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Year 8, Maths Practice Test Papers

1.
MATHEMATICS ENTRANCE EXAMINATION

ENTRY TO YEAR 8, SAMPLE PAPER

Time Allowed: 60 minutes

Write down all your working and put your answers in the spaces

provided.

Calculators are not allowed.

Try to answer all the questions.

Some of the questions may seem unfamiliar. Do not spend too much

time on these at first, but move on to questions you like more. You can

always return to the unusual ones later.

Your full name:

Your current school:

ENTRY TO YEAR 8, SAMPLE PAPER

Time Allowed: 60 minutes

Write down all your working and put your answers in the spaces

provided.

Calculators are not allowed.

Try to answer all the questions.

Some of the questions may seem unfamiliar. Do not spend too much

time on these at first, but move on to questions you like more. You can

always return to the unusual ones later.

Your full name:

Your current school:

2.
1. Work out the following:

a) 635+239+75 b) 4042 - 1578

(1) (1)

c) 736 × 7 d) 2688 ÷ 8

(1) (1)

e) 4122÷ 5 f) 225 × 34

[Give the remainder as a fraction]

(2) (2)

(Total 8 Marks)

a) 635+239+75 b) 4042 - 1578

(1) (1)

c) 736 × 7 d) 2688 ÷ 8

(1) (1)

e) 4122÷ 5 f) 225 × 34

[Give the remainder as a fraction]

(2) (2)

(Total 8 Marks)

3.
Work out the answers to the following calculations. You can draw a

number line to help you.

a) −3 − 8 =

b) (−4) − (−8) =

c) −7 × 8 =

d) −72 ÷ 8 =

e) −27 ÷ −3 =

(Total 5 marks)

Peter has a £10 note to spend on stickers.

A packet of stickers costs 79p.

He buys as many packets of stickers as possible.

Work out how much change Peter should get from his £10 note.

£........................

(Total 3 marks)

number line to help you.

a) −3 − 8 =

b) (−4) − (−8) =

c) −7 × 8 =

d) −72 ÷ 8 =

e) −27 ÷ −3 =

(Total 5 marks)

Peter has a £10 note to spend on stickers.

A packet of stickers costs 79p.

He buys as many packets of stickers as possible.

Work out how much change Peter should get from his £10 note.

£........................

(Total 3 marks)

4.
(a) Simplify 6p – 2w + p + 5w

……………………..

(2)

(b) Simplify 5c – 8d – 4c + 3d

……………………..

(2)

(c) Simplify t + 8 – 7m + 4 – 3m

……………………..

(2)

(d) Simplify 4a× 4b

……………………..

(2)

(e) Simplify p×p×p×p×p×p

……………………..

(1)

(f) Simplify 6𝑥 2 + 6𝑥 − 3𝑥 2 + 𝑥𝑦 − 2𝑥

………………………

(3)

(Total 12 Marks)

……………………..

(2)

(b) Simplify 5c – 8d – 4c + 3d

……………………..

(2)

(c) Simplify t + 8 – 7m + 4 – 3m

……………………..

(2)

(d) Simplify 4a× 4b

……………………..

(2)

(e) Simplify p×p×p×p×p×p

……………………..

(1)

(f) Simplify 6𝑥 2 + 6𝑥 − 3𝑥 2 + 𝑥𝑦 − 2𝑥

………………………

(3)

(Total 12 Marks)

5.
5. Find the value of x.

120o 𝑥

x=

(Total 2 marks)

A man rows 25038 miles on a rowing machine in 13 years.

He rows the same amount of miles each year.

Work out how many miles per year the man rows

(2)

(Total 2 marks)

120o 𝑥

x=

(Total 2 marks)

A man rows 25038 miles on a rowing machine in 13 years.

He rows the same amount of miles each year.

Work out how many miles per year the man rows

(2)

(Total 2 marks)

6.
7. a) Write these fractions in order of size.

Start with the smallest fraction.

3 5 2 7

4 6 3 12

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

7 1

b) Work out −

8 4

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

5 3

b) Work out the value of +

6 4

Give your answer as a mixed number.

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

(Total 6 marks)

Start with the smallest fraction.

3 5 2 7

4 6 3 12

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

7 1

b) Work out −

8 4

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

5 3

b) Work out the value of +

6 4

Give your answer as a mixed number.

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

(Total 6 marks)

7.
8. Find the value of x. You must show your working.

𝑥o

80o

120o

x=

(Total 3 marks)

9. There are 332 children in a school. One coach holds 50 children. How

many coaches are needed for a whole school trip?

(Total 2 marks)

𝑥o

80o

120o

x=

(Total 3 marks)

9. There are 332 children in a school. One coach holds 50 children. How

many coaches are needed for a whole school trip?

(Total 2 marks)

8.
10. Solve the following equations. You must show what you have done to

both sides of the equation to gain full marks.

a) 4𝑥 = 20

x = ……………

(2)

b) 𝑥 + 5 = 1

x = ……………

(2)

𝑥

c) = 5

2

x = ……………(2)

(Total 6 marks)

both sides of the equation to gain full marks.

a) 4𝑥 = 20

x = ……………

(2)

b) 𝑥 + 5 = 1

x = ……………

(2)

𝑥

c) = 5

2

x = ……………(2)

(Total 6 marks)

9.
yº

138o xº 34o

Diagram NOT accurately drawn

(a) Work out the value of x.

x = ………….

(1)

(b) Give a reason for your answer.

……………………………………………………………………………

……………………………………………………………………………

(1)

(c) Work out the value of y.

y = ………….

(2)

(d) Give a reason for your answer.

……………………………………………………………………………

……………………………………………………………………………

(1)

(Total 5 marks)

138o xº 34o

Diagram NOT accurately drawn

(a) Work out the value of x.

x = ………….

(1)

(b) Give a reason for your answer.

……………………………………………………………………………

……………………………………………………………………………

(1)

(c) Work out the value of y.

y = ………….

(2)

(d) Give a reason for your answer.

……………………………………………………………………………

……………………………………………………………………………

(1)

(Total 5 marks)

10.
12. Here is a map of Great Britain.

The map shows the temperatures in some cities at midnight on 20th January.

(a) Which city had the lowest temperature at midnight?

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

(1)

In Brighton, the temperature rose by 5°C between midnight on 20th January and

midday on 21st January.

(b) What was the temperature in Brighton at midday on 21st January?

........................................................... °C

(1)

At midnight on 20th January, the temperature in Nottingham was halfway between

the temperature in Truro and the temperature in Edinburgh.

(c) What was the temperature in Nottingham?

........................................................... °C

(2)

(Total 4 marks)

The map shows the temperatures in some cities at midnight on 20th January.

(a) Which city had the lowest temperature at midnight?

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

(1)

In Brighton, the temperature rose by 5°C between midnight on 20th January and

midday on 21st January.

(b) What was the temperature in Brighton at midday on 21st January?

........................................................... °C

(1)

At midnight on 20th January, the temperature in Nottingham was halfway between

the temperature in Truro and the temperature in Edinburgh.

(c) What was the temperature in Nottingham?

........................................................... °C

(2)

(Total 4 marks)

11.
13. Given that 357 × 101 = 36057, work out 358 × 101 without multiplying.

(Total 2 Marks)

End of test

Check your answers

Total Test Mark = 60

(Total 2 Marks)

End of test

Check your answers

Total Test Mark = 60

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