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AHL 1.11—Partial fractions - IB Questionbank | RevisionDojo

Practice AHL 1.11—Partial fractions with authentic IB Mathematics Analysis and Approaches (AA) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like functions and equations, calculus, complex numbers, sequences and series, and probability and statistics. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

HLPaper 1

Let $f(x) = \frac{5x^2 - 14x + 13}{(x-1)(x-3)^2}$ .

Express $f(x)$ in partial fractions.

[5]

Question 2

HLPaper 1

Let $f(x) = \frac{5x+2}{(x+1)(x^2+4)}$ .

Express $f(x)$ in the form $\frac{A}{x+1} + \frac{Bx+C}{x^2+4}$ .

[4]

Question 3

HLPaper 1

Express $\frac{7x-4}{(x-2)^2(2x+1)}$ in partial fractions.

[5]

Question 4

HLPaper 1

Express $\frac{1}{x(3x-2)}$ in partial fractions.

[2]

Question 5

HLPaper 1

Let $f(x) = \frac{3x^2 - 2x + 1}{(x-2)(x+1)}$ .

Express $f(x)$ in partial fractions.

[5]

Question 6

HLPaper 1

Let $f(x) = \frac{4x^2 - x + 10}{(x-3)(x^2+5)}$ .

Express $f(x)$ in partial fractions.

[5]

Question 7

HLPaper 1

Let $f(x) = \frac{5x^2 - 10x + 10}{(x-1)(x+2)(x-3)}$ .

Express $f(x)$ in partial fractions.

[4]

Question 8

HLPaper 1

Decompose the function $\frac{2x+3}{(x+1)(x+2)}$ into partial fractions.

[4]

Question 9

HLPaper 1

Consider the rational function $f(x) = \frac{2x^2 + 3x + 1}{(x+1)^2(x-2)}$ .

Express $f(x)$ as a sum of partial fractions.

[7]

Hence, or otherwise, find $\int\!f(x)dx$ with only one $\ln$ term

[4]

Question 10

HLPaper 1

Consider the rational function $g(x) = \frac{3x^2 + 5x + 2}{(x-1)^2(x+2)}$ .

Express $g(x)$ as a sum of partial fractions.

[8]

Hence, or otherwise, compute $\int_0^2\! g(x)dx$

[5]

AHL 1.11—Partial fractions Questionbank