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