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Year 7 · Key Stage 3 · free KS3 maths weekly check

Weekly check: Year 7 part 2

20 mixed questions from 7 Year 7 topics, 50 marks. It covers fractions, decimals and percentages to ratio and proportion, the second third of the year in the order schools usually teach it.

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The questions

1

Make x the subject of the formula

y = 2x + 9

2 marks
Show answer
x = y - 92
See the working
y=2x + 9
-9y - 9=2x-9
÷2y - 92=x÷2

x = y - 92

2

Ben's rent is £240 each week.

His rent is increased by 35%.

Work out Ben's new weekly rent.

3 marks
Show answer
£324
See the working
10% of £240=£24
30% of £240=3 × 24
30% of £240=£72
5% of £240=£12
35% of £240=72 + 12
35% of £240=£84
New rent=240 + 84
New rent=£324

£324

3

Write down the ratio 45 cm : 1.5 m in its simplest form.

2 marks
Show answer
3 : 10
See the working

Same units first

1.5 m=150 cm

45 : 150

HCF of 45 and 150=15

Divide both parts by 15

3 : 10

3 : 10

4

The nth term of a sequence is 20 − 4n

  1. Write down the first four terms of the sequence.
  2. Work out the 10th term of the sequence.
2 marks
Show answer
a) 16, 12, 8, 4 b) -20
See the working

a)

n = 1: 20 - 4 × 1 = 16

n = 2: 20 - 4 × 2 = 12

n = 3: 20 - 4 × 3 = 8

n = 4: 20 - 4 × 4 = 4

16, 12, 8, 4

b)

20 - 4 × 10 = 20 - 40 = -20

-20

5

Oliver expands 4(3m − 2) and writes

4(3m − 2) = 12m − 2

Explain the mistake Oliver has made and write the correct answer.

2 marks
Show answer
He did not multiply the 2 by 4. Correct answer 12m - 8
See the working

The 4 multiplies BOTH terms

4 × 3m = 12m

4 × 2 = 8 (Oliver forgot this)

12m - 8

6

A bottle contains 850 ml of juice.

34% of the juice is orange juice.

Work out how many millilitres of orange juice are in the bottle.

2 marks
Show answer
289 ml
See the working
34%=0.34
Orange juice=0.34 × 850
Orange juice=289

289 ml

7

Ella and Ravi share some sweets in the ratio 3 : 5

Ravi gets 12 more sweets than Ella.

How many sweets do they share altogether?

3 marks
Show answer
48
See the working

difference = 5 - 3 = 2 parts

2 parts = 12, so 1 part = 6

total = 3 + 5 = 8 parts

8 × 6 = 48

Check: 18 and 30, 30 - 18 = 12

48 sweets

8

The grid is made of 100 equal squares. Some of the squares are shaded.

  1. What percentage of the grid is shaded?
  2. What percentage of the grid is not shaded?
  3. Write the shaded part of the grid as a decimal.
3 marks
Show answer
a) 37% b) 63% c) 0.37
See the working

a) count the shaded squares

3 × 10 + 7=37

per cent means out of 100

37%

b)

100 - 37=63

63%

c)

37%=37100
=0.37

0.37

9

The nth term of a sequence is 5n − 3

  1. Work out the 12th term of the sequence.
  2. Is 122 a term of the sequence? You must show how you get your answer.
3 marks
Show answer
a) 57 b) Yes, 5n - 3 = 122 gives n = 25, a whole number
See the working

a)

12th term=5 × 12 - 3
12th term=60 - 3
12th term=57

57

b)

5n - 3=122
+35n=125+3
÷5n=25÷5

25 is a whole number

Yes, it is the 25th term

10

Write these numbers in order of size, starting with the smallest.

25   0.44   39%   14

2 marks
Show answer
14, 39%, 25, 0.44
See the working

Change all to decimals

25=0.4
0.44=0.44
39%=0.39
14=0.25

0.25 < 0.39 < 0.4 < 0.44

14, 39%, 25, 0.44

11

Write these numbers in order of size, starting with the smallest.

