June 2019 · Paper 2R (4MB1/02R) (Edexcel IGCSE Maths): Exam Questions

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

ℰ = {positive integers less than 13}

A = {multiples of 5}

B = {even numbers}

C = {factors of 8}

The Venn diagram below can be used to show these sets.

Complete the Venn diagram for the sets ℰ, A, B and C.

List the elements of the sets

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

ℰ = {positive integers less than 13}

A = {multiples of 5}

B = {even numbers}

C = {factors of 8}

The Venn diagram below can be used to show these sets.

B ∩ C

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

ℰ = {positive integers less than 13}

A = {multiples of 5}

B = {even numbers}

C = {factors of 8}

The Venn diagram below can be used to show these sets.

A ∪ B

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

ℰ = {positive integers less than 13}

A = {multiples of 5}

B = {even numbers}

C = {factors of 8}

The Venn diagram below can be used to show these sets.

(A ∪ B ∪ C)′

Find

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

ℰ = {positive integers less than 13}

A = {multiples of 5}

B = {even numbers}

C = {factors of 8}

The Venn diagram below can be used to show these sets.

n(B ∪ C)

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

ℰ = {positive integers less than 13}

A = {multiples of 5}

B = {even numbers}

C = {factors of 8}

The Venn diagram below can be used to show these sets.

n(B′ ∩ C′)

................................................................

Solve the inequality 6x + 10 > 2x + 2

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

Solve the inequality (4x + 3)(2x — 1) < (6x + 5)(x — 2)

Represent your solution on the same number line.

Write down the set of values for which

both $6x + 10 > 2x + 2$ and $(4x + 3)(2x - 1) < (6x + 5)(x - 2)$

-5 -4 -3 -2 -1 0 1 2 3 4 5

A bag contains 15 counters.

There are

5 orange counters

3 blue counters

7 white counters.

Priya takes at random 2 counters from the bag.

Complete the probability tree diagram.

First

Second

counter

counter

orange

blue

orange

3 fe)

white

orange

blue

blue

white

orange

white

blue

white

A bag contains 15 counters.

There are

5 orange counters

3 blue counters

7 white counters.

Priya takes at random 2 counters from the bag.

Calculate the probability that Priya takes 2 white counters.

A bag contains 15 counters.

There are

5 orange counters

3 blue counters

7 white counters.

Priya takes at random 2 counters from the bag.

Calculate the probability that the counters Priya takes are not of the same colour.

................................................................

The total amount of money that was spent last March by Marco’s family was $4200

The table below gives information about the amount Marco’s family spent on each of

four items last March.

Item Amount

healthcare $336

insurance $504

food $546

travel $630

housing

entertainment

other items

Calculate the percentage of the total amount that was spent on healthcare.

The amount spent on travel was divided between Marco’s car, his wife’s car and other

transport in the ratios 4 : 3 : 2

The total amount of money that was spent last March by Marco’s family was $4200

The table below gives information about the amount Marco’s family spent on each of

four items last March.

Item Amount

healthcare $336

insurance $504

food $546

travel $630

housing

entertainment

other items

Calculate the amount, in $, that was spent on Marco’s car.

The amount that was spent on food last March was 12% more than was spent on food

last February.

The total amount of money that was spent last March by Marco’s family was $4200

The table below gives information about the amount Marco’s family spent on each of

four items last March.

Item Amount

healthcare $336

insurance $504

food $546

travel $630

housing

entertainment

other items

Calculate the amount, in $, that was spent on food last February.

The amount of money spent on entertainment last March was 12.5% of the total amount

of money that was not spent on healthcare, insurance, food and travel.

The total amount of money that was spent last March by Marco’s family was $4200

The table below gives information about the amount Marco’s family spent on each of

four items last March.

Item Amount

healthcare $336

insurance $504

food $546

travel $630

housing

entertainment

other items

Calculate the amount, in $, that was spent on entertainment.

Marco draws a pie chart for the amounts his family spent on all the items last March.

The total amount of money that was spent last March by Marco’s family was $4200

The table below gives information about the amount Marco’s family spent on each of

four items last March.

Item Amount

healthcare $336

insurance $504

food $546

travel $630

housing

entertainment

other items

Calculate the size of the angle, in degrees, for insurance.

The angle in the pie chart for housing is 114°

The total amount of money that was spent last March by Marco’s family was $4200

The table below gives information about the amount Marco’s family spent on each of

four items last March.

Item Amount

healthcare $336

insurance $504

food $546

travel $630

housing

entertainment

other items

Calculate the amount, in $, that was spent on housing.

................................................................

Triangles A and B are drawn on the grid opposite.

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

Triangle A is reflected in the y-axis to give triangle C.

Triangles A and B are drawn on the grid opposite.

On the grid, draw and label triangle C.

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

(2 «0

M 0 2

Triangles A and B are drawn on the grid opposite.

On the grid, draw and label triangle D.

Triangle D is the image of triangle A under the transformation with matrix N.

Triangles A and B are drawn on the grid opposite.

Find the matrix N.

................................................................

U

<S =

Diagram NOT

accurately drawn

gj 140" OS R as

Sem an y : 12cm >

P 12cm Q 7

Figure 1

Figure 1 shows a right pentagonal prism, with a horizontal square base PORS of side 12cm.

