IGCSE Mathematics: Number — Practice Questions

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 — examination boards hold copyright in their own papers. Use these alongside the official past papers available free from your board.

Related: Number revision notes

Core or Extended: questions marked (Extended) use content in the Extended syllabus only: bounds of the result of a calculation (E1.10), reverse percentages (E1.13), and three-set Venn diagrams with the notation ∈, ∉, ∅, ⊆ and ⊈ (E1.2). All other questions use Core content.

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Section A

1. Write 84 as a product of its prime factors. [2]

2. Find the HCF and LCM of 84 and 126. [3]

Section B

3. Work out, giving your answers as fractions in their lowest terms:

(a) 3/4 + 2/5 [2] (b) 5/6 ÷ 10/9 [3]

4. A shop increases all prices by 8%, then reduces the new prices by 8% in a sale.

(a) Show that the final price is not the same as the original. [3] (b) Calculate the overall percentage change. [2]

5. $3600 is shared between A, B and C in the ratio 2 : 3 : 7.

(a) Calculate each share. [3] (b) C gives one third of his share to A. Calculate the new ratio A : B : C in its simplest form. [3]

6. Simple interest of $270 is earned on $1500 over 3 years. Calculate the annual rate. [3]

7. Calculate, giving your answer in standard form: (6.4 × 10⁻³) ÷ (1.6 × 10²) [3]

8. (Extended, E1.10) A rectangle measures 12.4 cm by 7.8 cm, each to 1 decimal place. Calculate the lower bound of its perimeter. [3]

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Section C

9. (Extended, E1.13) A price is $84 after a 20% increase. Calculate the original price. [2]

10. Calculate (4 × 10⁵) × (3 × 10³), giving your answer in standard form. [3]

11. Convert a speed of 72 km/h to m/s. [2]

12. (a) Write 0.000 405 in standard form. [1]

(b) Round 3.4567 to 3 significant figures. [1]

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Section D

13. ℰ = {x : x is an integer and 1 ⩽ x ⩽ 15}, P = {multiples of 3} and Q = {factors of 12}.

(a) List the elements of P ∩ Q. [1] (b) Find n(P ∪ Q). [1] (c) List the elements of (P ∪ Q)′. [1]

14. In a group of 40 students, 24 play football (F), 19 play basketball (B) and 6 play neither.

(a) Find the number of students who play both. [2] (b) Find n(F ∩ B′). [1] (c) Find n(F′). [1]

15. (Extended, E1.2) ℰ = {1, 2, 3, …, 12}, A = {even numbers}, B = {multiples of 3} and C = {factors of 12}.

(a) List the elements of A ∩ B ∩ C. [1] (b) List the elements of (A ∪ B ∪ C)′. [1] (c) Say whether each statement is true or false: (i) 9 ∈ C (ii) B ⊆ A (iii) A ∩ B ∩ C′ = ∅. [3] (d) Find n(A ∪ C). [1]

16. (a) Write 3/8 as (i) a decimal, (ii) a percentage. [2] (b) Write 45% as a fraction in its simplest form. [1] (c) Write 2⅗ as an improper fraction. [1] (d) Write 0.72 as a fraction in its simplest form. [2]

17. (a) Write these numbers in order of size, starting with the smallest: 0.65, 2/3, 64%, 5/8, 0.6 [2] (b) Write the correct symbol, <, > or =, between each pair: (i) −7 … −4 (ii) 0.3 … 3/10 (iii) 0.45 … 0.405 [3] (c) List all the integers n such that −2 < n ⩽ 3. [1]

18. (a) Write down the value of (i) √196, (ii) ∛1000. [2] (b) Work out 3⁴ − ∛64. [2] (c) Use your calculator to find the fifth root of 7776. [1]

19. A cyclist rides 27 km in 1 hour 48 minutes. She rests for 12 minutes, then rides a further 13 km in 42 minutes.

(a) Calculate her average speed for the first 27 km, in km/h. [2] (b) Calculate her average speed for the whole journey, including the rest, in km/h. Give your answer correct to 3 significant figures. [3]

20. (a) Use your calculator to work out (5.8 + 3.46) ÷ (2.1 × 1.7). Write down all the figures on your calculator display, then give your answer correct to 3 significant figures. [2] (b) A calculation gives a time of 4.35 hours. Write this time in hours and minutes. [1] (c) The answer to a calculation of a cost in dollars is displayed as 7.5. Write the cost as it should be written in money. [1] (d) A student types −4² into a calculator to work out (−4)² and gets −16. Explain the error and give the correct value. [2]

21. (a) Write 7.45 p.m. in the 24-hour clock. [1] (b) Write 00 20 in the 12-hour clock. [1] (c) A film starts at 18 50 and lasts 2 hours 25 minutes. At what time does it finish? [1] (d) Part of a train timetable is shown.

