**Basic Algebra/Precalculus**

**Precalculus**

Example of Arithmetic Sequence

Geometric Proof of Integer Sum Formula

Example of Proof By Induction 1: Sum 3n+2 = n(3n+7)/2

Example of Proof by Induction 2: 3 divides 5^n-2^n

Example of Proof by Induction 3: n! <= n^n

Example of Proof by Induction 4: Increasing Sequence (Hard)

Example of a Piecewise-Defined Function

Domain of sqrt(x+1) - 1/sqrt(9-x^2)

Example of Composition of Functions

Inverse Function for f(x) = (x-2)/(x+2)

Using Synthetic Division to Evaluate a Polynomial

Fast Factorization of Polynomial

Complex Conjugate Roots of a Real Polynomial

Factoring 3x^4-2x^3+3x-2 Over The Complex Numbers

Domain and Range of 1/(x^2-2x-8)

Partial Fraction Expansion of (x^4+x^3+1)/(x(x^2+1)^2)

Domain of ln((x+1)/(x-1)) +ln(x-1)-ln(x+1)

Evaluation of 3ln(2e^2) + 2ln(3/e) - ln(72e)

Solving an Exponential Equation

Example of Exponential Growth - Two Populations

Examples of Values of Trig Functions

Examples of Inverse Trig Evaluations

Graph of y = 2 sec(pi x - pi/3)

Example of Converting to Polar Coordinates

Example of Graph of Polar Equation

Example of Proof of Trig Identity

Example of Double Angle Formulas

Trig Values for Multiples of pi/5