13 marks
Work out an estimate for the value of
39.6 × 5.120.48
You must show your working.
Show answer
400
See the working
round each number to 1 s.f.
39.6 × 5.120.48 ≈ 40 × 50.5
| 40 × 5 | = | 200 |
| 200 ÷ 0.5 | = | 400 |
400
Weekly check: Year 9 part 1
20 mixed questions from 7 Year 9 topics, 50 marks. It covers rounding and estimating to ratio and proportion, the first third of the year in the order schools usually teach it.
Type your answers below for an instant mark and a score, or print the sheet, mark it with the answers sheet, and use the solutions to see every step written out. Set one a week and watch the score climb.
The questions
22 marks
Kofi makes two jugs of orange squash.
Jug A: 150 ml of squash mixed with 600 ml of water.
Jug B: 200 ml of squash mixed with 900 ml of water.
Which jug has the stronger taste of orange? Show your working by writing each ratio of squash to water in the form 1 : n
Show answer
Jug A (1 : 4 compared with 1 : 4.5)
See the working
Jug A ÷ 150
150 : 600 = 1 : 4
Jug B ÷ 200
200 : 900 = 1 : 4.5
less water for each 1 ml of squash
Jug A
33 marks
- Work out 35 of 2 km. Give your answer in metres.
- Work out 512 of an hour. Give your answer in minutes.
- Sana has a 2 kg bag of flour. She uses 38 of the flour to bake bread. How many grams of flour are left in the bag?
Show answer
a) 1200 m b) 25 minutes c) 1250 g
See the working
a)
2 km = 2000 m
2000 ÷ 5 = 400
400 × 3 = 1200
1200 m
b)
1 hour = 60 minutes
60 ÷ 12 = 5
5 × 5 = 25
25 minutes
c)
2 kg = 2000 g
2000 ÷ 8 = 250
Used: 250 × 3 = 750 g
Left: 2000 - 750 = 1250 g
1250 g
42 marks
Write
- 0.4 as a percentage,
- 135% as a decimal.
Show answer
a) 40% b) 1.35
See the working
a)
| 0.4 × 100 | = | 40 |
40%
b)
| 135 ÷ 100 | = | 1.35 |
1.35
53 marks
Work out 313 ÷ 212
Give your answer as a mixed number in its simplest form.
Show answer
113
See the working
Improper fractions
| 313 | = | 103 |
| 212 | = | 52 |
| Flip the second, then multiply | ||
| 103 ÷ 52 | = | 103 × 25 |
| 103 ÷ 52 | = | 2015 |
| 2015 | = | 43 |
4 ÷ 3 = 1 remainder 1
| 43 | = | 113 |
113
63 marks
Work out each of these. Give each answer in its simplest form.
- 45 ÷ 2
- 37 ÷ 6
- 58 ÷ 1516
Show answer
a) 25 b) 114 c) 23
See the working
a)
45 ÷ 2 = 45 × 12
= 410
25
b)
37 ÷ 6 = 37 × 16
= 342
114
c)
58 ÷ 1516 = 58 × 1615
Cancel 5 with 15, 16 with 8
= 11 × 23
23
72 marks
- Write (53)4 as a single power of 5
- Write down the value of 80
Show answer
a) 512 b) 1
See the working
a)
Power of a power: multiply
| (53)4 | = | 53 × 4 |
| = | 512 |
512
b)
Anything to the power 0 is 1
| 80 | = | 1 |
1
82 marks
Work out (9 × 108) ÷ (3 × 10−2)
Give your answer in standard form.
Show answer
3 × 1010
See the working
Divide numbers, subtract powers
| 9 ÷ 3 | = | 3 |
| 108 ÷ 10-2 | = | 108 - (-2) |
| 108 ÷ 10-2 | = | 1010 |
3 × 1010
92 marks
- Write the ratio 8 : 28 in the form 1 : n
- A school has 15 teachers and 360 pupils. Write the ratio of teachers to pupils in the form 1 : n
Show answer
a) 1 : 3.5 b) 1 : 24
See the working
a)
÷ both sides by 8
8 : 28
1 : 3.5
1 : 3.5
b)
÷ both sides by 15
15 : 360
1 : 24
1 : 24
102 marks
Write
- 35% as a fraction in its simplest form,
- 325 as a percentage.
Show answer
a) 720 b) 12%
See the working
a)
| 35% | = | 35100 |
| ÷ top and bottom by 5 | ||
| 35100 | = | 720 |
720
b)
× top and bottom by 4
| 325 | = | 12100 |
12%
113 marks
Ravi is choosing between two vouchers for the same online shop.
Voucher A gives 24% off a £75 order.
Voucher B gives 32% off a £55 order.
Which voucher saves more money?
You must show your working.
Show answer
Voucher A. It saves 24% of £75 = £18, while Voucher B saves 32% of £55 = £17.60, so Voucher A saves £0.40 more.
