Physics & Maths Tutoring

# Algebra

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## Function & Graph Transformations

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

## Calculus

The formula for a general quadratic is given by

$y=a⁢x2+b⁢x+c$

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

## Basics

(from www.savemyexams.co.uk)

## Harder Factorising

(from corbettmaths.com)

## General Factorising

(from www.savemyexams.co.uk)

## More Factorising

(from thirdspacelearning.com)

## the Parabola (A level)

(from astarmathsandphysics.com)

## Rules for Logs

Power rule for logs $a⁢logbx=logbxa$

Addition rule for logs $logbx+logby=logbx⁢y$

Difference rule for logs $logbx-logby=logbxy$

## Modulus Function

find more at duckduckgo.com

Contact Michael Andrew Smith on 0 77 86 69 56 06 or via mike.smith@physics.org

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