Teacher: Derek Owens
Date/Time: Thursday - 10:45 AM to 12:15 PM
Rooms: FH2, FH3
Grade Level: High School (9th-12th)
This course will cover the topics normally covered in a high
school pre-calculus course. This course is normally taken by students
in grade eleven or twelve. Students should have completed Algebra 2
before enrolling in Pre-Calculus. A detailed course outline is shown
Lecture Notes and Class Time
Class time will primarily be spent on instruction. Students should
bring their Student Workbook to each class, or a printout of the pages
for that week. The pages of the workbook are identical to the
instructor's lecture notes, except the student version has the solutions
and answers deleted. During the lecture the students take notes and
solve the example problems in the workbook.
Videos of the lectures are also available online, and
these videos go through the same lecture notes, point by point. Students
use the videos to cover any material that time constraints did not
permit us to cover in our weekly class. Or, if a student misses a class
or needs to review the material, all of the course content is available
online. It is possible to take the entire course online via distance
learning, and many students have done so.
Precalculus by Michael Sullivan, 4th edition, published by Prentice Hall, 1996, ISBN:
This is an excellent text, known for its clarity. It has received
many excellent reviews. The topics covered in this course will
correspond closely to the topics covered in this book. Students will be
assigned reading and practice problems from the textbook.
Homework, Tests and Grades
Students will be given specific assignments to complete each week.
Assignments will consist of Practice Problems from the workbook and
textbook, instructional videos online, and written assignments.
In this class there is a distinction between Practice Problems and
Homework Problems. Practice Problems are found in the workbook and
textbook, and students check their answers with the solutions provided.
Homework assignments and tests are printed from the website, completed,
and turned in for a grade.
To maximize instructional time in class, tests will be given at
home. One final exam for each semester will be taken in class at the end
of each semester. Students will receive a numerical grade for each
semester and for the year. The grade is calculated based on tests,
graded homework and the final exams.
Not all students require the same pace and difficulty level. Some
may need or prefer a class that is more challenging and at a faster
pace, while some may desire a class that is not accelerated. This class
is offered simultaneously on two difficulty levels, regular and honors.
The lectures are the same for both. The honors students will have
additional homework problems that are more difficult, and on each test
will have an extra page with more challenging questions. Note that the
honors class is not an AP class. It is simply a more challenging version
of the same course. The goal is for the classes to closely correspond
to “Regular Precalculus" and “Honors Precalculus" classes at a good
private school. Students may decide whether they will take the standard
or honors version of the course after completing one or two chapters.
Access to a computer with a high speed internet connection is
strongly recommended. Instructional materials such as lecture videos,
lecture notes, homework assignments and tests will be available over the
internet. Graded assignments and tests may also be returned via email
in order to provide more timely feedback. Progress reports will be put
on the website and updated regularly.
Derek Owens graduated from Duke University in 1988 with a degree in mechanical engineering and
physics. He taught physics, honors physics, AP Physics, and AP computer science at The Westminster Schools
in Atlanta, GA from 1988-2000. He worked at the TIP program at Duke for two years, teaching physics and
heading the Satellite Science Program. He received a National Science Foundation scholarship and
studied history and philosophy of science at L’Abri Fellowship in England. He worked as a software
developer for six years before returning to teaching. Since 2006, he has been a full time teacher for
homeschoolers in the Atlanta area. He and his wife Amor and their two children Claire and David
attend Twelve Stone Church, a non-denominational church near their home in Norcross, GA.
These topics comprise the material normally taught in a high school precalculus course.
- Chapter 1: Preliminaries
Review of topics from Algebra and Geometry; Equations; Setting Up
Equations; Inequalities; Complex Numbers; Rectangular Coordinates and
Graphs; Straight Lines
Chapter 2: Functions and Their Graphs
Functions; Graphing Techniques; Operations of Functions; Composite
Functions; One-to-One Functions; Inverse Functions; Mathematical Models
Chapter 3: Polynomial and Rational Functions
Quadratic Functions; Polynomial Functions; Rational Functions;
Synthetic Division; Zeros of Polynomial Functions; Approximating Real
Zeros; Complex Polynomials; The Fundamental Theorem of Algebra;
Chapter 4: Exponential and Logarithmic Functions
Exponential Functions and Graphs; Logarithmic Functions and Graphs;
Properties of Logarithms; Exponential and Logarithmic Equations;
Compound Interest; Growth and Decay; Logarithmic Scales
Chapter 5: Trigonometric Functions
Radian and Degree Measure; The Unit Circle; Properties of Trigonometric Functions; Right Triangle Trigonometry; Applications
Chapter 6: Graphs of Trigonometric Functions
Graphs of the Sine and Cosine Functions; Sinusoidal Graphs;
Applications; Graphs of Tangent, Cosecant, Secant, and Cotangent
Functions; Inverse Trigonometric Functions
Chapter 7: Analytic Trigonometry
Trigonometric Identities; Sum and Difference Formulas; Double-angle and
Half-angle Formulas; Product-to-Sum and Sum-to-Product Formulas;
Chapter 8: Additional Applications of Trigonometry
The Law of Sines; The Law of Cosines; The Area of a Triangle; Polar
Coordinates; Polar Equations and Graphs; The Complex Plane: DeMoivre’s
Chapter 9: Analytic Geometry
The Parabola; The Ellipse; The Hyperbola; Rotation of Axes: General
Form of a Conic; Polar Equations of Conics; Plane Curves and Parametric
Chapter 10: Systems of Equations and Inequalities
Solving Systems of Equations by Substitution and Elimination; Matrices;
Determinants; Systems of Nonlinear Equations; Systems of Inequalities;
Chapter 11: Sequences, Induction, Counting, and Probability
Sequences; Arithmetic Sequences; Geometric Sequences and Series; Mathematical Induction; The Binomial Theorem;