IB Maths AA HL AA 1.5 Partial fractions and linear systems questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper

Paper 1, no calculator Paper 2, calculator

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Question 1

Paper 1, no calculatorMedium12 marks

Let

f(x)=\frac{x+8}{x^2+x-6}, \qquad x\in\mathbb R,

where $f(x)$ is defined only when its denominator is non-zero.

(a)

Write $x^2+x-6$ as a product of linear factors, and state the values of $x$ for which $f(x)$ is undefined.

[2]

(b)

Write $f(x)$ in partial fractions.

[4]

(c)

For parts (i) and (ii), consider $-3<x<2$

(i)

Hence determine an antiderivative $F$ of $f$

[3]

(ii)

Hence evaluate $\displaystyle\int_0^1 f(x)\,dx$ giving your answer exactly. Explain why the sign of your answer is consistent with the sign of $f(x)$ on $[0,1]$

[3]

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