R Y10 End of Year Exam ‘Review Exercise’ Academic€¦ · 30. r cm R cm Diagram accurately drawn NOT The diagram represents two metal spheres of different sizes. The radius of

Y10 End of Year Exam ‘Review Exercise’_Academic

1.

5 cm

12.5 cm

R

Q Px°

Diagram accurately drawn

NOT

PQR is a triangle.

Angle PQR = 90.

PQ = 12.5 cm.

QR = 5 cm.

Calculate the value of x.

Give your answer correct to 1 decimal place.

......................................... (Total 3 marks)

2. The diagram represents a vertical flagpole, AB.

The flagpole is supported by two ropes, BC and BD, fixed to the horizontal ground at C and at D.


NOT

12.8 m

42°A

B

C D6.8 m

AB = 12.8 m.

AC = 6.8 m.

Angle BDA = 42.

(a) Calculate the size of angle BCA.

Give your answer correct to 3 significant figures.

………………………… (3)

(b) Calculate the length of the rope BD.


………………………… m (3)

(Total 6 marks)

3. A lighthouse, L, is 3.2 km due West of a port, P.

A ship, S, is 1.9 km due North of the lighthouse, L.

(a) Calculate the size of the angle marked x.


x = ……………….. ° (3)

(b) Find the bearing of the port, P, from the ship, S.


…………………... (1)

4.

D = ut + kt2

u = 20

t = 1.2

k = –5

(a) Work out the value of D.

..................................... (2)

D = 50

t = 5

k = –5

(b) Work out the value of u. (2)

(c) Make u the subject of the formula

D = ut + kt2

u = ................................... (2)

(Total 6 marks) 5. You can use this rule to work out the number of minutes it takes to cook a turkey.

Multiply the turkey’s weight, in kg, by 40.

Then add 30.

A turkey’s weight is 4.5 kg.

Use the rule to work out the number of minutes it will take to cook this turkey. (Total 2 marks)

6. The fraction, p, of an adult’s dose of medicine which should be given to a child who weighs w kg is given by

the formula

200

203

wp

A child weighs 35 kg.

(a) Work out the fraction of an adult’s dose which should be given to this child.

Give you answer as a fraction in its simplest form.

……………………… (2)

(b) Use the formula 200

203

wp to find the weight of a child whose dose is the same as an adult’s dose.

……………………… kg (3)

(Total 5 marks) 7. Julie does a statistical experiment. She throws a dice 600 times.

She scores six 200 times.

(a) Is the dice fair? Explain your answer. (1)

Julie then throws a fair red dice once and a fair blue dice once.

(b) Complete the probability tree diagram to show the outcomes.

Label clearly the branches of the probability tree diagram.

The probability tree diagram has been started in the space below.

16

RedDice

BlueDice

Six

NotSix

(3)

(c) (i) Julie throws a fair red dice once and a fair blue dice once. Calculate the probability that Julie

gets a six on both the red dice and the blue dice.

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

(ii) Calculate the probability that Julie gets at least one six.

..................................... (5)

(Total 9 marks)

8. The probability that a biased dice will land on a four is 0.2

Pam is going to roll the dice 200 times.

(a) Work out an estimate for the number of times the dice will land on a four.

......................... (Total 2 marks)

9.

x°

y°

126°

P Q

RDiagram accurately drawn

NOT

PQ is a straight line.

(a) Work out the size of the angle marked x°. (1)

(b) (i) Work out the size of the angle marked y°.

(ii) Give reasons for your answer. (3)

(Total 4 marks) 10.

y°

x°


NOT

This is part of the design of a pattern found at the theatre of Diana at Alexandria.

It is made up of a regular hexagon, squares and equilateral triangles.

(a) Write down the size of the angle marked x°. (1)

(b) Work out the size of the angle marked y°. (2)

The area of each equilateral triangle is 2 cm2.

(c) Work out the area of the regular hexagon.

.....................................cm2

(2)

(Total 5 marks)

11. The diagram shows a 5-sided shape.

All the sides of the shape are equal in length.

x°

y°


NOT

(a) (i) Find the value of x.

x = ………………..

(ii) Give a reason for your answer. (2)

(b) Work out the value of y.

y = ……………….. (2)

(Total 4 marks) 12.

D E F G

A B C

38º

xº yº

Diagram NOT accurately drawn

ABC is parallel to DEFG.

BE = EF.

Angle ABE = 38°.

(a) (i) Find the value of x.

x = .............................

(ii) Give a reason for your answer. (2)

(b) Work out the value of y.

y = ............................. (2)

(Total 4 marks)

13.

A

D

G

F

CB

56º

x

y

E


BEG and CFG are straight lines.

ABC is parallel to DEF.

