=>

It follows that

<=>

If and only if

N

Natural numbers

POSITIVE integers

Z

Integer

Q

quotients / rational numbers

Expressed as a FRACTION

R

Real numbers

not IMAGINARY

a ^ m/n

n rt(a^ m)

b^2 - 4ac > 0

2 disctint roots

b^2 - 4ac = 0

1 repeated root

b^2 - 4ac < 0

No roots

Turning point (a,b)

(x - a) + b

x = (quadratic formula)

-b +- sqrt(b^2 -4ac) / 2a

=< when region drawing

SOLID line

< when region drawing

DOTTED line

=< on number line

FILLED dot

< on number line

OPEN dot

=< in interval notation

SQUARE bracket [

< in interval notation

CURVED bracket (

Interval bracket for infinity

CURVED ( as <

define polynomial

Finite expression with N indices

state factor theorem

If f(a) = 0 then (x-a) is a factor

When to use identity symbol

Simplifying expressions

y = k / x

top right, bottom left

Gets flatter when k increases

fg(x) meaning

f of g(x)

Inverse function notation

f ^-1 (x)

Inverse function of e ^x

ln x

midpoint

( x1 + x2 / 2 , y1 + y2 / 2)

Collinear definition

Of the SAME LINE

tangent definition

Gradient at one point on a curve

When b^2 - 4ac = 0

Point which only touches at one point

Normal defintion

Line 90 degrees to tangent at one point

r^2 =

(x-a) + (y-b) with centre (a,b)

Define circumcircle

unique circle around 3 vertices of a triangle

Why is a = 1 not an exponential graph

Because 1^x is always 1

a^x = b

loga b = x

loga (a^x) =

x

a ^ (loga x) =

x

e =

2.71819

differentiate e^kx

ke^kx

Exponential decay

Ae^kx

Exponential decay

Ae^-kx

Differentiate e^-kx

-ke^kx

loga 1 =

0

log a (1/x) =

- loga x

log (x + y) =

CAN’T BE SIMPLIFIED

y = (exponential graph)

A (coefficient of e)

Make linear graph with logs

Logs of both sides

Separate RHS

constant is gradient

Variables are axis

loga y = kx + loga b (what on axis)

y = loga y

x = loga b

gradient = k

Derivation from first principles

lim h-> 0 f(x + h) - f(x) / h

As h -> 0 …

nh -> 0 and nh^2 -> 0

Find equation on normal at point (x,y)

dy/dx to find tangent

x -1/grad is gradient

Solve y=mx+c

is interval () strict or not?

NOT

Is interval[] strict or not

STRICT

find if maximum or minimum

d2y / dx2 using value for x

If n > 0 then MINIMUM

If n < 0 then MAXIMUM

If n = 0 then point of INFLECTION/ MAX/ MIN (use table)

Define dV / dr

rate of change in volume WRT radius

|a| =

sqrt( Δx^2 + Δy^2 + Δz^2)

a hat = (unit vector)

a / |a|

Find vector angle with y axis

cosθ = y / |a|

Find vector angle with x axis

cosθ = x / |a|

Find vector angle with z axis

cosθ = z / |a|