Department/Grade:  Math/11-12                        Course:  Precalculus                 Revision Date:  January, 2008

                                               

Required/Elective:  Elective                              Course Length:  1 year             Prerequisite:  Algebra II

 

Course Description:  This course is an integrated sequence of advanced topics in algebra and trigonometry.  Students will further develop equation-solving and graphing skills. It is designed for those students with above average mathematical ability and who wish to take calculus in high school or intend to pursue a career in a mathematics or science related major in college.

 

COURSE OBJECTIVES

CONTENT OUTLINE

Sketch and analyze graphs

·          Identify parent graphs and their transformations (multiple)

·          Sketch step functions and other piecewise-defined functions

·          Identify odd and even functions graphically

·          Use zeros of a function as a sketching aid

·          Sketch inverse functions

·          Use the Leading Coefficient Test to determine end behaviors

·          Use the Intermediate Value Theorem to help locate zeros of polynomial functions

·          Identify domains and ranges of functions

·          Find horizontal, vertical, and slant asymptotes

·          Sketch six  trigonometric parent graphs

·          Sketch transformations of sine and cosine graphs

Manipulate and analyze algebraic representations

·          Find and interpret zeros algebraically

·          Find compositions of functions

·          Find inverse functions algebraically

·          Use polynomial division

·          Work with complex numbers

·          Use the Fundamental Theorem of Algebra to determine the numbers of zeros of polynomial functions

·          Use Descartes’ Rule of Signs and the Upper and Lower Bound Rules to find zeros of polynomials

Use Mathematical Modeling

·          Use combinations of functions to model and solve real-life problems

·          Use mathematical models to approximate sets of data points

·          Write mathematical models for direct variation, direction variation as an nth power, inverse variation, and joint variation

·          Use regression analysis to find mathematical models

·          Use rational functions to model and solve real-life problems

·          Model cyclic situations using trigonometric equations

Use trigonometry

·          Convert between radians and degrees

·          Use the unit circle to find trigonometric functions of special angles

·          Evaluate trigonometric functions of any angle

·          Use the fundamental trigonometric identities

·          Evaluate the inverse trigonometric functions

·          Evaluate the compositions of trigonometric functions and inverse trigonometric functions

·          Use fundamental trigonometric identities to evaluate trigonometric functions and simplify trigonometric expressions

·          Verify trigonometric identities

·          Solve trigonometric equations

Explore sequences, series, and probability

·          Use sequence, factorial, and summation notation to write the terms and sum of a sequence

·          Recognize, write, and manipulate arithmetic sequences and geometric sequences

·          Solve counting problems using the Fundamental Counting Principle, permutations, and combinations

Preview calculus topics

·          Algebraically calculate derivatives

·          Explore and evaluate difference quotients

·          Identify composite functions

·          Find maximums and minimums of functions

Use graphing technologies

·          Work with functions (linear and nonlinear, continuous and discontinuous) on a graphing calculator

·          Create simple programs on the graphing calculator

·          Use the graphing calculator to find roots and intersections of functions

·          Use an online grapher to further enhance understanding of functions and their relationships (one example can be found at http://www.shodor.org/interactivate/activities/DataFlyer/

RESOURCE MATERIALS

ASSESSMENT OPTIONS

·          Major Text – Precalculus  (Houghton Mifflin)

·          TI-83+ Graphing Calculators

·          Online graphers

·          Unit Tests

·          Cumulative Tests

·          Midterm Exam

·          Final Exam

·          Standardized Tests

·          Open-Ended Assessments

·          Quizzes

·          Projects

·          Math Journal

·          Oral Presentations

·          Observation

·          Evaluate written work

·          Performance assessments

·          Tests, quizzes

·          Problem solving journal/activity

·          Evaluate oral response

·          Anecdotal records

·          Performance tasks