Lesson 8.6.1

8.6.1 Integration using partial fractions Quiz: Pearson Edexcel Maths, Unit 8

20 questions

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Lesson 8.6.1, Integration using partial fractions: 20 multiple choice questions for the Pearson Edexcel Maths (9MA0), Unit 8: Integration, written with Revision Ninja.

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The 20 questions

  1. What algebraic technique is required first to integrate 1 / (x^2 - 1)?

    • Partial fractions
    • Completing the square
    • Integration by parts
    • Substitution

  2. Express 1 / (x(x + 2)) in partial fractions with unknown constants A and B.

    • (Ax + B)/(x(x + 2))
    • A/x + Bx/(x + 2)
    • A/x + B/(x + 2)
    • A/(x - 2) + B/x

  3. What type of partial fraction expansion is needed for 1 / (x(x + 1)^2)?

    • Repeated linear factor
    • Single linear factor
    • Improper fraction
    • Quadratic factor

  4. When integrating 1 / (2x - 1), what multiplier arises from standard results?

    • Negative one half
    • One half
    • Two
    • One quarter

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

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

  6. Evaluate the integral of 3 / (x + 2) dx.

    • ln|3x + 6|
    • ln|x + 2| + 3
    • 3ln|x + 2|
    • 3 / (x + 2)^2

  7. Which substitution method is often equivalent to integrating via linear partial fractions?

    • Weierstrass substitution
    • Integration by parts
    • Trigonometric substitution
    • Logarithmic substitution

  8. What must be true about an algebraic fraction before applying partial fractions?

    • Zero constant term
    • Proper fraction
    • Improper fraction
    • Quadratic numerator

  9. If the degree of the numerator equals the denominator, what step is needed first?

    • Polynomial division
    • Rationalisation
    • Integration by parts
    • Partial fractions

  10. Find the partial fraction term for an irreducible quadratic factor x^2 + 1.

    • Ax / (x^2 + 1)
    • (Ax + B) / (x^2 + 1)
    • A / (x + 1)^2
    • A / (x^2 + 1)

  11. Integrate 5 / (2x + 1) with respect to x.

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

  12. Split 2x / ((x + 1)(x + 3)) into partial fraction numerators A and B.

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

  13. When using the cover-up method for partial fractions, what is substituted for x?

    • Derivative of factor
    • Infinity
    • Zero
    • Root of factor

  14. What is the integral of -2 / (3 - x) with respect to x?

    • -2ln|3 - x|
    • 2ln|3 - x|
    • -2 / (3 - x)^2
    • 2 / (3 - x)^2

  15. Which calculus rule is fundamentally used to integrate each resulting partial fraction?

    • Integration by parts
    • Product rule
    • Quotient rule
    • Chain rule reverse

  16. What is the integral of 4 / (2x - 3)^2 with respect to x?

    • -2 / (2x - 3)
    • 4ln|2x - 3|
    • 2 / (2x - 3)^2
    • -4 / (2x - 3)

  17. Express (3x + 5) / ((x + 1)(x + 2)) with partial fraction numerators.

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

  18. Why can ln(A) + ln(B) be combined after partial fraction integration?

    • Partial fraction rules
    • Binomial expansion
    • Logarithm laws
    • Indices rules

  19. What does ln(A) - ln(B) simplify to in integration final answers?

    • ln(B / A)
    • ln(A B)
    • ln(A - B)
    • ln(A / B)

  20. What integration method simplifies rational functions with factorisable denominators before integrating?

    • Integration by parts
    • Partial fractions
    • Trigonometric substitution
    • Integration by substitution

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