Things to Remember - StudyWell

SUVAT equations

$\hspace{10pt}V=U+AT$
$\hspace{10pt}S=\left(\frac{U+V}{2}\right)T$
$\hspace{10pt}V^2=U^2+2AS$
$\hspace{10pt}S=UT+\frac{1}{2}AT^2$
$\hspace{10pt}S=VT-\frac{1}{2}AT^2$

where

Variable	Description	SI unit
S	displacement	m (metres)
U	initial velocity	m/s (metres per second)
V	final velocity	m/s (metres per second)
A	acceleration	9.8 m/s/s (metres per second per second)
T	total time	s (seconds)

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Trigonometric Identities

Fundamental Formulae

$\frac{\sin(\theta)}{\cos(\theta)}=\tan(\theta)$

$\cos^2(\theta)+\sin^2(\theta)=1$

Double Angle Formulae

$\sin(2\theta)=2\sin(\theta)\cos(\theta)$

$\cos(2\theta)=\cos(\theta)^2-\sin^2(\theta)$
$\cos(2\theta)=2\cos^2(\theta)-1$
$\cos(2\theta)=1-2\sin^2(\theta)$

Compound Angle Formulae

$\sin(\alpha\pm\beta)=\sin(\alpha)\cos(\beta)\pm\cos(\alpha)\sin(\beta)$

$\cos(\alpha\pm\beta)=\sin(\alpha)\sin(\beta)\mp\cos(\alpha)\cos(\beta)$
$\tan(\alpha\pm\beta)=\frac{\tan(\alpha)\pm\tan(\beta)}{1\mp\tan(\alpha)\tan(\beta)}$

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Indices & Surds

IndicesSurdsNotes

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Quadratics

QuadraticsNotes

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Transformations

y-transformations

A y-transformation affects the y coordinates of a curve. You can identify a y-transformation as changes are made outside the brackets of y=f(x).

$f(x)\rightarrow f(x)+4$ , this is a shift in y, the x coordinates are unaffected but all the y coordinates go up by 4.
$f(x)\rightarrow f(x)-3$ , this is a shift in y, the x coordinates are unaffected but all the y coordinates go down by 3.
$f(x)\rightarrow 2f(x)$ , this is a stretch in y, the x coordinates are unaffected but all the y coordinates are doubled.
$f(x)\rightarrow -f(x)$ , this is a flip in y, the x coordinates are unaffected but all the y coordinates are flipped across the x-axis.

x-transformations

x-transformations always behave in the opposite way to what is expected. They can be identified when changes are made inside the brackets of y=f(x).

$f(x)\rightarrow f(x+4)$ , this is a shift in the x direction, the y coordinates are unaffected but all the x coordinates go to the left by 4, the opposite direction to what is expected.
$f(x)\rightarrow f(x-3)$ , this is a shift in the x direction, the y coordinates are unaffected but all the x coordinates go to the right by 3, the opposite direction to what is expected.
$f(x)\rightarrow f(2x)$ , this is a stretch in the x direction, the y coordinates are unaffected but all the x coordinates are halved, the opposite to what is expected.
$f(x)\rightarrow f(-x)$ , this is a flip in the x direction, the y coordinates are unaffected but all the x coordinates are flipped across the y-axis.

Go to Transformations page.

The Equation of a Circle

The equation of the circle whose centre is at the point (a,b) and whose radius is r is given by

$(x-a)^2+(y-b)^2=r^2$ .

DIFFERENTIATION FROM FIRST PRINCIPLES

$f$