Foundations of Algebra

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Course Description for Foundations of Algebra 1A and Algebra 1B

0.    Preparing for Algebra


                        Prime Factorization

                        Least Common Multiples

                        Greatest Common Factors

                        Real Numbers

                        Adding & Subtracting Integers 

                        Multiplying & Dividing Integers 

                        Adding & Subtracting Rational Numbers 

                        Multiplying & Dividing Rational Numbers

                        The Percent Proportions




                        Surface Area

                        Simple Probability and Odds

                        Mean, Median, Mode, Range and Quartiles

                        Representing Data

1.    Expressions, Equations, and Functions

                        Variables and Expressions

                        Order of Operations

                        Properties of Numbers

                        The Distributive Property      




                        Logical Reasoning and Counterexamples

2.   Linear Equations

Writing Equations

Solving One-Step Equations

Solving Multi-Step Equations

Solving Equations with the Variable on Each Side

Solving Equations Involving Absolute Value

Ratios and Proportions

Percent of Change

Literal Equations and Dimensional Analysis

Weighted Averages

3.   Linear Functions

Graphing Linear Equations

Solving Linear Equations by Graphing

Rates of Change and Slope

Direct Variation

Arithmetic Sequences as Linear Functions

Proportional and Nonproportional Relationships

4.  Linear Functions and Relations

Graphing Equations in Slope-Intercept Form

Writing Equations in Slope-Intercept Form

Writing Equations in Point-Slope Form

Parallel and Perpendicular Lines

Scatter Plots and Lines of Fit

Regression and Median-fit Lines

Special Functions

5.   Linear Inequalities

Solving Inequalities by Addition and Subtraction

Solving Inequalities by Multiplication and Division

Solving Multi-Step Inequalities

Solving Compound Inequalities

Inequalities Involving Absolute Value

Graphing Inequalities in Two Variables

6.      Systems of Linear Equations and Inequalities

Solving Systems of Equations by Graphing

 Solving Systems of Equations by Substitution

Solving Systems of Equations by Elimination

Applying Systems of Linear Functions

Systems of Inequalities

7.      Polynomials

Multiplying Monomials

Dividing Monomials

Scientific Notation


Adding and Subtracting Polynomials

Multiplying a Polynomial by a Monomial

Multiplying Polynomials

Special Products

8.      Factoring and Quadratic Equations

Monomials and Factoring

Using the Distributive Property

Quadratic Equations: x+ bx + c

Quadratic Equations: ax+ bx + c

Quadratic Equations: Difference of Squares

Quadratic Equations: Perfect Squares

9.      Quadratic and Exponential Functions

Graphing Quadratic Functions

Solving Quadratic Equations by Graphing

Transformations of Quadratic Functions

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Using the Quadratic Formula

Exponential Functions

Growth and Decay

Geometric Sequences as Exponential Functions

Analyzing Functions with Successive Difference and Ratios

10.  Radical Functions and Geometry

Square Root Functions

Simplifying Radical Expressions

Operations with Radical Expressions

Radical Equations

The Pythagorean Theorem

The Distance and Midpoint Formulas

Similar Triangles

Trigonometric Ratios

11.  Rational Functions and Equations

Inverse Variation

Rational Functions

Simplifying Rational Expressions

Multiplying and Dividing Polynomials

Adding and Subtracting Rational Expressions

Mixed Expressions and Complex Fractions

Rational Equations

12.  Statistics

                        Designing a Survey

                        Analyzing Survey Results

                        Statistics and Parameter