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Key Features of our AccuPlacer Math Test Prep Courses

ACCUPLACER MATH LESSONS WITH A TEACHER

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Our AccuPlacer math lessons cover all the math on the test.  Every lesson includes videos, guided practice, self-tests, worksheets and more.

PRE-TESTS BEFORE EVERY ACCUPLACER MATH LESSON

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Every lesson in our AccuPlacer math prep course features a quick diagnostic pre-test so you don’t have to waste time on material you already know!

AUTO-GENERATED BACKGROUND LESSONS

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GRADE REPORTING AND PROGRESS TRACKING

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We offer detailed grade reporting and progress tracking to keep on task while completing your AccuPlacer math prep course!

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ACCUPLACER Math Test Prep Courses

CHAPTER 1: WHOLE NUMBERS

Unit 1: Addition and Subtraction

Addition

Subtraction

Estimating Sums and Differences

Addition and Subtraction Word Problems

Unit 2: Multiplication and Division

Multiplication

Division

Estimating Products and Quotients

Multiplication and Division Word Problems

CHAPTER 2: INTEGERS

Unit 1: Positives and Negatives

Comparing Integers

Addition and Subtraction

Multiplication and Division

Unit 2: Order of Operations / Evaluation

Order of Operations

Evaluation

Unit 3: Absolute Value

Absolute Value

CHAPTER 3: FRACTIONS

Unit 1: Factors and Multiples

Divisibility Rules

Factors and Primes

Prime Factorization

Multiples and Least Common Multiples

Greatest Common Factor

Unit 2: Fractions and Mixed Numbers

Introduction to Fractions

Equivalent Fractions (Part I)

Lowest Terms

Equivalent Fractions (Part II)

Improper Fractions and Mixed Numbers

Unit 3: Comparing Fractions

Comparing Proper Fractions

Comparing Mixed Numbers and Improper Fractions

Word Problems

Unit 4: Addition and Subtraction

Adding and Subtracting Like Fractions

Adding and Subtracting Unlike Fractions

Adding Mixed Numbers

Subtracting Mixed Numbers

Unit 5: Multiplication and Division

Multiplying Fractions

Multiplying Mixed Numbers

Dividing Fractions

Dividing Mixed Numbers

Unit 6: Positive and Negative Fractions

Least Common Multiple

Addition and Subtraction

Multiplication and Division

Order of Operations

Evaluation

Absolute Value

CHAPTER 4: DECIMALS

Unit 1: Decimal Concept

Understanding Decimals

Converting Decimals to Fractions

Converting Fractions to Decimals

Comparing Decimals

Rounding Decimals

Word Problems

Unit 2: Addition and Subtraction

Estimating Sums and Differences

Adding Decimals

Subtracting Decimals

Word Problems

Unit 3: Multiplication and Division

Multiplying Decimals by Whole Numbers

Multiplying Decimals by Decimals

Dividing Decimals by Whole Numbers

Dividing Decimals by Decimals

Word Problems

CHAPTER 5: EXPRESSIONS, EQUATIONS, & WORD PROBLEMS

Unit 1: Variables and Expressions

Combining Like Terms

Distributive Property

Distributive / Like Terms

Unit 2: Beginning Equations

One-Step Equations

Two-Step Equations

Unit 3: Intermediate Equations

Equations with Fractions

Equations Involving Distributive

Unit 4: Advanced Equations

Variable on Both Sides

Variable on Both Sides / Fractions

Variable on Both Sides / Distributive

Unit 5: Literal Equations

Beginning Formulas

Advanced Formulas

Unit 6: Word Problems

Number Problems

Value Problems

CHAPTER 6: INEQUALITIES & FUNCTIONS

Unit 1: Inequalities

Solving and Graphing Inequalities

Unit 2: Functions

The Coordinate System

Domain and Range

Definition of a Function

Function and Arrow Notation

CHAPTER 7: LINEAR EQUATIONS & SYSTEMS OF EQUATIONS

Unit 1: Slope

Using the Graph of a Line to Find Slope

Using Slope to Graph a Line

Using Coordinates to Find Slope

Unit 2: Slope-Intercept Form

Using Slope-Intercept Form to Graph a Line

Converting to Slope-Intercept Form and Graphing

Unit 3: Writing Equations of Lines

Standard Form

The Point-Slope Formula

Given Two Points

Parallel and Perpendicular

Unit 4: Systems of Equations

By Addition

By Substitution

CHAPTER 8: EXPONENTS & POLYNOMIALS

Unit 1: Exponent Rules

The Product Rule

The Power Rule

The Quotient Rule

Unit 2: Multiplying Polynomials

The Distributive Property

F.O.I.L.

