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C3 Cheat Sheet
Chapter Usual types of questions Tips What can go ugly
1 ­ Algebraic Almost always adding or subtracting Factorise everything in each fraction first. e.g. If denominators Blindly multiplying the two denominators when
Fractions fractions. and , common denominator will be there might be a common factor,…

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(unless numerator is 0), thus range of is functions work.
. Use sketch! For exponential functions, output is
(strictly) positive:
o Min/max value of a quadratic (or any polynomial whose
highest power is even). Note bound is non-strict as
min/max value included.
Range of is
For composite functions, if given…

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Some questions are `quadratics in disguise':
Since , this suggest we multiply everything by , which
gives us: . Rearranging:

Then we could make the substitution and factorise, or just
factorise immediately to get
Thus , thus
If you'd managed to factorise an expression to say ,
remember that can't…

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5 ­ Transforming Using an existing function The way to remember | | vs | | is remember that changes Forgetting to add key coordinates to your
graphs of to sketch | | and/or inside the function brackets affects the values and changes diagrams, e.g. intercepts with the axis, turning…

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As with C2 questions, when you have a combination of say
and , then change the squared term using the identity, so that
you end up with a quadratic equation in terms of one trig function.
As per C2, if you're given a range for your solutions, then rewrite

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You will often have to simplify a differentiated expression. negatives floating about), you are advised to
Remember that when factorising things with indices, factor out the work out and separately first rather than
smallest power, and factor out any fraction using the lowest write all in one go.
common multiple:…


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