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Study Guides

ALGEBRA / TRIG I

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Unit 1

Why It Matters: Exponents
Why It Matters: Geometry
Introduction to Applying Exponent Rules
Introduction to Using Properties of Angles, Triangles, and the Pythagorean Theorem
Evaluating Exponential Expressions
Using Properties of Angles to Solve Problems
Simplifying Variable Expressions Using Exponent Properties I
Using the Properties of Triangles to Solve Problems
Simplifying Variable Expressions Using Exponent Properties II
Using the Pythagorean Theorem to Solve Problems
Simplifying Expressions with Negative Exponents and Exponents of 0 and 1
Summary: Using the Properties of Angles, Triangles, and the Pythagorean Theorem
Simplifying Complex Expressions I
Introduction to Using Properties of Rectangles, Triangles, and Trapezoids
Simplifying Complex Expressions II
Using Linear, Square, and Cubic Measure Appropriately
Summary: Simplifying Expressions With Exponents
Using the Properties of Rectangles to Solve Problems
Finding All the Factors of a Number
Using the Properties of Triangles to Solve Problems
Summary: Finding Multiples and Factors
Using the Properties of Trapezoids to Solve Problems
Introduction to Prime Factorization and the Least Common Multiple
Summary: Using Properties of Rectangles, Triangles, and Trapezoids
Finding the Prime Factorization of a Composite Number
Using the Properties of Circles to Solve Problems
Finding the Least Common Multiple of Two Numbers
Introduction to Solving Problems Using Volume and Surface Area
Summary: Prime Factorization and the Least Common Multiple
Finding the Volume and Surface Area of Rectangular Solids
Putting It Together: The Language of Algebra
Finding the Volume and Surface Area of a Sphere
Why It Matters: Factoring
Finding the Volume and Surface Area of a Cylinder
Introduction to Solving Simple Polynomial Equations
Finding the Volume of a Cone
The Zero Product Principle
Summary: Solving Problems Using Volume and Surface Area
Finding the Greatest Common Factor
Introduction to Systems of Measurement
Finding the Greatest Common Factor of a Polynomial
Making Unit Conversions in the U.S. System of Measurement
Solving a Polynomial in Factored Form
Making Unit Conversions in the Metric System of Measurement
Summary: Solving Simple Polynomial Equations
Converting Between U.S. and Metric Systems of Measurement
Introduction to Factoring Methods
Summary: Systems of Measurement
Factoring a Four Term Polynomial by Grouping
Putting It Together: Geometry
Factoring by Grouping
Introduction to Scientific Notation
Factoring a Trinomial with a Leading Coefficient of 1
Converting Between Scientific Notation and Decimal Notation
Summary: Factoring Methods
Multiplying and Dividing Numbers in Scientific Notation
Introduction to Factoring Special Cases
Problem Solving With Scientific Notation
Special Cases - Squares
Summary: Scientific Notation
Special Cases - Cubes
Putting It Together: Exponents
More Factoring Methods

Unit 2

Summary: Factoring Special Cases
Introduction to Problem Solving Strategies for Word Problems
Putting It Together: Factoring
Translating and Solving Word Problems and Applications

