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Royal Russell School Year 7 Maths Paper with Step by Step Solutions.

1.
SAMPLE PAPER

YEAR 7 ENTRANCE EXAMINATION

MATHEMATICS

Practice Questions

Equipment: pen, pencil, ruler

No Calculator

Remember to show workings where appropriate

YEAR 7 ENTRANCE EXAMINATION

MATHEMATICS

Practice Questions

Equipment: pen, pencil, ruler

No Calculator

Remember to show workings where appropriate

2.
1. Look at the menu below:

Tea 60p

Coffee 80p

Cola 60p

Sandwiches £1.80

Beef burger £2.95

(a) Work out the cost of three beef burgers.

………………………………………………………………………………………….

………………………………………………………………………………………….

(b) Work out the cost of two sandwiches and five cups of coffee.

………………………………………………………………………………………….

………………………………………………………………………………………….

(c) How many cups of tea can be bought with £5?

………………………………………………………………………………………….

………………………………………………………………………………………….

6 marks

2. Work out the next three numbers in each of these sequences:

(a) 20 17 14 .…….. ……… ………

(b) 1 4 9 16 …….. ……… ………

(c) 5 6 8 11 15 20 ……… ……… ……….

5 marks

3. How many cubes would you need to build the following cuboid?

Volume = ………………….. 2 marks

Tea 60p

Coffee 80p

Cola 60p

Sandwiches £1.80

Beef burger £2.95

(a) Work out the cost of three beef burgers.

………………………………………………………………………………………….

………………………………………………………………………………………….

(b) Work out the cost of two sandwiches and five cups of coffee.

………………………………………………………………………………………….

………………………………………………………………………………………….

(c) How many cups of tea can be bought with £5?

………………………………………………………………………………………….

………………………………………………………………………………………….

6 marks

2. Work out the next three numbers in each of these sequences:

(a) 20 17 14 .…….. ……… ………

(b) 1 4 9 16 …….. ……… ………

(c) 5 6 8 11 15 20 ……… ……… ……….

5 marks

3. How many cubes would you need to build the following cuboid?

Volume = ………………….. 2 marks

3.
4. (a) For each of the shapes below, choose a description and write it on the dotted

line:

(i) parallelogram (ii) isosceles triangle (iii) trapezium

(iv) scalene triangle (v) kite (vi) pentagon

(b) Draw in any lines of symmetry that the shapes have.

……………………… ……………………… ……………………… 6 marks

5. An equilateral triangle has three sides the same length. What is the size of one of

the angles?

2 marks

…………………………………………………………………………………

6. (a) Convert 13.2 metres into centimetres …………………

(b) Convert 430 millimetres into centimetres …………………

(c) Convert 2.1 kilometres into metres …………………

3 marks

1

7. (a) What is of 68 ? …………………

4

3

(b) What is of 20? ………………….

5

(c) What is 0.1 of £40 ? ………………….

24

(d) Simplify the fraction ………………….

36

(e) What is 0.03 re-written as a fraction ? ………………….

(f) Find 1% of 200 kg ………………….

1 1

(g) Work out …………………. 9 marks

2 4

line:

(i) parallelogram (ii) isosceles triangle (iii) trapezium

(iv) scalene triangle (v) kite (vi) pentagon

(b) Draw in any lines of symmetry that the shapes have.

……………………… ……………………… ……………………… 6 marks

5. An equilateral triangle has three sides the same length. What is the size of one of

the angles?

2 marks

…………………………………………………………………………………

6. (a) Convert 13.2 metres into centimetres …………………

(b) Convert 430 millimetres into centimetres …………………

(c) Convert 2.1 kilometres into metres …………………

3 marks

1

7. (a) What is of 68 ? …………………

4

3

(b) What is of 20? ………………….

5

(c) What is 0.1 of £40 ? ………………….

24

(d) Simplify the fraction ………………….

36

(e) What is 0.03 re-written as a fraction ? ………………….

(f) Find 1% of 200 kg ………………….

1 1

(g) Work out …………………. 9 marks

2 4

4.
8. Work out the answers to the following. Show your workings clearly.

(a) 23.1 – 16.7 (b) 821 x 16

(c) 4.1 x 7 (d) 42.3 ÷ 3

5 marks

9. In New York it is 23°C and in Moscow it is

–5°C. What is the temperature difference?

2 marks

………………..……………………..

10. If a = 5 and b = 10

Work out:

(i) b - a …………………………………………………………………

(ii) 4b ………………………………………………………………….

(iii) 2a2 …………………………………………………………………. 4 marks

11. (a) Write down the factors of 25 …………………………………………

(b) Write down the factors of 30 . ……………………………………….

(c) Write down the highest common factor of 25 and 30 ………………

(d) Write down the prime factors of 30 …………………………………

5 marks

(a) 23.1 – 16.7 (b) 821 x 16

(c) 4.1 x 7 (d) 42.3 ÷ 3

5 marks

9. In New York it is 23°C and in Moscow it is

–5°C. What is the temperature difference?

2 marks

………………..……………………..