See the working
Voucher A saving
| 24% of £75 | = | 0.24 × 75 |
| 24% of £75 | = | £18 |
| Voucher B saving | ||
| 32% of £55 | = | 0.32 × 55 |
| 32% of £55 | = | £17.60 |
£18 > £17.60
Voucher A (saves £18, B saves £17.60)
122 marks
Write down two numbers, both greater than 20, whose highest common factor (HCF) is 7
Show answer
Any valid pair, e.g. 21 and 28 (21 = 3 × 7 and 28 = 4 × 7, and 3 and 4 share no common factor greater than 1, so HCF = 7).
See the working
Multiples of 7 above 20
21, 28, 35, 42, ...
| 21 | = | 3 × 7 |
| 28 | = | 4 × 7 |
| 3 and 4 share no factor except 1 | ||
| HCF(21, 28) | = | 7 |
e.g. 21 and 28
133 marks
Ellie scored 17 out of 20 in a French test. She scored 42 out of 50 in a Spanish test.
In which test did Ellie do better? You must show your working.
Show answer
French (85% compared with 84%)
See the working
French
| 1720 | = | 85100 |
| = | 85% | |
| Spanish | ||
| 4250 | = | 84100 |
| = | 84% |
85% > 84%
French
143 marks
- Work out an estimate for 62.3 × 4.87
- You are given that 623 × 487 = 303,401
Use this fact to write down the exact value of 62.3 × 4.87
Show answer
a) 300 b) 303.401
See the working
a)
62.3 ≈ 60, 4.87 ≈ 5
| 60 × 5 | = | 300 |
300
b)
| 62.3 | = | 623 ÷ 10 |
| 4.87 | = | 487 ÷ 100 |
| 62.3 × 4.87 | = | 303,401 ÷ 1000 |
| 62.3 × 4.87 | = | 303.401 |
Close to 300, so sensible
303.401
152 marks
3 identical machines take 10 hours to print an order of leaflets.
Work out how long 5 of these machines would take to print the same order.
Show answer
6 hours
See the working
Total work in machine-hours
| 3 × 10 | = | 30 |
| Share the work between 5 machines | ||
| 30 ÷ 5 | = | 6 |
6 hours
162 marks
Rosa puts £3000 into a savings account.
The account pays 2% compound interest per year.
Work out the value of her savings at the end of 2 years.
Show answer
£3121.20
See the working
Multiplier for +2%
| 100% + 2% | = | 102% |
| Multiplier | = | 1.02 |
| Value | = | 3000 × 1.022 |
| Value | = | 3121.2 |
£3121.20
172 marks
- Write 507,000 in standard form.
- Write 2.6 × 10−3 as an ordinary number.
Show answer
a) 5.07 × 105 b) 0.0026
See the working
a)
| 507,000 | = | 5.07 × 100,000 |
| 507,000 | = | 5.07 × 105 |
5.07 × 105
b)
| 2.6 × 10-3 | = | 2.6 ÷ 1000 |
Digits move 3 places right
0.0026
183 marks
Work out how many positive whole numbers less than 100 are multiples of both 4 and 6.
Show answer
8
See the working
Multiples of 4 and 6
4: 4, 8, 12, ...
6: 6, 12, ...
LCM = 12
Multiples of 12 under 100
12, 24, 36, 48, 60, 72, 84, 96
8
192 marks
- Kai scored 18 out of 25 in a spelling test. Write his score as a percentage.
- Write £6 as a percentage of £40
Show answer
a) 72% b) 15%
See the working
a)
| 1825 | = | 72100 |
72%
b)
| 640 | = | 320 |
| 320 | = | 15100 |
15%
204 marks
Tia and Sam each ran 100 m.
Tia's time was 12.4 seconds, correct to 1 decimal place.
Sam's time was 12.4 seconds, truncated to 1 decimal place.
- Write down the error interval for Tia's time, t seconds.
- Write down the error interval for Sam's time, s seconds.
- Tia says, "I definitely ran faster than Sam." Is Tia right? Give a reason for your answer.
Show answer
a) 12.35 ≤ t < 12.45 b) 12.4 ≤ s < 12.5 c) No, the intervals overlap
See the working
a) rounding: half of 0.1 either side
| 12.4 - 0.05 | = | 12.35 |
| 12.4 + 0.05 | = | 12.45 |
12.35 ≤ t < 12.45
b) truncating: up to the next 0.1
12.4 ≤ s < 12.5
c) the intervals overlap
Tia could be 12.44, Sam could be 12.40
No, Sam could have been faster
Your score
Answer the questions above and your score appears here.
Every question here is original and written by Robinson Tuition, drawn from the Year 9 topic worksheets. It follows the Key Stage 3 programme of study.
All weekly checks
- Weekly check: Year 7 part 1
- Weekly check: Year 7 part 2
- Weekly check: Year 7 part 3
- Weekly check: Year 7 whole year
- Weekly check: Year 8 part 1
- Weekly check: Year 8 part 2
- Weekly check: Year 8 part 3
- Weekly check: Year 8 whole year
- Weekly check: Year 9 part 1
- Weekly check: Year 9 part 2
- Weekly check: Year 9 part 3
- Weekly check: Year 9 whole year