Rhea County High School

Semester Syllabus

Math #003126 Pre-Calculus

Mr. Zac Brown

Course Description:

This course is an elective course.  It includes college preparatory material such as equations and inequalities, functions and graphs, linear and quadratic functions, polynomial and rational functions, exponential and logarithmic functions, system of equations, trigonometric functions, applications of trigonometry, sequences and series and conic sections.

Prerequisites: 

Algebra I, Algebra II, and Geometry

Textbook and other reference materials:

Larson, Roland E., and Robert P. Hostetler.  Precalculus, 6^th edition. Houghton Mifflin Company, 2004.

A graphing calculator is available for class use, but having your own is recommended.  Instructor will use a Texas Instrument TI-84 plus graphing calculator.  A calculator with a computer algebra system, such as the TI-89 and TI-92, is not allowed.  

Instructional Objectives:

The student will be able to:

Prerequisite (only if necessary)

• Real Numbers and Properties
• Exponents and Radicals
• Polynomials and Factoring
• Rational Expressions
• Solving Equations
• Solving Inequalities
• Errors and the Algebra Calculus
• Graphical Representation of Data

1.1     Graphs of Equations

• The graph of an equation
• Intercepts of a graph
• Symmetry
• Circles
• Application

1.2     Linear equations in Two Variables

• Using slope
• Finding the Slope of a Line
• Writing Linear Equations
• Parallel and Perpendicular Lines
• Applications

1.3     Functions

• Introductions to Functions
• Function Notation
• The Domain of a Function
• Applications

1.4     Analyzing Graphs of Functions

• The graph of a function
• Increasing and decreasing functions
• Step functions
• Even and odd functions
• Summary of graphs of common functions

1.5     A Library of Functions

• Linear and Squaring Functions
• Identify cubic, square root and reciprocal functions
• Piecewise Functions

1.6     Shifting, Reflecting, and Stretching graphs

• Vertical and Horizontal shifts
• Reflections
• Non rigid transformations

1.7     Combinations of Functions

• Add, subtract functions
• Composition
• Real life problems

1.8     Inverse Functions

• The inverse of a function
• Finding the inverse of a function
• The graph of the inverse of a function

1.9     Mathematical Modeling

• Direct, inverse, and joint variations

2.1 Quadratic Functions

• The graph of a quadratic function
• The standard form of a quadratic function

2.2 Polynomial Functions of Higher degree

• Graphs of polynomial functions
• The leading coefficient test
• Zeros of polynomial functions
• The Intermediate Value theorem

2.3 Polynomial and Synthetic Division

• Long division of polynomials
• Synthetic division
• The Remainder and Factor Theorems

2.4 Complex Numbers

• The imaginary unit I
• Operations with complex numbers
• Complex conjugates and division
• Complex solutions of quadratic equations

2.5 Real Zeros of Polynomials Functions

• Descartes’ Rules of Signs
• The Rational Zero Test
• Bounds for real zeros of polynomial functions

• The fundamental theorem of algebra
• Conjugate pairs
• Factoring a polynomial

2.6 Rational Functions

• Horizontal and Vertical asymptotes
• Sketching the graph of a rational function
• Slant asymptotes

3.1 Exponential Functions and Their Graphs

• Exponential functions
• Graphs of exponential functions
• The natural base e
• Applications

3.2 Logarithmic Functions and Their Graphs

• Logarithmic functions
• Graphs of logarithmic functions
• The natural logarithmic function
• Applications

3.3 Properties of Logarithms

• Change of base
• Properties of Logarithms
• Rewriting logarithmic expressions
• Application

3.4 Exponential and Logarithmic Equations

• Solving exponential equations
• Solving logarithmic equations
• Application

3.5 Exponential and Logarithmic Models

• Exponential growth and decay
• Logistics growth models
• Logarithmic models

4.1 Radian and Degree Measure

• Describe angles
• Radian Measure
• Degree Measure
• Real life application

4.2 Trigonometric Functions: The Unit Circle

• Identify a Unit Cicle
• Evaluate Trig Functions
• Domain and Period
• Use the calculator to evaluate trig functions

4.3 Right Triangle Trigonometry

• Trig Functions of acute angles
• Fundamental Trig Identities
• Use a Calculator

4.4 Trigonometric Functions of Any angle

• Evaluate Trig functions of any angle
• Reference angles

4.5 Graphs of Sine and Cosine Functions

• Sketch Graphs
• Amplitude and Period
• Sketch translations

4.6 Graphs of Other Trigonometric Functions

• Sketch Graphs

4.7 Inverse Trigonometric Functions

• Evaluate Inverse functions
• Evaluate Composition functions

4.8 Applications and Models

• Real life problems with right triangles
• Directional Bearing