Algebra II        

Mr. Al Bierschbach

Al.Bierschbach@k12.sd.us

Madison High School

Textbook:              Algebra And Trigonometry:  Structure And Method, Book 2                    Houghton/Mifflin 1990

ISBN# - 0-395-47056-0

Description of Course:  The course begins with a review of mathematical methods covered in algebra and geometry.  Algebraic topics new to students such as complex numbers, synthetic division and sequences will be explored.  A study of conic sections and logarithms will also be part of this course.

SPECIFIED COURSE OBJECTIVES

A.  Basic Concepts of Algebra

                        1. Real Numbers and Their Graphs

                        2.  Simplifying Expressions

                        3.  Basic Properties of Real Numbers

                        4.  Sums and Differences

                        5.  Products and Quotients

                        6.  Equation Solving with One Variable

                        7.  Problem Solving with Equations

            B.  Inequalities

                        1.  Solving Inequalities in One Variable

                        2.  Solving Combined Inequalities

                        3.  Problem Solving Using Inequalities

                        4.  Absolute Value in Open Sentences

            C.  Linear Equations and Functions

                        1.  Open Sentences in Two Variables

                        2.  Graphs of Linear Equations in Two Variables

                        3.  The Slope of a Line

                        4.  Finding the Equation of a Line

                        5.  Systems of Linear Equations in Two Variables

                        6.  Problem Solving using Systems

                        7.  Linear Inequalities in Two Variables

                        8.  Function and Relations

D.  Products and Factors of Polynomials

                        1.  Polynomials

                        2.  Using Laws of Exponents

                        3.  Multiplying Polynomials

                        4.  Using Prime Factorization

                        5.  Factoring Polynomials

                        6.  Solving Polynomial Equations

                        7.  Problem Solving using Polynomial Equations

                        8.  Solving Polynomial Inequalities

            E.  Rational Expressions

                        1.  Quotients of Monomials

                        2.  Zero and Negative Exponents

                        3.  Scientific Notation and Significant Digits

                        4.  Rational Algebraic Expressions

                        5.  Products and Quotients of Rational Expressions

                        6.  Sums and Differences of Rational Expressions

                        7.  Complex Fractions

                        8.  Fractional Coefficients

                        9.  Fractional Equations

            F.  Irrational and Complex Numbers

                        1.  Roots of Real Numbers

                        2.  Properties of Radicals

                        3.  Sums of Radicals

                        4.  Binomials Containing Radicals

                        5.  Equations Containing Radicals

                        6.  Rational and Irrational Numbers

                        7.  The Imaginary Number           

                        8.  The Complex Numbers

            G.  Quadratic Equations and Functions

                        1.  Completing the Square

                        2.  The Quadratic Formula

                        3.  The Discriminant

                        4.  Equations in Quadratic Form

                        5.  Parabolas

                        6.  Quadratic Functions

                        7.  Writing Quadratic Equations and Functions

      H.  Variation and Polynomial Equations

                        1.  Direct Variation and Proportion

                        2. Inverse and Joint Variations

                        3.  Polynomial Long Division

                        4.  Synthetic Division

                        5.  The Remainder and Factor Theorems

                        6.  Conjugate Root Theorem and Descartes Rule of Signs

                        7.  Finding Rational Roots

            I.  Conic Sections

                        1.  Distance and Midpoint Formulas

                        2.  Circles

                        3.  More Parabolas

                        4.  Ellipses

                        5.  Hyperbolas

                        6.  Solving Quadratic Systems

            J.  Exponential and Logarithmic Functions

                        1.  Rational Exponents

                        2.  Real Number Exponents

                        3.  Composition and Inverses of Functions

                        4.  Definition of Logarithms

                        5.  Laws of Logarithms

                        6.  Applications of Logarithms

                        7.  The Natural Logarithm Function

            K.  Sequences and Series

                        1.  Types of Sequences

                        2.  Arithmetic Sequences

                        3.  Geometric Sequences

                        4.  Series and Sigma Notation

                        5.  Sums of Arithmetic and Geometric Series

                        6.  Infinite Geometric Series

Grading of Course

35% - Quiz Grade – Quizzes will be taken after every two to four topics (sections) in each chapter.

65% - Test Grade – A chapter test will be taken at the end of each chapter.

Rules/Guidelines of the class:

Students will have respect for the classroom, its property, their fellow students and the teacher.  Pop or food is not allowed in the classroom.