Northgate    06 55   07 35   08 20
Hill Road    07 09   07 49   08 34
Central      07 31   08 11   08 56
Harbour      07 48   08 28   09 13

(i) How long does the journey from Northgate to Harbour take? [1] (ii) Sam arrives at Hill Road at 07 55. What is the earliest time he can arrive at Central? [1] (e) City B is 4 hours behind City A. A plane leaves City A at 23 20 local time and the flight takes 6 hours 55 minutes. Find the local time in City B when the plane lands. [2]

22. On one day the exchange rate is £1 = €1.15.

(a) Change £240 into euros. [1] (b) Change €92 into pounds. [2] (c) A jacket costs £65 in London and €78 in Paris. In which city is it cheaper, and by how much in pounds? [3]

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Answers

1. 84 = 2 × 2 × 3 × 7 [1] = 2² × 3 × 7 [1].

2. 126 = 2 × 3² × 7 [1]. HCF = 2 × 3 × 7 = 42 [1]; LCM = 2² × 3² × 7 = 252 [1].

3. (a) 15/20 + 8/20 [1] = 23/20 (or 1 3/20) [1]. (b) 5/6 × 9/10 [1] = 45/60 [1] = 3/4 [1].

4. (a) Take an original price of $100. After the increase: 100 × 1.08 = $108 [1]. After the reduction: 108 × 0.92 = $99.36 [1], which is less than $100, because the 8% reduction is calculated on the larger amount [1]. (b) Change = −0.64 ÷ 100 [1] = a decrease of 0.64% [1].

5. (a) Total parts = 12 [1]; one part = $300 [1]; A = $600, B = $900, C = $2100 [1]. (b) C gives away $700 [1]; A = 1300, B = 900, C = 1400 [1]; ratio = 1300 : 900 : 1400 = 13 : 9 : 14 [1].

6. I = PRT ÷ 100, so 270 = 1500 × R × 3 ÷ 100 [1]; 270 = 45R [1]; R = 6% per year [1].

7. 6.4 ÷ 1.6 = 4 [1]; 10⁻³ ÷ 10² = 10⁻⁵ [1]; = 4 × 10⁻⁵ [1].

8. Lower bounds are 12.35 cm and 7.75 cm [1]; perimeter = 2(12.35 + 7.75) [1] = 40.2 cm [1].

9. 84 ÷ 1.2 [1] = $70 [1]. Dividing (not subtracting 20%) is essential — 20% of $84 is not the same as 20% of the original price.

10. 4 × 3 = 12 [1]; 10⁵ × 10³ = 10⁸ [1]; 12 × 10⁸ = 1.2 × 10⁹ (renormalised, since 12 lies outside 1 ⩽ a < 10) [1].

11. 72 km/h = 72 000 m/h [1]; ÷ 3600 = 20 m/s [1]. Both the distance unit (km→m) and the time unit (h→s) must be converted — converting only one is the standard error.

12. (a) 4.05 × 10⁻⁴ [1]. (b) 3.46 [1].

Common mistake: writing 40.5 × 10⁻⁵ (the first number must be between 1 and 10), or counting decimal places instead of significant figures.

13. (a) P = {3, 6, 9, 12, 15} and Q = {1, 2, 3, 4, 6, 12}, so P ∩ Q = {3, 6, 12} [1]. (b) P ∪ Q = {1, 2, 3, 4, 6, 9, 12, 15}, so n(P ∪ Q) = 8 [1]. (c) (P ∪ Q)′ = {5, 7, 8, 10, 11, 13, 14} [1]. Check: 8 + 7 = 15 = n(ℰ).

14. (a) n(F ∪ B) = 40 − 6 = 34 [1]; both = 24 + 19 − 34 = 9 [1]. (b) F ∩ B′ is “football only”: 24 − 9 = 15 [1]. (c) n(F′) = 40 − 24 = 16 [1] (basketball only, 10, plus neither, 6). Check: 15 + 9 + 10 + 6 = 40.

Common mistake: adding 24 + 19 = 43 and not noticing that this is more than the 34 students who play at least one sport: the 9 who play both have been counted twice.

15. (a) A = {2, 4, 6, 8, 10, 12}, B = {3, 6, 9, 12}, C = {1, 2, 3, 4, 6, 12}; A ∩ B ∩ C = {6, 12} [1]. (b) 1 is in C, 2, 4, 8 and 10 are in A, 3 and 9 are in B, so the only elements in none of the sets are {5, 7, 11} [1]. (c) (i) False: 9 is not a factor of 12 [1]. (ii) False: 3 ∈ B but 3 ∉ A [1]. (iii) True: A ∩ B = {6, 12}, and both are in C, so no element is in A and B but not C [1]. (d) A ∪ C = {1, 2, 3, 4, 6, 8, 10, 12}, so n(A ∪ C) = 8 [1].

The full three-set Venn diagram: A only {8, 10}; B only {9}; C only {1}; A and C only {2, 4}; B and C only {3}; A and B only: empty; all three {6, 12}; outside all three {5, 7, 11}. The regions hold 2 + 1 + 1 + 2 + 1 + 0 + 2 + 3 = 12 elements.