Advanced Problems

CHAPTER 9: FACTORING

Unit 1: Greatest Common Factor

Rules for Finding the G.C.F.

Factoring Out the G.C.F.

Unit 2: Factoring Special Polynomials

Special Trinomials with Positive Constant

Special Trinomials with Negative Constant

Difference of Two Squares

Unit 3: Advanced Trinomial Factoring

Coefficient on x^2 Term, Positive Constant

Coefficient on x^2 Term, Negative Constant

Unit 4: Factoring Completely

Factoring Out G.C.F. as First Step

Unit 5: Polynomial Equations

Beginning Equations

CHAPTER 10: RATIONAL EXPRESSIONS

Unit 1: Beginning Rational Expressions

Simplifying Rational Expressions

Multiplying and Dividing Rational Expressions

Unit 2: Advanced Rational Expressions

Adding Rational Expressions

Subtracting Rational Expressions

Unit 3: Rational Equations

Beginning Rational Equations

CHAPTER 11: RADICALS

Unit 1: Operations with Radicals

Simplifying Radicals

Multiplying Radicals

Dividing Radicals

Addition and FOILing

Unit 2: Radical Equations

Radical Equations

CHAPTER 12: QUADRATICS

Unit 1: Graphing Quadratic Functions

Graphs of Quadratic Functions and Beginning Transformations

Unit 2: Completing the Square

Square Rooting Both Sides

Beginning Completing The Square

Unit 3: The Quadratic Formula

Beginning Quadratic Formula

CHAPTER 13: RATIO, PROPORTION, & PERCENT

Unit 1: Ratio

Introduction to Ratios

Equal Ratios

Unit Rate

Unit Price

Unit 2: Proportion

Introduction to Proportion

Solving Proportions

Word Problems

Unit 3: Percent Concept

Percent Problems

Sales Tax

CHAPTER 14: GEOMETRY

Unit 1: Segments and Angles

Segments, Rays, and Length

Segment Addition Postulate and Midpoint

Angles and Measure

Angle Addition Postulate and Angle Bisector

Unit 2: Angles of a Triangle

Vocabulary and Triangle Sum Theorem

Unit 3: Right Triangles

The Pythagorean Theorem

30-60-90 and 45-45-90 degree Triangles (Part I)

Sine, Cosine, and Tangent (Part I)

CHAPTER 15: MEASUREMENT

Unit 1: Perimeter and Circumference

Perimeter

Circumference

Word Problems

Unit 2: Area

Area of Squares and Rectangles

Area of Triangles

Area of Parallelograms and Trapezoids

Area of a Circle

Word Problems

CHAPTER 16: PROBABILITY & STATISTICS

Unit 1: Common Graphs and Charts

Bar Graphs

Line Graphs

Circle Graphs

Unit 2: Central Tendency

Mean

Unit 3: Counting Methods

Permutations

Combinations

CHAPTER 17: COORDINATE GEOMETRY

Unit 1: Segments in the Coordinate Plane

Distance Formula

Midpoint Formula

Unit 2: Circles in the Coordinate Plane

Equation of a Circle

CHAPTER 18: NEGATIVE & RATIONAL EXPONENTS

Unit 1: Simplifying Expressions with Negative Exponents

Negative Exponents

Negative Exponent Rules

Multiplying and Dividing with Negative Exponents

Unit 2: Operations with Scientific Notation

Multiplying and Dividing Scientific Notation

Unit 3: Rational Exponents and Radical Expressions

Rational Exponents

Fractional Exponents

Writing Radicals in Exponential Form

Unit 4: Equations with Rational Exponents and Simplifying with Radical Exponents

Solving Equations with Rational Exponents

Radical Exponents

CHAPTER 19: COMPOSITE FUNCTIONS & INVERSES

Unit 1: Composite Functions

Composite Functions: f(g(x)) and g(f(x))

