# Pre-Calculus

## Fundamental Algebra Concepts

Solving Equations with 2 Absolute Value Functions or More

## Introduction to Functions and their Graphs

Visually identifying key characteristics of graphs.

Even and Odd Functions Many Examples

Graphing Absolute Value Functions as Piecewise Functions 3 Examples

Graphing Absolute Value Functions with Transformations 6 Examples

Determining Domain of Functions

## Linear Functions and Slope

Rate of Change Slope & Point Slope Equation of Lines

Equations of Lines and Graphing

Equations of parallel and perpendicular lines

## Combining Functions, Composition of Functions, and Inverse Functions

Combining Functions & Function Operations

Combining Square Root Functions & Domain 4 Examples

## Modeling Real World Settings with Functions

Modeling with Functions Part 1

Modeling with Functions Part 2

Modeling with Functions Part 3

## Understanding Complex Numbers

Complex (imaginary) Numbers Part 1

Complex (imaginary) Numbers Part 2

Powers of Imaginary Numbers Higher Powers of i (4 Examples)

Solving Equations with Complex Numbers 4 Examples

## Graphing Polynomials

Graphing Parabolas w/ vertex & intercepts

Parabola Applications Maximizing Minimizing Reflectors, etc

Basic graphing with a TI-NSPIRE

## Solving Quadratics and Higher Order Polynomials

Synthetic Division & Remainder Theorem

Solving Higher Order Polynomials Part 1

Solving Higher Order Polynomials Part 2

Finding polynomials using the Linear Factorization Theorem

## Rational Functions

Horizontal Asymptotes of rational equations

Graphing Rational Functions with Slant Asymptotes

Finding vertical asymptotes and holes of rational equations

Graphing Rational Functions Part 1

Graphing Rational Functions Part 2

## Solving Polynomial & Rational Inequalities

Solving Polynomial Inequalities

Solving Polynomial Inequalities a Graphical Approach

## Exponential Functions and Logarithms

Graphing Exponential Functions

Change of Base Formula Logarithms

Using Properties of Logarithms to Expand Logs

Using Properties of Logarithms to Condense Logs

Graphing Logarithms without a Calculator 3 Examples

Solving Equations with Logarithms Pt 1

Solving Equations with Logarithms Pt 2

Solving Equations with Logarithms Pt 3

Solving Natural Exponential Functions with Natural Logarithms

Logarithm Equations with Different Bases

Solving Compound Interest Problems

System of Equations Involving Logarithms of Different Bases

## Standard Position Angles and Unit Circle

Standard Position Angles & Radians Part 1

Standard Position Angles & Radians Part 2

Setting up the Unit Circle Part 1 and Reference Angle

Setting Up the Unit Circle Part 2

Evaluating Trig Functions w/ Unit Circle Degrees & Radians

## Linear & Angular speed

## More Unit Circle and Right Triangle Trigonometry

Fundamental Trigonometric Identities Intro & Proofs

Trig Expressions & Finding Trig Functions Given another Trig Ratio

Right Triangle Trigonometry Part 1

Right Triangle Trigonometry Part 2

Trigonometric Functions of Any Angle

## Graphs of Trigonometric Functions

Understanding Basic Sine & Cosine Graphs

Graphing Sine & Cosine w/out a Calculator Pt1

Graphing Sine & Cosine w/out a Calculator Pt 2

Equation of Sine and Cosine from a Graph

Water Depth Word Problem Modeled with Cosine Sine Function

Intro Tangent & Cotangent Graphs

Tangent & Cotangent Graphs w/ Transformations

Graphing Secant & Cosecant w/ t-table

Evaluating Inverse Trigonometric Functions

## Analytic Trigonometry and Trig Proofs

Verifying Trigonometric Identities Pt 1.mov

Verifying Trigonometric Identities Pt2

Verifying Trigonometric Identities Pt3

Sum and Difference Trigonometric Identities

Verifying Trigonometric Identities Involving Sum & Difference

Evaluating Trigonometry Expressions with Half and Double Angles Pt1

Evaluating Trigonometry Expressions with Half and Double Angles Pt2

Trigonometry Proofs Involving Half and Double Angles

Product to Sum and Sum to Product Formulas

## Solving Trigonometric Equations

Trigonometric Equations Single Angle 0 to 2pi Restriction

Single Angle Trigonometric Equations All Solutions

Trigonometric Equations Multiple Angles 0 to 2pi Restriction

Trigonometric Equations Multiple Angles All Solutions

## Law of Sine and Law of Cosine

Law of Sine Introduction Solving Oblique Triangles (New)

Oblique Triangles Law of Sines

Ambiguous Case for Law of Sines (New)

Ambiguous Case for Law of Sines

Introduction to Law of Cosine (New)

Area of oblique triangles with Heron's Formula

Applications of Law of Sine and Law of Cosine

Bearing Word Problems 4 Examples

## Polar Coordinate System

Understanding Polar Coordinates

Graphing Polar Equations, Test for Symmetry & 4 Examples

Converting Coordinates between Polar and Rectangular Form

Converting Equations Between Polar & Rectangular Form

## Complex Numbers in Polar Form

Product & Quotient of Polar Complex Numbers

De Moivre's Theorem powers of Polar Complex Numbers

De Moivre's Theorem Roots of Polar Complex Numbers

## Vectors

Writing Vector in terms of Magnitude & Direction Example

Dot Product & Angle Between Vectors

Projection of a Vector onto another Vector

## Systems of Equations

Solving Linear Systems with Substitution and LInear Combination

Solving 3 Variable Linear Systems Gaussian Elimination

Applications of 3 Variable Systems

Non-Square 3 Variable Linear Systems

Partial Fraction Decomposition Part 1

Partial Fractions Decomposition Part 2

2 Variable Non Linear Systems Substitution Method

2 Variable Non Linear Systems Addition/Elimination Method

## Graphing Inequalities

Graphing 1 Variable Inequalities

Graphing Non-Linear Inequalities

Graphing System of Inequalities

## Conic Sections: Parabolas, Ellipses & Circles, Hyperbolas

Graphing Hyperbolas in Standard Form

Graphing Parabolas in Standard Form

Finding Equations of Conics from Given Conditions

Applications of Parabolas in Standard Form

Rotated Conic Section Identifying & Graphing 4 Examples

## Parametric Equations

Introduction to Parametric Equations

Parametric Equations Eliminating Parameter T

## Intro to Sequences, Arithmetic & Geometric

Arithmetic Sequence Introduction

Partial Sum Arithmetic Sequence

Geometric Means in a Geometric Sequence

Partial Sum Geometric Sequences

Converting Repeating Decimal to a Fraction

## Induction Proofs

Introduction to Induction Proofs

Induction Proof for Divisibility

## Binomial Theorem

Binomial Theorem Introduction to Raise Binomials to High Powers

Binomial Theorem Introduction (New) 3 More Examples

Binomial Theorem & Transformation of Functions

## Introduction to Calculus

Why Limits are Important in Calculus

Finding Real limits Graphical & Numerical Approach