# Pre-Calculus Syllabus 2002-2003

Chapter 1 **Linear Relations and Functions**

1-1 Relations and Functions

1-2 Composition and Inverses of Functions

1-3A Graphing Calculators : Graphing Linear Equations and Inequalities

1-3 Linear Functions and Inequalities

1-4 Distance and Slope

1-5 Forms of Linear Equations

1-6 Parallel and Perpendicular Lines

**** Complete chapter 1 in about one week as review **
**

Chapter 2

**Systems of Equations and Inequalities**

2-1A Graphing Calculators: Graphing Systems of Linear Equations

2-1 Solving Systems of Equations

2-2A Graphing Calculators: Matrices

2-2 Introduction to Matrices

2-3 Determinants and Multiplicative Inverses of Matrices

2-4 Solving Systems of Equations by Using Matrices

2-5A Graphing Calculators: Graphing Systems of Linear Inequalities

2-5 Solving Systems of Inequalities

2-6 Linear Programming

Chapter 3

**The Nature of Graphs**

3-1A Graphing Calculators: Graphing Polynomial Functions

3-1 Symmetry

3-2 Families of Graphs

3-3A Graphing Calculators: Graphing Radical Functions

3-3 Inverse Functions and Relations

3-4A Graphing Calculators: Graphing Rational Functions

3-4 Rational Functions and Asymptotes

3-5 Graphs of Inequalities

3-6 Tangent to a Curve

3-7A Graphing Calculators: Locating Critical Points of Polynomial

Functions

3-7 Graphs and Critical Points of Polynomial Functions

3-8 Continunity and End Behavior

Chapter 4

**Polynomial and Rational Functions**

4-1 Polynomial Functions

4-2A Graphing Calculators: Graphing Quadratic Functions

4-2 Quadratic Equations and Inequalities

4-3 The Remainder and Factor Theorems

4-4 The Rational Root Theorem

4-5A Graphing Calculators: Locating Zeros of Polynomial Functions

4-5 Locating the Zeros of a Function

4-6 Rational Equations and Partial Fractions

4-7A Graphing Calculators: Solving Radical Equations and Inequalities

4-7 Radical Equations and Inequalities

**** Complete chapter 4 in about one week ****

Chapter 5 **The Trigonometric Functions**

5-1 Angles and Their Measures

5-2 Central Angles and Arcs

5-3 Circular Functions

5-4 Trigonometric Functions of Special Angles

5-5 Right Triangles

5-6 The Law of Sines

5-7 The Law of Cosines

5-8 Area of Triangles

Chapter 6 **Graphs and Inverses of the Trigonometric Functions**

6-1 Graphs of the Trigonometic Functions

6-2 Amplitude, Period, and Phase Shift

6-3A Graphing Calculators: Graphing Trigonometric Functions

6-3 Graphing Trigonometric Functions

6-4 Inverse Trigonometric Functions

6-5 Principal Values of the Inverse

6-6A Graphing Calculators: Graphing Inverses of Trigonometric

Functions

6-6 Graphing Inverses of Trigonometric Functions

6-7 Simple Harmonic Motion

Chapter 7 **Trigonometric Identities and Equations**

7-1 Basic Trigonometric Identities

7-2 Verifying Trigonometric Identities

7-2B Graphing Calculators: Verifying Trigonometric Identities

7-3 Sum and Difference Identities

7-4 Double-Angle and Half-Angle Identities

7-5A Graphing Calculators: Solving Trigonometric Equations

7-5 Solving Trigonometric Equations

7-6 Normal Form of a Linear Equation

7-7 Distance from a Point to a Line

**** Complete chapter 7 in about one week ****

Chapter 8** Vectors and Parametric Equations**

8-1 Geometric Vectors

8-2 Algebraic Vectors

8-3 Vectors in Three-Dimensional Space

8-4 Perpendicular Vectors

8-5 Applications with Vectors

8-6 Vectors and Parametric Equations

8-7 Using Parametric Equations to Model Motion

Chapter 9 **Polar Coordinates and Complex Numbers **

9-1 Polar Coordinates

9-2A Graphing Calculators: Graphing Polar Equations

9-2 Graphs of Polar Equations

9-3 Polar and Rectangular Coordinates

9-4 Polar Form of a Linear Function

9-5 Simplifying Complex Numbers

9-6 Polar Form of Complex Numbers

9-7 Products and Quotients of Complex Numbers in Polar Form

9-8 Powers and Roots of Complex Numbers

Chapter 15 **Statistics and Data Analysis**

15-1 The Frequency Distribution

15-2 Measures of Central Tendency

15-3 Measures of Variability

15-4 The Normal Distribution

15-5 Sample Sets of Data

15-6A Graphing Calculators: Scatter Plots and Lines of Regression

15-6 Scatter Plots

15-6B Graphing Calculators: Curve Fitting

**** Optional Material if time permits in first three quarters ****

Chapter 11 **Exponential and Logarithmic Functions **

11-1 Rational Exponents

11-2A Graphing Calculators: Graphing Exponential Functions

11-2 Exponential Functions

11-3 The Number e

11-4A Graphing Calculators: Graphing Logarithmic Functions

11-4 Logarithmic Functions

11-5 Common Logarithms

11-6A Graphing Calculators: Exponential and Logarithmic Equations and

Inequalities

11-6 Exponential and Logarithmic Equations

11-7 Natural Logarithms

**** Put at beginning of Fourth Quarter ****

Chapter 12** Sequences and Series**

12-1 Arithmetic Sequences and Series

12-2 Geometric Sequences and Series

12-3 Infinite Sequences and Series

12-4 Convergent and Divergent Series

12-5 Sigma Notation and the nth Term

12-6 The Binomial Theorem

12-7 Special Sequences and Series

12-8 Mathematical Induction

Chapter 17** Limits, Derivatives, and Integrals**

17-1 Limits

17-2 Derivatives and Differentiation Techniques

17-3 Area Under a Curve

17-4 Integration

17-5 The Fundamental Theorem of Calculus

**** Most of the Fourth Quarter will be spent on chapter 17 with supplementary
materials ****

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