# Math 3

Math 3, Precalculus, is a preparatory course for students in economics, engineering, or the physical or biological sciences.

## Prerequisites

Before enrolling in Math 3, you must satisfy one of the following prerequisites:

MP tier 200 or higher, or
completion of Math 2 with a grade of C or better.

## Who should take Math 3?

Math 3 is the recommended preparatory course for students intending to take Math 11AB or Math 19AB whose best MP tier after reassessment is 200, and who do not have an AP Calculus score or 3 or higher.

Math 3 is recommended for calculus-bound students who whose most advanced math course is advanced algebra or the equivalent. Students who have successfully completed a precalculus or trigonometry course are strongly encouraged to improve their placement through review in their ALEKS Learning Module and reassessment.

## Topics and text

Usual text for Math 3, Precalculus:
Precalculus, 7th edition, by David Cohen, Theodore Lee, and David Sklar.

Gray sections are skipped and chapters not covered aren't shown.

WARNING: The text may be changed at the instructor's discretion.

#### 3. FUNCTIONS

3.1 The Definition of a Function
3.2 The Graph of a Function
3.3 Shapes of Graphs, Average Rate of Change
3.4 Techniques in Graphing
3.5 Methods of Combining Functions, Iteration
3.6 Inverse Functions

#### 4. POLYNOMIAL AND RATIONAL FUNCTIONS: APPLICATIONS TO OPTIMIZATION

4.1 Linear Functions
4.3 Using Iteration to Model Populations Growth (Optional Section)
4.4 Setting Up Equations That Define Functions
4.5 Maximum and Minimum Problems
4.6 Polynomial Functions
4.6 Rational Functions

#### 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS

5.1 Exponential Functions
5.2 The Exponential Function y = ex
5.3 Logarithmic Functions
5.4 Properties of Logarithms
5.5 Equations and Inequalities with Logs and Exponents
5.6 Compound Interest
5.7 Exponential Growth and Decay

#### 6. AN INTRODUCTION TO TRIGONOMETRY VIA RIGHT TRIANGLES

6.1 Trigonometric Functions of Acute Angles
6.2 Right-Triangle Applications
6.3 Trigonometric Functions of Angles
6.4 Trigonometric Identities

#### 7. THE TRIGONOMETRIC FUNCTIONS

7.2 Trigonometric Functions of Angles
7.3 Evaluating the Trigonometric Functions
7.4 Algebra and the Trigonometric Functions
7.5 Right-Triangle Trigonometry

#### 8. GRAPHS OF TRIGONOMETRIC FUNCTIONS

8.1 Trigonometric Functions of Real Numbers
8.2 Graphs of the Sine and Cosine Functions
8.3 Graphs of y = A sin(Bx-C) and y = A cos(Bx-C)
8.4 Simple Harmonic Motion
8.5 Graphs of the Tangent and the Reciprocal Functions

#### 9. ANALYTICAL TRIGONOMETRY

9.2 The Double-Angle Formulas
9.3 The Product-to-Sum and Sum-to-Product Formulas
9.4 Trigonometric Equations
9.5 The Inverse Trigonometric Functions

#### 10. ADDITIONAL TOPICS IN TRIGONOMETRY

10.1 Right-Triangle Applications
10.2 The Law of Sines and the Law of Cosines
10.3 Vectors in the Plane: A Geometric Approach
10.4 Vectors in the Plane: An Algebraic Approach
10.5 Parametric Equations
10.6 Introduction to Polar Coordinates
10.7 Curves in Polar Coordinates
10.8 DeMoivre’s Theorem