Angle ABE = 56°

EF = EG

(a) (i) Write down the size of the angle marked x

x = ………..…..°

(ii) Give a reason for your answer.

..................................................................................................................................... (2)

(b) Work out the size of the angle marked y

Give reasons for your answer.

y = ……………..° (3)

(Total 5 marks) 14.

3 cm

3 cm

2 c

m

Diagrams NOT accurately drawn

This cuboid is made up of a number of small cubes.

Each small cube has side 1 cm.

1 cm1 cm

1 cm

Work out the volume of the cuboid (Total 2 marks)

15.

12 cm

4 cm

10 cm


The diagram shows a box in the shape of a cuboid.

(a) Work out the volume of the box.

…………………………. cm3

(2) The box is full of sugar lumps.

Each sugar lump is in the shape of a cuboid.

Each lump is 1 cm by 1 cm by 2 cm.

(b) Work out the number of sugar lumps in the box.

(1)

(Total 3 marks)

16. Ben fills a container with boxes.

Each box is a cube of side 0.5 m.

The container is a cuboid of

length 9 m,

width 4 m and

height 3 m.

Work out how many boxes will fit exactly into the container.

……………… (Total 3 marks)

17. Here are the plan and front elevation of a prism.

The front elevation shows the cross section of the prism.

Plan

Front elevation

(a) On the grid below, draw a side elevation of the prism.

(3)

(b) In the space below, draw a 3-D sketch of the prism. (2)

18. The diagram shows a solid object.

(a) In the space below, sketch the front elevation from the direction marked with an arrow. (2)

(b) In the space below, sketch the plan of the solid object. (2)

(Total 4 marks)

19. Here are the plan, front elevation and side elevation of a 3-D shape.

plan

frontelevation

sideelevation

In the space below, draw a sketch of the 3-D shape. (Total 2 marks)

20.

12 cm

Calculate the area of a circle with diameter 12 cm.

……………………….. (Total 3 marks)

21. Jerry has a new garden roller.

Part of the roller is a cylinder.

The diameter of the cylinder is 0.7 m.

Jerry pushes the roller along.

The cylinder goes around exactly 16 times.

Picture NOT accurately drawn

Work out how far the roller moves.


……………. m (Total 3 marks)

22. The radius of a circle is 6.4 cm.

Work out the circumference of this circle.

Give your answer correct to 1 decimal place.

6.4 cm


....................... cm (Total 2 marks)

23. Amy is going to play one game of snooker and one game of billiards.

The probability that she will win the game of snooker is 4

3

The probability that she will win the game of billiards is 3

1

(a) Complete the probability tree diagram.

(2)

(b) Work out the probability that Amy will win exactly one game.

……………………. (3)

Amy played one game of snooker and one game of billiards on a number of Fridays.

She won at both snooker and billiards on 21 Fridays.

(c) Work out an estimate for the number of Fridays on which Amy did not win either game.

……………………. (3)

(Total 8 marks)

24. Salika travels to school by train every day.

The probability that her train will be late on any day is 0.3

(a) Complete the probability tree diagram for Monday and Tuesday.

0.3

0.3

late

late

late

notlate

notlate

notlate

Monday Tuesday

(2)

(b) Work out the probability that her train will be late on at least one of these two days.

…………………………… (3)

(Total 5 marks)

25. Change 28 miles to kilometres.

………………………… km (Total 2 marks)

26. Prendeep bought a necklace in the United States of America.

Prendeep paid 108 dollars ($).

Arthur bought an identical necklace in Germany.

Arthur paid 117 Euros ( )

£1 = $1.44

£1 = 1.6

Calculate, in pounds, the difference between the prices paid for the two necklaces.

Show how you worked out your answer.

£ ……………………… (Total 5 marks)

27. A crate contains 48 apples. Each apple has approximately the same weight.

The weight of 12 of these apples is 2 kg.

Estimate the weight of the apples in the crate in pounds.

…………………. pounds (Total 3 marks)

28.


NOT

A

B C8.5 cm

38°

The diagram shows triangle ABC.

BC = 8.5 cm.

Angle ABC = 90°.

Angle ACB = 38°.

Work out the length of AB.


......................... cm (Total 3 marks)

29.

A

B C

6.2 cm

24º


Angle ABC = 90°.

Angle ACB = 24°.

AC = 6.2 cm.

Calculate the length of BC.


…………………………. cm (Total 3 marks)

30.

r cm R cm


NOT

The diagram represents two metal spheres of different sizes.

The radius of the smaller sphere is r cm.

The radius of the larger sphere is R cm.

r = 1.7 correct to 1 decimal place.

R = 31.0 correct to 3 significant figures.

(a) Write down the upper and lower bounds of r and R.

