Free Partial fractions questions for IB Mathematics: Analysis & Approaches (SL & HL), HL only, part of Number & algebra. Each question has the answer and the marking points an examiner would look for.
Generate a full Partial Fractions worksheet →All Number & algebra questionsExpress 3x − 1(x + 1)(x) in partial fractions.
Hence find ∫253x − 1(x + 1)(x)dx, giving your answer in the form ln k, where k ∈ ℚ.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 4x + 1 − 1x 3x − 1 ≡ A(x) + B(x + 1) M1 A = 4 A1 B = −1 A1 | 3 |
| (b) | ln 325 [4ln|x + 1| − ln|x|]25 A1 substituting limits (M1) use of log laws to combine M1 ln 325 A1 | 4 |
Express 3x + 1(x + 1)(x) in partial fractions.
Hence find ∫143x + 1(x + 1)(x)dx, giving your answer in the form ln k, where k ∈ ℚ.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 2x + 1 + 1x 3x + 1 ≡ A(x) + B(x + 1) M1 A = 2 A1 B = 1 A1 | 3 |
| (b) | ln 25 [2ln|x + 1| + ln|x|]14 A1 substituting limits (M1) use of log laws to combine M1 ln 25 A1 | 4 |
Express −x + 8(x + 2)(x − 3) in partial fractions.
Hence find ∫47−x + 8(x + 2)(x − 3)dx, giving your answer in the form ln k, where k ∈ ℚ.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | −2x + 2 + 1x − 3 −x + 8 ≡ A(x − 3) + B(x + 2) M1 A = −2 A1 B = 1 A1 | 3 |
| (b) | ln 169 [−2ln|x + 2| + ln|x − 3|]47 A1 substituting limits (M1) use of log laws to combine M1 ln 169 A1 | 4 |
Express 7x − 22(x − 2)(x − 4) in partial fractions.
Hence find ∫577x − 22(x − 2)(x − 4)dx, giving your answer in the form ln k, where k ∈ ℚ.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 4x − 2 + 3x − 4 7x − 22 ≡ A(x − 4) + B(x − 2) M1 A = 4 A1 B = 3 A1 | 3 |
| (b) | ln 6253 [4ln|x − 2| + 3ln|x − 4|]57 A1 substituting limits (M1) use of log laws to combine M1 ln 6253 A1 | 4 |
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Meet Riyaz →Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in