Precalculus – Homeschool

Course Description

The Cool Math Guy Precalculus Course (formerly Chalk Dust) is a comprehensive, college-preparatory program that combines the full scope of College Algebra and Trigonometry, along with additional advanced topics. It is ideal for students preparing for Calculus or for college-level placement exams.

Key features of this course include:

  • A complete and integrated curriculum covering algebraic functions, trigonometry, vectors, conic sections, logarithms, and more

  • Extensive use of graphing calculator techniques throughout the course

  • A strong academic foundation that prepares students for success in Calculus and beyond

Note: Because Precalculus includes all topics from both College Algebra and Trigonometry, it is not necessary to take those courses separately. However, Cool Math Guy does offer both as stand-alone courses, and some homeschool families prefer to complete them individually at a slower pace. If you are considering that option, feel free to contact Cool Math Guy for guidance.


How the Course Works

  1. The student begins by watching a video lesson, then starts the corresponding textbook assignment the same day, working until their scheduled math time ends.

  2. The next day, the student continues the assignment until it is completed or time runs out. A third day may be needed—and that’s okay.

  3. On the following day, the student moves on to the next section.

  4. After completing several sections—or at the end of a chapter—the student takes a practice test and checks their answers using the provided key. Parents may assist in this process.

  5. Once ready, the student takes the chapter test under parent supervision. Test keys include point values for grading. If there are any grading questions, contact Cool Math Guy—we’re happy to help.


When Help Is Needed

If students or parents encounter difficulties, support is available through multiple methods:

  1. Re-watch the video lesson.
  2. Review similar examples in the textbook.
  3. Consult the solutions manual for step-by-step guidance.
  4. Submit a question through the Cool Math Guy website. Replies typically arrive within 24 hours.

Sample Videos from this Course

Section 2.2 Polynomial Functions of Higher Degree
Section 3.4 Solving Exponential and Logarithmic Equations
Section 6.3 Vectors in the Plane
Section 9.2 Ellipses

Table of Contents

  • 1.1  Lines in the Plane
  • 1.2  Functions
  • 1.3  Graphs of Functions
  • 1.4  Shifting, Reflecting, and Stretching Graphs
  • 1.5  Combinations of Functions
  • 1.6  Inverse Functions
  • 1.7  Linear Models and Scatter Plots
  • 2.1  Quadratic Functions
  • 2.2  Polynomial Functions of Higher Degree
  • 2.3  Real Zeros of Polynomial Functions
  • 2.4  Complex Numbers
  • 2.5  The Fundamental Theorem of Algebra
  • 2.6  Rational Functions and Asymptotes
  • 2.7  Graphs of Rational Functions
  • 2.8  Quadratic Models
  • 3.1  Exponential Functions and Their Graphs
  • 3.2  Logarithmic Functions and Their Graphs
  • 3.3  Properties of Logarithms
  • 3.4  Solving Exponential and Logarithmic Equations
  • 3.5  Exponential and Logarithmic Models
  • 3.6  Nonlinear Models
  • 4.1  Radian and Degree Measure
  • 4.2  Trigonometric Functions: The Unit Circle
  • 4.3  Right Triangle Trigonometry
  • 4.4  Trigonometric Functions of Any Angle
  • 4.5  Graphs of Sine and Cosine Functions
  • 4.6  Graphs of Other Trigonometric Functions
  • 4.7  Inverse Trigonometric Functions
  • 4.8  Applications and Models
  • 5.1  Using Fundamental Identities
  • 5.2  Verifying Trigonometric Identities
  • 5.3  Solving Trigonometric Equations
  • 5.4  Sum and Difference Formulas
  • 5.5  Multiple-Angle and Product-to-Sum Formulas
  • 6.1  Law of Sines
  • 6.2  Law of Cosines
  • 6.3  Vectors in the Plane
  • 6.4  Vectors and Dot Products
  • 6.5  Trigonometric Form of a Complex Number
  • 7.1  Solving Systems of Equations
  • 7.2  Systems of Linear Equations in Two Variables
  • 7.3  Multivariable Linear Systems
  • 7.4  Matrices and Systems of Equations
  • 7.5  Operations with Matrices
  • 7.6  The Inverse of a Square Matrix
  • 7.7  The Determinant of a Square Matrix
  • 7.8  Applications of Matrices and Determinants
  • 8.1  Sequences and Series
  • 8.2  Arithmetic Sequences and Partial Sums
  • 8.3  Geometric Sequences and Series
  • 8.4  Mathematical Induction
  • 8.5  The Binomial Theorem
  • 8.6  Counting Principles
  • 8.7  Probability
  • 9.1  Circles and Parabolas
  • 9.2  Ellipses
  • 9.3  Hyperbolas
  • 9.4  Rotation and Systems of Quadratic Equations
  • 9.5  Parametric Equations
  • 9.6  Polar Coordinates
  • 9.7  Graphs of Polar Equations
  • 9.8  Polar Equations of Conics
  • 10.1  The Three-Dimensional Coordinate System
  • 10.2  Vectors in Space
  • 10.3  The Cross Product of Two Vectors
  • 10.4  Lines and Planes in Space
  • 11.1  Introduction to Limits
  • 11.2  Techniques for Evaluating Limits
  • 11.3  The Tangent Line Problem
  • 11.4  Limits at Infinity and Limits of Sequences
  • 11.5  The Area Problem

Supporting Parents

We understand that questions can come up, especially in the beginning. Personal support is available via text, email, or phone. We’re here to help both parents and students every step of the way.


Course Materials

Textbook Recommendations

Below are the recommended textbook and companion solutions guide for this course. The textbook includes answers to selected problems, while the solutions manual provides detailed, step-by-step explanations—which are especially helpful at this level.

Precalculus: Functions and Graphs, A Graphing Approach, 5th Edition by Larson

Note: This is a very robust Precalculus program. Some sections—and the final chapter—are intentionally omitted, as they are typically reviewed in the first days of a Calculus 1 course. Assignment lists will reflect these omissions.

Even with some content skipped, the course may take up to 10 months to complete. That’s normal—most schools don’t finish every section in a single year. If time becomes tight, you may safely omit additional sections without compromising the integrity of the course.

Also: We suggest completing Section 4.3 before Section 4.2 for improved learning flow.

 

Practice Tests, Tests, and Answer Keys

All assignments and testing materials are available to subscribers through a password-protected link.


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