10. If a = 5 and b = 10

Work out:

(i) b - a …………………………………………………………………

(ii) 4b ………………………………………………………………….

(iii) 2a2 …………………………………………………………………. 4 marks

11. (a) Write down the factors of 25 …………………………………………

(b) Write down the factors of 30 . ……………………………………….

(c) Write down the highest common factor of 25 and 30 ………………

(d) Write down the prime factors of 30 …………………………………

5 marks

5.
12. Calculate the area of the triangle (remember to write down the correct units)

(a)

…………………………………………

…………………………………………

10cm

…………………………………………

…………………………………………

6 cm

(b) Find the perimeter of the rectangles p and q

(i) (ii)

p 3 cm q W

8 cm L

p……………………………………… q………….…………………………

……………………………………….. ……………………………………..

……………………………………….. ……………………………………..

7 marks

……………………………………….. ……………………………………..

13. (a) In a survey 30% of people were left handed only, 10% were both left and right

handed. What percentage were right handed only ?

………………………………………………………….

(b) Find 50% of 80 ………………………………………

(c) 400 × 30 ………………………………………

4 marks

14. Draw the lines of symmetry on the shape below :

1 mark

(a)

…………………………………………

…………………………………………

10cm

…………………………………………

…………………………………………

6 cm

(b) Find the perimeter of the rectangles p and q

(i) (ii)

p 3 cm q W

8 cm L

p……………………………………… q………….…………………………

……………………………………….. ……………………………………..

……………………………………….. ……………………………………..

7 marks

……………………………………….. ……………………………………..

13. (a) In a survey 30% of people were left handed only, 10% were both left and right

handed. What percentage were right handed only ?

………………………………………………………….

(b) Find 50% of 80 ………………………………………

(c) 400 × 30 ………………………………………

4 marks

14. Draw the lines of symmetry on the shape below :

1 mark

6.
15. (a) How many pieces of ribbon of 30cm length can be cut from a piece

of length 7 m ?

………………………………………………………………………………….

………………………………………………………………………………….

(b) How many cm of ribbon are left over ?………………………………..

………………………………………………………………………………….

…………………………………………………………………………………. 3 marks

16. Work out:

(a) 10 2 3 ………………………………………..………………..

(b) 4 (8 2) ………………………………………………………….

2 marks

17. Solve:

(a) x + 7 = 12

…………………………………………………………………………………

…………………………………………………………………………………

(b) 10 – x = 6

…………………………………………………………………………………

…………………………………………………………………………………

(c) 3 x + 7 = 46

…………………………………………………………………………………

…………………………………………………………………………………

x

(d) 1 7

2

…………………………………………………………………………………

…………………………………………………………………………………

6 marks

of length 7 m ?

………………………………………………………………………………….

………………………………………………………………………………….

(b) How many cm of ribbon are left over ?………………………………..

………………………………………………………………………………….

…………………………………………………………………………………. 3 marks

16. Work out:

(a) 10 2 3 ………………………………………..………………..

(b) 4 (8 2) ………………………………………………………….

2 marks

17. Solve:

(a) x + 7 = 12

…………………………………………………………………………………

…………………………………………………………………………………

(b) 10 – x = 6

…………………………………………………………………………………

…………………………………………………………………………………

(c) 3 x + 7 = 46

…………………………………………………………………………………

…………………………………………………………………………………

x

(d) 1 7

2

…………………………………………………………………………………

…………………………………………………………………………………

6 marks

7.
18. The Archer family has 4 children who receive £2, £5, £3 and £2 pocket money

each week.

(a) Calculate the average pocket money (use the “mean” average).

………………………………………………………………………………….

………………………………………………………………………………….

(b) Calculate the range of pocket money.

…………………………………………………………………………………

…………………………………………………………………………………

(c) The Jones family have 5 children who each receive an average of £3.50 a

week and the range of amounts is £1.

Compare the amounts given to the children in these two families.

…………………………………………………………………………………

………………………………………………………………………………… 5 marks

19. Alex and Emma buy the same type of bike.

Alex pays £169.99 cash from his birthday money.

Emma pays a deposit of £70.00 and then pays instalments of £10 per month over

the course of one year (12 months).

Who pays the most and by how much ? Show all of your working clearly.

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

3 marks

each week.

(a) Calculate the average pocket money (use the “mean” average).

………………………………………………………………………………….

………………………………………………………………………………….

(b) Calculate the range of pocket money.

…………………………………………………………………………………

…………………………………………………………………………………

(c) The Jones family have 5 children who each receive an average of £3.50 a

week and the range of amounts is £1.

Compare the amounts given to the children in these two families.

…………………………………………………………………………………

………………………………………………………………………………… 5 marks

19. Alex and Emma buy the same type of bike.

Alex pays £169.99 cash from his birthday money.

Emma pays a deposit of £70.00 and then pays instalments of £10 per month over

the course of one year (12 months).

Who pays the most and by how much ? Show all of your working clearly.

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

3 marks

8.
20. The entry prices at a theme park are: Adults £20.00 & Children £15.00.

