O Level / IGCSE Mathematics chapter 2: Algebra and graphs MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

107 exam-style questions on Algebra and graphs, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

107 questions · 12 topics · 10 per test

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What chapter 2 covers

Ten Algebra and graphs questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. 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.

2. 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.

3. Solve 5(x − 3) = 2x + 6.

  1. A
    x = 3
  2. B
    x = 21
  3. C
    x = 7
  4. D
    x = −7
Show answer

Answer: C. Expand: 5x − 15 = 2x + 6. Then 3x = 21, so x = 7. Multiplying only the x by 5 (5x − 3) gives x = 3.

4. Write x/3 − (x − 2)/5 as a single fraction in its simplest form.

  1. A
    (2x − 6)/15
  2. B
    (2x + 6)/15
  3. C
    (2x − 2)/15
  4. D
    (8x − 6)/15
Show answer

Answer: B. Common denominator 15: (5x − 3(x − 2))/15 = (5x − 3x + 6)/15 = (2x + 6)/15. The minus sign in front multiplies the whole bracket, so −3 × −2 = +6.

5. How many integer values of n satisfy −3 < 2n ≤ 6?

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

Answer: C. Divide through by 2: −1.5 < n ≤ 3. The integers are −1, 0, 1, 2, 3: five values. Remember 0 counts and 3 is included because of ≤.

6. Write 1/(x − 1) − 1/(x + 1) as a single fraction.

  1. A
    0
  2. B
    2x/(x2 − 1)
  3. C
    −2/(x2 − 1)
  4. D
    2/(x2 − 1)
Show answer

Answer: D. Common denominator (x − 1)(x + 1) = x2 − 1. Numerator: (x + 1) − (x − 1) = 2. So the answer is 2/(x2 − 1). 2x/(x2 − 1) is the sum, not the difference.

7. Find the coordinates of the turning point of y = x2 + 4x + 1.

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

Answer: C. Complete the square: y = (x + 2)2 − 3. The minimum is where the bracket is zero, x = −2, giving y = −3. The turning point is (−2, −3); note the x-coordinate has the opposite sign to the +2 in the bracket.

8. Find the next term of the sequence 3, 5, 9, 15, 23, …

  1. A
    31
  2. B
    33
  3. C
    35
  4. D
    38
Show answer

Answer: B. The differences are 2, 4, 6, 8, going up by 2 each time, so the next difference is 10 and the next term is 23 + 10 = 33. Repeating the last difference gives 31.

9. Solve x2 − 5x − 14 = 0.

  1. A
    x = 7 or x = −2
  2. B
    x = −7 or x = 2
  3. C
    x = 7 or x = 2
  4. D
    x = −7 or x = −2
Show answer

Answer: A. Find two numbers with product −14 and sum −5: −7 and +2. So (x − 7)(x + 2) = 0, giving x = 7 or x = −2. The solutions have the opposite signs to the numbers in the brackets.

10. What is the next term of the sequence 2, 6, 18, 54, …?

  1. A
    108
  2. B
    72
  3. C
    216
  4. D
    162
Show answer

Answer: D. Each term is 3 times the previous one (a geometric sequence), so the next term is 54 × 3 = 162. The differences 4, 12, 36 are not constant, so it is not linear.

Start the chapter testAbout the O Level / IGCSE Mathematics test

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Ways to practise this chapter

Algebra and graphs: questions students ask

How many Algebra and graphs MCQs are there?

107, each with the answer and a short explanation, across 12 topics: Introduction to algebra, Algebraic manipulation, Algebraic fractions, Indices II, Equations, Inequalities, Sequences, Proportion, Graphs in practical situations, Graphs of functions, Sketching curves, Functions. Every chapter test draws ten of them, so you can take it many times.

Is the O Level / IGCSE Mathematics chapter 2 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

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