Pre-Calculus / Trigonometry

Pre-Requisites

Algebra I

Geometry

Algebra II

Description

This upper level course is important for any student planning to take Calculus or a college Algebra class. The first semester of this course is Pre-Calculus which covers chapters P-4 and extends topics introduced in Algebra II including exponential and logarithmic functions. The second semester of this course is Trigonometry which covers chapter 5-7 and focuses on angles, trigonometric functions and identities, vectors and complex numbers.

Textbook

Precalculus Common Core (Pearson 2015)

Course Outline

Chapter P - Prerequisites

Real Numbers

Cartesian Coordinate System

Linear Equations and Inequalities

Lines in the Plane

Solving Equations Graphically, Numerically, and Algebraically

Complex Numbers

Solving Inequalities Algebraically and Graphically

Chapter 1 - Functions and Graphs

Modeling and Equation Solving

Functions and Their Properties

Twelve Basic Functions

Building Functions from Functions

Parametric Relations and Inverses

Graphical Transformations

Modeling with Functions

Chapter 2 - Polynomial, Power & Rational Functions

Linear and Quadratic Functions and Modeling

Power Functions with Modeling

Polynomial Functions of Higher Degree with Modeling

Real Zeros of Polynomial Functions

Complex Zeros and the Fundamental Theorem of Algebra

Graphs of Rational Functions

Solving Equations in One Variable

Chapter 3 - Exponential, Logistic, and Logarithmic Functions

Exponential and Logistic Functions

Exponential and Logistic Modeling

Logarithmic Functions and Their Graphs

Properties of Logarithmic Functions

Equation Solving and Modeling

Mathematics of Finance

Chapter 4 - Trigonometric Functions

Angles and Their Measures

Trigonometric Functions of Acute Angles

The Circular Functions

Graphs of Sine and Cosine

Inverse Trigonometric Functions

Solving Problems with Trigonometry

Chapter 5 - Analytic Trigonometry

Fundamental Identities

Proving Trigonometric Identities

Sum and Difference Identities

Multiple Angle Identities

The Law of Sines

The Law of Cosines

Area of a Triangle and Heron’s Formula

Chapter 6 - Applications of Trigonometry

Vectors in the Plane

Dot Product of Vectors

Polar Coordinates

De Moivre’s Theorem and nth Roots

Chapter 7 - Systems and Matrices

Solving Systems of Two Equations

Matrix Algebra

Multivariate Linear Systems and Row Operations