YP =WQO=5cm

ZWXY = 140°

ZYPO = ZWOP = 90°

M is the midpoint of PO so that XM is an axis of symmetry of the pentagon.

Calculate the size, in degrees to one decimal place, of ZVMR.

U

<S =

Diagram NOT

accurately drawn

gj 140" OS R as

Sem an y : 12cm >

P 12cm Q 7

Figure 1

Figure 1 shows a right pentagonal prism, with a horizontal square base PORS of side 12cm.

YP =WQO=5cm

ZWXY = 140°

ZYPO = ZWOP = 90°

M is the midpoint of PO so that XM is an axis of symmetry of the pentagon.

Calculate the length, in cm to one decimal place, of PU.

................................................................

The equation of a curve is $y = 5 - \dfrac{x}{2} - x^2$

Complete the table of values for $y = 5 - \dfrac{x}{2} - x^2$

The equation of a curve is $y = 5 - \dfrac{x}{2} - x^2$

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

a smooth curve.

The equation of a curve is $y = 5 - \dfrac{x}{2} - x^2$

Using your curve, find an estimate of the maximum value, to one decimal place,

x

of y=5- a x?

The equation of a curve is $y = 5 - \dfrac{x}{2} - x^2$

Use your curve to find the range of values of x, to one decimal place, for which

5 - 5 -x?>3

x

The equation of a curve is $y = 5 - \dfrac{x}{2} - x^2$

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

for the solutions of the equation 3 — x — x? = 0

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20

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Question 7 continued

. 5 y

mM | EECCCEEEEREEEEECECEEE EEE EEE

<x SEREREE SERS BE Be ee ee eee 6 ERE SE SE ee Oe eee eee ee

z PEE EEE EEE CEE EEE EE EEE EEE EEE EEE EEE EEE ECEEEEEEEE EEE EEE EEE EEE EEE EEE EEE EEE

. BREESE SEES Pe Pe ee eee Ht 55 EERE BR Be ee ee ee eee

BREED BERGE PR Pe Pe Be Be Be Pe ee Be ee ee

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i EERE E BERG S SR PO Be Be Be ee ee Oe ee eee

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ERED BEERS PR Be ee ee ——- 34 BREED BRR BR Be Pe ee ee

owed BREESE Be ee ee ee eee ERE SR Pe ee ee eee

=m BREED SERGE CR Pe Pe Pe eB Be Pe ee eee ee

ERED BERS PR ee ee eee tt ERREE BERR PR ee Pe ee ee

a FEEEEEEEE EEE EEE EERE EERE EEE EEEEEEEEEEEEEEEEEEEEEHEEEEEEEEEEEEEE EEE EEE

The functions f and g are defined as

fixr3x-5

1

gixre

2x —3

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

The functions f and g are defined as

fixr3x-5

1

gixre

2x —3

Find gf

The function h is defined as

h:ixre where x # 3

x

x _

The functions f and g are defined as

fixr3x-5

1

gixre

2x —3

Solve fh(x) = 7

The functions f and g are defined as

fixr3x-5

1

gixre

2x —3

Express the inverse function h™! in the form ht! : x +>...

The functions f and g are defined as

fixr3x-5

1

gixre

2x —3

Solve the equation g(x) + h(x) = 1

Show your working clearly.

Give your solutions in the form a + Vb where a and b are integers.

—b+vVb? - we]

soto of ax? + bx +c = Oarex = 5

................................................................

A

Diagram NOT

accurately drawn

Figure 2

Figure 2 shows a solid right square-based pyramid with height 20cm.

The volume of the pyramid is 960 cm?

The pyramid is standing with its square base on a horizontal table.

Diagram NOT

accurately drawn

LD

Figure 3

The pyramid is divided into a smaller right square-based pyramid of height 10cm and a

frustum of the pyramid, as shown in Figure 3, by a horizontal cut.

Calculate the volume, in cm’, of the smaller pyramid.

A

Diagram NOT

accurately drawn

Figure 2

Figure 2 shows a solid right square-based pyramid with height 20cm.

The volume of the pyramid is 960 cm?

The pyramid is standing with its square base on a horizontal table.

Diagram NOT

accurately drawn

LD

Figure 3

The pyramid is divided into a smaller right square-based pyramid of height 10cm and a

frustum of the pyramid, as shown in Figure 3, by a horizontal cut.

Calculate the total surface area, in cm? to 3 significant figures, of the frustum of the pyramid.

................................................................

A particle, P, is moving along a straight line through the fixed point O.

The displacement, s metres, of P from O at time ¢ seconds is given by

s=f-7P —5t+ 121 t>0

Find the displacement, in metres, of P from O when P is instantaneously at rest.

................................................................

B ;

R

; —

A

Figure 4

Figure 4 shows triangle OAB in which OA =a and OB =b

. . . . =~ =~

P is the point on AB such that AP : PB=2: 1

Q is the point on OP such that OO : OP = 1 : 3

R is the point on OB such that RQA is a straight line.

Calculate, in its simplest form, the ratio OR : RB

................................................................