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GCSE Maths (AQA) MCQs with answers

Practise GCSE Maths (AQA) (AQA 8300) with 284 exam-style MCQs, each with the answer and a short explanation. Every test is marked the moment you finish and shows your score chapter by chapter, so you know what to revise next. It is free and needs no sign-up.

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GCSE Maths (AQA) MCQs with answers

Practise GCSE Maths (AQA) (AQA 8300) with 284 exam-style MCQs, each with the answer and a short explanation. Every test is marked the moment you finish and shows your score chapter by chapter, so you know what to revise next. It is free and needs no sign-up.

284 questions · 6 chapters

What each chapter covers 6 chapters

The questions follow the syllabus chapter by chapter. You can test the whole subject or one chapter at a time.

  1. Number 46 questionsN1–N5 Structure and calculation, N6–N7, N9 Powers, roots, indices and standard form, N8 Surds and exact calculation, N10–N12 Fractions, decimals and percentages, N13–N16 Measures, estimation and bounds
  2. Algebra 74 questionsA1–A4 Algebraic expressions, A5–A7 Formulae, identities, proof and functions, A8–A10 Coordinates and straight-line graphs, A11–A13 Quadratic and other graphs, A14–A16 Graphs in context, gradients, areas and circles, A17–A18, A20 Solving equations, A19, A21–A22 Simultaneous equations and inequalities, A23–A25 Sequences
  3. Ratio, proportion and rates of change 46 questionsR1–R8 Units, scale and ratio, R9 Percentages, R10, R13 Direct and inverse proportion, R11, R14–R15 Compound measures and rates of change, R16 Growth and decay
  4. Geometry and measures 77 questionsG1–G4, G15 Angles, polygons and bearings, G7–G8 Transformations, G9–G10 Circle theorems, G14, G16–G18 Area, volume and surface area, G5–G6, G19 Congruence and similarity, G20–G21 Pythagoras and trigonometry, G22–G23 Sine rule, cosine rule and area of a triangle, G24–G25 Vectors
  5. Probability 20 questionsP1–P5 Probability and expected outcomes, P6–P9 Combined events and conditional probability
  6. Statistics 21 questionsS1–S3 Sampling and statistical diagrams, S4–S6 Averages, spread and scatter graphs
Sample GCSE Maths (AQA) MCQs with answers 12 questions

12 questions from the test, one or two from each chapter. Try each one, then open the answer.

1. Write √72 in the form a√2.

  1. A
    6√2
  2. B
    36√2
  3. C
    3√2
  4. D
    12√2
Show answer

Answer: A. 72 = 36 × 2, so √72 = √36 × √2 = 6√2. The 36 must be square-rooted when it comes out of the root.

2. A circle has centre (0, 0) and passes through (5, −12). What is its equation?

  1. A
    x2 + y2 = 169
  2. B
    x2 + y2 = 13
  3. C
    x2 + y2 = 17
  4. D
    x2 + y2 = 289
Show answer

Answer: A. r2 = 52 + (−12)2 = 25 + 144 = 169, so x2 + y2 = 169. The right-hand side is r2, not r (r = 13).

3. a : b = 3 : 4 and b : c = 6 : 5. What is a : c in its simplest form?

  1. A
    3 : 5
  2. B
    9 : 10
  3. C
    1 : 2
  4. D
    18 : 15
Show answer

Answer: B. Make b the same in both: a : b = 9 : 12 and b : c = 12 : 10, so a : c = 9 : 10. Just taking the first and last numbers (3 : 5) ignores that b is different in each ratio.

4. OA = a and OB = b. M is the midpoint of AB. Which expression is the vector OM?

  1. A
    ½(b − a)
  2. B
    a + ½b
  3. C
    ½(a + b)
  4. D
    b − a
Show answer

Answer: C. OM = OA + ½AB = a + ½(b − a) = ½a + ½b = ½(a + b). ½(b − a) is only AM.

5. A and B are independent events with P(A) = 0.3 and P(B) = 0.6. What is P(A and B)?

  1. A
    0.9
  2. B
    0.72
  3. C
    0.18
  4. D
    0.09
Show answer

Answer: C. For independent events multiply: 0.3 × 0.6 = 0.18. Adding (0.9) is for mutually exclusive events with "or".

6. A table shows times t minutes: 0 < t ≤ 10, frequency 4; 10 < t ≤ 20, frequency 10; 20 < t ≤ 30, frequency 6. What is an estimate of the mean?

  1. A
    106.7 minutes
  2. B
    16 minutes
  3. C
    15 minutes
  4. D
    20 minutes
Show answer

Answer: B. Use midpoints: 4 × 5 + 10 × 15 + 6 × 25 = 20 + 150 + 150 = 320, and 320 ÷ 20 = 16 minutes. Dividing by 3 (the number of classes) gives 106.7.

7. Rationalise the denominator of 4/(3 − √5), simplifying fully.

  1. A
    (12 + 4√5)/14
  2. B
    3 − √5
  3. C
    3 + √5
  4. D
    12 + 4√5
Show answer

Answer: C. Multiply top and bottom by 3 + √5: the denominator becomes 9 − 5 = 4, so 4(3 + √5)/4 = 3 + √5. Using 9 + 5 in the denominator is the common slip.

8. Line L has equation y = 2x − 7. Find the equation of the line perpendicular to L that passes through (4, 1).

  1. A
    y = −2x + 9
  2. B
    y = ½x − 1
  3. C
    y = −½x − 1
  4. D
    y = −½x + 3
Show answer

Answer: D. Perpendicular gradient = −1 ÷ 2 = −½. Then 1 = −½ × 4 + c, so c = 3. Using −2 changes the sign but forgets to take the reciprocal.

9. Vn+1 = 0.9Vn + 50 and V0 = 1000. Find V2.

  1. A
    950
  2. B
    860
  3. C
    910
  4. D
    905
Show answer

Answer: D. V1 = 0.9 × 1000 + 50 = 950. V2 = 0.9 × 950 + 50 = 855 + 50 = 905. Adding 50 only once, after 0.92, gives 860.

10. Two similar solids have surface areas 45 cm2 and 80 cm2. The smaller has volume 54 cm3. What is the volume of the larger?

  1. A
    96 cm3
  2. B
    128 cm3
  3. C
    72 cm3
  4. D
    170.7 cm3
Show answer

Answer: B. Area factor 80/45 = 16/9, so the length factor is 4/3 and the volume factor is 64/27. 54 × 64/27 = 128 cm3. Multiplying by the area factor gives 96 cm3.

11. A bag holds only red, blue and green balls. P(red) = 0.35 and P(blue) = 0.4. What is P(green)?

  1. A
    0.25
  2. B
    0.75
  3. C
    0.14
  4. D
    0.65
Show answer

Answer: A. The probabilities of all outcomes add to 1: 1 − 0.35 − 0.4 = 0.25. 0.75 is P(red or blue).

12. The mean of five numbers is 12. A sixth number is added and the mean becomes 13. What is the sixth number?

  1. A
    18
  2. B
    13
  3. C
    1
  4. D
    78
Show answer

Answer: A. The totals are 5 × 12 = 60 and 6 × 13 = 78, so the sixth number is 78 − 60 = 18.

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Ways to practise 5 ways

When you get a question wrong, a short note called "The idea behind this" explains the topic it belongs to, with the rules to remember and a worked example.

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How many GCSE Maths (AQA) questions are there?

284 MCQs with answers, covering 6 chapters of the syllabus. Each test draws new questions, so you can practise many times.

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No. The 284 MCQs are our own, written to the syllabus in the style of the exam.

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