Lesson A6

A6 Equations, identities and algebraic proof Quiz: AQA Maths, Unit 2

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson A6, Equations, identities and algebraic proof: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 2: Algebra, written with Revision Ninja.

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The 20 questions

  1. Which equation has exactly one solution: x + 3 = 7, 2x = 2x + 1 or x + 1 = x + 1?

    • 2x = 2x + 1
    • x + 3 = 7
    • All three have one solution
    • x + 1 = x + 1

  2. Which shows that the sum of two consecutive whole numbers is always odd?

    • n + (n + 1) = n², which is odd whenever n is odd
    • n + (n + 1) = 2n, which is even, so the sum is always even
    • n + (n + 1) = 2n + 2, which is even because it doubles n + 1
    • n + (n + 1) = 2n + 1, which is one more than an even number

  3. Solve 5x - 3 = 2x + 9.

    • x = -4
    • x = 2
    • x = 4
    • x = 6

  4. Solve 4(x - 2) = 20.

    • x = 3
    • x = 7
    • x = 22
    • x = 5

  5. Solve x/3 + 4 = 10.

    • x = 2
    • x = 14
    • x = 6
    • x = 18

  6. Solve 3x + 2 = x - 6.

    • x = 2
    • x = -4
    • x = -2
    • x = 4

  7. The expression 2(x + 3) - 2x simplifies to 6 for every value of x. What does this show?

    • It is an identity, true for all values of x
    • It is only true when x = 3
    • It is an inequality
    • It is an equation with solution x = 6

  8. Solve 2x - 7 = 3x + 4.

    • x = -11
    • x = -3
    • x = 3
    • x = 11

  9. Which argument proves that n² - n is always even for whole numbers n?

    • Trying n = 2 proves it for every whole number n
    • n² - n = n² - n, so it must be even by definition
    • n² - n is odd whenever n is an odd number
    • n² - n = n(n - 1), and one factor is always even

  10. Solve 6 - 2x = 14.

    • x = 4
    • x = -4
    • x = -10
    • x = 10

  11. Solve (x + 2)/5 = 3.

    • x = 1
    • x = 17
    • x = 15
    • x = 13

  12. Solve 7x - 4 = 3x + 12.

    • x = 16
    • x = -2
    • x = 2
    • x = 4

  13. Which equation has no solution?

    • x + 2 = x + 5
    • x - 3 = 0, which gives x = 3 as its only solution
    • 2x = 8, which gives x = 4 as its only solution
    • x + 2 = 5, which gives x = 3 as its only solution

  14. Show algebraically that the sum of three consecutive integers is a multiple of 3.

    • n + (n + 1) + (n + 2) = 3n + 2
    • n + (n + 1) + (n + 2) = 3(n + 1)
    • n + (n + 1) + (n + 2) = 2n + 3
    • n + (n + 1) + (n + 2) = 3n + 1

  15. Solve 3(2x - 1) = 5x + 4.

    • x = -7
    • x = 1
    • x = 3
    • x = 7

  16. A number is tripled and then 4 is subtracted, giving 26. Which equation is correct, and what is the number?

    • 3n - 4 = 26, so n = 10
    • 3n + 4 = 26, so n = 22/3
    • 3n - 4 = 22, so n = 26/3
    • 3(n - 4) = 26, so n = 38/3

  17. Solve 3x/4 = 9.

    • x = 6
    • x = 36
    • x = 27/4
    • x = 12

  18. Solve 0.5x + 1.5 = 4.

    • x = 2.5
    • x = 5
    • x = 11
    • x = 3

  19. Expanding 3(x + 2) gives 3x + 6, so 3(x + 2) = 3x + 6 for every x. What does this mean?

    • The statement holds for every x
    • It holds only when x = 2, because both sides match there
    • It is never true, because the bracket cannot be expanded
    • It holds only when x = 0, because the bracket is zero

  20. Which equation models 'a number less 4 is 12'?

    • n - 12 = 4
    • n + 4 = 12
    • 4 - n = 12
    • n - 4 = 12

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