Unit 4

Apply a Problem-Solving Strategy to Word Problems
Why It Matters: Rational Expressions and Equations
Using a Problem-Solving Strategy to Solve Number Problems
Introduction to Operations With Rational Expressions I
Summary: Problem Solving Strategies for Word Problems
Simplifying Rational Expressions
Introduction to Solving Word Problems Containing Decimals
Multiplying and Dividing Rational Expressions
Solving Problems Involving Tickets and Stamps
Introduction to Operations With Rational Expressions II
Introduction to Using Formulas to Solve Word Problems
Adding and Subtracting Rational Expressions Part I
Problems Involving Formulas I
Adding and Subtractracting Rational Expressions Part II
Problems Involving Formulas II
Complex Rational Expressions
Summary: Using Formulas to Solve Word Problems
Introduction to Rational Equations and Their Applications
Putting It Together: Linear Equations
Solving Rational Equations
Why It Matters: Graphs
Proportions
Introduction to The Coordinate Plane
Applications with Rational Equations
Plotting Points on the Coordinate Plane
Why It Matters: Roots and Rational Exponents
Identifying Points on a Rectangular Coordinate System
Introduction to Simplifying Roots
Finding Solutions to Equations in Two Variables
Square Roots
Graphing Linear Equations Using Ordered Pairs
Simplifying Square Roots with Variables
Summary: The Coordinate Plane
Cube Roots and Nth Roots
Introduction to Finding Slope
Introduction to Simplifying Expressions with Radicals and Rational Exponents
Finding the Slope of a Line from its Graph
Radical Expressions and Rational Exponents
Using the Slope Formula to Find the Slope between Two Points
Simplifying Radical Expressions
Summary: Finding Slope
Introduction to Algebraic Operations with Radical Expressions
Introduction to Using Intercepts to Graph Lines
Multiplying and Dividing Radical Expressions
Identifying the Intercepts on the Graph of a Line
Adding and Subtracting Radicals
Graphing Lines Using X- and Y- Intercepts
Multiple Term Radicals
Summary: Using Intercepts to Graph Lines
Rationalizing Denominators
Introduction to Writing Equations of Lines
Why It Matters: Quadratic Equations and Complex Numbers
Graphing a Line Using Slope and a Point
Introduction to Quadratic Equations
Introduction to Applications of Graphs
Quadratic Equations
Interpreting Slope in Equations and Graphs
Square Roots and Completing the Square
Interpreting the y-Intercept and Making Predictions
The Quadratic Formula
Why It Matters: Linear Functions and Function Notation
Applications of Quadratic Equations
Introduction to Functions
Why It Matters: Quadratic, Polynomial, and Piecewise Functions
Defining a Function
Introduction to Piecewise Functions
Function Notation
Writing Piecewise Functions
Evaluating Functions
Graphing Piecewise Functions
Introduction to Linear Functions
Introduction to Quadratic and Radical Functions
Graphing Linear Functions
Graphing Quadratic Functions
Characteristics of Linear Functions
Graphing Radical Functions
Introduction to Domain and Range
Introduction to Polynomial Functions
Domain Restrictions
Identifying Polynomial Functions
Finding Domain and Range From a Graph
Graphs of Polynomial Functions
Putting It Together: Linear Functions and Function Notation
Algebra of Polynomial Functions
Why It Matters: Linear Systems
Introduction to Applications of Quadratic Functions
Introduction to Solutions to Systems of Equations
Projectiles
Ordered Pairs as Solutions to Systems
Putting It Together: Quadratic, Polynomial, and Piecewise Functions
Classify Solutions for Systems

Unit 5

Graphing Systems
Introduction to Complex Numbers
Summary: Solutions to Systems of Equations
Pythagorean Theorem
Introduction to Algebraic Methods for Solving Systems
Imaginary and Complex Numbers
The Substitution Method
Adding and Subtracting Complex Numbers
The Elimination Method Without Multiplication
Multiplying and Dividing Complex Numbers
The Elimination Method With Multiplication
Introduction to Quadratic Equations with Complex Solutions
Introduction to Systems of Equations in Three Variables
Quadratic Equations With Complex Solutions
Systems of Three Equations in Three Variables

Resources: Problem Sets

Inconsistent and Dependent Systems in Three Variables
Problem Set: Whole Numbers
Applications of Linear Equations in Three Variables
Problem Set: The Language of Algebra
Introduction to Problem Solving With Systems
Problem Set: Integers
Cost and Revenue Problems
Problem Set: Fractions

Unit 3

Problem Set: Decimals
Why It Matters: Linear Inequalities
Problem Set: Ratios, Rates, Probabilities, and Averages
Introduction to Solving Single- and Multi-Step Inequalities
Problem Set: Percents
Representing Inequalities on a Number Line and with Interval Notation
Problem Set: Geometry
Solving Inequalities
Problem Set: Real Numbers
Summary: Solving Single- and Multi-Step Inequalities
Problem Set: Multi-Step Linear Equations
Introduction to Solving Compound Inequalities
Problem Set: Polynomials
Describing Sets as Intersections or Unions
Problem Set: Graphs
Solving Compound Inequalities