January 2021 · Paper 2 (4MB1/02) (Edexcel IGCSE Maths): Exam Questions

The following formula can be used to change a temperature f degrees Fahrenheit to a

temperature c degrees Celsius.

(

)

f −

c = 5

32

9

(

)

f −

Make f the subject of c = 5

32

9

Sean and Kate measure the temperature of a heated iron bar.

Sean measures the temperature of the iron bar as x degrees Fahrenheit.

Kate measures the temperature of the iron bar as y degrees Celsius.

Given that x = 2y ,

The following formula can be used to change a temperature f degrees Fahrenheit to a

temperature c degrees Celsius.

(

)

f −

c = 5

32

9

(

)

f −

find the temperature, in degrees Fahrenheit, of the iron bar.

Question 1 continued

The Earth is assumed to move around the Sun in a circular orbit of radius 1.5$\times$108 km.

Assuming that the Earth takes 365 days to complete one orbit of the Sun,

calculate the average speed, in m/s to 3 significant figures, of the Earth as it orbits the Sun.

Question 2 continued

T

Diagram NOT

S

accurately drawn

50 mm

40 mm

O

R

60 mm

Q

Figure 1

Figure 1 shows circle QRST with centre O.

SQ is a diameter of the circle.

QR = 60 mm RS = 40 mm ST = 50 mm

Without using a calculator, find the exact length, in mm, of QT.

Give your answer in the form a b where a is an integer and b is a prime number.

Show your working clearly.

Question 3 continued

Over the course of a week of seven days, Alan plays a series of games.

He plays exactly one game each day.

On Sunday, the probability that Alan wins his game is 1

2

On a day other than Sunday, the probability that Alan wins his game is 1

3

The incomplete probability tree diagram below is to give information about Alan’s result

on a randomly chosen day in a week of seven days.

Complete the probability tree diagram below.

Day

Alan’s result

Alan wins

Sunday

Alan does not win

Alan wins

Not Sunday

Alan does not win

Over the course of a week of seven days, Alan plays a series of games.

He plays exactly one game each day.

On Sunday, the probability that Alan wins his game is 1

2

On a day other than Sunday, the probability that Alan wins his game is 1

3

The incomplete probability tree diagram below is to give information about Alan’s result

on a randomly chosen day in a week of seven days.

Find the expected number of games Alan will win in a week of seven days.

Question 4 continued

E is the universal set and A, B and C are three sets.

Here is information about these sets.

n ( A ) = 45

n ( B ) = 48

n ( C ) = 55

n ( A ∩ B ) = 24

n ( A ∩ C ) = 25

n ( B ∩ C ) = 27

n ( A ∩ B ∩ C ) = x

n ( A ' ∩ B ' ∩ C ' ) = y

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

each appropriate subset, in terms of x or y.

E

A

B

C

Given that n(E ) = 100

E is the universal set and A, B and C are three sets.

Here is information about these sets.

n ( A ) = 45

n ( B ) = 48

n ( C ) = 55

n ( A ∩ B ) = 24

n ( A ∩ C ) = 25

n ( B ∩ C ) = 27

n ( A ∩ B ∩ C ) = x

n ( A ' ∩ B ' ∩ C ' ) = y

find an expression for y in terms of x.

Give your answer in its simplest form.

E is the universal set and A, B and C are three sets.

Here is information about these sets.

n ( A ) = 45

n ( B ) = 48

n ( C ) = 55

n ( A ∩ B ) = 24

n ( A ∩ C ) = 25

n ( B ∩ C ) = 27

n ( A ∩ B ∩ C ) = x

n ( A ' ∩ B ' ∩ C ' ) = y

Using your Venn diagram and your answer to part (b), find the greatest possible

value of x.

Give reasons for your answer.

An element is selected at random from the 100 elements in the universal set.

E is the universal set and A, B and C are three sets.

Here is information about these sets.

n ( A ) = 45

n ( B ) = 48

n ( C ) = 55

n ( A ∩ B ) = 24

n ( A ∩ C ) = 25

n ( B ∩ C ) = 27

n ( A ∩ B ∩ C ) = x

n ( A ' ∩ B ' ∩ C ' ) = y

Find the probability that this element is in the set ( B ∩ C ' ) ∪ ( B ' ∩ C ).

Question 5 continued

Solve the inequality 3x + 5 > 7x − 9

Represent your solution on the number line on the next page.

Solve the inequality x2 + 5x − 6 ≥ 0

Represent your solution on the number line on the next page.

Write down the set of values for which

both 3x + 5 > 7x − 9 and x2 + 5x − 6 ≥ 0

Question 6 continued

Given that

b and b is inversely proportional to c3

a is inversely proportional to

complete the following table.

Question 7 continued

B

Diagram NOT

accurately drawn

8 cm

6 cm

A

C

E

D

Figure 2

Figure 2 shows a kite ABCD in which

AB = 6 cm BC = 8 cm ∠ABC = 90°

AEC and BED are straight lines.

Calculate the length, in cm, of AC.

B

8 cm

6 cm

A

C

E

D

Figure 2

Figure 2 shows a kite ABCD in which

AB = 6 cm BC = 8 cm ∠ABC = 90°

AEC and BED are straight lines.

Calculate the area, in cm², of ABCD.

B

Diagram NOT

accurately drawn

8 cm

6 cm

A

C

E

D

Figure 2

Figure 2 shows a kite ABCD in which

AB = 6 cm BC = 8 cm ∠ABC = 90°

AEC and BED are straight lines.

Show that BE = 4.8 cm

B

Diagram NOT

accurately drawn

8 cm

6 cm

A

C

E

D

Figure 2

Figure 2 shows a kite ABCD in which

AB = 6 cm BC = 8 cm ∠ABC = 90°

AEC and BED are straight lines.