0.3    725    31%    38    0.295

3 marks
Show answer
725, 0.295, 0.3, 31%, 38
See the working

change them all to decimals

725=28100
=0.28
31%=0.31
38=3 × 0.125
=0.375

compare with 3 decimal places

0.300 0.280 0.310 0.375 0.295

725, 0.295, 0.3, 31%, 38

12

Make x the subject of each equation.

  1. x + 5 = y
  2. x − 3 = p
  3. 4x = t
3 marks
Show answer
a) x = y - 5 b) x = p + 3 c) x = t4
See the working

a)

x + 5=y
-5x=y - 5-5

x = y - 5

b)

x - 3=p
+3x=p + 3+3

x = p + 3

c)

4x=t
÷4x=t4÷4

x = t4

13

The nth term of a sequence is 6n − 1

Write down the first three terms of the sequence.

2 marks
Show answer
5, 11, 17
See the working

Substitute n = 1, 2, 3

6 × 1 - 1=5
6 × 2 - 1=11
6 × 3 - 1=17

5, 11, 17

14

Expand and simplify 2(x + 5) + 3(x + 1)

2 marks
Show answer
5x + 13
See the working
2(x + 5) + 3(x + 1)=2x + 10 + 3x + 3
=5x + 13

5x + 13

15

Amy is x years old.

Ben is 5 years older than Amy.

Chloe is twice as old as Amy.

  1. Write down an expression, in terms of x, for Ben's age.
  2. Write down an expression, in terms of x, for Chloe's age.
2 marks
Show answer
a) x + 5 (accept 5 + x) b) 2x
See the working

a)

5 years older: add 5

Ben=x + 5

x + 5

b)

Twice as old: × 2

Chloe=2 × x
Chloe=2x

2x

16
  1. Simplify  8x + 5 − 3x + 2
  2. Simplify  2g × 5g
3 marks
Show answer
a) 5x + 7 (accept 7 + 5x) b) 10g2
See the working

a)

Collect x terms

8x - 3x=5x
Collect the numbers
5 + 2=7

5x + 7

b)

Multiply the numbers

2 × 5=10
Multiply the letters
g × g=g2

10g2

17

A plumber charges a fixed call-out fee of £40 plus £28 for each hour of work.

The plumber works for h hours on a job.

The total charge for the job is £C.

Write a formula for C in terms of h.

3 marks
Show answer
C = 40 + 28h
See the working

£28 for each of h hours

Hourly part=28 × h
Hourly part=28h

Add the £40 call-out fee

C = 40 + 28h

18

5 packets of football stickers cost £3.50

Work out the cost of 8 packets of the same stickers.

2 marks
Show answer
£5.60
See the working

1 packet = 3.50 ÷ 5 = £0.70

8 packets = 8 × 0.70 = £5.60

£5.60

19

Three friends compare their scores in a science test.

  • Leah scored 17 out of 20
  • Omar scored 82%
  • Grace got 0.84 of the marks

Put the friends in order, starting with the highest score.

You must show your working.

3 marks
Show answer
Leah, Grace, Omar
See the working

change them all to percentages

1720=85100
=85%
0.84=84%

Leah 85%, Grace 84%, Omar 82%

Leah, Grace, Omar

20

Asha thinks of a number, n.

She multiplies her number by 4 and then subtracts 7. Her answer is 25.

  1. Write an equation in n.
  2. Solve your equation to find Asha's number.
3 marks
Show answer
a) 4n - 7 = 25 b) n = 8
See the working

a) × 4, then - 7, equals 25

4n - 7 = 25

b)

4n - 7=25
+74n=32+7
÷4n=8÷4

n = 8

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Every question here is original and written by Robinson Tuition, drawn from the Year 7 topic worksheets. It follows the Key Stage 3 programme of study.

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