
PreCalculus
Syllabus 20022003
Text: Merrill, Advanced Mathematical Concepts: Precalculus with Applications
Chapter 1 Linear Relations and Functions
11 Relations and Functions
12 Composition and Inverses of Functions
13A Graphing Calculators: Graphing Linear Equations and Inequalities
13 Linear Functions and Inequalities
14 Distance and Slope
15 Forms of Linear Equations
16 Parallel and Perpendicular Lines
** Complete chapter 1 in about one week as review **
Chapter 2 Systems of Equations and Inequalities
21A Graphing Calculators: Graphing Systems of Linear Equations
21 Solving Systems of Equations
22A Graphing Calculators: Matrices
22 Introduction to Matrices
23 Determinants and Multiplicative Inverses of Matrices
24 Solving Systems of Equations by Using Matrices
25A Graphing Calculators: Graphing Systems of Linear Inequalities
25 Solving Systems of Inequalities
26 Linear Programming
Chapter 3 The Nature of Graphs
31A Graphing Calculators: Graphing Polynomial Functions
31 Symmetry
32 Families of Graphs
33A Graphing Calculators: Graphing Radical Functions
33 Inverse Functions and Relations
34A Graphing Calculators: Graphing Rational Functions
34 Rational Functions and Asymptotes
35 Graphs of Inequalities
36 Tangent to a Curve
37A Graphing Calculators: Locating Critical Points of Polynomial Functions
37 Graphs and Critical Points of Polynomial Functions
38 Continunity and End Behavior
Chapter 4 Polynomial and Rational Functions
41 Polynomial Functions
42A Graphing Calculators: Graphing Quadratic Functions
42 Quadratic Equations and Inequalities
43 The Remainder and Factor Theorems
44 The Rational Root Theorem
45A Graphing Calculators: Locating Zeros of Polynomial Functions
45 Locating the Zeros of a Function
46 Rational Equations and Partial Fractions
47A Graphing Calculators: Solving Radical Equations and Inequalities
47 Radical Equations and Inequalities
** Complete chapter 4 in about one week **
Chapter 5 The Trigonometric Functions
51 Angles and Their Measures
52 Central Angles and Arcs
53 Circular Functions
54 Trigonometric Functions of Special Angles
55 Right Triangles
56 The Law of Sines
57 The Law of Cosines
58 Area of Triangles
Chapter 6 Graphs and Inverses of the Trigonometric Functions
61 Graphs of the Trigonometic Functions
62 Amplitude, Period, and Phase Shift
63A Graphing Calculators: Graphing Trigonometric Functions
63 Graphing Trigonometric Functions
64 Inverse Trigonometric Functions
65 Principal Values of the Inverse
66A Graphing Calculators: Graphing Inverses of Trigonometric Functions
66 Graphing Inverses of Trigonometric Functions
67 Simple Harmonic Motion
Chapter 7 Trigonometric Identities and Equations
71 Basic Trigonometric Identities
72 Verifying Trigonometric Identities
72B Graphing Calculators: Verifying Trigonometric Identities
73 Sum and Difference Identities
74 DoubleAngle and HalfAngle Identities
75A Graphing Calculators: Solving Trigonometric Equations
75 Solving Trigonometric Equations
76 Normal Form of a Linear Equation
77 Distance from a Point to a Line
** Complete chapter 7 in about one week **
Chapter 8 Vectors and Parametric Equations
81 Geometric Vectors
82 Algebraic Vectors
83 Vectors in ThreeDimensional Space
84 Perpendicular Vectors
85 Applications with Vectors
86 Vectors and Parametric Equations
87 Using Parametric Equations to Model Motion
Chapter 9 Polar Coordinates and Complex Numbers
91 Polar Coordinates
92A Graphing Calculators: Graphing Polar Equations
92 Graphs of Polar Equations
93 Polar and Rectangular Coordinates
94 Polar Form of a Linear Function
95 Simplifying Complex Numbers
96 Polar Form of Complex Numbers
97 Products and Quotients of Complex Numbers in Polar Form
98 Powers and Roots of Complex Numbers
Chapter 15 Statistics and Data Analysis
151 The Frequency Distribution
152 Measures of Central Tendency
153 Measures of Variability
154 The Normal Distribution
155 Sample Sets of Data
156A Graphing Calculators: Scatter Plots and Lines of Regression
156 Scatter Plots
156B Graphing Calculators: Curve Fitting
** Optional Material if time permits in first three quarters **
Chapter 11 Exponential and Logarithmic Functions
111 Rational Exponents
112A Graphing Calculators: Graphing Exponential Functions
112 Exponential Functions
113 The Number e
114A Graphing Calculators: Graphing Logarithmic Functions
114 Logarithmic Functions
115 Common Logarithms
116A Graphing Calculators: Exponential and Logarithmic Equations and
Inequalities
116 Exponential and Logarithmic Equations
117 Natural Logarithms
** Put at beginning of Fourth Quarter **
Chapter 12 Sequences and Series
121 Arithmetic Sequences and Series
122 Geometric Sequences and Series
123 Infinite Sequences and Series
124 Convergent and Divergent Series
125 Sigma Notation and the nth Term
126 The Binomial Theorem
127 Special Sequences and Series
128 Mathematical Induction
Chapter 17 Limits, Derivatives, and Integrals
171 Limits
172 Derivatives and Differentiation Techniques
173 Area Under a Curve
174 Integration
175 The Fundamental Theorem of Calculus
** Most of the Fourth Quarter will be spent on chapter 17 with supplementary
materials **
TWB 2002