Unit 2: Inverses

Inverse Relations

Inverse Functions

CHAPTER 20: LOGARITHMS & EXPONENTIAL FUNCTIONS

Unit 1: Introduction to Logarithms

Logarithms and Logarithmic Functions

Solving Logarithmic Equations

Unit 2: Properties of Logarithms

Logarithm Rules and Properties

Evaluating Logarithms by Condensing or Expanding

Solving Advanced Log Equations

Unit 3: Evaluating Logarithms with a Calculator

Log Calculator Problems

Unit 4: Exponential Equations and Logarithms

Exponential Equations and Change of Base Formula

Exponential Growth and Decay

Half Life Formula and Doubling Time Formula

Unit 5: The Natural Logarithm

Natural Logarithms

Solving Natural Logarithm Equations with ln and e

CHAPTER 1: WHOLE NUMBERS

Unit 1: Number Concepts

Place Value

Comparing Numbers

Rounding

Unit 2: Addition and Subtraction

Addition

Subtraction

Estimating Sums and Differences

Addition and Subtraction Word Problems

Unit 3: Multiplication and Division

Multiplication

Exponents

Division

Estimating Products and Quotients

Multiplication and Division Word Problems

Unit 4: Properties and Rules

Order of Operations

Grouping Symbols

Variables

Addition Properties

Multiplication Properties

CHAPTER 2: INTEGERS

Unit 1: Integers and the Number Line

Graphing and Writing Integers

Comparing Integers

Opposites and Absolute Value

Unit 2: Integer Operations

Addition

Subtraction

Multiplication

Division

CHAPTER 3: FRACTIONS

Unit 1: Factors and Multiples

Divisibility Rules

Factors and Primes

Prime Factorization

Multiples and Least Common Multiples

Greatest Common Factor

Unit 2: Fractions and Mixed Numbers

Introduction to Fractions

Equivalent Fractions (Part I)

Lowest Terms

Equivalent Fractions (Part II)