Prove that triangle ABE is similar to triangle BCE.

Question 8 continued

The points with coordinates (1, 2), (1, 5) and (3, 2) are the vertices of triangle A.

On the grid, draw and label triangle A.

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

The points with coordinates (1, 2), (1, 5) and (3, 2) are the vertices of triangle A.

On the grid, draw and label triangle B.

Triangle C is the image of triangle A under the transformation with the matrix M where

−

0

1

M =

1

0

1

1

3

The points with coordinates (1, 2), (1, 5) and (3, 2) are the vertices of triangle A.

Find the matrix product M

2

5

2

The points with coordinates (1, 2), (1, 5) and (3, 2) are the vertices of triangle A.

Hence, on the grid, draw and label triangle C.

The points with coordinates (1, 2), (1, 5) and (3, 2) are the vertices of triangle A.

Describe fully the single transformation that maps triangle B onto triangle C.

The single transformation that maps triangle B onto triangle C is represented by the

matrix N

The points with coordinates (1, 2), (1, 5) and (3, 2) are the vertices of triangle A.

State, giving a reason, the matrix N2

Question 9 continued

y

x

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

Question 9 continued

Question 9 continued

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

y

x

B

Diagram NOT

accurately drawn

N

P

A

O

M

Figure 3

→ = 12a and OB

→ = 6b

Figure 3 shows the triangle OAB where OA

M is the midpoint of OA and N is the midpoint of AB.

The point P on BM is such that BP : BM = 2 : 3

Simplifying your answer, find, in terms of a and b

→

BM

B

Diagram NOT

accurately drawn

N

P

A

O

M

Figure 3

→ = 12a and OB

→ = 6b

Figure 3 shows the triangle OAB where OA

M is the midpoint of OA and N is the midpoint of AB.

The point P on BM is such that BP : BM = 2 : 3

OP

B

Diagram NOT

accurately drawn

N

P

A

O

M

Figure 3

→ = 12a and OB

→ = 6b

Figure 3 shows the triangle OAB where OA

M is the midpoint of OA and N is the midpoint of AB.

The point P on BM is such that BP : BM = 2 : 3

Hence show that O, P and N are collinear.

Given that | a | = | b | = 1 cm and that ∠AOB = 70°

B

Diagram NOT

accurately drawn

N

P

A

O

M

Figure 3

→ = 12a and OB

→ = 6b

Figure 3 shows the triangle OAB where OA

M is the midpoint of OA and N is the midpoint of AB.

The point P on BM is such that BP : BM = 2 : 3

find the length, in cm to 3 significant figures, of OP.

[ Cosine rule: a2 = b2 + c2 − 2bc cos A ]

Question 10 continued

Question 10 continued

Question 10 continued

The equation of a curve is y = f (x) where f (x) = x3 − 10x2 + 20

Complete the table of values for y = x3 − 10x2 + 20

Give your values of y to one decimal place where necessary.

The equation of a curve is y = f (x) where f (x) = x3 − 10x2 + 20

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

form a smooth curve.

A curve C has equation y = g (x) where B = g (x) and d

B

x = f (x)

d

The curve C has two turning points in −2 ≤ x ≤ 3

The equation of a curve is y = f (x) where f (x) = x3 − 10x2 + 20

Using your graph, find the x coordinates of these two turning points on the curve C.

The equation of a curve is y = f (x) where f (x) = x3 − 10x2 + 20

Referring to your graph, determine which of these two turning points is a maximum

and which is a minimum.

You should explain your reasoning clearly.

Question 11 continued

y

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

Question 11 continued

Question 11 continued

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

y

Indre buys 1000 Hungarian dolls in Budapest to sell in Austria.

She pays in Hungarian forints.

Indre pays 1900 forints for each small doll she buys.

She pays 10 300 forints for each large doll she buys.

The number of small dolls that Indre buys is 4 times the number of large dolls that she buys.

Calculate the total cost, in forints, of the 1000 dolls that Indre buys.

Indre has to pay 100 euros to transport the dolls from Hungary so that she can sell them

in Austria.

Initially the price of each small doll that Indre sells is 8 euros and the price of each large

doll that Indre sells is 40 euros.

She sells 80% of the small dolls and 7

8 of the large dolls at these prices.

Indre then reduces the price of each of her remaining dolls by 40%

She sells all of the remaining dolls.

When Indre bought the dolls, the exchange rate was 1 euro = 327.6 forints.

Indre buys 1000 Hungarian dolls in Budapest to sell in Austria.

She pays in Hungarian forints.

Indre pays 1900 forints for each small doll she buys.

She pays 10 300 forints for each large doll she buys.

The number of small dolls that Indre buys is 4 times the number of large dolls that she buys.

Calculate the total profit, in euros to 2 decimal places, that Indre made by selling all

1000 dolls.

Indre buys 1000 Hungarian dolls in Budapest to sell in Austria.

She pays in Hungarian forints.

Indre pays 1900 forints for each small doll she buys.

She pays 10 300 forints for each large doll she buys.

The number of small dolls that Indre buys is 4 times the number of large dolls that she buys.

Calculate the percentage profit, to 3 significant figures, that Indre made.

Indre buys 1000 Hungarian dolls in Budapest to sell in Austria.

She pays in Hungarian forints.

Indre pays 1900 forints for each small doll she buys.

She pays 10 300 forints for each large doll she buys.

The number of small dolls that Indre buys is 4 times the number of large dolls that she buys.

State how the percentage profit in part (c) (i) would be affected if the total profit

calculated in part (b) had been in forints.

Question 12 continued

Question 12 continued