure 1

Figure 1 shows 3 sectors, OAF, OBE and OCD

The three sectors have the same centre O

OABC and OFED are straight lines.

80 and OD = 6 6. cm

DOC

Calculate the area, in cm² to 3 significant figures, of the shaded region ABEF

Given that OA = 1 1. cm

D

Diagram NOT

accurately drawn

E

F

C

B

A

O

Figure 1

Figure 1 shows 3 sectors, OAF, OBE and OCD

The three sectors have the same centre O

OABC and OFED are straight lines.

80 and OD = 6 6. cm

DOC

calculate the length, in cm, of AB

Question 4 continued

A bag contains 8 red counters and 5 blue counters only.

Imran takes at random 2 counters from the bag.

Calculate the probability that these 2 counters are the same colour.

A box contains 11 black counters and w white counters only.

Nathalie takes at random 2 counters from the box.

The probability that these 2 counters are both white is 10

21

A bag contains 8 red counters and 5 blue counters only.

Imran takes at random 2 counters from the bag.

Calculate the value of w

Show all your working.





2

b

b

ac

4

2

ax

bx

c

x

Solutions of

0

are





a

2









Question 5 continued

h cm

r cm

Figure 2

Figure 2 shows a solid shape S, made by fixing a solid right circular cone to the flat

circular face of a solid hemisphere.

The centre of the base of the cone coincides with the centre of the hemisphere.

The base radius of the cone and the radius of the hemisphere are each r cm

The height of the cone is h cm

The total volume of S is 1660 cm³

the volume of the hemisphere : the total volume of S = 8 25

:

Find, in cm to 3 significant figures, the value of r

h cm

r cm

Figure 2

Figure 2 shows a solid shape S, made by fixing a solid right circular cone to the flat

circular face of a solid hemisphere.

The centre of the base of the cone coincides with the centre of the hemisphere.

The base radius of the cone and the radius of the hemisphere are each r cm

The height of the cone is h cm

The total volume of S is 1660 cm³

the volume of the hemisphere : the total volume of S = 8 25

:

Find, in cm to 3 significant figures, the value of h

1



2

r h

Volume of cone



3



4



3

r

Volume of sphere





3

Question 6 continued

B

Diagram NOT

accurately drawn

A

a

O

C

2b

Figure 3

Figure 3 shows quadrilateral OABC

1

= a

b

a

= 2b

3

2

= 3

5

The point D lies on OB such that

in terms of a and b

Find a simplified expression for

= k

such that

The point E lies on

Given that ADE is a straight line

B

Diagram NOT

accurately drawn

A

a

O

C

2b

Figure 3

Figure 3 shows quadrilateral OABC

1

= a

b

a

= 2b

3

2

= 3

5

The point D lies on OB such that

in terms of a and b

find the value of k

B

Diagram NOT

accurately drawn

A

a

O

C

2b

Figure 3

Figure 3 shows quadrilateral OABC

1

= a

b

a

= 2b

3

2

= 3

5

The point D lies on OB such that

in terms of a and b

find the ratio AD : DE in the form x : y where x and y are integers.

Question 7 continued

Question 7 continued

Question 7 continued

Chetan owns a fruit shop.

In January, Chetan sold 560 kg of citrus fruit.

In February, Chetan sold 518 kg of citrus fruit.

Calculate the percentage decrease in the weight of citrus fruit sold.

The table below shows the weight of citrus fruit, the weight of berries and the weight of

tropical fruit Chetan sold in March.

Chetan is going to draw a pie chart for this information.

Chetan owns a fruit shop.

In January, Chetan sold 560 kg of citrus fruit.

In February, Chetan sold 518 kg of citrus fruit.

Calculate the size, in degrees, of the angle of the sector in the pie chart for the

weight of berries sold in March.

The table below gives information about the weight, in kg, of berries sold on each of the

30 days in April.

Chetan owns a fruit shop.

