## Pre-Calculus Course Outline

The first semester of Pre-calculus explores trig functions and sinusoids. The second semester examines a variety of topics from analytic geometry to probability to polar coordinates and complex numbers. The course should also contain review of earlier algebraic concepts. This course uses Pre-Calculus by P. Foerster.

## Semester I

Chapter 1: Functions and Mathematical Models

• dilations, translations, and transformations
• composition of functions
• inverses of functions
• reflections and absolute values

Chapter 2: Periodic Functions and Right Triangle Problems

• periodic functions
• measurements of rotation
• trig functions
• inverse trig functions

Chapter 3: Applications of Trigonometric and Circular Functions

• sinusoids
• amplitudes, period, and cycles
• circular functions

Chapter 4: Trigonometric Functions, Properties, Identities, and Parametric Functions

• the Pythagorean property
• trig identities
• arcsines, arccosines, and arctangents
• inverse trig relations

Chapter 5: Properties of Combined Sinusoids

• combination of sinusoids
• composition argument properties
• sum and product properties
• double and half argument properties

## Semester II

Chapter 6: Triangle Trigonometry

• oblique triangles
• law of sines and law of cosines
• area of triangles
• vectors
• triangle problems

Chapter 7: Properties of Elementary Functions

• shapes of functions
• graphical patterns
• numerical patterns
• properties of logarithms
• logarithmic functions
• logistic functions for growth

Chapter 8: Fitting Functions to Data

• regression equations
• correlations
• regression for nonlinear data
• residual plots

Chapter 9: Probability and Functions of Random Variability

• principles of probability
• counting principles
• permutations and combinations
• functions of a random variable
• mathematical expectation

Chapter 12: Analytic Geometry of Conic Selections and Quadratic Surfaces

• conic sections
• parametric equations of conics
• analytic geometry
• application of conics

Chapter 13: Polar Coordinates, Complex Numbers, and Moving Objects

• polar coordinates
• polar equations of conics and other curves
• intersection of polar coordinates
• complex numbers in complex form