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May 24th

May 24th

# Precalculus Mathematics

I. COURSE DESCRIPTION FROM CATALOG:
Review of algebra and trigonometry ; relations and functions and their graphs, including
polynomial and rational functions; conic sections; inequalities, polar coordinates,
complex numbers; advanced topics in algebra. Lec. 5. Cr. 5.

II. PREREQUISITE(S):
Two years of high school algebra, one year of high school geometry, and 12 weeks of
trigonometry.

III. COURSE OBJECTIVE(S):
Build on (not replicate) the competencies gained through the study of two years of high
school algebra and one year of high school geometry. Use mathematics to solve problems
and de termine if the solutions are reasonable. Use mathematics to model real world
behaviors and apply mathematical concepts to the solution of real-life problems. Make
meaningful connections between mathematics and other disciplines. Use technology for
mathematical reasoning and problem solving. Apply mathematical and/or basic statistical
reasoning to analyze data and graphs. Refine the algebraic, geometric, trigonometric, and
reading com prehension skills necessary in the study of calculus.

IV. TOPICS TO BE COVERED:

Chapter 1: Equations and Inequalities
1.3 Complex Numbers

Chapter 2: Graphs and Functions
2.1 Rectangular Coordinates and
Graphs

2.2 Circles
2.3 Functions
2.4 Linear Functions
2.5 Equations of Lines ; Curve
Fitting
2.6 Graphs of Basic Functions
2.7 Graphing Techniques
2.8 Function Operations and
Composition

Chapter 3: Polynomial and Rational
Functions

Models
3.2 Synthetic Division
3.3 Zeros of Polynomials
3.4 Polynomial Functions: Graphs,
Applications and Models
3.5 Rational Functions: Graphs,
Applications, and Models
3.6 Variation - Omit

Chapter 4: Inverse, Exponential, and
Logarithmic Functions
4.1 Inverse Functions
4.2 Exponential Functions
4.3 Logarithmic Functions
4.4 Evaluating Logarithms and the
Change-of-Base Theorem
4.5 Exponential and Logarithmic
Equations

Chapter 5: Trigonometric Functions
5.1 Angles
5.2 Trigonometric Functions
5.3 Evaluating Trigonometric
Functions
5.4 Solving Right Triangles

Chapter 6: The Circular Functions and
Their Graphs

6.2 The Unit Circle and Circular
Functions
6.3 Graphs of the Sine and Cosine
Functions
6.4 Translations of the Graphs of
the Sine and Cosine Functions
6.5 Graphs of the Tangent,
Cotangent, Secant, and
Cosecant Functions
6.6 Harmonic Motion - Omit

Chapter 7: Trigonometric Identities and
Equations

7.1 Fundamental Identities
7.2 Verifying Trigonometric
Identities
7.3 Sum and Difference Identities
7.4 Double-Angle Identities and
Half-Angle Identities
7.5 Inverse Circular Functions
7.6 Trigonometric Equations
7.7 Equations Involving Inverse
Trigonometric Functions

Chapter 8: Applications of Trigonometry
8.1 The Law of Sines
8.2 The Law of Cosines
8.3 Vectors, Operations, and Dot
Product
8.4 Applications of Vectors
8.5 Trigonometric (Polar) Form of
Complex Numbers: Products
and Quotients
8.6 De Moivre’s Theorem; Powers
and Roots of Complex
Numbers
8.7 Polar Equations and Graphs
8.8 Parametric Equations, Graphs,
and Application

Chapter 9: Systems and Matrices
9.4 Partial Fractions

Chapter 11: Further Topics in Algebra
11.1 Sequences and Series
11.2 Arithmetic Sequences and
Series
11.3 Geometric Sequences and
Series
11.4 The Binomial Theorem
11.5 Mathematical Induction
11.6 Counting Theory - Omit
11.7 Basics of Probability – Omit

VI. POSSIBLE TEXTS AND REFERENCES:

Precalculus, 4th edition Margaret L. Lial, John Hornsby and David I. Schnieder

VII. ANY TECHNOLOGY THAT MAY BE USED:
MyMathLab
Scientific Calculator

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