Precalculus Topics

Functions and Mathematical Modeling
Functions
f(x) Terminology
Types of Functions
Restricted Domains and Boolean Variables
Friendly Windows
Translations and Dilations of Function Graphs
Translations and Dilations of Function Graphs - Practice on the TI83/TI 84
Composition of Functions
Domain of a Composite Function
Inverse of Functions
Reflections of Function Graphs
Absolute Value Transformations
Even and Odd Functions

Periodic Functions and Right Triangle Problems
Standard Position of an Angle
Coterminal Angles
Reference Angles
Sine and Cosine Functions
The Six Trigonometric Functions
Inverse Trigonometric Functions
Right Triangle Problems

Applications of Trigonometric and Circular Functions
General Sinusoidal Graphs
General Sinusoidal Graphs - Examples
Graphs of Tangent, Cotangent, Secant, and Cosecant Functions
Radian Measure of Angles
Circular Functions
The Inverse Cosine Relation
Sinusoidal Functions as Mathematical Models

Properties of Trigonometric Functions; Identities; Parametric Functions
Reciprocal, Quotient, and Pythagorean Properties
Identities and Algebraic Transformation of Expressions
Arcsine, Arctangent, and Arccosine
Trigonometric Equations
Parametric Functions
Using Parametric Equations to Plot Solids
Inverse Trigonometric Relation Graphs
Exact Values of Inverse Circular Functions

Combined Sinusoids
Linear Combination Property
Composite Argument Property for Cos ( A - B )
The Odd-Even Properties
The Cofunction Properties
Other Composite Argument Properties
Composition of Ordinates
Harmonic Analysis
The Sum and Product Properties
Products and Squares of Cosine and Sine
Double Argument Properties
Half Argument Properties
Combined SInusoids - Review

Triangle Trigonometry
The Law of Cosines
Area of a Triangle
The Law of Sines
The Ambiguous Case
Vector Addition
Applications of Triangle Problems

Properties of Elementary Functions
Identifying Functions from Graphical Patterns
Identifying Functions from Graphical Patterns - Problems
Using Matrices to Solve Systems of Equations
Identifying Functions from Numerical Patterns
Introduction to Logarithms
Properties of Logarithms
Solving Logarithmic and Exponential Equations
Logarithmic Functions
Logistic Functions for Restrained Growth

Fitting Functions to Data
Linear Regression
Regression for Nonlinear Data
Linearizing Data and Logarithmic Graph Paper
Residual Plots and Mathematical Models

Probability and Functions of a Random Variable
Words Associated with Probability
Two Counting Principles
Probabilities of Various Permutations
Probabilities of Various Combinations
Properties of Probability
Functions of a Random Variable
Mathematical Expectation

Three Dimensional Vectors
Review of Two-Dimensional Vectors
Two-Dimensional Vector Practice
Vectors in Space
Scalar Products and Projections of Vectors
Planes in Space
Vector Product of Two Vectors
Direction Angles and Direction Cosines
Vector Equations of Lines in Space

Matrix Transformations and Fractal Figures
Matrix Operations and Solutions of Linear Systems
Rotation and Dilation Matrices
Strange Attractors for Several Iterated Transformations
Fractal Dimensions

Conic Sections and Quadric Surfaces
Introduction to Conic Sections
Parametric and Cartesian Equations of the Conic Sections
Quadric Surfaces and Inscribed Figures
Analytic Geometry of the Conic Sections
Parametric and Cartesian Equations for Rotated Conics
Applications of Conic Sections

Polar Coordinates
Polar Equations of Conics and Other Curves
Intersections of Polar Curves
Complex Numbers in Polar Form
Parametric Equations for Moving Objects

Sequences and Series
Arithmetic, Geometric, and Other Sequences
Series and Partial Sums
Binomial Series

Polynomial and Rational Functions; Limits and Derivatives
Long Division of Polynomials
Graphs and Zeros of Polynomial Functions
Sums and Products of Zeros
Fitting Polynomial Functions to Data
Rational Functions: Discontinuities and Limits
Rational Functions: Partial Fractions
Instantaneous Rate of Change of a Function: The Derivative