Lesson B1-B2

B1-B2 Indices and surds Quiz: AQA Maths, Unit 2

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson B1-B2, Indices and surds: 20 multiple choice questions for the AQA Maths (7357), Unit 2: Algebra and functions, written with Revision Ninja.

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The 20 questions

  1. What is the value of 8^(2/3)?

    • 16
    • 6
    • 2
    • 4

  2. Which expression equals a^m / a^n?

    • a^(m+n)
    • a^(mn)
    • a^(m/n)
    • a^(m-n)

  3. What is the rationalised form of 1/sqrt(3)?

    • sqrt(3) - 1
    • 3 sqrt(3)
    • sqrt(3)/3
    • 1/3

  4. Which of the following is a surd?

    • 1.5
    • 27^(1/3)
    • sqrt(16)
    • sqrt(7)

  5. Which index law is represented by the identity (a^m)^n = a^(mn)?

    • Power of a power
    • Product law
    • Quotient law
    • Distributive law

  6. What does a^(-n) equal for non-zero a?

    • -a^n
    • 1/a^n
    • 1/(na)
    • a^n

  7. What square factor must the integer under a fully simplified square root have?

    • An even number
    • Only 1
    • No prime factors
    • Any prime number

  8. Simplify sqrt(50) + sqrt(8).

    • sqrt(58)
    • 10 sqrt(2)
    • 7 sqrt(2)
    • 14

  9. Solve 3^(x+1) = 27.

    • x = 2
    • x = 4
    • x = 1
    • x = 3

  10. Simplify (27x^6)^(2/3) for x > 0.

    • 3x^4
    • 18x^4
    • 9x^4
    • 9x^2

  11. Express 1/(2 + sqrt(3)) with a rational denominator.

    • sqrt(3) - 2
    • 2 + sqrt(3)
    • 2 - sqrt(3)
    • (2 - sqrt(3))/2

  12. What is the value of 16^(3/4)?

    • 12
    • 8
    • 64
    • 4

  13. Expand and simplify (sqrt(5) + 2)^2.

    • 9 + 4 sqrt(5)
    • 9 + 2 sqrt(5)
    • 5 + 4 sqrt(5)
    • 7 + 4 sqrt(5)

  14. Rationalise the denominator of (3 - sqrt(2))/(3 + sqrt(2)).

    • (7 - 6 sqrt(2))/7
    • (11 + 6 sqrt(2))/7
    • (11 - 6 sqrt(2))/7
    • (11 - 6 sqrt(2))/9

  15. Solve 2^(2x) - 5 x 2^x + 4 = 0.

    • x = 2 only
    • x = 0 or x = -2
    • x = 1 or x = 2
    • x = 0 or x = 2

  16. Given 5^x = 2, what is the value of 25^x?

    • 25
    • 2
    • 4
    • 10

  17. Solve 2^x = 8^y and 9^y = 3^(x+1) simultaneously.

    • x = -3, y = -1
    • x = 3, y = 1
    • x = 3, y = -1
    • x = -1, y = -3

  18. How many real solutions exist for the equation 4^x + 2^(x+1) = 0?

    • Two
    • Infinitely many
    • One
    • Zero

  19. Given a = sqrt(5) + sqrt(3) and b = sqrt(5) - sqrt(3), find ab.

    • 2 sqrt(15)
    • 8
    • 2
    • 4 sqrt(2)

  20. Simplify 1/(3 + 2 sqrt(2)).

    • 3 + 2 sqrt(2)
    • 1/3 + sqrt(2)
    • 6 - 4 sqrt(2)
    • 3 - 2 sqrt(2)

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