Warwick School District

Course Description

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This rigorous course is designed for students interested in college level mathematics and is intended to develop the background necessary to study Calculus. Topics considered are properties of polynomials, rational, exponential and logarithmic functions; solving polynomial, rational, exponential, and logarithmic equations algebraically and graphically, fields of complex numbers, solving systems of equations algebraically and graphically, matrices and determinants, sequences, series, mathematical induction,vectors, limits and basic rules for differentiation.

Core Curriculum Content Standards

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PA Common Core: Mathematics (2013)

• Algebraic Concepts

• GRADE 8

• Understand the connections between proportional relationships, lines, and linear equations.(2.2.8.B2)

• GRADE High School

• Use the concept and notation of functions to interpret and apply them in terms of their context.(2.2.HS.C1)
• Graph and analyze functions and use their properties to make connections between the different representations.(2.2.HS.C2)
• Write functions or sequences that model relationships between two quantities.(2.2.HS.C3)
• Interpret the effects transformations have on functions and find the inverses of functions.(2.2.HS.C4)
• Construct and compare linear, quadratic and exponential models to solve problems.(2.2.HS.C5)
• Interpret functions in terms of the situation they model.(2.2.HS.C6)
• Apply radian measure of an angle and the unit circle to analyze the trigonometric functions.(2.2.HS.C7)
• Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs.(2.2.HS.C8)
• Prove the Pythagorean identity and use it to calculate trigonometric ratios.(2.2.HS.C9)
• Write expressions in equivalent forms to solve problems.(2.2.HS.D2)
• Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs.(2.2.HS.D4)
• Use polynomial identities to solve problems.(2.2.HS.D5)
• Extend the knowledge of rational functions to rewrite in equivalent forms.(2.2.HS.D6)
• Create and graph equations or inequalities to describe numbers or relationships.(2.2.HS.D7)
• Apply inverse operations to solve equations or formulas for a given variable.(2.2.HS.D8)
• Represent, solve and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.(2.2.HS.D10)

• Measurement, Data and Probability

• GRADE High School

• Apply the rules of probability to compute probabilities of compound events in a uniform probability model.(2.4.HS.B7)

Units

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Unit #1 - Relations, Functions, and Graphs

Unit #2 - More on Functions

Unit #3 - Quadratic Functions and Operations on Functions

Unit #4 - Polynomial and Rational Functions

Unit #5 - Exponential and Logarithmic Functions

Unit #6 - Right Triangle and Unit Circle Trig

Unit #7 - Graphing Trig Functions and Secondary Trig functions

Unit #8 - Trig Equations and Identities

Unit #9 - Sequences and Series

Unit #10 - Introduction to Limits

Course Resources

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Textbook: Precalculus Graphs & Models by John Coburn and JD Herdlick. 1st Edition.