June 2020 · Paper 2 (4MB1/02) (Edexcel IGCSE Maths): Exam Questions

A

Diagram NOT

accurately drawn

x°

9.3 cm

5 cm

10.8 cm

124°

B

C

y°

D

Figure 1

Figure 1 shows a quadrilateral ABCD.

AB = 9.3 cm AC = 5 cm AD = 10.8 cm

∠ACD = 124° ∠ACB = 90° ∠CAB = x° ∠ADC = y°

Calculate to one decimal place,

the value of x,

A

Diagram NOT

accurately drawn

x°

9.3 cm

5 cm

10.8 cm

124°

B

C

y°

D

Figure 1

Figure 1 shows a quadrilateral ABCD.

AB = 9.3 cm AC = 5 cm AD = 10.8 cm

∠ACD = 124° ∠ACB = 90° ∠CAB = x° ∠ADC = y°

Calculate to one decimal place,

the value of y.

a

b

c

=

=

Sine rule:

A

B

C

sin

sin

sin

Question 1 continued

On the grid below, by drawing suitable straight lines and using shading, show the

region R that satisfies the inequalities

2x + 3y ≥ 6 1 ≤ x ≤ 3 y ≤ 4

Label the region R.

y

5

x

The point P with coordinates (x, y) lies in the region that satisfies the inequalities

2x + 3y > 6 1 < x < 3 y < 4

Given that x and y are integers,

write down the coordinates of all possible points P.

Question 2 continued

Express (5x - 6)$\div$25

36

1

2

−

as a single fraction in its simplest form.

x

x

3

2

Show clear algebraic working.

Question 3 continued

A

9 cm

9 cm

10 cm

B

C

Figure 2

Figure 2 shows triangle ABC.

AB = 9 cm AC = 9 cm BC = 10 cm

Calculate the area, in cm² to one decimal place, of triangle ABC.

Figure 3 shows two solid right prisms, each of length 7 cm.

One of the prisms has triangle ABC as a cross section of the prism.

The other prism has trapezium DEFG as a cross section of the prism.

Diagram NOT

A

accurately drawn

F

E

5.5 cm

9 cm

9 cm

4.5 cm

7 cm

D

G

7 cm

10 cm

B

C

Figure 3

In trapezium DEFG,

DE = 4.5 cm

FG = 5.5 cm

The perimeter of trapezium DEFG is equal to the perimeter of triangle ABC.

A

9 cm

9 cm

10 cm

B

C

Figure 2

Figure 2 shows triangle ABC.

AB = 9 cm AC = 9 cm BC = 10 cm

Calculate the difference, in cm³ to one decimal place, between the volumes of the

two prisms.

Area of trapezium = 1

a

b h

2 (

)

Question 4 continued

Question 4 continued

Question 4 continued

Tahina travels to work by bus.

Her total bus fare last week was £12.50

This week her total bus fare has increased by 8%

Calculate her total bus fare for this week.

Tahina works in a kiosk selling hot drinks.

She sells coffee, tea and hot chocolate.

On Monday, Tahina sold a total of 378 hot drinks.

The numbers of cups of coffee, tea and hot chocolate she sold were in the ratios 5 : 3 : 1

Tahina travels to work by bus.

Her total bus fare last week was £12.50

This week her total bus fare has increased by 8%

Calculate the difference between the number of cups of coffee and the number of

cups of hot chocolate that Tahina sold on Monday.

On Monday, 3

14 of the number of cups of coffee Tahina sold were sold without milk.

Tahina travels to work by bus.

Her total bus fare last week was £12.50

This week her total bus fare has increased by 8%

Calculate the number of cups of coffee that Tahina sold without milk.

The cost of each cup of coffee that Tahina sells from the kiosk is £2.80

Tahina went on holiday to the USA and to Canada.

She bought a cup of coffee in the USA for $3.20

Using an exchange rate of £1 = $1.24

Tahina travels to work by bus.

