Pre-Calculus Syllabus 2002-2003
Merrill, Advanced Mathematical Concepts: Precalculus with Applications

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 **

TWB 2002