16. (a) (i) 3 ÷ 8 = 0.375 [1]; (ii) 0.375 × 100 = 37.5% [1]. (b) 45/100 = 9/20 (dividing top and bottom by 5) [1]. (c) 2 × 5 + 3 = 13, so 2⅗ = 13/5 [1]. (d) 0.72 = 72/100 [1] = 18/25 (dividing top and bottom by 4) [1].

17. (a) As decimals: 0.65, 0.666…, 0.64, 0.625, 0.6 [1]. In order: 0.6, 5/8, 64%, 0.65, 2/3 [1]. (b) (i) −7 < −4 [1] (ii) 0.3 = 3/10 [1] (iii) 0.45 > 0.405 [1] (compare the hundredths: 5 > 0). (c) n is greater than −2 (so −2 itself is not included) and less than or equal to 3: −1, 0, 1, 2, 3 [1].

18. (a) (i) 14 [1] (ii) 10 [1]. (b) 3⁴ = 81 and ∛64 = 4 [1]; 81 − 4 = 77 [1]. (c) 6 [1] (check: 6⁵ = 7776).

19. (a) 1 hour 48 minutes = 1 + 48/60 = 1.8 hours [1]; 27 ÷ 1.8 = 15 km/h [1]. (b) Total distance = 27 + 13 = 40 km [1]. Total time = 108 + 12 + 42 = 162 minutes = 2.7 hours [1]. Average speed = 40 ÷ 2.7 = 14.81… = 14.8 km/h [1].

Common mistake: leaving out the rest, or writing 1 hour 48 minutes as 1.48 hours.

20. (a) Display: 2.593837535 [1]; 2.59 (3 s.f.) [1]. Brackets are needed around both the top and the bottom. (b) 0.35 × 60 = 21 minutes, so 4 hours 21 minutes [1] (not 4 hours 35 minutes). (c) $7.50 [1]. (d) The calculator squares 4 first and then applies the minus sign, giving −(4²) [1]. Using brackets, (−4)² = 16 [1].

21. (a) 19 45 [1]. (b) 12.20 a.m. [1] (20 minutes after midnight). (c) 18 50 + 2 h = 20 50; + 25 min = 21 15 (9.15 p.m.) [1]. (d) (i) 06 55 to 07 48 is 53 minutes [1] (the same for every train). (ii) The 07 49 has already left, so he catches the 08 34 and arrives at Central at 08 56 [1]. (e) 23 20 + 6 h 55 min = 06 15 the next day, in City A time [1]. City B is 4 hours behind: 02 15 the next day [1].

22. (a) 240 × 1.15 = €276 [1]. (b) 92 ÷ 1.15 [1] = £80 [1]. (c) €78 = 78 ÷ 1.15 = £67.826… = £67.83 [1]. It is cheaper in London [1], by 67.83 − 65 = £2.83 [1].

Common mistake: multiplying by 1.15 when changing euros into pounds. Each pound buys more than one euro, so the amount in pounds must be the smaller number.

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Where marks are usually lost

• Assuming an 8% rise followed by an 8% fall returns to the original price.
• Dividing the total by the number of names rather than by the number of parts.
• Using the upper bound of one dimension and the lower bound of the other.
• Giving a standard form answer with a first factor outside 1 ≤ a < 10.
• Subtracting the percentage directly from the final value in a reverse-percentage question, instead of dividing by the multiplier.
• Counting the overlap of a Venn diagram twice, or putting the “in both” total into the “only” regions of a three-set diagram.
• Subtracting clock times as decimals, or reading 4.35 hours as 4 hours 35 minutes.
• Multiplying instead of dividing in a currency conversion.

Examiner report insight

• Working left to right instead of following the order of operations (BIDMAS/PENDMAS) – e.g. treating 28 - 8 / 2 as (28 - 8) / 2 rather than 28 - (8 / 2).
• Rounding only the final answer when a question specifically instructs each value to be rounded first (e.g. “correct each number to 1 significant figure, then calculate”) – the instruction applies before the calculation, not after.
• (Extended) Misreading which digits recur in a recurring decimal before applying the standard “multiply by 10 to the n, subtract” method – treating it as terminating, or misidentifying the repeating block, invalidates the rest of a correct method.
• After multiplying or dividing two numbers in standard form, mishandling the index arithmetic – indices are added when multiplying and subtracted when dividing, separately from renormalising the mantissa back into the range 1 <= a < 10.
• In a compound unit conversion, converting only the unit that catches the eye and forgetting the other – how many parts need converting depends on what’s changing: km/h to m/h only requires converting the distance unit (km to m), since the time unit (h) is unchanged, but km/h to m/s requires converting both the distance (km to m) AND the time (h to s), since both units differ between the two forms.

Source: Cambridge International, 0580 Mathematics Principal Examiner Report, June 2024 series, Papers 11, 12, 13, 21, 23 (verified 2026-09-02).