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Precalculus
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Currently enrolled students login here
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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 syllabus is shown below.
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Fees
The cost of the course is $78 per month for nine months for students attending the class, $58 per month for distance learners. Registration fees for homeschool classes at various locations (LAC, SNA, Dunwoody, etc) will also apply. Students will need to purchase a copy of the “Student Notes and Workbook”, which should be less than $20. Students may borrow a copy of the textbook from the teacher at no charge, and videos of the class lectures will be provided on computer disc or via the internet at no additional cost.
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Lecture Notes and Class Time
Class time will primarily be spent on instruction. The lecture notes are a key part of the class. These notes are prepared in advance and given to the students, but with much of the material deleted and replaced by blank space on the page. During the lecture, the students fill in the blank areas, solve the example problems, and add any notes they need to. By the end of the year, the students will have what amounts to their own complete text made from the lectures delivered and the problems worked in class. A sample of these lecture notes is available on the website.
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Textbook
Precalculus by Michael Sullivan, 4th edition, published by Prentice Hall, 1996. 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.
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Homework, Tests and Grades
Students will be given specific assignments to do on their own each week. Assignments will consist of additional lectures delivered on the computer, problems to practice, and homework assignments that will be collected and graded. To allow for the maximum amount of 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 the 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 that is more difficult, and will have more challenging tests. 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 “Standard Precalculus" and “Honors Pre-Calculus" classes at a good private school. Students will decide whether they would prefer the standard or honors version of the course about a month into the course, after having had a chance to look at some tests and assignments.
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Computer Access
Access to a computer (Windows, Mac, or Linux) with either a CD drive or a high speed internet connection is strongly recommended for this course. Videos of the lectures will be available to the students over the web or on CD. These lectures contain both audio and video and cover the same material covered in class. The videos allow students to review the material, to hear the explanations again if needed, and to see example problems being worked out with detailed explanations. They also insure that the students receive all of the instruction, even if they miss a class or if all of the material is not covered given the limited class time.
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The Instructor
Derek Owens taught physics, honors physics, AP Physics, and AP computer science at The Westminster Schools in Atlanta, GA from 1988-2000. He currently teaches Physics in the summer school program at Westminster as well as AP Calculus at Providence Christian Academy. He graduated from Duke University in 1988 with a degree in mechanical engineering and physics, and 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 five years before returning to teaching. This will be his sixth school year teaching homeschoolers in the Atlanta area. He and his wife Amor and their two children Claire and David attend Grace Fellowship Church, a non-denominational church near their home in Lawrenceville.
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Course Syllabus
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; Counting Principles; Permutations and Combinations; Probability
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Chapter 12: Miscellaneous Topics
Matrix Algebra; Partial Fraction Decomposition; Vectors; The Dot Product
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