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

Weekly check: Year 7 part 1

20 mixed questions from 7 Year 7 topics, 50 marks. It covers place value, addition and subtraction to fractions, the first third of the year in the order schools usually teach it.

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The questions

1

Amir has £20

He buys a book costing £7.65 and a magazine costing £4.80

Work out how much money Amir has left.

2 marks
Show answer
£7.55
See the working

Total spent

£7.65 + £4.80=£12.45
Money left
£20 - £12.45=£7.55

£7.55

2

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

23   34   712   56

2 marks
Show answer
712, 23, 34, 56
See the working

Common denominator 12

23=812
34=912
712=712
56=1012

712 < 812 < 912 < 1012

712, 23, 34, 56

3

Here are the lowest temperatures, in °C, recorded in five cities one winter night.

−3   −11   −0.5   −8   −1

Write the temperatures in order. Start with the coldest.

2 marks
Show answer
-11, -8, -3, -1, -0.5
See the working

further below zero = colder

-11 < -8 < -3 < -1 < -0.5

-11, -8, -3, -1, -0.5

4

Amira has £25 in her bank account.

She spends £40 on a pair of trainers using her bank card.

The next day she pays in £12

What is her bank balance now?

2 marks
Show answer
-£3
See the working

25 - 40 = -15

-15 + 12 = -3

-£3

5

Aisha finished a swimming session at 16:10.

The session lasted 1 hour 35 minutes.

Work out the time the session started.

2 marks
Show answer
14:35
See the working

Count back from 16:10

16:10 - 1 hour → 15:10

15:10 - 10 minutes → 15:00

15:00 - 25 minutes → 14:35

Check: 14:35 + 1 h 35 min

14:35 + 1 h 35 min → 16:10 ✓

14:35

6

On the clock face, draw the hour hand and the minute hand to show the time quarter to four.

123456789101112
2 marks
Show answer
Minute hand pointing at 9; hour hand three quarters of the way from 3 to 4
See the working

quarter to four = 3:45

45 ÷ 5 = 9, so the minute hand points at 9

hour hand: 45 minutes is 34 of an hour

so it is 34 of the way from 3 to 4

long hand on 9, short hand just before 4

7

Work out

  1. 34 + 16
  2. 56 − 29
4 marks
Show answer
a) 1112 b) 1118
See the working

a) common denominator 12

34 + 16=912 + 212
=1112

1112

b) common denominator 18

56 - 29=1518 - 418
=1118

1118

8

Use the grid method to work out 58 × 37

2 marks
Show answer
2146
See the working

split 58 = 50 + 8 and 37 = 30 + 7

50 × 30 = 1500

50 × 7 = 350

8 × 30 = 240

8 × 7 = 56

1500 + 350 + 240 + 56 = 2146

2146

9
  1. Write the number 4738 correct to 2 significant figures.
  2. Write the number 0.05372 correct to 2 significant figures.
2 marks
Show answer
a) 4700 b) 0.054
See the working

a)

4700 < 4738 < 4800

Next digit is 3

3 < 5, round down

Zeros keep the place value

4700

b)

Leading zeros do not count

0.053 < 0.05372 < 0.054

Next digit is 7

7 ≥ 5, round up

0.054

10

Write 360 as a product of powers of its prime factors.

3 marks
Show answer
23 × 32 × 5
See the working

Divide by primes

360 ÷ 2=180
180 ÷ 2=90
90 ÷ 2=45
45 ÷ 3=15
15 ÷ 3=5
5 is prime
360=2 × 2 × 2 × 3 × 3 × 5

360 = 23 × 32 × 5

11

Use short division to work out 1438 ÷ 6

  1. Give your answer with a remainder.
  2. Give your answer as a mixed number in its simplest form.
2 marks
Show answer
a) 239 remainder 4 b) 239 23
See the working

a)

6 into 14 = 2 r 2

6 into 23 = 3 r 5

6 into 58 = 9 r 4

239 r 4

b) remainder 4 out of 6

46 = 23

239 23

12

180 = 22 × 32 × 5

84 = 22 × 3 × 7

  1. Complete the Venn diagram to show the prime factors of 180 and 84
  2. Find the highest common factor (HCF) of 180 and 84
  3. Find the lowest common multiple (LCM) of 180 and 84
18084
4 marks
Show answer
a) 180 only: 3, 5; both: 2, 2, 3; 84 only: 7 b) 12 c) 1260
See the working

a)

