GCSE Maths (AQA) chapter 2: Algebra MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

74 exam-style questions on Algebra, 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.

74 questions · 8 topics · 10 per test

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What chapter 2 covers

Ten Algebra questions with answers

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

1. 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).

2. 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.

3. Solve 5(x − 3) = 2x + 6.

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

Answer: B. 5x − 15 = 2x + 6, so 3x = 21 and x = 7. Writing 5x − 3 (not multiplying the 3) gives x = 3.

4. Make x the subject of a(x + 3) = bx + 7.

  1. A
    x = (7 − 3a)/(b − a)
  2. B
    x = (7 + 3a)/(a − b)
  3. C
    x = (7 − a)/(a − b)
  4. D
    x = (7 − 3a)/(a − b)
Show answer

Answer: D. Expand: ax + 3a = bx + 7. Collect x terms: ax − bx = 7 − 3a, so x(a − b) = 7 − 3a and x = (7 − 3a)/(a − b). Remember a multiplies the 3 as well.

5. The geometric sequence 2, 2√3, 6, 6√3, … continues. What is the next term?

  1. A
    12
  2. B
    9√3
  3. C
    6 + 6√3
  4. D
    18
Show answer

Answer: D. Each term is multiplied by √3. 6√3 × √3 = 6 × 3 = 18.

6. f(x) = x2 + 1 and g(x) = 2x − 3. Find gf(x).

  1. A
    4x2 − 12x + 10
  2. B
    2x2 − 2
  3. C
    2x3 − 3x2 + 2x − 3
  4. D
    2x2 − 1
Show answer

Answer: D. gf(x) = g(x2 + 1) = 2(x2 + 1) − 3 = 2x2 − 1. 4x2 − 12x + 10 is fg(x), and multiplying f(x) by g(x) is not a composite function.

7. Factorise 9x2 − 25y2.

  1. A
    (3x − 5y)2
  2. B
    (9x + 25y)(x − y)
  3. C
    (3x + 5y)(3x − 5y)
  4. D
    3(3x2 − 5y2)
Show answer

Answer: C. This is a difference of two squares: (3x)2 − (5y)2 = (3x + 5y)(3x − 5y). (3x − 5y)2 would give a middle term of −30xy.

8. Expand and simplify (2x − 3)(x + 5).

  1. A
    2x2 − 15
  2. B
    2x2 + 13x − 15
  3. C
    2x2 − 7x − 15
  4. D
    2x2 + 7x − 15
Show answer

Answer: D. 2x2 + 10x − 3x − 15 = 2x2 + 7x − 15. Multiplying only the first terms and the last terms misses the 7x.

9. Where does the curve y = x2 − 2x − 8 cross the x-axis?

  1. A
    (4, 0) and (−2, 0)
  2. B
    (−4, 0) and (2, 0)
  3. C
    (0, −8) only
  4. D
    (8, 0) and (−1, 0)
Show answer

Answer: A. Set y = 0: (x − 4)(x + 2) = 0, so x = 4 or x = −2. (0, −8) is the y-intercept.

10. Find the equation of the tangent to the circle x2 + y2 = 25 at the point (3, 4).

  1. A
    y = (4/3)x
  2. B
    4x + 3y = 25
  3. C
    3x − 4y = −7
  4. D
    3x + 4y = 25
Show answer

Answer: D. The radius to (3, 4) has gradient 4/3, so the tangent has gradient −3/4. y − 4 = −¾(x − 3) rearranges to 3x + 4y = 25. 3x − 4y = −7 passes through the point but has gradient +3/4.

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How many Algebra MCQs are there?

74, each with the answer and a short explanation, across 8 topics: A1–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. Every chapter test draws ten of them, so you can take it many times.

Is the GCSE Maths (AQA) 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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