# AMS 3

AMS 3, Precalculus for the Social Sciences, is a preparatory course for students in social science majors other than Economics, particularly Psychology.

## Prerequisites

Before enrolling in AMS 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 AMS 3?

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

AMS 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 AMS 3, Precalculus for the Social Sciences:
Precalculus, 7th edition, by Sullivan and Sullivan

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

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

#### 2. Functions and Their Graphs

2.1 Functions
2.2 The Graph of a Function
2.3 Properties of Functions
2.4 Library of Functions; Piecewise-defined Functions
2.5 Graphing Techniques: Transformations
2.6 Mathematical Models: Building Functions

#### 3. Linear and Quadratic Functions

3.1 Properties of Linear Functions and Linear Models
3.2 Building Linear Models from Data
3.3 Quadratic Functions and Their Properties
3.4 Build Quadratic Models from Verbal Descriptions and from Data

#### 4. Polynomial and Rational Functions

4.1 Polynomial Functions and Models
4.2 The Real Zeros of a Polynomial Function
4.3 Complex Zeros; Fundamental Theorem of Algebra
4.4 Properties of Rational Functions
4.5 The Graph of a Rational Function
4.6 Polynomial and Rational Inequalities

#### 5. Exponential and Logarithmic Functions

5.1 Composite Functions
5.2 One-to-One Functions; Inverse Functions
5.3 Exponential Functions
5.4 Logarithmic Functions
5.5 Properties of Logarithms
5.6 Logarithmic and Exponential Equations
5.7 Financial Models
5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
5.9 Building Exponential, Logarithmic, and Logistic Models from Data

#### 6. Trigonometric Functions

6.1 Angles and Their Measure
6.2 Trigonometric Functions: Unit Circle Approach
6.3 Properties of the Trigonometric Functions
6.4 Graphs of the Sine and Cosine Functions
6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
6.6 Phase Shift; Sinusoidal Curve Fitting

#### 7. Analytic Trigonometry

7.1 The Inverse Sine, Cosine, and Tangent Functions
7.2 The Inverse Trigonometric Functions (Continued)
7.3 Trigonometric Equations
7.4 Trigonometric Identities
7.5 Sum and Difference Formulas
7.6 Double-angle and Half-angle Formulas
7.7 Product-to-Sum and Sum-to-Product Formulas

#### 8. Applications of Trigonometric Functions

8.1 Right Triangle Trigonometry; Applications
8.2 The Law of Sines
8.3 The Law of Cosines
8.4 Area of a Triangle
8.5 Simple Harmonic Motion; Damped Motion; Combining Waves

#### 9. Polar Coordinates; Vectors

9.1 Polar Coordinates
9.2 Polar Equations and Graphs
9.3 The Complex Plane; DeMoivre’s Theorem
9.4 Vectors
9.5 The Dot Product
9.6 Vectors in Space
9.7 The Cross Product