180 = 2 × 2 × 3 × 3 × 5

84 = 2 × 2 × 3 × 7

shared: 2, 2, 3 go in the middle

180 only: 3, 5

84 only: 7

middle 2, 2, 3; left 3, 5; right 7

b) multiply the middle

2 × 2 × 3 = 12

HCF = 12

c) multiply everything

3 × 5 × 2 × 2 × 3 × 7 = 1260

LCM = 1260

13

Use your calculator to work out

  1. 2.33
  2. √17.64
  3. 37
3 marks
Show answer
a) 12.167 b) 4.2 c) 2187
See the working

a) cube means × itself three times

2.33=2.3 × 2.3 × 2.3
2.33=12.167

12.167

b) check: 4.2 × 4.2 = 17.64

4.2

c) power button, then 7

2187

14

Mr Hussain has 42 pencils and 56 rubbers.

He puts them all into identical packs, with nothing left over.

  1. What is the greatest number of packs he can make?
  2. How many pencils and how many rubbers are in each pack?
3 marks
Show answer
a) 14 b) 3 pencils and 4 rubbers
See the working

a) number of packs divides 42 and 56: HCF

42: 1, 2, 3, 6, 7, 14, 21, 42

56: 1, 2, 4, 7, 8, 14, 28, 56

HCF = 14

14 packs

b)

42 ÷ 14 = 3

56 ÷ 14 = 4

3 pencils and 4 rubbers

15

Here are five numbers.

126   245   312   430   594

  1. Write down the numbers that are multiples of 9
  2. Write down the numbers that are multiples of 6
2 marks
Show answer
a) 126 and 594 b) 126, 312 and 594
See the working

a) digits add to a multiple of 9

1 + 2 + 6 = 9

2 + 4 + 5 = 11

3 + 1 + 2 = 6

4 + 3 + 0 = 7

5 + 9 + 4 = 18

126 and 594

b) even, and digits add to a multiple of 3

126: even, 9

312: even, 6

594: even, 18

245 is odd, 430 has digit sum 7

126, 312 and 594

16

96 pupils go on a school trip. 58 of the pupils are in Year 7.

13 of the Year 7 pupils bring a packed lunch.

How many Year 7 pupils do not bring a packed lunch?

3 marks
Show answer
40
See the working

Year 7 pupils

96 ÷ 8=12
5 × 12=60
packed lunch
60 ÷ 3=20
do not bring one
60 - 20=40

40 pupils

17

Write true or false for each statement.

  1. −6 ≥ −6
  2. −4 ≠ 4
  3. −3 ≤ −8
3 marks
Show answer
a) true b) true c) false
See the working

a) ≥ means greater than or equal to

-6 = -6

true

b) ≠ means not equal to

-4 and 4 are different

true

c) ≤ means less than or equal to

-3 > -8

false

18

Here is a list of numbers.

21   34   37   45   51   58   59

  1. Write down the even numbers in the list.
  2. Write down the prime numbers in the list.
2 marks
Show answer
a) 34 and 58 b) 37 and 59
See the working

a)

even numbers end in 0, 2, 4, 6 or 8

34, 58

b)

check the odd numbers for factors

21 = 3 × 7

45 = 5 × 9

51 = 3 × 17

37 and 59 have only 1 and themselves

37, 59

19

Sophie adds up odd numbers, starting from 1.

1 = 1
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16

  1. Write down the next line of the pattern.
  2. What type of numbers are the answers?
  3. Use the pattern to work out 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 without adding the numbers one by one.
3 marks
Show answer
a) 1 + 3 + 5 + 7 + 9 = 25 b) square numbers c) 100
See the working

a) next odd number is 9

1 + 3 + 5 + 7 + 9=25

1 + 3 + 5 + 7 + 9 = 25

b) 1, 4, 9, 16, 25

square numbers

c) count the odd numbers from 1 to 19

1, 3, 5, 7, 9, 11, 13, 15, 17, 19

that is 10 odd numbers

102=100

100

20

Zara works out 39.8 + 61.3 − 19.6

She gets 181.5

Use estimation to show that Zara must be wrong.

2 marks
Show answer
40 + 60 - 20 = 80, so the answer should be about 80, not 181.5 (it is 81.5)
See the working

round each number

39.8 ≈ 40

61.3 ≈ 60

19.6 ≈ 20

40 + 60 - 20 = 80

about 80, so 181.5 is wrong

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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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