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Precalculus Algebra and Trigonometry: Course Competencies and Study Guide

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Algebraic Expressions

Exponents

Polynomials Intro

Multiplying Polynomials

Factoring Polynomials

Rational Exponents

Rationalize Denominator

Linear Equations

Intro to Quadratic Equations

The Square Root Property

Completing the Square

The Quadratic Formula

Complex Numbers

Rational Equations

Choosing a Method to Solve Quadratics

Linear Inequalities

Graphs and Coordinates

Two-Variable Equations

Lines

Circles

Intro to Functions & Their Graphs

Common Functions

Transformations

Function Operations

Quadratic Functions

Understanding Polynomial Functions

Graphing Polynomial Functions

Introduction to Rational Functions

Asymptotes

Graphing Rational Functions

Introduction to Exponential Functions

Graphing Exponential Functions

The Number e

Introduction to Logarithms

Graphing Logarithmic Functions

Properties of Logarithms

Solving Exponential and Logarithmic Equations

Angles in Standard Position

Coterminal Angles

Complementary and Supplementary Angles

Radians

Trigonometric Functions on Right Triangles

Special Right Triangles

Cofunctions of Complementary Angles

Solving Right Triangles

Defining the Unit Circle

Trigonometric Functions on the Unit Circle

Common Values of Sine, Cosine, & Tangent

Reference Angles

Reciprocal Trigonometric Functions on the Unit Circle

Graphs of the Sine and Cosine Functions

Graphs of Secant and Cosecant Functions

Graphs of Tangent and Cotangent Functions

Phase Shifts

Inverse Sine, Cosine, & Tangent

Evaluate Composite Trig Functions

Linear Trigonometric Equations

Introduction to Trigonometric Identities

Sum and Difference Identities

Double Angle Identities

Solving Trigonometric Equations Using Identities

Law of Sines

Law of Cosines

Area of SAS & ASA Triangles

Polar Coordinate System

Convert Points Between Polar and Rectangular Coordinates

Convert Equations Between Polar and Rectangular Forms

Graphing Other Common Polar Equations

Graphing Complex Numbers

Polar Form of Complex Numbers

Products and Quotients of Complex Numbers

Powers of Complex Numbers (DeMoivre's Theorem)

Geometric Vectors

Vectors in Component Form

Direction of a Vector

Unit Vectors and i & j Notation

Dot Product

Introduction to Conic Sections

Parabolas

Ellipses: Standard Form

Hyperbolas at the Origin

Hyperbolas NOT at the Origin

Graphing Parametric Equations

Eliminate the Parameter

Writing Parametric Equations

Two Variable Systems of Linear Equations

Introduction to Matrices

Determinants and Cramer's Rule

Graphing Systems of Inequalities

Sequences

Arithmetic Sequences

Geometric Sequences

Factorials

Combinatorics

Probability