Algebra 1 Syllabus
This course is offered exclusively as a one-on-one class and is not available in a small-group format.
Introduction
In Algebra 1, the language of algebra is studied intensely.
Students begin their study of the real number system and its properties.
The course is designed to convey an understanding of the meaning and use of variables, formulas, equations and inequalities, exponents, functions, and graphs.
Several real life applications are used to enhance these concepts.
The significance of word problems and of strategic problem solving is emphasized throughout the course.
Syllabus
1 The Language and Tools of Algebra
1.1 Variables and Expressions
1.2 Order of Operations
1.3 Open Sentences
1.4 Identity and Equality Properties.
1.5 The Distributive Property
1.6 Commutative and Associative Properties
1.7 Logical Reasoning and Counterexamples
1.8 Number Systems
1.9 Functions and Graphs
2 Solving Linear Equations
2.1 Writing Equations
2.2 Solving Equations by Using Addition and Subtraction
2.3 Solving Equations by Using Multiplication and Division
2.4 Solving Multi.Step Equations
2.5 Solving Equations with the Variable on Each Side
2.6 Ratios and Proportions
2.7 Percent of Change.
2.8 Solving for a Specific Variable
2.9 Weighted Averages
3 Functions and Patterns
3.1 Representing Relations
3.2 Representing Functions.
3.3 Linear Functions
3.4 Arithmetic Sequences
3.5 Proportional and Nonproportional Relationships
4 Analyzing Linear Equations
4.1 Rate of Change and Slope
4.2 Slope and Direct Variation
4.3 Graphing Equations in Slope Intercept Form
4.4 Writing Equations in Slope Intercept Form
4.5 Writing Equations in Point Slope Form
4.6 Statistics: Scatter Plots and Lines of Fit
4.7 Geometry: Parallel and Perpendicular Lines
5 Solving Systems of Linear Equations
5.1 Graphing Systems of Equations
5.2 Substitution
5.3 Elimination Using Addition and Subtraction.
5.4 Elimination Using Multiplication
5.5 Applying Systems of Linear Equations
6 Solving Linear Inequalities
6.1 Solving Inequalities by Addition and Subtraction
6.2 Solving Inequalities by Multiplication and Division
6.3 Solving Multi.Step Inequalities.
6.4 Solving Compound Inequalities
6.5 Solving Open Sentences Involving Absolute Value
6.6 Solving Inequalities Involving Absolute Value
6.7 Graphing Inequalities in Two Variables
6.8 Graphing Systems of Inequalities
7 Polynomials
7.1 Multiplying Monomials
7.2 Dividing Monomials
7.3 Polynomials
7.4 Adding and Subtracting Polynomials
7.5 Multiplying a Polynomial by a Monomial
7.6 Multiplying Polynomials
7.7 Special Products
8 Factoring
8.1 Monomials and Factoring
8.2 Factoring Using the Distributive Property
8.3 Factoring Trinomials: x^2 + bx + c
8.4 Factoring Trinomials: ax^2 + bx + c
8.5 Factoring Differences of Squares
8.6 Perfect Squares and Factoring
9 Quadratic and Exponential Functions
9.1 Graphing Quadratic Functions
9.2 Solving Quadratic Equations by Graphing
9.3 Solving Quadratic Equations by Completing the Square
9.4 Solving Quadratic Equations by Using the Quadratic Formula
9.5 Exponential Functions
9.6 Growth and Decay
10 Radical Expressions and Triangles
10.1 Simplifying Radical Expressions
10.2 Operations with Radical Expressions
10.3 Radical Equations
10.4 The Pythagorean Theorem
10.5 The Distance Formula.
10.6 Similar Triangles
11 Rational Expressions and Equations
11.1 Inverse Variation
11.2 Rational Expressions
11.3 Multiply Rational Expressions.
11.4 Dividing Rational Expressions
11.5 Dividing Polynomials
11.6 Rational Expressions with Like Denominators
11.7 Rational Expressions with Unlike Denominators
11.8 Mixed Expressions and Complex Fractions
11.9 Rational Equations and Functions
12 Statistics and Probability
12.1 Sampling and Bias
12.2 Counting Outcomes
12.3 Permutations and Combinations
12.4 Probability of Compound Events
12.5 Probability Distributions
12.6 Probability Simulations