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		Algebra is generous; she often gives more than is asked of her. - D'Alembert

Algebra

Algebra is the matematics of generalized arithmetical operations in which symbols represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set. Classical algebra uses equation solving to find the unknown number. Abstract algebra, or modern algebra, is the study of groups, rings, and fields.

Assignments for 2008/09

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Class Notes

As time permits, class notes will be made available in PDF format. Be advised that these notes are not representative of all the material covered in class and are not a substitue for attending class. (In other words, do not expect them to make up for missed classes!)

Section 1 - Connections to Algebra

1.1 Variables of Algebra
1.2 Exponents and Powers
1.3 Order of Operations
1.4 Equalities and Inequalities
1.5 A Problem Solving Plan Using Models
1.6 Tables and Graphs (see book, page 40)
1.7 An Introduction to Functions
 

Section 2 - Properties of Real Numbers

2.1 The Real Number Line
2.2 Addition of Real Numbers
2.3 Subtraction of Real Numbers
2.4 Adding and Subtracting Matrices
2.5 Multiplication of Real Numbers
2.6 The Distributive Property
2.7 Division of Real Numbers
2.8 Probability and Odds
 

Section 3 - Solving Linear Equations

3.1 Solving Equations Using Addition and Subtraction
3.2 Solving Equations and Using Multiplication and Division (same as 3.1)
3.3 Solving Multi-Step Equations
3.4 Solving Equations with Variables on Both Sides
3.5 Linear Equations and Problem Solving
3.6 Solving Decimal Equations
3.7 Formulas and Functions
3.8 Rates, Ratios, and Percents
 

Section 4 - Graphing Linear Equations and Functions

4.1 Coordinates and Scatter Plots
4.2 Graphing Linear Equations
4.3 Quick Graphs Using Intercepts
4.4 The Slope of a Line
4.5 Direct Variation
4.6 Quick Graphs Using Slope-Intercept Form
4.7 Solving Linear Equations Using Graphs
4.8 Functions and Relations
 

Section 5 - Writing Linear Equations

5.1 Writing Linear Equations in Slope-Intercept Form
5.2 Writing Linear Equations Given the Slope and a Point
5.3 Writing Linear Equations Given Two Points
5.4 Fitting a Line to Data
5.5 Point-Slope Form of a Linear Equation
5.6 The Standard Form of a Linear Equation
5.7 Predicting with Linear Models
 

Section 6 - Solving and Graphing Linear Inequities

6.1 Solving One-Step Linear Inequalities
6.2 Solving Multi-Step Linear Inequalities
6.3 Solving Compound Interest
6.4 Solving Absolute-Value Equations and Inequalities
6.5 Graphing Linear Inequalities in Two Variables
6.6 Stem-and-Leaf Plots and Mean, Median, and Mode
6.7 Box-and-Whisker Plots
 

Section 7 - Systems of Linear Equations and Inequalities

7.1 Solving Linear Systems by Graphing
7.2 Solving Linear Systems by Substitution
7.3 Solving Linear Systems by Linear Combinations
7.4 Applications of Linear Systems
7.5 Special Types of Linear Systems
7.6 Solving Systems of Linear Inequalities
 

Section 8 - Exponents and Exponential Functions

8.1 Multiplication Properties of Exponents
8.2 Zero and Negative Exponents
8.3 Division Properties of Exponents
8.4 Scientific Notation
8.5 Exponential Growth Functions
8.6 Exponential Decay Functions
 

Section 9 - Quadratic Equations and Functions

9.1 Solving Quadratic Equations by Finding Square Roots
9.2 Simplifying Radicals
9.3 Graphing Quadratic Functions
9.4 Solving Quadratic Equations by Graphing
9.5 Solving Quadratic Equations by the Quadratic Formula
9.6 Applications of the Discriminant
9.7 Graphing Quadratic Inequalities
9.8 Comparing Linear, Exponential, and Quadratic Models
 

Section 10 - Polynomials and Factoring

10.1 Adding and Subtracting Polynomials
10.2 Multiplying Polynomials
10.3 Special Products of Polynomials
10.4 Solving Polynomial Equations in Factored Form
10.5 Factoring x² + bx + c
10.6 Factoring ax² + bx + c
10.7 Factoring Special Products
10.8 Factoring Using the Distributive Property
 

Section 11 - Rational Equations and Functions

11.1 Ratio and Proportion
11.2 Percents
11.3 Direct and Inverse Variation
11.4 Simplifying Rational Expressions
11.5 Multiplying and Dividing Rational Expressions
11.6 Adding and Subtracting Rational Expressions
11.7 Dividing Polynomials
11.8 Ration Equations and Functions
 

Section 12 - Radicals and Connections to Geometry

12.1 Functions Involving Square Roots
12.2 Operations with Radical Expressions
12.3 Solving Radical Equations
12.4 Completing the Square
12.5 The Pythagorean Theorem and Its Converse
12.6 The Distance and Midpoint Formulas
12.7 Trigonometric Ratios
12.8 Logical Reasoning Proof
 

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