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C3 Cheat Sheet
Chapter Usual types of questions Tips What can go ugly 1 ­ Algebraic Fractions
· Almost always adding or subtracting fractions.
· Simplifying top heavy fraction using algebraic division.
· Simplifying fractions by first factorising numerator and denominator, where possible.
· Factorise everything in each fraction first.…

Page 2

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· Blindly multiplying the two denominators when there might be a common factor, e.g.
and should become rather than
.
· Classic sign errors when subtracting a fraction.
Note use of brackets around ensures -2 becomes +2.
2 ­ Functions · Specifying range or domain of
function.
· Finding inverse…

Page 3

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Page 4

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functions work.
3 ­ Exponential and Log Functions
· Be able to draw the graphs of and .
· Sketch more complicated exponential graphs, e.g.
· Solve equations involving and (see right).
· Solve equations which are quadratic in terms of (see right).
· Find the `long term' value of…

Page 5

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· Misremembering C2 laws of logs.
· Thinking particularly in applied questions (e.g. population growth).
www.drfrostmaths.com
(unless numerator is 0), thus range of is
. 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…

Page 6

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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…

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Pages in this set

Page 1

Preview of page 1
C3 Cheat Sheet
Chapter Usual types of questions Tips What can go ugly 1 ­ Algebraic Fractions
· Almost always adding or subtracting fractions.
· Simplifying top heavy fraction using algebraic division.
· Simplifying fractions by first factorising numerator and denominator, where possible.
· Factorise everything in each fraction first.…

Page 2

Preview of page 2
· Blindly multiplying the two denominators when there might be a common factor, e.g.
and should become rather than
.
· Classic sign errors when subtracting a fraction.
Note use of brackets around ensures -2 becomes +2.
2 ­ Functions · Specifying range or domain of
function.
· Finding inverse…

Page 3

Preview of page 3

Page 4

Preview of page 4
functions work.
3 ­ Exponential and Log Functions
· Be able to draw the graphs of and .
· Sketch more complicated exponential graphs, e.g.
· Solve equations involving and (see right).
· Solve equations which are quadratic in terms of (see right).
· Find the `long term' value of…

Page 5

Preview of page 5
· Misremembering C2 laws of logs.
· Thinking particularly in applied questions (e.g. population growth).
www.drfrostmaths.com
(unless numerator is 0), thus range of is
. 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…

Page 6

Preview of page 6
· 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…

Comments

No comments have yet been made