Two sets of 12 multiple-choice questions on GCSE Maths. Choose one answer for each question, press “Check my answers” at the end of the set, and read the short explanation under each question. Nothing is saved or sent anywhere, and you can clear a set and try again.
Set 1 covers number, algebra and ratio. Set 2 covers geometry, probability and statistics. Work out each answer on paper first, as you would in the non-calculator paper, then pick your option. These are practice questions written for Sessioned, not past exam questions. If you are unsure of a method, look it up in the glossary or read the revision guide .
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Set 1: number, algebra and ratio Question 1 of 12. What is the value of 3 + 4 × 2²? A. 19 B. 28 C. 49 D. 11 Powers come first: 2² = 4. Multiplication is next: 4 × 4 = 16. Then add 3 to get 19.
Question 2 of 12. What is the highest common factor of 24 and 36? A. 6 B. 12 C. 72 D. 4 Factors of 24 include 1, 2, 3, 4, 6, 8, 12 and 24. Factors of 36 include 12 and 18. Largest factor they share: 12.
Question 3 of 12. Write 0.00045 in standard form. A. 4.5 × 10−5 B. 4.5 × 104 C. 4.5 × 10−3 D. 4.5 × 10−4 First non-zero digit is 4, which is four places after the decimal point, so the power is −4: 4.5 × 10−4 .
Question 4 of 12. Solve 3x − 7 = 11. A. x = 18B. x = 6C. x = 4/3D. x = 5Add 7 to both sides to get 3x = 18, then divide by 3 to get x = 6. Check: 18 − 7 = 11.
Question 5 of 12. Expand and simplify (x + 3)(x + 5). A. x ² + 15B. x ² + 8x + 8C. x ² + 8x + 15D. x ² + 15x + 8Multiply each term: x ² + 5x + 3x + 15. Collect the middle terms to get x ² + 8x + 15.
Question 6 of 12. Factorise x ² + 5x + 6. A. (x + 1)(x + 6) B. (x + 2)(x + 3) C. (x − 2)(x − 3) D. (x + 5)(x + 1) Look for two numbers that multiply to 6 and add to 5. Those are 2 and 3, so the answer is (x + 2)(x + 3).
Question 7 of 12. Make y the subject of x = 3y + 2. A. y = (x + 2)/3B. y = 3(x − 2)C. y = x /3 − 2D. y = (x − 2)/3Subtract 2 from both sides to get x − 2 = 3y , then divide everything on the left by 3. Test with y = 1: x = 5, and (5 − 2)/3 = 1.
Question 8 of 12. £60 is shared in the ratio 2 : 3. How much is the larger share? A. £24 B. £30 C. £36 D. £40 There are 2 + 3 = 5 parts, so one part is £60 ÷ 5 = £12. Larger share: 3 × £12 = £36.
Question 9 of 12. A price of £80 is increased by 15%. What is the new price? A. £95 B. £12 C. £68 D. £92 An increase of 15% means multiplying by 1.15. 80 × 1.15 = 92. (15% of 80 is £12, which is only the increase.)
Question 10 of 12. 5 pens cost £3.50. Assuming the same price for each pen, how much do 8 pens cost? A. £5.60 B. £5.50 C. £6.40 D. £4.90 One pen costs £3.50 ÷ 5 = £0.70. Eight pens cost 8 × £0.70 = £5.60.
Question 11 of 12. Which of these numbers is irrational? A. √49 B. 0.25 C. 3/8 D. √7 √49 = 7, 0.25 = 1/4 and 3/8 are all fractions of integers. √7 is not a whole number, and its decimal never ends or repeats, so it is irrational.
Question 12 of 12. What is the value of 2−3 ? A. −8 B. −6 C. 1/8 D. 1/6 A negative power means a reciprocal: 2−3 = 1/23 = 1/8.
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Set 2: geometry, probability and statistics Question 1 of 12. A triangle has angles of 48° and 67°. What is the third angle? A. 115° B. 65° C. 75° D. 55° Angles in a triangle add to 180°. 48 + 67 = 115, and 180 − 115 = 65, so the third angle is 65°.
Question 2 of 12. What is the sum of the interior angles of a pentagon? A. 360° B. 450° C. 720° D. 540° A pentagon can be split into 3 triangles, and 3 × 180° = 540°. General rule: (n − 2) × 180°.
Question 3 of 12. A circle has radius 5 cm. What is its area, in terms of π? A. 10π cm² B. 25π cm² C. 5π cm² D. 100π cm² Area = πr ² = π × 5² = 25π cm². (10π would be the circumference.)
Question 4 of 12. A right-angled triangle has shorter sides of 6 cm and 8 cm. How long is the hypotenuse? A. 14 cm B. 12 cm C. 10 cm D. 7 cm Pythagoras: 6² + 8² = 36 + 64 = 100, and √100 = 10. Hypotenuse = 10 cm.
Question 5 of 12. A cuboid measures 4 cm by 5 cm by 3 cm. What is its volume? A. 94 cm³ B. 60 cm³ C. 12 cm³ D. 60 cm² Volume = 4 × 5 × 3 = 60, in cubic centimetres. (94 is the surface area, and that would be in cm².)
Question 6 of 12. B is on a bearing of 070° from A. What is the bearing of A from B? A. 110° B. 290° C. 070° D. 250° Return bearings differ by 180°. 70 + 180 = 250, so the bearing of A from B is 250°.
Question 7 of 12. A fair six-sided dice is rolled. What is the probability of getting a prime number? A. 1/3 B. 1/6 C. 1/2 D. 2/3 Primes on a dice are 2, 3 and 5, which is 3 outcomes out of 6. That is 3/6 = 1/2. (1 is not prime.)
Question 8 of 12. A fair coin is flipped and a fair six-sided dice is rolled. What is the probability of a head and a six? A. 1/12 B. 2/3 C. 1/8 D. 1/2 These events are independent, so multiply: 1/2 × 1/6 = 1/12.
Question 9 of 12. What is the mean of 4, 7, 7, 9 and 13? A. 7 B. 8 C. 9 D. 10 Add the values: 4 + 7 + 7 + 9 + 13 = 40. Divide by 5 to get 8. (7 is the median and the mode.)
Question 10 of 12. What is the median of 3, 9, 4, 12, 6 and 8? A. 6 B. 8 C. 7 D. 9 In order: 3, 4, 6, 8, 9, 12. There are six values, so take the number halfway between the middle two: (6 + 8) ÷ 2 = 7.
Question 11 of 12. Score 1 has frequency 2, score 2 has frequency 3 and score 3 has frequency 5. What is the mean score? A. 2 B. 3.3 C. 23 D. 2.3 Multiply each score by its frequency: 2 + 6 + 15 = 23. Total frequency is 10, so the mean is 23 ÷ 10 = 2.3.
Question 12 of 12. What is the gradient of the straight line through (1, 2) and (3, 8)? A. 1/3 B. 3 C. 6 D. 2 Change in y is 8 − 2 = 6 and the change in x is 3 − 1 = 2. Gradient = 6 ÷ 2 = 3.
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Part of the GCSE Maths revision set: the revision guide , glossary of key terms and comparison of the three exam boards .