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

Gary buys furniture and sells it in a shop.

In the shop on Monday, Gary has tables and chairs such that

number of tables : number of chairs = 2 : 7

Gary has 42 chairs in the shop on Monday.

Calculate the number of tables Gary has in the shop on Monday.

Gary buys a table for $240 and sells it for $276

Gary buys furniture and sells it in a shop.

In the shop on Monday, Gary has tables and chairs such that

number of tables : number of chairs = 2 : 7

Gary has 42 chairs in the shop on Monday.

Calculate the percentage profit from the sale of the table.

Gary buys some chairs and sells them for $513

Gary’s percentage profit from the sale of the chairs is 35%

Gary buys furniture and sells it in a shop.

In the shop on Monday, Gary has tables and chairs such that

number of tables : number of chairs = 2 : 7

Gary has 42 chairs in the shop on Monday.

Calculate the price at which Gary bought the chairs.

The cost of a table that Gary buys is $732

An identical table costs 684 euros in France.

Using the exchange rate $1 = 0.95 euros

Gary buys furniture and sells it in a shop.

In the shop on Monday, Gary has tables and chairs such that

number of tables : number of chairs = 2 : 7

Gary has 42 chairs in the shop on Monday.

find the difference in the costs of the tables.

State whether your answer is in euros or $.

Question 1 continued

C

D

B

125°

125°

125°

125°

E

Diagram NOT

F

A

accurately drawn

L

y°

G

K

H

J

I

Figure 1

Figure 1 shows a hexagon ABCDEL and a regular octagon EFGHIJKL

125°

BAL

ABC

CDE

DEL

y°

BCD

ALE

ALK

Calculate the value of y

A different regular polygon has T sides and is such that

°

°

x

x

an interior angle

an exterior angle

(

10

25

)

(

7

83

)

C

D

B

125°

125°

125°

125°

E

Diagram NOT

F

A

accurately drawn

L

y°

G

K

H

J

I

Figure 1

Figure 1 shows a hexagon ABCDEL and a regular octagon EFGHIJKL

125°

BAL

ABC

CDE

DEL

y°

BCD

ALE

ALK

Calculate the value of T

[Sum of interior angles of polygon

right angles]

n

(

2

4

)

Question 2 continued

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

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

Triangle A is transformed to triangle C by a reflection in the line with equation y 1

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

On the grid, draw and label triangle C

Triangle A is transformed to triangle D by an enlargement with centre (0, 3) and

scale factor 2

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

On the grid, draw and label triangle D

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

M



2

1





0

2

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

On the grid, draw and label triangle E

Question 3 continued

y

7

x

−7

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

Question 3 continued

Question 3 continued

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

y

7

x

−7

Solve the inequality 4

x +

3

31

Solve the inequality 1

x

2

3

21

Hence represent on the number line opposite, the set of values of x for which

≤

and 1

x +

x

4

3

31

2

3

21

Question 4 continued

x

0

3

4

5

6

7

8

9

−2

−1

1

2

10

Complete the table of values for y

x

x

3

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 on your grid, find estimates to one decimal place,

in the range −2

2

for the solutions of the equation 2

3x

x

x

5

3

2

Question 5 continued

y

x

80 gardeners were asked if they grow potatoes (P), carrots (C) or lettuce (L)

Of these gardeners

9 grow potatoes, carrots and lettuce

17 grow potatoes and carrots

23 grow carrots and lettuce

19 grow potatoes and lettuce

48 grow carrots

49 grow lettuce

2 grow none of these three crops

Using this information, complete the Venn diagram below to show the number of

gardeners in each subset.

E

P

C

L

80 gardeners were asked if they grow potatoes (P), carrots (C) or lettuce (L)

Of these gardeners

9 grow potatoes, carrots and lettuce

17 grow potatoes and carrots

23 grow carrots and lettuce

19 grow potatoes and lettuce

48 grow carrots

49 grow lettuce

2 grow none of these three crops

Find n(C ∩ L' )

One of the gardeners is chosen at random.

Given that this gardener grows carrots,

80 gardeners were asked if they grow potatoes (P), carrots (C) or lettuce (L)

Of these gardeners

9 grow potatoes, carrots and lettuce

17 grow potatoes and carrots

23 grow carrots and lettuce

19 grow potatoes and lettuce

48 grow carrots

49 grow lettuce

2 grow none of these three crops

find the probability that this gardener also grows lettuce.

