Northern IrelandMathsQuick questions

A2 1 Pure Mathematics

Quick questions on Functions and partial fractions: composite, inverse, modulus and partial fractions - CCEA A-Level Mathematics

6short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is the modulus function?

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The modulus

|x|

is the non-negative size of

x

, so

|x| = x

x \ge 0

and

|x| = -x

x < 0

. The graph of

y = |f(x)|

reflects any part of

y = f(x)

below the

x

-axis up above it. To solve

|f(x)| = k

, solve both

f(x) = k

and

f(x) = -k

What are partial fractions?

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Before decomposing, check the fraction is proper (the numerator has lower degree than the denominator); if not, divide first to separate a polynomial part. Then factorise the denominator fully, because each factor produces its own partial fraction.

What is wrong partial-fraction form for a repeated factor?

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A factor

(x + a)^2

needs both

\frac{A}{x + a}

and

\frac{B}{(x + a)^2}

, not a single term.

What is q1?

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For

f(x) = 3x + 2

, find

f^{-1}(x)

. [2 marks]

What is q2?

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Solve

|x + 1| = 4

. [2 marks]

What is q3?

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For

f(x) = x + 1

and

g(x) = 2x

, find

fg(x)

. [2 marks]

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