Algebra II Syllabus

Angel Website:  http://pcps.myelearning.org/frameIndex.htm
Angela Schmit's Website:  http://manila.esu4.org/angelaschmit/

Algebra II Quizaroo's:  http://www.geocities.com/ojjk/indexaq.html

Course Syllabus

Description of Course

Prerequisites

• Algebra I (one full academic year)

The Objectives of the Course

• Understand and realize the value of the symbolism of algebra language.
• Use the language of algebra as a natural way of expressing mathematical ideas.
• Help students become independent thinking using various learning strategies.
• Learn through "trial and error" and realize that real learning takes place through asking questions, trying guesses, starting down false paths, and trying new methods of approach to algebraic problems.
• Learn problem solving strategies that can help with algebra, as well as other academic courses.
• Appreciate the power of mathematics and see the connections mathematics has with other subject areas, as well as everyday and career applications.
• Improve students' thinking skills, use them more effectively, and acquire additional skills.

Texts

Explanation of Instruction

• Lecture and discussion every day.
• Quizzes every two or three lessons.
• Tests after every unit.
• Spelling/Writing assignments as needed.
• Angel Website--On-Line Learning
  

Visual Aids, Utilized Films, Film Strips, Etc.

• Marker board
• Calculators (Texas Instruments--TI 83, TI 85, and TI 92) provided by the school district
• Computer Software/Technology
• Supplementary Workbooks

Units and Contents

Chapter 1:  Basic Concepts of Algebra

• Real Numbers and Their Graphs
• Simplifying Expressions
• Basic Properties of Real Numbers
• Sums and Differences
• Products
• Quotients
• Solving Equations in One Variable
• Words into Symbols
• Problem Solving with Equations

Chapter 2:  Inequalities and Proof

• Solving Inequalities in One Variable
• Solving Combined Inequalities
• Problem Solving Using Inequalities
• Absolute Value in Open Sentences
• Solving Absolute Value Sentences Graphically
• Theorems and Proof
• Theorems about Order and Absolute Value

Chapter 3:  Linear Equations and Functions

• Open Sentences in Two Variables
• Graphs of Linear Equations in Two Variables
• The Slope of a Line
• Finding an Equation of a Line
• Systems of Linear Equations in Two Variables
  
• Problem Solving:  Using Systems
• Linear Inequalities in Two Variables

Chapter 4:  Products and Factors of Polynomials

• Polynomials
• Using Laws of Exponents
• Multiplying Polynomials
• Using Prime Factorization
• Factoring Polynomials
• Factoring Quadratic Polynomials
• Solving Polynomial Equations
• Problem Solving Using Polynomial Equations
• Solving Polynomial Inequalities

Chapter 5:  Rational Expressions

• Quotients of Monomials
• Zero and Negative Exponents
• Scientific Notation and Significant Digits
• Rational Algebraic Functions
• Products and Quotients of Rational Expressions
• Sums and Differences of Rational Expressions
• Complex Fractions
• Fractional Coefficients
• Fractional Equations

Chapter 6:  Irrational and Complex Numbers

• Roots of Real Numbers
• Properties of Radicals
• Sums of Radicals
• Binomials Containing Radicals
• Equations Containing Radicals
• Rational and Irrational Numbers
• The Imaginary Number i
• The Complex Numbers

Chapter 7:  Quadratic Equations and Functions

• Completing the Square
• The Quadratic Formula
• The Discriminant
• Equations in Quadratic Form
• Graphing y - k = a (x - h)^2
• Quadratic Functions
• Writing Quadratic Equations and Functions

Chapter 8:  Variation and Polynomial Equations

• Direct Variation and Proportion
• Inverse and Joint Variation
• Dividing Polynomials
• Synthetic Division
• The Remainder and Factor Theorems
• Some Useful Theorems
• Finding Rational Roots
• Approximating Irrational Roots
• Linear Interpolation

Chapter 9:  Analytic Geometry

• Distance and Midpoint Formulas
• Circles
• Parabolas
• Ellipses
• Hyperbolas
• More on Central Conics
• The Geometry of Quadratic Systems
• Solving Quadratic Systems
• Systems of Linear Equations in Three Variables

Chapter 10:  Exponential and Logarithmic Functions

• Rational Exponents
• Real Number Exponents
• Composition and Inverses of Functions
• Definition of Logarithms
• Laws of Logarithms
• Applications of Logarithms
• Problem Solving:  Exponential Growth and Decay
• The Natural Logarithmic Function

Chapter 11:  Sequences and Series

• Types of Sequences
• Arithmetic Sequences
• Geometric Sequences
• Series and Sigma Notation
• Sums of Arithmetic and Geometric Series
• Infinite Geometric Series
• Powers of Binomials
• The General Binomial Expansion

Chapter 12:  Triangle Trigonometry

• Angles and Degree Measure
• Trigonometric Functions of Acute Angles
• Trigonometric Functions of General Angles
• Values of Trigonometric Functions
• Solving Right Triangles
• The Law of Cosines
• The Law of Sines
• Solving General Triangles
• Areas of Triangles

Chapter 13:  Trigonometric Graphs; Identities

• Radian Measure
• Circular Functions
• Periodicity and Symmetry
• Graphs of Sine and Cosine
• Graphs of the Other Functions
• The Fundamental Identities
• Trigonometric Addition Formulas
• Double-Angle and Half-Angle Formulas
• Formulas for the Tangent

Chapter 14:  Trigonometric Applications

• Vector Operations
• Vectors in the Plane
• Polar Coordinates
• The Geometry of Complex Numbers
• De Moivre's Theorem
• The Inverse Cosine and Inverse Sine
• Other Inverse Functions
• Trigonometric Equations

Chapter 15:  Statistics and Probability

• Presenting Statistical Data
• Analyzing Statistical Data
• The Normal Distribution
• Correlation
• Fundamental Counting Principles
• Permutations
• Combinations
• Sample Spaces and Events
• Probability
• Mutually Exclusive and Independent Events

Chapter 16:  Matrices and Determinants

• Definition of Terms
• Addition and Scalar Multiplication
• Matrix Multiplication
• Applications of Matrices
• Determinants
• Inverses of Matrices
• Expansion of Determinants by Minors
• Properties of Determinants
• Cramer's Rule

This Page was last update: Friday, November 2, 2007 at 9:34:49 AM
This page was originally posted: 5/31/2006; 5:37:06 PM.
Copyright 2008 Pawnee City Schools

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