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Precalculus
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Description
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 below.
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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.
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Textbook
This course was originally based on Precalculus by Michael Sullivan, ISBN:
0132285940.
As of fall of 2021, the textbook is no longer necessary for this course. All of the course content is found in the
student workbook and the lecture videos. Before 2021, students used the textbook mainly for practice problems.
Practice problems are now included in the student workbook instead.
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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.
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Difficulty Level
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.
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Internet Access
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.
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The Instructor
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 Dunwoody Community Church, a non-denominational church near their home in Norcross, GA.
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Course Outline
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
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Chapter 2: Functions and Their Graphs
Functions; Graphing Techniques; Operations of Functions; Composite Functions; One-to-One Functions; Inverse Functions; Mathematical Models
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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;
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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
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Chapter 5: Trigonometric Functions
Radian and Degree Measure; The Unit Circle; Properties of Trigonometric Functions; Right Triangle Trigonometry; Applications
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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
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Chapter 7: Analytic Trigonometry
Trigonometric Identities; Sum and Difference Formulas; Double-angle and Half-angle Formulas; Product-to-Sum and Sum-to-Product Formulas; Trigonometric Equations
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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 Theorem
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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 Equations
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Chapter 10: Systems of Equations and Inequalities
Solving Systems of Equations by Substitution and Elimination; Matrices; Determinants; Systems of Nonlinear Equations; Systems of Inequalities; Linear Programming
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Chapter 11: Sequences, Induction, Counting, and Probability
Sequences; Arithmetic Sequences; Geometric Sequences and Series; Mathematical Induction; The Binomial Theorem;
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