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Function & Graph Transformations

$y = f (x) + C$	$C > 0$ moves the function up $C < 0$ moves the function down
$y = f (x + C)$	$C > 0$ moves the function left $C < 0$ moves the function right
$y = C f (x)$	$C > 1$ stretches the function in the y-direction $0 < C < 1$ compresses the function
$y = f (C x)$	$C > 1$ compresses the function in the x-direction $0 < C < 1$ stretches the function
$y = - f (x)$	Reflects the function about x-axis
$y = f (- x)$	Reflects the function about y-axis

Function & Graph Transformations from mathsisfun.com

Trigonometry

Calculus

Quadratic Function

The formula for a general quadratic is given by

y = a x^{2} + b x + c

where
$y$ is the dependent variable,
$x$ is the independent variable,
& $a$ , $b$ & $c$ are real valued constants.

Factorisation

Basics

(from www.savemyexams.co.uk)

Harder Factorising

(from corbettmaths.com)

General Factorising

(from www.savemyexams.co.uk)

More Factorising

(from thirdspacelearning.com)

Quadratic Inequalities

the Parabola (A level)

(from astarmathsandphysics.com)

Linking into Conic Sections

Conics

(from www.khanacademy.org)

Rules for Logs

Power rule for logs $a \log_{b} x = \log_{b} x^{a}$

Addition rule for logs $\log_{b} x + \log_{b} y = \log_{b} x y$

Difference rule for logs $\log_{b} x - \log_{b} y = \log_{b} \frac{x}{y}$

Binomial Expansion

Modulus Function

from mathsmadeeasy.co.uk

from www.savemyexams.co.uk

from mkhometuition.co.uk

from curriculum-press.co.uk

from alevelmathsrevision.com

find more at duckduckgo.com

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