Dept./Grade:  Math/Grades 10-12     Course:  Advanced Algebra               Revision Date:  April, 2008

                                               

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

 

Course Description:  This course is designed to strengthen and extend the study of topics introduced in Algebra I and Algebra II.  The course includes the following topics:  fundamental concepts of algebra, equations and inequalities, functions and graphs, polynomial and rational functions, exponential and logarithmic functions, and systems of equations and inequalities.

 

COURSE OBJECTIVES

CONTENT OUTLINE

Know Fundamental Algebraic Concepts

·          Classify, perform arithmetic operations on, and know properties of real numbers

·          Determine domains

·          Use approximation techniques

·          Use laws and properties of exponents (integer and rational)

·          Add, subtract, multiply, and divide polynomials

·          Factor polynomials

·          Simplify rational expressions

·          Simplify radicals

Solve and Use Equations and Inequalities

·          Solve advanced linear and quadratic equations and inequalities

·          Use linear and quadratic equations and inequalities to solve applied problems

·          Use interval notation

·          Solve polynomial and rational inequalities

·          Solve equations and inequalities involving absolute value

Use and Interpret Graphs

·          Graph equations

·          Find and interpret intercepts

·          Identify and interpret slope

·          Test equations/graphs for symmetry

·          Find equations of parallel and perpendicular lines

·          Graph circles

·          Construct models using direct, indirect, and joint or combined variations

·          Use curve fitting techniques to understand situations

Know Function Basics

·          Distinguish between functions and relations

·          Find values and domains of functions

·          Interpret graphs of functions

·          Determine whether a function is odd or even, increasing or decreasing

·          Graph piecewise-defined functions

·          Graph parent functions for quadratic, cubic, square root, absolute value, and reciprocal functions

·          Perform operations on functions

·          Form composite functions

·          Determine domains and ranges of complex functions

·          Use mathematical models to construct and analyze functions

Explore Polynomial and Rational Functions

·          Identify polynomials and their degree

·          Graph polynomials using transformations

·          Find domains, ranges, and asymptotes of rational functions

·          Analyze graphs of polynomial and rational functions

·          Find zeros (real and complex) of and solve polynomial equations

·          Perform operations on complex numbers

·          Solve quadratic equations with negative discriminants

 

Explore Exponential and Logarithmic Functions

·          Determine whether a function is one-to-one

·          Find an inverse function

·          Find equations of populations

·          Use logistic growth models

·          Use properties of logarithms

·          Solve exponential equations

·          Solve logarithmic equations

Use Systems of Equations and Inequalities

·          Solve systems of linear and nonlinear equations

·          Graph inequalities

·          Solve systems of inequalities

RESOURCE MATERIALS

ASSESSMENT OPTIONS

·          Major Text – College Algebra (Prentice Hall)

·          www.studyisland.com

·          www.prenhall.com/sullivan

 

·          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