Catholic Central High School
Course Syllabus
Course: Precalculus
Department: Mathematics
Length: One Year
Credit: 1
I.
Pre-requisites: “B” in Algebra II
II.
Text Book: PRECALCULUS
(Seventh Addition)
Ron Larson
Robert Hostetler
David C. Falvo
Published by: Houghton and Mifflin Company
Boston New York
III.
Course Goals: To teach the following topics: mathematical induction, analytic
geometry, vector algebra, sequences and series, quadratic relations,
transformations in a plane, and trigonometry with some applications in
order to directly prepare students for college calculus.
IV.
Detailed List of Topics:
A. 1st Quarter
1. Review of Fundamental Concepts of Algebra
a. Real Numbers and Their Properties
b. Exponents and Radicals
c. Polynomials and Factoring
d. Rational Expressions
e. Solving Equations
f. Linear Inequalities in One Variable
g. Errors and the Algebra of Calculus
2. Functions and Their Graphs
a. Rectangular Coordinates
b. Graphs of Equations
c. Linear Equations in Two Variables
d. Functions
e. Analyzing Graphs of Functions
f. A Library of Parent Functions
g. Transformations of Functions
h. Combinations of Functions: Composite Functions
i. Inverse Functions
j. Mathematical Modeling and Variation
3. Polynomial and Rational Functions
a. Quadratic Functions and Models
b. Polynomial Functions of Higher Degree
c. Polynomial and Synthetic Division
d. Complex Numbers
e. Zeros of Polynomial Functions
f. Rational Functions
g. Nonlinear Inequalities
B. 2nd Quarter
1. Exponential and Logarithmic Functions
a. Exponential Functions and Their Graphs
b. Logarithmic Functions and Their Graphs
c. Properties of Logarithms
d. Exponential and Logarithmic Equations
e. Exponential and Logarithmic Models
2. Trigonometry
a. Radian and Degree Measure
b. Trigonometric Functions: The Unit Circle
c. Right Triangle Trigonometry
d. Trigonometric Functions of Any Angle
e. Graphs of Sine and Cosine Functions
f. Graphs of Other Trigonometric Functions
g. Inverse Trigonometric Functions
h. Applications and Models
3. Analytic Trigonometry
a. Using Fundamental Identities
b. Verifying Trigonometric Identities
c. Solving Trigonometric Equations
d. Sum and Difference Formulae
e. Multiple-Angle and Product to Sum Formulae
C. Mid-Term Exam
D. 3rd Quarter
1. Additional Topics in Trigonometry
a. Law of Sines
b. Law of Cosines
c. Vectors in the Plane
d. Vectors and Dot Products
e. Trigonometric Form of a Complex Number
2. Systems of Equations and Inequalities
a. Linear and Nonlinear Systems of Equations
b. Two-Variable Linear Systems
c. Multivariable Linear Systems
d. Partial Fractions
e. Systems of Inequalities
f. Linear Programming
3. Matrices and Determinants
a. Matrices and Systems of Equations
b. Operations with Matrices
c. The Inverse of a Square Matrix
d. The Determinant of a Square Matrix
e. Applications of Matrices and Determinants
E. 4th Quarter
1. Sequences, Series, and Probability
a. Sequences and Series
b. Arithmetic Sequences and Partial Sums
c. Geometric Sequences and Series
d. Mathematical Induction
e. The Binomial Theorem
f. Counting Principles
g. Probability
2. Topics in Analytic Geometry
a. Lines
b. Introduction to Conics: Parabolas
c. Ellipses
d. Hyperbolas
e. Rotation of Conics
f. Parametric Equations
g. Polar Coordinates
h. Graphs of Polar Equations
i. Polar Equations of Conics
F. Final Exam
V.
Course Assignments and Requirements:
Homework is assigned nightly.
Tests or quizzes are given weekly.