Write down the value of
(a) 5^3 [1]
(b) √121. [1]
Show model answer
(a) 125
(b) 11
5^3 = 5 × 5 × 5; 11 × 11 = 121 so the square root is 11 (±11 also accepted).
O Level Mathematics: Number, questions with answers
Practise 118 real questions on Number from 2021 to 2026. See the answer and explanation as soon as you answer.
118real questions
2papers covered
11exam sessions
About Number in O Level Mathematics
Number is one of the 5 main topics in our O Level Mathematics (Cambridge (CAIE) 4024) question bank, and about 30% of its real questions come from it. Tayyari Karo has 118 real questions on this topic from 2021 to 2026, from Paper 1, Paper 2. By difficulty: 64 easy, 48 medium, 6 hard.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
Try 8 real questions
These are real past-paper questions. Think of your answer first, then open the explanation.
In a sale, a shop reduces all prices by 32%. Before the sale, a dress costs $56. Work out the sale price of the dress. [2]
Show model answer
$38.08
56 × 0.68 = 38.08
Multiply by 100% − 32% = 68%.
Chris wants to exchange $350 for euros (€) at the bank. The bank only gives euros in multiples of €5. The exchange rate is $1 = €0.92.
Calculate the number of euros he receives and his change from $350.
Show model answer
$350 at the given rate = 350 × 0.92 = €322
The bank only gives multiples of €5, so round down to €320.
Cost of €320 in dollars = 320 ÷ 0.92 = $347.83 (2 d.p.)
Change = 350 − 347.83 = $2.17
Chris receives €320 and his change is $2.17
Convert at the given rate, round down to the nearest allowed multiple, then convert back to find the leftover dollars.
(a) Simplify √8 × √6 + √3.
(b) Rationalise the denominator and simplify.
3/(2 − √5)
Show model answer
(a) √8 × √6 = √48 = √(16×3) = 4√3
4√3 + √3 = 5√3
(b) Multiply top and bottom by the conjugate (2 + √5):
3/(2 − √5) × (2 + √5)/(2 + √5) = 3(2 + √5) / [(2)² − (√5)²]
= (6 + 3√5) / (4 − 5)
= (6 + 3√5) / (−1)
= −6 − 3√5
Combine surds using √a × √b = √(ab); multiply by the conjugate to remove a surd from the denominator.
Tom's pet eats 3/5 of a tin of food each day. Tom needs food for his pet for 12 days.
Calculate the number of tins of food Tom needs to buy.
Show model answer
Total tins needed = 3/5 × 12 = 36/5 = 7.2 tins
Since tins can only be bought whole, and 7 tins would not be enough,
Tom needs to buy 8 tins.
Multiply the daily amount by the number of days, then round up since partial tins can't be bought.
(a) Work out 1 1/3 × 8/9. Give your answer as a mixed number in its simplest form.
(b) Kate has a bunch of grapes. She ate 1/4 of the grapes in the morning. She ate 2/3 of the grapes in the afternoon.
Work out the fraction of the grapes that she has not eaten.
Show model answer
(a) 1 1/3 = 4/3
4/3 × 8/9 = 32/27
= 1 5/27
(b) Fraction not eaten = 1 − 1/4 − 2/3
Common denominator 12: 1 = 12/12, 1/4 = 3/12, 2/3 = 8/12
= 12/12 − 3/12 − 8/12
= 1/12
Convert the mixed number to an improper fraction before multiplying; use a common denominator to subtract from 1.
(a) Write down the value of the 5 in the number 253 624.
(b) The crowd at a sports event is exactly 35 687. Write this number correct to the nearest ten.
Show model answer
(a) The 5 is in the ten-thousands column.
Value = 50 000
(b) The units digit is 7, so round up.
35 687 = 35 690 (nearest ten)
Identify the column for the digit's value; look at the next digit down to round.
Work out.
(a) 74.6 × 10 − 3.89 × 100
(b) 5 + 3 × 2 − 1
Show model answer
(a) 74.6 × 10 = 746
3.89 × 100 = 389
746 − 389 = 357
(b) Multiply first: 3 × 2 = 6
5 + 6 − 1 = 10
Multiply before you add or subtract (order of operations).
Sessions with Number questions
| Session | Paper 1 | Paper 2 |
|---|---|---|
| May/June 2026 | 9 | 7 |
| May/June 2025 | 7 | 7 |
| Oct/Nov 2025 | 9 | 7 |
| May/June 2024 | 7 | 2 |
| Oct/Nov 2024 | 7 | 1 |
| May/June 2023 | 8 | 1 |
| Oct/Nov 2023 | 9 | 1 |
| May/June 2022 | 8 | 1 |
| Oct/Nov 2022 | 7 | 1 |
| May/June 2021 | 11 | 1 |
| Oct/Nov 2021 | 6 | 1 |
Common questions
What does the Number topic cover on this page?
118 real O Level Mathematics (4024) questions on Number from 2021 to 2026, from Paper 1, Paper 2. Each one shows the year, session and paper it came from.
Do I get the answers and explanations?
Yes. Every question shows the correct answer and a short explanation the moment you answer.
Is it free?
You can start free with no signup. A small set of papers per subject is free, and Premium unlocks every paper, the full question bank and the paper PDFs.