Her total bus fare last week was £12.50

This week her total bus fare has increased by 8%

compare the cost of each cup of coffee sold from Tahina’s kiosk with the cost of the

cup of coffee that Tahina bought in the USA.

In Canada, Tahina bought a sandwich for 5.28 Canadian dollars.

Using exchange rates of

£1 = $1.24 and 1 Canadian dollar = $0.75

Tahina travels to work by bus.

Her total bus fare last week was £12.50

This week her total bus fare has increased by 8%

convert 5.28 Canadian dollars to pounds (£)

Give your answer to 2 decimal places.

Question 5 continued

Question 5 continued

Question 5 continued

Solve the simultaneous equations

x2 + y2 = 26

2x + y = 9

Show clear algebraic working.

Question 6 continued

10b

A

C

4a

Diagram NOT

accurately drawn

O

B

6b

Figure 4

Figure 4 shows a trapezium OACB.

→ = 4a OB

→ = 6b AC

→ = 10b

OA

P is the point on AB such that OPC is a straight line.

→ in terms of a and b.

Find an expression for PC

Give your answer in its simplest form.

Question 7 continued

The diagram shows kite A.

Kite B is the image of kite A under a reflection in the line with equation y = –1

On the grid opposite, draw and label kite B.

Kite A is transformed to kite C by a reflection in the line with equation x = 4 followed by

the translation −

8

−

6

Kite C is the image of kite B under a rotation through 180° about the point P.

The diagram shows kite A.

Kite B is the image of kite A under a reflection in the line with equation y = –1

On the grid opposite, draw and label kite C.

The diagram shows kite A.

Kite B is the image of kite A under a reflection in the line with equation y = –1

Find the coordinates of P.

−

−

0

1

0

1

M =

N =

−

2

0

1

0

Kite A is transformed to kite D under the combined transformation with matrix MN.

The diagram shows kite A.

Kite B is the image of kite A under a reflection in the line with equation y = –1

On the grid opposite, draw and label kite D.

D

Given that area of kite

A = k

area of kite

The diagram shows kite A.

Kite B is the image of kite A under a reflection in the line with equation y = –1

find the value of k.

Question 8 continued

y

x

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

Question 8 continued

Question 8 continued

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

y

x

90 students from a sixth form college were each asked the following question.

“Do you study any of Biology (B), Chemistry (C) or Physics (P)?”

Of these 90 students

7 study all three subjects

15 study Biology and Chemistry

20 study Chemistry and Physics

37 study Chemistry

14 study Biology only

15 study Physics only

The number of these students who study Biology and Physics but not Chemistry is three

times the number of these students who study none of these three subjects.

Let x be the number of these students who study none of these three subjects.

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

appropriate subset, in terms of x where necessary.

E

C

B

P

90 students from a sixth form college were each asked the following question.

“Do you study any of Biology (B), Chemistry (C) or Physics (P)?”

Of these 90 students

7 study all three subjects

15 study Biology and Chemistry

20 study Chemistry and Physics

37 study Chemistry

14 study Biology only

15 study Physics only

The number of these students who study Biology and Physics but not Chemistry is three

times the number of these students who study none of these three subjects.

Let x be the number of these students who study none of these three subjects.

Find the value of x.

90 students from a sixth form college were each asked the following question.

“Do you study any of Biology (B), Chemistry (C) or Physics (P)?”

Of these 90 students

7 study all three subjects

15 study Biology and Chemistry

20 study Chemistry and Physics

37 study Chemistry

14 study Biology only

15 study Physics only

The number of these students who study Biology and Physics but not Chemistry is three

times the number of these students who study none of these three subjects.

Let x be the number of these students who study none of these three subjects.

n(B¢ ∩ C)

90 students from a sixth form college were each asked the following question.

“Do you study any of Biology (B), Chemistry (C) or Physics (P)?”

