FSc Part 1 Maths chapter 5: Partial fractions MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

10 exam-style questions on Partial fractions, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

10 questions · 1 topics · 10 per test

Test this chapter freeAll FSc Part 1 Maths chapters

What chapter 5 covers

Ten Partial fractions questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. Which of the following is an identity?

  1. A
    x2 = 4
  2. B
    x2 − 5x + 6 = 0
  3. C
    2x + 3 = 7
  4. D
    (x + 1)2 = x2 + 2x + 1
Show answer

Answer: D. An identity is true for every value of x. The others are conditional equations, true only for particular values.

2. The partial fractions of (5x + 1)/((x − 1)(x + 2)) are

  1. A
    2/(x − 1) + 3/(x + 2)
  2. B
    3/(x − 1) + 2/(x + 2)
  3. C
    2/(x − 1) − 3/(x + 2)
  4. D
    6/(x − 1) − 1/(x + 2)
Show answer

Answer: A. 5x + 1 = A(x + 2) + B(x − 1). x = 1: 6 = 3A, A = 2. x = −2: −9 = −3B, B = 3. Check: 2(x + 2) + 3(x − 1) = 5x + 1.

3. (x2 + 1)/(x2 − 1) resolved into partial fractions is

  1. A
    x + 1/(x − 1) − 1/(x + 1)
  2. B
    1/(x − 1) − 1/(x + 1)
  3. C
    1 + 1/(x − 1) + 1/(x + 1)
  4. D
    1 + 1/(x − 1) − 1/(x + 1)
Show answer

Answer: D. The fraction is improper, so divide first: (x2 + 1)/(x2 − 1) = 1 + 2/(x2 − 1), and 2/(x2 − 1) = 1/(x − 1) − 1/(x + 1).

4. The correct form of the partial fractions of (2x + 1)/((x + 1)(x2 + 4)) is

  1. A
    (Ax + B)/(x + 1) + C/(x2 + 4)
  2. B
    A/(x + 1) + B/(x2 + 4)
  3. C
    A/(x + 1) + B/(x + 2) + C/(x − 2)
  4. D
    A/(x + 1) + (Bx + C)/(x2 + 4)
Show answer

Answer: D. x2 + 4 cannot be factorised over the reals, so its numerator must be linear, Bx + C. Factorising it as (x + 2)(x − 2) is wrong: that is x2 − 4.

5. The partial fractions of x/(x − 1)2 are

  1. A
    x/(x − 1) + 1/(x − 1)2
  2. B
    1/(x − 1) − 1/(x − 1)2
  3. C
    1/(x − 1)2
  4. D
    1/(x − 1) + 1/(x − 1)2
Show answer

Answer: D. x = A(x − 1) + B. Put x = 1: B = 1. Compare x coefficients: A = 1. Check: (x − 1) + 1 = x.

6. The correct form of the partial fractions of (x + 3)/((x − 1)(x + 2)2) is

  1. A
    A/(x − 1) + B/(x + 2)2
  2. B
    A/(x − 1) + B/(x + 2) + C/(x + 2)2
  3. C
    A/(x − 1) + (Bx + C)/(x + 2)2
  4. D
    A/(x − 1) + B/(x + 2) + C/(x − 1)2
Show answer

Answer: B. A repeated linear factor (x + 2)2 needs a term for each power: B/(x + 2) and C/(x + 2)2. The factor x − 1 is not repeated.

7. If 1/(x2(x + 1)) = A/x + B/x2 + C/(x + 1), then A is

  1. A
    −1
  2. B
    1
  3. C
    0
  4. D
    2
Show answer

Answer: A. 1 = Ax(x + 1) + B(x + 1) + Cx2. x = 0 gives B = 1; x = −1 gives C = 1; the x2 terms give A + C = 0, so A = −1.

8. The partial fractions of 1/((x + 1)(x2 + 1)) are

  1. A
    1/(2(x + 1)) + (x + 1)/(2(x2 + 1))
  2. B
    1/(2(x + 1)) + (1 − x)/(2(x2 + 1))
  3. C
    1/(x + 1) − x/(x2 + 1)
  4. D
    1/(2(x + 1)) − 1/(2(x2 + 1))
Show answer

Answer: B. 1 = A(x2 + 1) + (Bx + C)(x + 1). x = −1 gives A = 1/2; x2 terms: A + B = 0, B = −1/2; constants: A + C = 1, C = 1/2.

9. Which of the following is an improper rational fraction?

  1. A
    (2x − 1)/((x + 1)(x + 3))
  2. B
    (x + 1)/(x2 + 1)
  3. C
    3/(x − 2)
  4. D
    (x3 + 1)/(x2 − 4)
Show answer

Answer: D. A fraction is improper when the degree of the numerator is at least the degree of the denominator. Here 3 ≥ 2; in the others the numerator has lower degree.

10. The partial fractions of 1/(x2 − 1) are

  1. A
    1/(x − 1) − 1/(x + 1)
  2. B
    1/(2(x − 1)) − 1/(2(x + 1))
  3. C
    1/(2(x + 1)) − 1/(2(x − 1))
  4. D
    1/(x − 1) + 1/(x + 1)
Show answer

Answer: B. 1 = A(x + 1) + B(x − 1). x = 1 gives A = 1/2; x = −1 gives B = −1/2. Without the 1/2 the difference would be 2/(x2 − 1).

Start the chapter testAbout the FSc Part 1 Maths test

Read the notes for this chapter

Ways to practise this chapter

Partial fractions: questions students ask

How many Partial fractions MCQs are there?

10, each with the answer and a short explanation, across 1 topics: Resolving into partial fractions. Every chapter test draws ten of them, so you can take it many times.

Is the FSc Part 1 Maths chapter 5 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

Can I read the explanations in Urdu?

Yes. In practice mode and on your results you can switch the explanations to Urdu.

Keep going

← Chapter 4: Quadratic equationsChapter 6: Sequences and series →All chaptersStuck? Ask a question