Upper bound of r = ………………………………

Lower bound of r = ………………………………

Upper bound of R = ………………………………

Lower bound of R = ……………………………… (2)

(b) Find the smallest possible value of R – r.

…………………………… (1)

The larger sphere of radius R cm was melted down and used to make smaller spheres of radius r cm.

(c) Calculate the smallest possible number of spheres that could be made.

…………………………… (4)

(Total 7 marks)

31. Each side of a regular pentagon has a length of 101 mm, correct to the nearest millimetre.

(i) Write down the least possible length of each side.

................ mm

(ii) Write down the greatest possible length of each side.

................ mm (Total 2 marks)

32. The length of a path is 14 m correct to the nearest metre.

(i) Write down the minimum possible length of the path.

……………………………m

(ii) Write down the maximum possible length of the path.

……………………………m (Total 2 marks)

33. Martin won the 400 metre race in the school sports with a time of 1 minute.

The distance was correct to the nearest centimetre.

The time was correct to the nearest tenth of a second.

(a) Work out the upper bound and the lower bound of Martin’s speed in km/h.

Give your answers correct to 5 significant figures.

Upper bound ......................................... km/h

Lower bound ........................................ km/h (5)

(b) Write down an appropriate value for Martin’s speed in km/h.

Explain your answer.

....................................................................................................................................... (1)

The table shows the number of people in each age group who watched the school sports.

Age group 0 – 16 17 – 29 30 – 44 45 – 59 60 +

Number of people 177 111 86 82 21

Martin did a survey of these people.

He used a stratified sample of exactly 50 people according to age group.

(c) Work out the number of people from each age group that should have been in his sample of 50.

Complete the table.

Age group 0 – 16 17 – 29 30 – 44 45 – 59 60 + Total

Number of people

in sample

(3)

(Total 9 marks)

34. This table shows some expressions.

The letters a, b, c, and d represent lengths.

and 4 are numbers that have no dimensions.

Three of the expressions could represent volumes.

Tick the boxes underneath the three expressions which could represent volumes.

d

abc 4a

3 4a2 a

3 + bd (a + b)cd (c

2 + d

2)

24ad

(Total 3 marks)

35. This table shows some expressions.

The letters x, y and z represent lengths.

Place a tick in the appropriate column for each expression to show whether the expression can be used to

represent a length, an area, a volume or none of these.

Expression Length Area Volume

None of

these

x + y + z

xyz

xy + yz + xz

(Total 3 marks) 36. Here are some expressions.

21 ac c 2b 2ab

2 abc a(b + c)

c

ab a

2

The letters a, b and c represent lengths.

, 2 and 21 are numbers which have no dimensions.

Three of the expressions could represent areas.

Tick ( ) the boxes underneath the three expressions which could represent areas. (Total 3 marks)

37. Here are some expressions.

(a + b)c ac + b 2abc πa2 + πb

2 2πc

The letters a, b, and c represent lengths. π and 2 are numbers that have no dimension.

Two of the expressions could represent areas.

Tick the boxes ( ) underneath these two expressions. (Total 2 marks)

38. (a) (i) Write 40 000 000 in standard form.

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

(ii) Write 3 10–5

as an ordinary number.

................................... (2)

(b) Work out the value of

3 10–5

40 000 000

Give your answer in standard form.

(2)

(Total 4 marks)

39. Work out (3.2 × 105) × (4.5 × 10

4)

Give your answer in standard form correct to 2 significant figures.

…………………….. (Total 2 marks)

40. The engine of a new aircraft had a major inspection after 1.2 × 104 hours flying time.

The aircraft flies at an average speed of 900 km/h.

Calculate the distance travelled by the new aircraft before its engine had a major inspection. Give your

answer in standard form.

……………….… km (Total 3 marks)

41. Work out (9.88 × 108) ÷ (2.6 × 10

2)

Give your answer in standard form.

………………………………….. (Total 2 marks)

42. (a) Write 65 200 in standard form.

........................................... (1)

(b) Write 8.36 10–2

as an ordinary number.

........................................... (1)

(Total 2 marks)

43.

x = pq

qp

p = 4 × 108

q = 3 × 106

Find the value of x.

Give your answer in standard form correct to 2 significant figures.

x = ....................................... (Total 3 marks)

44. The engine of a new aircraft had a major inspection after 1.2 × 104 hours flying time.

The aircraft flies at an average speed of 900 km/h.

(a) Calculate the distance travelled by the new aircraft before its engine had a major inspection. Give your

answer in standard form.

……………….… km (3)

In 2000 the aircraft carried a total of 1.2 × 105 passengers.

In 2001 the aircraft carried a total of 9 ×104 passengers.

