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O Level / IGCSE Mathematics MCQs with answers

Practise O Level / IGCSE Mathematics (4024 / 0580) with 576 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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O Level / IGCSE Mathematics MCQs with answers

Practise O Level / IGCSE Mathematics (4024 / 0580) with 576 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.

576 questions · 9 chapters

What each chapter covers 9 chapters

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

  1. Number 147 questionsTypes of number, Sets, Powers and roots, Fractions, decimals and percentages, Ordering, The four operations, Indices I, Standard form, Estimation, Limits of accuracy, Ratio and proportion, Rates, Percentages, Using a calculator, Time, Money, Exponential growth and decay, Surds
  2. Algebra and graphs 107 questionsIntroduction to algebra, Algebraic manipulation, Algebraic fractions, Indices II, Equations, Inequalities, Sequences, Proportion, Graphs in practical situations, Graphs of functions, Sketching curves, Functions
  3. Coordinate geometry 56 questionsCoordinates, Drawing linear graphs, Gradient of linear graphs, Length and midpoint, Equations of linear graphs, Parallel lines, Perpendicular lines
  4. Geometry 72 questionsGeometrical terms, Geometrical constructions, Scale drawings, Similarity, Symmetry, Angles, Circle theorems I, Circle theorems II
  5. Mensuration 44 questionsUnits of measure, Area and perimeter, Circles, arcs and sectors, Surface area and volume, Compound shapes and parts of shapes
  6. Trigonometry 36 questionsPythagoras’ theorem, Right-angled triangles, Non-right-angled triangles, Pythagoras’ theorem and trigonometry
  7. Transformations and vectors 27 questionsTransformations, Vectors in two dimensions, Magnitude of a vector
  8. Probability 27 questionsIntroduction to probability, Relative and expected frequencies, Probability of combined events
  9. Statistics 60 questionsClassifying statistical data, Interpreting statistical data, Averages and measures of spread, Statistical charts and diagrams, Scatter diagrams, Cumulative frequency diagrams, Histograms
Sample O Level / IGCSE Mathematics MCQs with answers 12 questions

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

1. Which of these has the largest value?

  1. A
    25
  2. B
    52
  3. C
    33
  4. D
    42
Show answer

Answer: A. 25 = 32, 52 = 25, 33 = 27 and 42 = 16. The largest is 25.

2. A speed–time graph is a straight line from 4 m/s at t = 0 to 16 m/s at t = 6 s. Find the acceleration.

  1. A
    2.67 m/s2
  2. B
    2 m/s2
  3. C
    0.67 m/s2
  4. D
    72 m/s2
Show answer

Answer: B. Acceleration = gradient = change in speed ÷ time = (16 − 4) ÷ 6 = 2 m/s2. Using 16 ÷ 6 ignores the starting speed.

3. Three vertices of a rectangle are (1, 2), (5, 2) and (5, 6). What are the coordinates of the fourth vertex?

  1. A
    (6, 1)
  2. B
    (1, −2)
  3. C
    (5, 1)
  4. D
    (1, 6)
Show answer

Answer: D. The fourth vertex is directly above (1, 2) and level with (5, 6), so it is (1, 6). x-coordinate first, then y.

4. A net consists of one square with a congruent isosceles triangle attached to each of its four sides. Which solid does it fold to make?

  1. A
    cube
  2. B
    tetrahedron
  3. C
    triangular prism
  4. D
    square-based pyramid
Show answer

Answer: D. The square is the base and the four triangles fold up to meet at the apex: a square-based pyramid. A tetrahedron has four triangular faces and no square.

5. The diagonals of a rhombus are 10 cm and 16 cm long. Find its area.

  1. A
    52 cm2
  2. B
    80 cm2
  3. C
    40 cm2
  4. D
    160 cm2
Show answer

Answer: B. The diagonals cross at right angles and split the rhombus into 4 right-angled triangles with legs 5 cm and 8 cm: 4 × ½ × 5 × 8 = 80 cm2. This equals ½ × 10 × 16. Forgetting the ½ gives 160.

6. An equilateral triangle has sides of 8 cm. Find its perpendicular height, correct to 3 significant figures.

  1. A
    8.94 cm
  2. B
    5.66 cm
  3. C
    4.00 cm
  4. D
    6.93 cm
Show answer

Answer: D. The height bisects the base into 4 cm and 4 cm: h = √(82 − 42) = √48 = 6.93 cm. Adding the squares gives √80 = 8.94.

7. The point (5, 7) is enlarged by scale factor 1/2 with centre (1, 1). Find the image of the point.

  1. A
    (2.5, 3.5)
  2. B
    (4, 5)
  3. C
    (9, 13)
  4. D
    (3, 4)
Show answer

Answer: D. From the centre (1, 1) to (5, 7) is 4 across and 6 up. Halve these: 2 across and 3 up from the centre gives (3, 4). Halving the coordinates themselves only works when the centre is the origin.

8. The probability that a bus is late on any day is 0.2, independently of other days. Find the probability that over two days it is late on exactly one day.

  1. A
    0.16
  2. B
    0.04
  3. C
    0.32
  4. D
    0.36
Show answer

Answer: C. On a tree diagram there are two branches: late then not late (0.2 × 0.8) and not late then late (0.8 × 0.2). Total 0.16 + 0.16 = 0.32. Counting only one branch gives 0.16.

9. A line of best fit passes through the points (10, 25) and (30, 65). Use it to estimate y when x = 20.

  1. A
    50
  2. B
    55
  3. C
    40
  4. D
    45
Show answer

Answer: D. The gradient is (65 − 25) ÷ (30 − 10) = 2, so from (10, 25) a rise of 10 in x adds 20: y = 25 + 20 = 45.

10. A = {x : x is an integer, −2 < x ≤ 3}. Find n(A).

  1. A
    5
  2. B
    6
  3. C
    4
  4. D
    3
Show answer

Answer: A. The integers greater than −2 and up to and including 3 are −1, 0, 1, 2, 3, so n(A) = 5. −2 is not included because of the strict <.

11. Solve the simultaneous equations 2x + 3y = 13 and 3x − y = 3.

  1. A
    x = 3, y = 2
  2. B
    x = 5, y = 1
  3. C
    x = 2, y = 3
  4. D
    x = 2, y = −3
Show answer

Answer: C. From the second equation y = 3x − 3. Substitute: 2x + 3(3x − 3) = 13, so 11x − 9 = 13 and x = 2, then y = 3. Always check in both equations: x = 5, y = 1 fits the first but not the second.

12. Find the equation of the line parallel to y = x/2 + 3 that passes through (4, −1).

  1. A
    y = x/2 + 1
  2. B
    y = −2x + 7
  3. C
    y = x/2 − 1
  4. D
    y = x/2 − 3
Show answer

Answer: D. Same gradient 1/2, so y = x/2 + c. Substitute (4, −1): −1 = 2 + c, so c = −3. Equation y = x/2 − 3.

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Ways to practise 5 ways

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The 576 MCQs are our own, written to the syllabus in the style of the exam.

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