Honors Pre-Calculus Course Syllabus

Course Name: Honors Pre-Calculus

I Course Information
Course Number: 3331
Level: Honors
Department: Mathematics

II Course Description
Prerequisite: Two Semesters of Honors Algebra Two/Trigonometry
Open to: Freshman, Sophomore, Junior, Senior
Length: Year
Credit: 1
Summary: This course is extremely rigorous and fast-paced.  Students should have a very strong algebra and trigonometry background.  Also, students should be highly motivated and be able to work independently.  This course prepares students to take calculus.

III Course Goals

1. Students will study vectors.

2. Students will expand their knowledge of graphs, inequalities, and functions.

3. Students will apply iteration and optimization.

4. Students will increase their understanding of exponential and logarithmic functions.

5. Students will study analytical trigonometry.

6. Students will expand their knowledge of analytical geometry.

7. Students will study the polar coordinate system.

8. Students will increase their understanding of systems of equations.

9. Students will write mathematical induction.

10. Students will study sequences and series.

11. Students will learn about parametric equations.

12. Students will study probability, permutations, and combinations.

13. Students will evaluate limits.

14. Students will study derivatives.

IV Textbooks and Materials        
Textbook: David Cohen, Pre-Calculus
Material: Paper, Pencils, Notebook/Binder, Graphing Calculator (TI – 83, TI – 84, TI – 83 Plus or TI – 84 Plus)

V  Course Outline

First Semester – Units of Instruction and Assessments

Unit One - Vectors

Vectors in the Plane, A Geometric Approach

Vectors in the Plane, An Algebraic Approach

Airplane Problems

3-D Geometry & Vectors

Norms, Cross Product – Equation of Lines

Equations of Planes

 

Unit Two - Coordinates, Graphs, Inequalities, and Functions

Rectangular Coordinates

Graphs and Equations, A Second Look

Equations of Lines

Symmetry and Graphs

The Definition of Function

The Graph of a Function

Techniques in Graphing

Methods of Combing Functions Iteration

Inverse Functions

 

Unit Three - Polynomial and Rational Functions, Applications to Iteration and Optimization

Quadratic Functions

Applied Functions: Setting up Equations

Maximum and Minimum Problems

 

Unit Four - Exponential and Logarithmic Functions

Exponential Functions

The Exponential Function y=e^x

Logarithmic Functions

Properties of Logarithms

Equations with Logs and Exponents

Compound Interest

Exponential Growth and Decay

 

Unit Five - Trigonometric Functions of Real Numbers and Analytical Trigonometry

Radian Measure

Radian Measure and Geometry

Trigonometric Functions of Real Number

Sum and Difference Formulas

The Double-Angle Formulas

The Product-to-Sum and Sum-to-Product Formulas

 

Unit Six - More on Trigonometric Functions of Real Numbers and Analytical Trigonometry

Graphs of the Sine and Cosine Functions

Graphs of y=Asin(Bx – C) and y = A cos(Bx – C)

Sinusoid Word Problems

Graphs of the Tangent and the Reciprocal Functions

Trigonometric Equations

The Inverse Trigonometric Functions

 

Unit Seven - Analytic Geometry

The Basic Equations

The Parabola

Tangents to Parabolas

The Ellipse

The Hyperbola

The Focus-Directrix Property of Conics

 

Unit Eight - Topics in Trigonometry, Analytic Geometry, and DeMoivre’s Theorem

Introduction to Polar Coordinates

Curves in Polar Coordinates

The Conics in Polar Coordinates

DeMoivre’s Theorem

 

Major Assessments:
Quizzes: TBA
Tests: Unit 1, Unit 2, Unit 3, Unit 4, Unit 5, Unit 6, Unit 7, Unit 8
Semester One Exam
Misc: Homework, Binder/Notebook, Bellwork

 

Second Semester Units of Instruction and Assessments:

Unit Nine - Systems of Equations

Gaussian Elimination

Matrices

The Inverse of a Square Matrix

Determinants and Cramer’s Rule

 

Unit Ten - Mathematical Induction

Mathematical Induction

 

Unit Eleven - Sequences and Series

The Binomial Theorem

Introduction to Sequences and Series

Arithmetic Sequences and Series

Geometric Sequences and Series

 

Unit Twelve - Parametric Equations

Parametric Equations

Packets

Parameters Equations and Graphs

Motion Problems and Parametric Equations

 

Unit Thirteen - Probability, Permutations, and Combinations

Probability, Permutations, and Combinations (Packet)

 

Unit Fourteen - Limits

Limits (Packet)

Limits

Continuous Functions

Sandwich Theorem

Limits Involving Infinity

Controlling Outputs

 

Unit Fifteen - Derivatives

Derivatives (Packet)

Slope, Tangent, Derivatives

Differentiation Rules

Derivatives of Trigonometric Functions

Chin Rule

 

Major Assessments:
Quizzes: TBA
Tests: Unit 9, Unit 10, Unit 11, Unit 12, Unit 13, Unit 14, Unit 15
Semester Two Exam
Misc: Homework, Binder/Notebook, Bellwork

  

(Parents and students: please consult individual teachers for grading policies, extra credit info, class procedures, etc.)