Of these 90 students

7 study all three subjects

15 study Biology and Chemistry

20 study Chemistry and Physics

37 study Chemistry

14 study Biology only

15 study Physics only

The number of these students who study Biology and Physics but not Chemistry is three

times the number of these students who study none of these three subjects.

Let x be the number of these students who study none of these three subjects.

n(B ∪ C ∪ P)

90 students from a sixth form college were each asked the following question.

“Do you study any of Biology (B), Chemistry (C) or Physics (P)?”

Of these 90 students

7 study all three subjects

15 study Biology and Chemistry

20 study Chemistry and Physics

37 study Chemistry

14 study Biology only

15 study Physics only

The number of these students who study Biology and Physics but not Chemistry is three

times the number of these students who study none of these three subjects.

Let x be the number of these students who study none of these three subjects.

n(B ∩ C ∩ P¢)

One of the students is to be chosen at random.

Given that this student studies Chemistry,

90 students from a sixth form college were each asked the following question.

“Do you study any of Biology (B), Chemistry (C) or Physics (P)?”

Of these 90 students

7 study all three subjects

15 study Biology and Chemistry

20 study Chemistry and Physics

37 study Chemistry

14 study Biology only

15 study Physics only

The number of these students who study Biology and Physics but not Chemistry is three

times the number of these students who study none of these three subjects.

Let x be the number of these students who study none of these three subjects.

find the probability that this student also studies Physics.

Question 9 continued

The function g is such that

g : x ↦ 12

x −

3

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

The function h is defined for all values of x by

h : x ↦ x2 + 4

The function g is such that

g : x ↦ 12

x −

3

Write down the range of h.

The function g is such that

g : x ↦ 12

x −

3

Find h(–9)

The function g is such that

g : x ↦ 12

x −

3

Find hg

The function g is such that

g : x ↦ 12

x −

3

Express the inverse function g–1 in the form $g^{-1}$ : x ↦ ...

x

x

−

The function g is such that

g : x ↦ 12

x −

3

Show that hg(x) can be written as 4 45

(

6

)

2

x

−

3

(

)

2

The function g is such that

g : x ↦ 12

x −

3

Solve hg(x) = 5

Show clear algebraic working.

Question 10 continued

Question 10 continued

Question 10 continued

Complete the table of values for y = 2x3 - 3x + 4

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

smooth curve.

By drawing on the grid a suitable tangent to the curve, find an estimate, to the nearest

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

Use your graph to find the range of values of x, in –2.5 ≤ x ≤ 2.5, for which

2x3 - 3x + 4 > 5x

Question 11 continued

y

30

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

30

x

Harvey has two bags of counters, bag A and bag B.

Bag A contains 8 red counters, 3 orange counters and 4 yellow counters only.

Bag B contains 3 red counters, 2 orange counters and 5 green counters only.

Harvey takes at random one counter from bag A and one counter from bag B.

Complete the probability tree diagram on the opposite page.

Harvey has two bags of counters, bag A and bag B.

Bag A contains 8 red counters, 3 orange counters and 4 yellow counters only.

Bag B contains 3 red counters, 2 orange counters and 5 green counters only.

Harvey takes at random one counter from bag A and one counter from bag B.

Calculate the probability that the two counters taken have different colours.

Harvey replaces the counters into the bags from which he took the counters.

Chen has a bag, bag C, that contains 10 red counters and x orange counters only.

Chen takes at random one counter from bag A, one counter from bag B and one counter

from bag C.

The probability that all three counters that Chen takes have the same colour is 1

15

Harvey has two bags of counters, bag A and bag B.

Bag A contains 8 red counters, 3 orange counters and 4 yellow counters only.

Bag B contains 3 red counters, 2 orange counters and 5 green counters only.

Harvey takes at random one counter from bag A and one counter from bag B.

Find the value of x.

Question 12 continued

Bag A

Bag B

red

red

orange

8

green

15

red

orange

orange

green

red

yellow

orange

green

Question 12 continued