Lesson 1.08j

1.08j Integration by partial fractions Quiz: OCR Maths, Unit 8

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.08j, Integration by partial fractions: 20 multiple choice questions for the OCR Maths (H240), Unit 8: Integration, written with Revision Ninja.

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The 20 questions

  1. Which decomposition is correct for 1/((x+1)(x-2))?

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

  2. What is the form of the partial fraction decomposition of (x+5)/((x+1)^2 (x-3))?

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

  3. What is the integral of 1/(x+3) with respect to x?

    • -1/(x+3)^2 + C
    • -ln|x+3| + C
    • ln|x+3| + C
    • 1/ln|x+3| + C

  4. What is the integral of 1/(ax+b) with respect to x, where a is not zero?

    • ln|ax+b| + C
    • (1/a) ln|ax+b| + C
    • a ln|ax+b| + C
    • -(1/a) ln|ax+b| + C

  5. Integrating a function decomposed into linear partial fractions typically produces which function type?

    • Polynomial
    • Exponential
    • Trigonometric
    • Logarithmic

  6. What process must be performed before partial fraction decomposition if the numerator degree is not smaller?

    • Binomial expansion
    • Integration by parts
    • Implicit differentiation
    • Algebraic division

  7. Which is an antiderivative of 1/((x-1)(x+1)) on a suitable interval?

    • ln|(x-1)(x+1)| + C
    • (1/2) ln|(x+1)/(x-1)| + C
    • (1/2) ln|(x-1)(x+1)| + C
    • (1/2) ln|(x-1)/(x+1)| + C

  8. Find the integral of (3x+1)/(x(x+1)) with respect to x.

    • ln|x| + 2 ln|x+1| + C
    • 2 ln|x| + ln|x+1| + C
    • ln|x(x+1)| + 3x + C
    • ln|x| + ln|x+1| + C

  9. Evaluate the integral of 1/(x^2 - 1) from x = 2 to x = 3, giving an exact answer.

    • ln(3/2)
    • (1/2) ln(3/2)
    • (1/2) ln 6
    • (1/2) ln(2/3)

  10. Find the integral of (5x-1)/((x-1)(x+2)) with respect to x.

    • (4/3) ln|x-1| - (11/3) ln|x+2| + C
    • (4/3) ln|x-1| + (11/3) ln|x+2| + C
    • (11/3) ln|x-1| + (4/3) ln|x+2| + C
    • (5/2) ln|x^2+x-2| + C

  11. Find the integral of (2x+3)/(x-1)^2 with respect to x.

    • 2 ln|x-1| - 3/(x-1) + C
    • 2 ln|x-1| + 5/(x-1) + C
    • 2 ln|x-1| - 5/(x-1) + C
    • ln|x-1| - 5/(x-1)^2 + C

  12. Find the integral of (x+4)/((x-1)(x+3)) with respect to x.

    • (5/4) ln|x+3| - (1/4) ln|x-1| + C
    • (5/4) ln|x-1| + (1/4) ln|x+3| + C
    • (1/4) ln|x-1| + (5/4) ln|x+3| + C
    • (5/4) ln|x-1| - (1/4) ln|x+3| + C

  13. Evaluate the integral of 1/((x+1)(x+2)) from x = 0 to x = 1, giving an exact answer.

    • ln(3/4)
    • ln(4/3)
    • ln(2/3)
    • ln(3/2)

  14. Find the integral of 2x/(x^2 - 1) with respect to x.

    • ln|x^2 + 1| + C
    • 2 ln|x^2 - 1| + C
    • ln|x^2 - 1| + C
    • ln|x-1| - ln|x+1| + C

  15. Evaluate the integral of x/((x+1)(x+2)) from x = 0 to x = 1, giving an exact answer.

    • ln(9/8)
    • ln(8/9)
    • ln(3/2)
    • ln(9/4)

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

    • 1/4
    • 1
    • -1/2
    • 1/2

  17. Find the integral of 1/(x(x+1)(x+2)) with respect to x.

    • ln|x| - ln|x+1| + ln|x+2| + C
    • (1/2) ln|x| - ln|x+1| + (1/2) ln|x+2| + C
    • -(1/2) ln|x| + ln|x+1| - (1/2) ln|x+2| + C
    • (1/2) ln|x| + ln|x+1| - (1/2) ln|x+2| + C

  18. Find the integral of (x^2+1)/(x-1) with respect to x.

    • x^2/2 + x - 2 ln|x-1| + C
    • x^2/2 - x + 2 ln|x-1| + C
    • x + 2 ln|x-1| + C
    • x^2/2 + x + 2 ln|x-1| + C

  19. Evaluate the integral of (x+3)/(x-1)^2 from x = 2 to x = 3, giving an exact answer.

    • 2 - ln 2
    • 1 + ln 2
    • 2 + ln 2
    • ln 2 - 2

  20. Evaluate the integral of 1/((x-1)(x+2)) from x = 2 to x = 4, giving an exact answer.

    • (1/3) ln(1/2)
    • (2/3) ln 2
    • (1/3) ln 2
    • ln 2

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