A group visited the theme park and were charged £105.00. How many adults &

children were in the party? There was at least one adult.

Show all of your working clearly.

………………………………………………………………………………….

………………………………………………………………………………….

………………………………………………………………………………….

4 marks

21. Mr Green is organising a school trip. In Year 5 there are 53 pupils and in Year 6

there are 46 pupils. There will also be 28 adults.

Mr Green has two options:

Apple Coaches Orange Coaches

Our coaches seat 41 Our coaches seat 44

Cost £200 per day Cost £250 per day

Help Mr Green find the best deal. Show your workings & give your choice.

…………………………………………………………………………………

………………………………………………………………………………….

………………………………………………………………………………….

………………………………………………………………………………….

………………………………………………………………………………….

………………………………………………………………………………….

5 marks

A group visited the theme park and were charged £105.00. How many adults &

children were in the party? There was at least one adult.

Show all of your working clearly.

………………………………………………………………………………….

………………………………………………………………………………….

………………………………………………………………………………….

4 marks

21. Mr Green is organising a school trip. In Year 5 there are 53 pupils and in Year 6

there are 46 pupils. There will also be 28 adults.

Mr Green has two options:

Apple Coaches Orange Coaches

Our coaches seat 41 Our coaches seat 44

Cost £200 per day Cost £250 per day

Help Mr Green find the best deal. Show your workings & give your choice.

…………………………………………………………………………………

………………………………………………………………………………….

………………………………………………………………………………….

………………………………………………………………………………….

………………………………………………………………………………….

………………………………………………………………………………….

5 marks

9.
22. Mrs Walker is planning a party for her grand-daughter and there will be 70 children

in total.

Each child will have a party bag to take home with a lollipop

and a toy.

Empty party bags are sold in packs of 12 and cost £2 per pack.

Lollipops are sold in packs of 8 and cost £4 per pack.

Toys are sold in packs of 9 and cost £10 per pack.

As a special new year offer, all prices are reduced by one quarter.

How many packs of each item will she need to buy and what will be her total cost?

Show all your working clearly.

………………………………………………………………………………….

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

6 marks

………………………………………………………………………….………

23. Mrs Suzie needs to cover a floor measuring 3m by 2m. There are three possible

options:

Acorn Tiles Beeching Tiles Carpet

50 cm × 50 cm 60 cm × 40 cm £14 per square metre

Fitting cost £30

Cost £4 each. Cost £3 each.

Which option is the cheapest? Show all your workings & explain clearly.

………………………………………………………………………………….

………………………………………………………………………………….

………………………………………………………………………………….

………………………………………………………………………………….

………………………………………………………………………………….

5 marks

in total.

Each child will have a party bag to take home with a lollipop

and a toy.

Empty party bags are sold in packs of 12 and cost £2 per pack.

Lollipops are sold in packs of 8 and cost £4 per pack.

Toys are sold in packs of 9 and cost £10 per pack.

As a special new year offer, all prices are reduced by one quarter.

How many packs of each item will she need to buy and what will be her total cost?

Show all your working clearly.

………………………………………………………………………………….

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

6 marks

………………………………………………………………………….………

23. Mrs Suzie needs to cover a floor measuring 3m by 2m. There are three possible

options:

Acorn Tiles Beeching Tiles Carpet

50 cm × 50 cm 60 cm × 40 cm £14 per square metre

Fitting cost £30

Cost £4 each. Cost £3 each.

Which option is the cheapest? Show all your workings & explain clearly.

………………………………………………………………………………….

………………………………………………………………………………….

………………………………………………………………………………….

………………………………………………………………………………….

………………………………………………………………………………….

5 marks

10.
24. (a) Plot the points (8, 12) and (5,12) on the grid below and join the points up to

make a straight line.

y

14

12

10

8

6

4

2

0 x

0 2 4 6 8 10 12 14

(b) Tick the correct statement:

This line is horizontal This line is vertical 3 marks

25. In a dancing competition, the four judges gave marks ranging from –5 to 5,

(whole numbers). There were 4 competitors.

Andrew got top marks from every judge.

Brian’s score was 4 less than Andrew.

Carla and Donna both had the same final score of 7.

Complete the table:

Judge 1 Judge 2 Judge 3 Judge 4 Total

Brian 5 4 3

Carla 4 2 0

Donna 0 –3 5

4 marks

End of Practice Paper (Total 105 marks)

make a straight line.

y

14

12

10

8

6

4

2

0 x

0 2 4 6 8 10 12 14

(b) Tick the correct statement:

This line is horizontal This line is vertical 3 marks

25. In a dancing competition, the four judges gave marks ranging from –5 to 5,

(whole numbers). There were 4 competitors.

Andrew got top marks from every judge.

Brian’s score was 4 less than Andrew.

Carla and Donna both had the same final score of 7.

Complete the table:

Judge 1 Judge 2 Judge 3 Judge 4 Total

Brian 5 4 3

Carla 4 2 0

Donna 0 –3 5

4 marks

End of Practice Paper (Total 105 marks)

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