Question 6 continued

5

A

C













14

8

2

4

2

A

B

Find 4

2

5

A

C













14

8

2

4

2

A

B

Find AC



1

0

5

A

C













14

8

2

4

2

A

B

Find the matrix D such that A

D

I

I =

1

2

where





0

1

d

b

a

b







1





The inverse of matrix

is





c

a

c

d



ad

bc







Question 7 continued

Aalia delivers letters and parcels.

Last week Aalia worked for 5 days and wrote down 5 integers that represent

the distance, in miles, she drove each day.

For these integers

the mode is 15

the median is 16

the largest − the smallest = 7

Find 5 integers that Aalia could have written down.

Aalia delivers letters and parcels.

Aalia has 8 letters to deliver to Tom.

The mean weight of the 8 letters is 104 grams.

5 of the letters are each of weight 89 grams.

The mean weight of the remaining letters is A grams.

Work out the value of A

The histogram shows information about the weights of all the parcels Aalia has in her

delivery van on Friday.

75 of the parcels in the van each have a weight between 2 kg and 6 kg.

Aalia takes 2 parcels at random from the van.

Aalia delivers letters and parcels.

Find an estimate for the probability that both parcels weigh more than 4 kg.

Q

Diagram NOT

accurately drawn

P

160°

R

37°

O

T

Figure 2

Figure 2 shows the points P, Q, R and T on a circle centre O

POR

ORT

160

37

Work out the size, in degrees, of ∠PTR

Q

Diagram NOT

accurately drawn

P

160°

R

37°

O

T

Figure 2

Figure 2 shows the points P, Q, R and T on a circle centre O

POR

ORT

160

37

Give a reason for your answer.

Q

P

160°

R

37°

O

T

Figure 2

Figure 2 shows the points P, Q, R and T on a circle centre O

POR

ORT

160

37

Work out the size, in degrees, of ∠TPO

Question 9 continued

The sector, OPQR, is cut out from the circle in Figure 2

A hollow right circular cone is formed by joining OP and OR together as shown in

Figure 3

O

Q

P

160°

P

R

R

Q

O

Figure 3

The curved surface area of the cone is 196

25 $\pi$ cm²

Q

P

160°

R

37°

O

T

Figure 2

Figure 2 shows the points P, Q, R and T on a circle centre O

POR

ORT

160

37

Calculate the volume, in cm³ to 3 significant figures, of the cone.



1

r h



2

Volume of cone



3



rl





Curved surface area of cone

Question 9 continued

Question 9 continued

f and g are two functions such that

where x >−1

f : x

x

x

↦

2

2

13

g : x

↦

x

2

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

f and g are two functions such that

where x >−1

f : x

x

x

↦

2

2

13

g : x

↦

x

2

Find f

f and g are two functions such that

where x >−1

f : x

x

x

↦

2

2

13

g : x

↦

x

2

Find the value of x for which g(x) = 5

f and g are two functions such that

where x >−1

f : x

x

x

↦

2

2

13

g : x

↦

x

2

Find fg

f and g are two functions such that

where x >−1

f : x

x

x

↦

2

2

13

g : x

↦

x

2

Find the value of x for which gf(x) = 4

Show your working clearly.

2 −

where x ≥ 1

The function h is such that h : x

x

x

−

↦5

10

4

f and g are two functions such that

where x >−1

f : x

x

x

↦

2

2

13

g : x

↦

x

2

Find the inverse of h(x) in the form h −1 :

x ↦

...





ac

b

b



4

2

ax

bx

c

a

x





2

The solutions of

0

where

0

are given by

a





2





Question 10 continued

Question 10 continued

Question 10 continued

Solve the simultaneous equations

5

x

y

x

y

xy

2

2

2

2

85

Show clear algebraic working.





ac

b

b



4

2

ax

bx

c

a

x





2

The solutions of

0

where

0

are given by

a





2





Question 11 continued

35

25

w

5

a



2

1

7 25

Find an expression for w in terms of a

Give your answer in the form na + m where n and m are integers.