Algebra I

Review of Algebra

• Introduction to Functions
• Graphing Linear Equations and Inequalities
• Writing the Equation of a Line
• Comparing Functions

Rational, Complex, and Polynomials

• Rational Exponents
• Properties of Rational Exponents
• Solving Radical Equations
• Complex Numbers
• Operations of Complex Numbers
• Review of Polynomials
• Polynomial Operations

Factoring and Quadratics

• Greatest Common Factors and Special Products
• Factoring by Grouping
• Sum and Difference of Cubes
• Graphing Quadratics
• Completing the Square
• Solving Quadratic Equations
• Solving Quadratic Equations with Complex Solutions
• Investigating Quadratics

Dividing and Solving Polynomials

• Polynomial Long Division
• Polynomial Synthetic Division
• Theorems of Algebra
• Rational Root Theorem and Descartes’ Rule of Signs
• Solving Polynomial Equations
• Graphing Polynomial Functions
• Polynomial Identities and Proofs

Rational Expressions

• Simplifying Rational Expressions
• Multiplying and Dividing Rational Expressions
• Adding and Subtracting Rational Expressions
• Simplifying Complex Fractions
• Discontinuities of Rational Expressions
• Asymptotes of Rational Functions
• Solving Rational Equations
• Applications of Rational Equations

Systems of Equations and Inequalities

• Solving Systems of Equations Algebraically
• Solving Systems of Non-Linear Equations
• Graphing Systems of Linear Equations
• Graphing Systems of Non-Linear Equations

Exponential and Logarithmic Functions

• Exponential Functions
• Logarithmic Functions
• Properties of Logarithms
• Solving Exponential Equations with Unequal Bases
• Graphing Exponential Functions
• Graphing Logarithmic Functions
• Exponential and Logarithmic Functions

Sequences and Series

• Arithmetic Sequences
• Arithmetic Series
• Geometric Sequences
• Geometric Series
• Sigma Notation
• Infinite, Convergent, and Divergent Series
• Graphing Sequences and Series

Statistics

• Events and Outcomes in a Sample Space
• Independent Probability
• Conditional Probability
• Normal Distribution
• Models of Populations
• Using Surveys
• Using Experiments

Trigonometry

• Introduction to the Unit Circle
• Unit Circle and the Coordinate Plane
• Trigonometric Functions with Periodic Phenomena
• Pythagoras, Trigonometry, and Quadrants
• Functions of All Types