Lesson B10

B10 Partial fractions Quiz: AQA Maths, Unit 2

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson B10, Partial fractions: 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. Decompose 1/((x + 1)(x + 2)) into partial fractions.

    • 1/(x + 1) + 1/(x + 2)
    • 1/(x + 1) - 2/(x + 2)
    • 1/(x + 1) - 1/(x + 2)
    • 2/(x + 1) - 1/(x + 2)

  2. Decompose (3x + 5)/((x + 1)(x + 2)) into partial fractions.

    • 2/(x + 1) + 1/(x + 2)
    • 1/(x + 1) + 2/(x + 2)
    • 3/(x + 1) + 5/(x + 2)
    • 2/(x + 1) - 1/(x + 2)

  3. Before partial fractions can be used, what must be true of a rational function?

    • The numerator's degree must be less than the denominator's degree
    • The numerator must be a constant
    • The numerator must be a perfect square
    • The denominator must have no linear factors

  4. For a repeated linear factor (x + 1)^2 in a denominator, which partial fraction terms are needed?

    • A/(x + 1)^2 + B/(x + 1)^3
    • A/(x + 1) + B/(x + 1)^2
    • A/(x + 1) + B/(x + 1)
    • A/(x + 1)^2 only

  5. Express 1/(x^2 - 1) in partial fractions.

    • (1/2)(1/(x - 1) - 1/(x + 1))
    • 1/(x - 1) - 1/(x + 1)
    • 1/(x - 1) + 1/(x + 1)
    • (1/2)(1/(x - 1) + 1/(x + 1))

  6. Express (2x + 3)/(x^2 + 3x + 2) in partial fractions.

    • 1/(x + 1) - 1/(x + 2)
    • 1/(x + 1) + 1/(x + 2)
    • 2/(x + 1) + 1/(x + 2)
    • 1/(x + 1) + 2/(x + 2)

  7. Express (x + 4)/(x^2 - x - 2) in partial fractions.

    • 2/(x - 2) + 1/(x + 1)
    • 2/(x - 2) - 1/(x + 1)
    • -2/(x - 2) + 1/(x + 1)
    • 1/(x - 2) + 2/(x + 1)

  8. Express (7x - 1)/((x - 1)(x + 2)) in partial fractions.

    • 2/(x - 1) - 5/(x + 2)
    • 2/(x - 1) + 5/(x + 2)
    • 7/(x - 1) - 1/(x + 2)
    • 5/(x - 1) + 2/(x + 2)

  9. Express (2x + 1)/(x - 1)^2 in partial fractions.

    • 2/(x - 1) + 1/(x - 1)^2
    • 2/(x - 1) + 3/(x - 1)^2
    • 3/(x - 1) + 2/(x - 1)^2
    • 2/(x - 1)^2 + 3/(x - 1)

  10. Express x/((x + 1)(x - 3)) in partial fractions.

    • 3/(4(x + 1)) + 1/(4(x - 3))
    • 1/(4(x - 1)) + 3/(4(x + 3))
    • 1/(x + 1) + 3/(x - 3)
    • 1/(4(x + 1)) + 3/(4(x - 3))

  11. If (ax + b)/((x + 1)(x - 2)) = 1/(x + 1) + 2/(x - 2), what are a and b?

    • a = 3, b = -4
    • a = 2, b = 3
    • a = 3, b = 0
    • a = 1, b = 2

  12. Express (4x - 1)/(x^2 - 1) in partial fractions.

    • 3/(x - 1) + 5/(x + 1)
    • 5/(2(x - 1)) + 3/(2(x + 1))
    • 3/(2(x - 1)) + 5/(2(x + 1))
    • 3/(2(x - 1)) - 5/(2(x + 1))

  13. What is the partial fraction form of 1/(x(x + 1))?

    • 1/(x + 1) - 1/x
    • 1/x + 1/(x + 1)
    • 1/x^2 + 1/(x + 1)
    • 1/x - 1/(x + 1)

  14. In (x + 3)/((x - 1)(x + 2)) = A/(x - 1) + B/(x + 2), what is A?

    • -4/3
    • 3/4
    • 4/3
    • 1/3

  15. How many unknown constants are needed for a partial fraction decomposition with two distinct linear factors?

    • Four
    • Two
    • One
    • Three

  16. For (x^3 + 1)/(x^2 - 1), which step should come first?

    • Cancel x^2 from the top and bottom
    • Divide to get a polynomial plus a proper fraction
    • Multiply out the denominator
    • Factorise the numerator as a cube

  17. What is the partial fraction form of 1/(x(x - 2))?

    • -1/(2x) + 1/(2(x - 2))
    • -1/x + 1/(x - 2)
    • 1/(2x) - 1/(2(x - 2))
    • 1/(2x) + 1/(2(x - 2))

  18. Express (x + 5)/(x + 1)^2 in partial fractions.

    • x/(x + 1) + 5/(x + 1)^2
    • 5/(x + 1) + 1/(x + 1)^2
    • 1/(x + 1) + 4/(x + 1)^2
    • 1/(x + 1)^2 + 4/(x + 1)

  19. In the decomposition of 1/((x + 1)(x - 1)(x + 2)), what is the coefficient of 1/(x - 1)?

    • 1/6
    • 1/2
    • -1/2
    • 1/3

  20. For (3x - 2)/((x - 2)(x + 2)) = A/(x - 2) + B/(x + 2), find A and B.

    • A = 1, B = 2
    • A = 2, B = 1
    • A = 1, B = -2
    • A = -1, B = 2

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