In January, Chetan sold 560 kg of citrus fruit.

In February, Chetan sold 518 kg of citrus fruit.

Find the class interval that contains the median weight.

Chetan owns a fruit shop.

In January, Chetan sold 560 kg of citrus fruit.

In February, Chetan sold 518 kg of citrus fruit.

Calculate an estimate for the mean weight, in kg, of berries sold on each day

in April.

Question 8 continued

Chetan wants to buy 60 kg of apples for his shop from one of the following

online traders.

US traders

French traders

12 kg box of apples for $29.50

1.72 euros per kg of apples

Free delivery

Total delivery cost of 22.80 euros

Buy 4 boxes and get a 5th box free

Special offer of 15% off

the cost of apples and the cost

of delivery

Using an exchange rate of

$1 = 0.92 euros

Chetan owns a fruit shop.

In January, Chetan sold 560 kg of citrus fruit.

In February, Chetan sold 518 kg of citrus fruit.

compare the cost, including delivery, of 60 kg of apples bought from US traders

with the cost of 60 kg of apples bought from French traders.

State which of the traders is the cheaper when buying 60 kg of apples.

Show all your working.

Question 8 continued

Question 8 continued

The function f is defined for all values of x by

2 − ≥

f : x

x

x

↦3

8

0

Write down the range of f

The function f is defined for all values of x by

2 − ≥

f : x

x

x

↦3

8

0

Find f 2

The function g is defined by

2

where x ≥−1

g : x

x

x

↦2

4

3

The function h is defined by

2

where x ≥−1

h : x

x

x

↦3

6

2

Given that hg

1

x

6 1

.

The function f is defined for all values of x by

2 − ≥

f : x

x

x

↦3

8

0

find the value of x

Show all your working.

Question 9 continued

Question 9 continued

Question 9 continued

Complete the table of values for y

3

x

x

2

5

3

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 (at least 3 cm long) on the grid, find an estimate

to the nearest whole number, of the gradient of the curve at the point where x 2

By drawing a suitable straight line on the grid, find the range of values of x,

≤

≤

3x

for which 2

to one decimal place, in the interval −2 5

x

x

5

3

1

.

2 5

.

Question 10 continued

y

25

x

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

Question 10 continued

Question 10 continued

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

y

25

x

Triangle A and triangle D are drawn on the grid opposite.

Triangle A is transformed to triangle B under a rotation of 180° about the point

with coordinates (3, 1)

On the grid, draw and label triangle B

Triangle A is transformed to triangle C under a reflection in the line

with equation y 0 5.

Triangle A and triangle D are drawn on the grid opposite.

Triangle A is transformed to triangle B under a rotation of 180° about the point

with coordinates (3, 1)

On the grid, draw and label triangle C

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

2

0



M





0

2

Triangle A and triangle D are drawn on the grid opposite.

Triangle A is transformed to triangle B under a rotation of 180° about the point

with coordinates (3, 1)

On the grid, draw and label triangle E

Triangle A and triangle D are drawn on the grid opposite.

Triangle A is transformed to triangle B under a rotation of 180° about the point

with coordinates (3, 1)

Describe fully the single transformation that maps triangle A onto triangle E

Triangle A is transformed to triangle F under a rotation of 90°anticlockwise about

the origin.

k

Triangle F is transformed to triangle G under the matrix 7

2

2





2

4

Triangle G is the image of triangle A under the matrix N

1

3



1

Given that N

1

1





2

10

Triangle A and triangle D are drawn on the grid opposite.

Triangle A is transformed to triangle B under a rotation of 180° about the point

with coordinates (3, 1)

find the value of k

[Inverse of matrix a

b

d

b

1



 is

 ]

c

d

c

a

ad

bc

Question 11 continued

y

11

x

−5

Turn to page 35 for a spare grid if you need to redraw your triangles.

Question 11 continued

Question 11 continued

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

y

11

x

−5