(b) Calculate the difference in the number of passengers the aircraft carried in 2000 and in 2001. Give your

answer as an ordinary number

……………….……. (2)

(Total 5 marks)

45.

15 cm


NOT

The diagram shows a semi-circle.

The diameter of the semi-circle is 15 cm. Calculate the area of the semi-circle.


............................ (Total 3 marks)

46. The diagram shows a sector of a circle with a radius of x cm and centre O.

PQ is an arc of the circle.

Angle POQ = 120.

120°

Q

PO x cm


NOT

(a) Write down an expression in terms of and x for

(i) the area of this sector,

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

(ii) the arc length of this sector.

................................ (2)

The sector is the net of the curved surface of this cone.

Arc PQ forms the circumference of the circle that makes the base of the cone.

h cmx cm

The curved surface area of the cone is A cm2.

The volume of the cone is V cm3.

The height of the cone is h cm.

Given that V = 3A,

(b) find the value of h.

............................. (3)

(Total 5 marks)

47.

y°

x°


NOT

This is part of the design of a pattern found at the theatre of Diana at Alexandria.

It is made up of a regular hexagon, squares and equilateral triangles.

(a) Write down the size of the angle marked x°. (1)

(b) Work out the size of the angle marked y°. (2)

The area of each equilateral triangle is 2 cm2.

(c) Work out the area of the regular hexagon.

.....................................cm2

(2) (d) In the space below, use ruler and compasses to construct an equilateral triangle with sides of length 4

centimetres.

You must show all construction lines. (2)

(Total 7 marks)

48. Here is a solid cube of side 2 cm.

2 cm

(a) Write down

(i) the number of faces of the cube, …………………..

(ii) the number of vertices of the cube, …………………..

(iii) the number of edges of the cube. ………………….. (3)

(b) Draw an accurate net of this cube. (3)

(Total 6 marks)

49. Here is a cuboid.

3 cm

6 cm

4 cm


(a) Write down

(i) the number of edges of this cuboid, .................................

(ii) the number of vertices of the cuboid .................................. (2)

(b) Draw an accurate net for the cuboid. (3)

(Total 5 marks)

50. Here is a list of seven numbers

6 8 9 12 14 20 23

From the list, write down

(a) a square number, (1)

(b) a number that is a multiple of 7, (1)

(c) two numbers that are factors of 40, (1)

(d) two numbers with a difference of 9. (1)

(Total 4 marks)

51. Michael picks one number from Box A.

He then picks one number from Box B.

Box A Box B

1

7

5

4

2

8

6

List all the pairs of numbers he could pick.

One pair (1, 2) is shown.

(1, 2) ...……………………………………………………………………………………... (Total 2 marks)

52.

20 cm

9 cm

4 cm

8 cm


NOT

The diagram shows a shape.

Work out the area of the shape.

…………………………… cm2

(Total 4 marks) 53.

10 cm

4 cm Diagram accurately drawn

NOT

The diagram shows a cylinder with a height of 10 cm and a radius of 4 cm.

(a) Calculate the volume of the cylinder.


...........................cm3

(2)

The length of a pencil is 13 cm.

The pencil cannot be broken.

(b) Show that this pencil cannot fit inside the cylinder. (3)

(Total 5 marks)

54. This is a map of part of Northern England.

X

X

X

X

X

X

X

X

Blackpool

Wigan

Manchester

Preston

Liverpool

Chester

Stoke-on-Trent

HalifaxN

Scale: 1 cm represents 10 km

Measure and write down the bearing of

(i) Halifax from Wigan,

.........................°

(ii) Preston from Manchester.

........................° (2)

A radio station in Manchester transmits programmes.

Its programmes can be received anywhere within a distance of 30 km.

(b) On the diagram, shade the region in which the programmes can be received. (2)

(Total 4 marks)

There are 12 inches in 1 foot.

There are 3 feet in 1 yard.

There are 2.54 centimetres in 1 inch.

Express 1 metre in yards. Give your answer correct to 3 decimal places.

There are 2.54 centimetres in 1 inch.

There are 12 inches in 1 foot.

There are 3 feet in 1 yard.

i Calculate the number of yards in 10 metres.

ii Calculate the number of metres in 10 yards.

There are 14 pounds in a stone.

There are 2.2 pounds in a kilogram.

A man weighs 13 stone 6 pounds.

Work out his weight in kilograms.

Give your answer to the nearest kilogram.

There are 6 groats in a florin and 5 florins in 10 shillings.

Work out how many

i groats there are in 5 florins,

ii florins there are in 24 shillings,

iii groats there are in 8 shillings.

Documents

R Y10 End of Year Exam ‘Review Exercise’ Academic€¦ · 30. r cm R cm Diagram accurately drawn NOT The diagram represents two metal spheres of different sizes. The radius of