# C3 Cheat Sheet

Credits to physicsandmathstutor.com

- Created by: Ayman!
- Created on: 11-07-15 23:38

First 532 words of the document:

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, e.g.

Simplifying top heavy fraction using and should become

algebraic division. Otherwise, just a case of practice! rather than

Simplifying fractions by first If adding/subtracting a constant, turn into a fraction. .

factorising numerator and Classic sign errors when subtracting a fraction.

denominator, where possible.

Suppose we were asked to turn into a mixed number. By

algebraic division we find the quotient is and the remainder Note use of brackets around ensures -2

becomes +2.

2. Remember we can express the result as where

is the quotient, the remainder and the divisor, just as

where 5 was the quotient and 1 the remainder.

Thus

In general, to simplify `fractions within fractions', multiply top and

bottom of the outer fraction by the denominator of the inner

fraction, e.g.:

2 Functions Specifying range or domain of You should know and understand why Having a lack of care in domains/ranges with the

function. I avoid getting domain and range mixed up by thinking "ddrrr" with strictness/nonstrictness of the bound. For

Finding inverse of function. a silly voice. i.e. Domain first (possible inputs) followed by Range , range is not .

Finding specific output of function, (possible outputs) Similarly range for quadratics are non-strict

e.g. or Learn the domains and ranges of each of the `common functions' because min/max point is included.

Finding specific output using graph ( , , , ...) Putting the range of a function in terms of

only (without explicit definition of instead of say the correct . Similarly for the

Domains can be restricted for 2 main reasons:

function) range of an inverse, if the domain of the original

o The denominator of a fraction can't be 0, so domain of

Finding composite function. function was say , then the range of the

is . Use symbol.

Sketching original function and inverse is (i.e. even though the

inverse function on same axis (i.e. o You can't square root a negative number, so range of inequality is effectively the same, we're

reflection in ) is . Similarly you can't log 0 or negative referring to the output of now so need to

Be able to find or for numbers so domain (notice it's strict) use rather than )

example, when the function is Range can be restricted for 3 main reasons: When finding , accidentally doing first

known. o The domain was restricted. e.g. If and domain is and then .

"If find all values of set to , then range is . Notice If , then you should recognise that

for which " strictness/non-strictness of bounds. , NOT , which would

o Asymptotes. For reciprocals a division can never yield 0 suggest you don't quite fully understand how

www.drfrostmaths.com

## Comments

No comments have yet been made