Pre-Calculus
MATH 100
Joseph Freymann, Adjunct Professor (jfreymann@catholicpolytechnic.org)

Pre-Calculus Course Syllabus

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Catholic Polytechnic University’s Online Academy provides dual-enrollment opportunities. This course counts for high school credit as well as credit towards a degree at Catholic Polytechnic University. (The CPU course code is MATH 100.)

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Course Description: This course covers the concepts of arithmetic and geometric functions, trigonometry, analytical geometry, linear algebra, sequences and series.  Some of these concepts will have already been introduced in previous courses, while others will be totally new to the students. Concepts are presented in a rigorous way that prepares each student thoroughly for Calculus. Problem-solving and real-life applications of mathematical principles are emphasized.

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Course Overview

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Course Duration: 30 weeks (2 semesters, 15 weeks each)

Cost: $500 for the whole year (register and pay with the links at the bottom of this page)

Prerequisites: Algebra I, Geometry, and Algebra II (or equivalent)

Textbook: Precalculus with Limits (7th Ed.), by Larson and Hostetler

Course Structure:

• Weekly Format: 2–3 hours of video lectures, homework problems, one hour of Q&A.

• Assessments: Weekly homework (50%), Chapter tests and final exams (50%).

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Textbook Sections

• Chapter 1: Functions and Their Graphs (1.1–1.10)

• Chapter 2: Polynomial and Rational Functions (2.1–2.7)

• Chapter 3: Exponential and Logarithmic Functions (3.1–3.5)

• Chapter 4: Trigonometric Functions (4.1–4.8)

• Chapter 5: Analytic Trigonometry (5.1–5.5)

• Chapter 6: Additional Topics in Trigonometry (6.1–6.6, skip 6.5 and 6.6)

• Chapter 7: Systems of Equations and Inequalities (7.1–7.6)

• Chapter 8: Matrices and Determinants (8.1–8.5, skip 8.4 and 8.5)

• Chapter 9: Sequences, Series, and Probability (9.1–9.7)

• Chapter 10: Topics in Analytic Geometry (10.1–10.9, skip 10.5, 10.6, and 10.9)

Semester 1: Weeks 1–15 (Chapters 1,2,3,7,8)​

Focus: Functions, polynomials, exponentials, logarithms, multivariable linear systems, matrices.

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1.1–1.3   Rectangular Coordinates, Graphs, Functions

1.4–1.6   Analyzing Graphs, Transformations, Composite Functions

1.7–1.9   Inverse Functions

1.10        Mathematical Modeling

2.1–2.2   Distance/Midpoint Formulas, Quadratic Functions, Polynomial Functions

2.3–2.5   Dividing Polynomials, Zeros, Rational Functions

2.6–2.7   Nonlinear Inequalities, Polynomial/Rational Inequalities

3.1–3.2   Exponential Functions, Logarithmic Functions

3.3–3.5   Properties of Logarithms, Exponential/Logarithmic Equations, Modeling

7.1–7.2    Linear/Nonlinear Systems, Two-Variable Systems

7.3–7.4   Partial Fractions, Systems of Inequalities

7.5–7.6   Linear Programming, Augmented Matrices

8.1–8.2  Matrix Operations

8.3         Inverse Matrices and Cryptography

Review/Final     Review Ch. 1,2,3,7,8

Semester 2: Weeks 16–30 (Chapters 4,5,6,9,10)

Focus: Trigonometry, sequences, series, probability, and conic sections.

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4.1–4.2    Radian/Degree Measure, Unit Circle

4.3–4.4    Right Triangle Trigonometry, Trig Functions

4.5–4.6    Graphs of Sine/Cosine, Other Trig Graphs

4.7–4.8    Inverse Trig Functions, Applications

5.1–5.3    Trig Identities, Sum/Difference Formulas

5.4–5.5    Multiple-Angle Formulas, Trig Equations

6.1–6.2    Law of Sines, Law of Cosines

6.3–6.4    Vectors

Buffer       This week is for catching up or getting ahead.

9.4–9.5    Binomial Theorem, Counting Principles

9.6–9.7    Probability, Modeling with Sequences

10.1–10.2  Conics: Circles, Parabolas

10.3–10.4  Ellipses, Hyperbolas

10.7–10.8  Polar Coordinates, Polar Graphs

Review/Final     Review Ch. 4,5,6,9,10

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To register, click here.

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