O Level Mathematics: Number Practice Questions (Cambridge 4024)

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs — Cambridge International holds copyright in its own papers. Use these alongside the official past papers available from your board.

Most questions practise a skill tested in the June 2025 papers. Questions marked (no calculator) are Paper 1 style; the rest allow a calculator, as in Paper 2. After each answer there is a tip and the real question to try next.

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Questions

1. (no calculator) Work out (a) 7 − 3 × (−5) (b) 60 × 0.3. [2]

2. (no calculator) Write 180 as a product of its prime factors. [2]

3. (no calculator) Find the highest common factor (HCF) and the lowest common multiple (LCM) of 84 and 90. [3]

4. (no calculator) In a sale, all prices are reduced by 15%. (a) A jacket costs $60 before the sale. Find its sale price. (b) The sale price of a bag is $68. Find its price before the sale. [3]

5. (a) Write the ratio 250 ml : 1.5 litres in its simplest form. (b) Share $720 in the ratio 2 : 3 : 4. Find the largest share. [3]

6. (no calculator) By rounding each number to 1 significant figure, estimate the value of (61.2 × 3.87) ÷ 0.198. [2]

7. (no calculator) (a) Simplify √75 − √12. (b) Rationalise the denominator of 6/√3. [3]

8. (no calculator) Write the recurring decimal 0.272727… as a fraction in its simplest form. [2]

9. $3000 is invested at 2% per year compound interest. Find the total interest after 2 years. [3]

10. A distance of 400 m is measured correct to the nearest 10 m. The time taken is 50 seconds, correct to the nearest second. Find the upper bound of the average speed. [3]

11. A country has a population of 4.8 × 10⁷ and an area of 6 × 10⁵ km². Find the population density, in people per km². [2]

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Answers

1. (a) 3 × (−5) = −15, so 7 − (−15) = 22 [1]. (b) 18 [1].

Tip: do the multiplication before the subtraction, and take care with two negative signs.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 1.

2. 180 = 2 × 90 = 2 × 2 × 45 = 2 × 2 × 3 × 3 × 5 [1] = 2² × 3² × 5 [1].

Tip: divide by the smallest prime each time, and check by multiplying back.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 10.

3. 84 = 2² × 3 × 7 and 90 = 2 × 3² × 5 [1]. HCF = 2 × 3 = 6 [1]. LCM = 2² × 3² × 5 × 7 = 1260 [1].

Tip: HCF uses the lowest power of each shared prime; LCM uses the highest power of every prime.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 10.

4. (a) 85% of 60 = 0.85 × 60 = $51 [1]. (b) 68 is 85% of the original price [1], so the original price = 68 ÷ 0.85 = $80 [1].

Tip: to reverse a percentage change, divide by the multiplier. Adding 15% of the sale price gives the wrong answer.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 13.

5. (a) 250 : 1500 = 1 : 6 [1]. (b) 2 + 3 + 4 = 9 parts, so one part = 720 ÷ 9 = $80 [1]. Largest share = 4 × 80 = $320 [1].

Tip: put both quantities in the same units before you simplify a ratio.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 3.

6. (60 × 4) ÷ 0.2 [1] = 240 ÷ 0.2 = 1200 [1].

Tip: show the rounded values; the method mark depends on them.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 9.

7. (a) √75 = 5√3 and √12 = 2√3 [1], so the answer is 3√3 [1]. (b) 6/√3 × √3/√3 = 6√3/3 = 2√3 [1].

Tip: look for the largest square factor inside each root.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 15.

8. Let x = 0.2727…; then 100x = 27.2727…, so 99x = 27 [1] and x = 27/99 = 3/11 [1].

Tip: multiply by 10 to the power of the length of the repeating block, then subtract.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 20.

9. Value = 3000 × 1.02² [1] = $3121.20 [1]. Interest = $121.20 [1].

Tip: the question asks for the interest, so subtract the amount invested at the end.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 11.

10. Upper bound of distance = 405 m; lower bound of time = 49.5 s [1]. Upper bound of speed = 405 ÷ 49.5 [1] = 8.18 m/s [1].

Tip: for the largest speed, divide the largest distance by the smallest time.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 23.

11. (4.8 × 10⁷) ÷ (6 × 10⁵) = 0.8 × 10² [1] = 80 people per km² [1].

Tip: divide the number parts and subtract the powers of 10 separately.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 16.

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Where marks are usually lost

• Dividing by the wrong bound in a bounds question.
• Adding the percentage back on instead of dividing by the multiplier.
• Leaving a surd or fraction not fully simplified.
• Giving the total amount when the question asks for the interest.