Kendall Park Learning Center
Course Title: Honors Precalculus & Trigonometry – Advanced Credit/Enrichment
Course Length: Six Weeks (120 Hours)
This course is designed to prepare students for Advanced Placement Calculus or the first
two semesters of college calculus. The principle objectives are to provide students with
a thorough understanding of advanced algebra and trigonometry and to show how this
area of mathematics can be used to model problems in the real world. An integrated
approach that uses algebraic, numerical, graphical and verbal methods for analyzing and
solving problems will be used. Graphing calculators will be used extensively; a TI-83+ or
TI-84+ is preferred.
Prerequisites:
Honors Precalculus -Advanced Credit is a course offered to students who have
successfully completed a high school course in Honors Algebra II with grade B+ or
higher.
Requirements:
Students must complete the 120 hours and finish the course with an A- average to
receive full credit.
Topics Covered:
1. Review of Fundamentals and Introduction to the Graphing Calculator
a. Review of Fundamentals
The emphasis will be on the topics most important for success in Pre-calculus:
Real numbers, simplifying algebraic and rational expressions, factoring, solving
equations and inequalities, coordinate geometry, lines, and variation.
b. Introduction to the Graphing Calculator
A brief introduction to the use of the graphing calculator. Additional specific uses of
the calculator will be integrated with the rest of the course.
2. Functions
Definition of a function
Graphs of functions and their properties
Increasing and decreasing functions and average rate of change
Transformations of functions
Quadratic functions; maxima and minima
Modeling with functions (applied problems)
Combining functions
One-to-One functions and their inverses
Data Modeling: Fitting Lines to Data
3.
Polynomial and Rational Functions
Polynomial Functions and Their Graphs
Dividing Polynomials
Real Zeros of Polynomials
Complex Numbers
Complex Zeros and the Fundamental Theorem of Algebra
Rational Functions
Data Modeling: Fitting Polynomial Curves to Data
4.
Exponential and Logarithmic Functions
Exponential and Logistic Functions
Logarithmic Functions
Laws of Logarithms
Exponential and Logarithmic Equations
Modeling with Exponential, Logarithmic, and Logistic Functions
Mathematics of Finance
Data Modeling: Fitting Exponential and Power Curves to Data
5.
Trigonometric Functions of Real Numbers
The Unit Circle
Trigonometric Functions of Real Numbers
Trigonometric Graphs
More Trigonometric Graphs
Modeling Harmonic Motion
6.
Trigonometric Functions of Angles
Angle Measure
Trigonometry of Right Triangles
Trigonometric Functions of Angles
The Law of Sines
The Law of Cosines
7. Analytic Trigonometry
Trigonometric Identities
Addition and Subtraction Formulas
Double-Angle, Half-Angle, and Sum-Product Formulas
Inverse Trigonometric Functions
Trigonometric Equations
8. Polar Coordinates and Vectors
Polar Coordinates
Graphs of Polar Equations
Polar Form of Complex Numbers; DeMoivre’s Theorem
Vectors
The Dot Product
9. Systems of Equations and Inequalities
Systems of Equations
Systems of Linear Equations in Two Variables
Systems of Linear Equations in Several Variables
Systems of Linear Equations: Matrices
The Algebra of Matrices
Inverses of Matrices and Matrix Equations
Determinants and Cramers’s Rule
Partial Fractions
Systems of Inequalities
Linear Programming
10. Analytic Geometry
Parabolas
Ellipses
Hyperbolas
Shifted Conics
Plane Curves and Parametric Equations (including path of a projectile)
11. Sequences and Series
Basic Combinatorics
Probability
Sequences and Summation Notation
Arithmetic Sequences
Geometric Sequences
Mathematical Induction
The Binomial Theorem
Modeling with Recursive Sequences
12.
Limits: A Preview of Calculus
Finding Limits Numerically and Graphically
Finding Limits Algebraically
Tangent Lines and Derivatives
Limits at Infinity: Limits of Sequences
Areas
Textbook: Precalculus - Mathematics for Calculus – Stewart, Redlin and Watson (5th Ed.)
New Jersey Department of Education Core Curriculum Standards for Mathematics.
www.state.nj.us/njded/cccs