Math

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Financial Applications

Simple Interest

A=P+I

I=Prt

Compounding Interest

The time, n, is the amount of time multiplied by the compounding period.

The interest is the rate, r, by the compounding period.

A=P(1+i)^n

Annuities

Annuities are compounding interests where you are adding more money into the account as time goes on, alongside with the interest earned on the money from before.

Future Value

FV=R(((1+i)^n)-1)/i

Present Value

PV=R(1-(1+i)^-n)/i

Math

Series / Sequences

Geometric

Geometric Series / Sum Formula

Sn=a(r^n-1)/r-1

Geometric Sequence

ar^n-1

Arithmetic

Arithmetic Sequence

a+d(n-1)

Arithmetic Series / Sum Formula

Sn=n(2a+d(n-1))/2

Sn=n(a+tn)/2

Sequence

A sequence is a set of numbers that have no set end to them.

Ex: 3, 6, 9, 12, 15, ... this would go on forever

Series

A series is a set of numbers that have an end to them.

Ex: the keys on a keyboard

General Trig

Trig Problems

Unit circle

This is the CAST rule

Special Angles

Angles for 45°

Angles for: 30° and 60°

2D Problems

Ambiguous Case

h=asinB

3D Problems

Identities

1=(cosx)^2+(sinx)^2

cotx=1/tanx

cscx=1/sinx

secx=1/cosx

tanx=sinx/cosx

Functions

Function Definitions

Continuous:

A function where numbers can be any value within a set.

Ex: time it took to complete some task at any point you could say 1/2 of a second, 1 microsecond, 1 minute but there is a defined set if the task for example took 10 minutes.

Recursive:

tn=t(n-1)....

A function that calls upon previous numbers within the function.

Ex: the Fibonacci sequence that uses the previous numbers in the sequence to make the new number.

Discrete:

A function that has specific data set. Aka: several points in data.

Ex: # of students in a class, only a set # as you cannot have 1/2 of a student.

Exponential Function

Growth Model

f(x)=A₀(1+i)^x

f(x)=ar^x

Decay Model

f(x)=ar^x (where r is a decimal / fraction)

4 Primary Functions

Reciprocal

f(x)=1/x

Absolute

f(x)=|x|

Rational

f(x)=√x

Quadradic

f(x)=x^2

Trig Functions

Cosine Waves

f(x)=acos(k(x-h))+c

Sine Waves

f(x)=asin(k(x-h))+c

(x,y)---}((x/k)+h,ay+c)