Improper Fractions and Mixed Numbers

Unit 3: Comparing Fractions

Comparing Proper Fractions

Comparing Mixed Numbers and Improper Fractions

Word Problems

Unit 4: Addition and Subtraction

Adding and Subtracting Like Fractions

Adding and Subtracting Unlike Fractions

Adding Mixed Numbers

Subtracting Mixed Numbers

Unit 5: Multiplication and Division

Multiplying Fractions

Multiplying Mixed Numbers

Dividing Fractions

Dividing Mixed Numbers

CHAPTER 4: DECIMALS

Unit 1: Decimal Concept

Understanding Decimals

Converting Decimals to Fractions

Converting Fractions to Decimals

Comparing Decimals

Rounding Decimals

Word Problems

Unit 2: Addition and Subtraction

Estimating Sums and Differences

Adding Decimals

Subtracting Decimals

Word Problems

Unit 3: Multiplication and Division

Multiplying Decimals by Whole Numbers

Multiplying Decimals by Decimals

Dividing Decimals by Whole Numbers

Dividing Decimals by Decimals

Word Problems

Unit 4: Scientific Notation

Powers of Ten

Converting from Scientific to Standard Notation

Converting from Standard to Scientific Notation

Unit 5: Rational and Irrational Numbers

Terminating and Repeating Decimals

Determining if a Number is Rational or Irrational

CHAPTER 5: ALGEBRAIC EXPRESSIONS & EQUATIONS

Unit 1: Algebraic Expressions

Evaluating Expressions

Modeling Expressions

Unit 2: Solving One-Step Equations

Introduction to Equations

Addition Equations

Subtraction Equations

Multiplication Equations

Division Equations

Unit 3: Writing and Solving Equations

Writing and Solving Equations

CHAPTER 6: RATIO, PROPORTION, & PERCENT

Unit 1: Ratio

Introduction to Ratios

Equal Ratios

Unit Rate

Unit Price

Unit 2: Proportion

Introduction to Proportion

Solving Proportions

Word Problems

Unit 3: Percent Concept

Understanding Percents

Fractions and Percents

Decimals and Percents

Unit 4: Percent Problems

Percent of a Number

Percent One Number is of Another

Using Percent to Find a Number

Percent Increase or Decrease

Unit 5: Percent Applications

Discount

Sales Tax

Interest

CHAPTER 7: GEOMETRY

Unit 1: Lines and Angles

Points, Lines, Segments, and Rays

Classifying Lines

Angles

Measuring Angles

Complementary and Supplementary Angles

Unit 2: Two-Dimensional Figures

Angles of a Triangle

Sides of a Triangle

Polygons

Quadrilaterals

Circles

Unit 3: Three-Dimensional Figures

Classifying 3-Dimensional Figures

Nets

Perspective Drawings

Unit 4: Congruent and Similar Figures

Congruent Figures

Similar Figures

Problem Solving with Similar Figures

Unit 5: Symmetry

Symmetry

CHAPTER 8: MEASUREMENT

Unit 1: Units of Measurement

Customary Unit Conversions

Metric Unit Conversions

Units of Measurement

Unit 2: Perimeter and Circumference

Perimeter

Circumference

Word Problems

Unit 3: Area

Area of Squares and Rectangles

Area of Triangles

Area of Parallelograms and Trapezoids

Area of a Circle

Word Problems

Unit 4: Square Roots and the Pythagorean Theorem

Square Roots

Using Square Roots to Solve Equations

Pythagorean Theorem

Pythagorean Triples

CHAPTER 9: PROBABILITY & STATISTICS

Unit 1: Common Graphs and Charts

Bar Graphs

Line Graphs

Circle Graphs

Unit 2: Central Tendency

Range, Median, and Mode

Mean

Word Problems

Unit 3: Probability

Simple Probability

CHAPTER 1: WHOLE NUMBERS & PROPERTIES

Unit 1: Exponents and Order of Operations

Exponents

Order of Operations

Grouping Symbols

Unit 2: Introduction to Variables

Variables

Unit 3: Properties of Real Numbers

Addition Properties

Multiplication Properties

CHAPTER 2: INTEGERS

Unit 1: Introduction to Integers

Graphing and Writing Integers

Comparing Integers

Opposites and Absolute Value

Unit 2: Operations with Integers

Addition and Subtraction

Multiplication and Division

Unit 3: Order of Operations and Evaluating Expressions

Order of Operations

Evaluation

Integers

CHAPTER 3: FRACTIONS

Unit 1: Factors and Multiples

Divisibility Rules

Factors and Primes

Prime Factorization

Multiples and Least Common Multiples

Greatest Common Factor

Unit 2: Fractions and Mixed Numbers

Introduction to Fractions

Equivalent Fractions (Part I)

Lowest Terms

Equivalent Fractions (Part II)

Unit 3: Comparing Fractions

Improper Fractions and Mixed Numbers

Comparing Proper Fractions

Comparing Mixed Numbers and Improper Fractions

Unit 4: Operations with Fractions

Adding and Subtracting Like Fractions

Adding and Subtracting Unlike Fractions

Multiplying Fractions

Dividing Fractions

Unit 5: Operations with Rational Numbers

Addition and Subtraction

Multiplication and Division

Order of Operations

Evaluation

CHAPTER 4: DECIMALS

Unit 1: Decimal Concepts

Understanding Decimals

Converting Decimals to Fractions

Converting Fractions to Decimals

Comparing Decimals

Rounding Decimals

Unit 2: Scientific Notation

Powers of Ten

Converting from Scientific to Standard Notation

Converting from Standard to Scientific Notation

Unit 3: Rational and Irrational Numbers

Terminating and Repeating Decimals

Determining if a Number is Rational or Irrational

CHAPTER 5: ALGEBRAIC EXPRESSIONS & EQUATIONS

Unit 1: Simplifying Algebraic Expressions

Combining Like Terms

Distributive Property

Distributive / Like Terms

Unit 2: Solving One- and Two-Step Equations

One-Step Equations

Two-Step Equations

Equations with Fractions

Unit 3: Multi-Step Equations

Equations Involving Distributive

Variable on Both Sides

Variable on Both Sides / Fractions

Variable on Both Sides / Distributive

Unit 4: Formulas

Beginning Formulas

Advanced Formulas

CHAPTER 6: WORD PROBLEMS

Unit 1: Modeling Expressions and Equations

Translating English to Algebra

Modeling Two-Step Equations

Unit 2: Solving Word Problems

Number Problems

Geometry Problems

Value Problems

CHAPTER 7: INEQUALITIES, FUNCTIONS, & GRAPHING

Unit 1: Solving Linear Inequalities in One Variable

Solving and Graphing Inequalities

Unit 2: Graphing and Functions

The Coordinate System

Domain and Range

Definition of a Function

Function and Arrow Notation

Unit 3: Graphing Linear Equations

Graphing Lines

The Intercept Method

Unit 4: Linear Inequalities in Two Variables

Graphing Inequalities in Two Variables

CHAPTER 8: LINEAR EQUATIONS & GRAPHING

Unit 1: Slope of a Line

Using the Graph of a Line to Find Slope

Using Slope to Graph a Line

Using Coordinates to Find Slope

Unit 2: Slope-Intercept Form

Using Slope-Intercept Form to Graph a Line

Converting to Slope-Intercept Form and Graphing

Unit 3: Writing Equations in Slope-Intercept Form

Using Graphs and Slope-Intercept Form

Using Tables and Slope-Intercept Form

Unit 4: Equations in Standard and Point-Slope Form

Standard Form

The Point-Slope Formula

Given Two Points

Parallel and Perpendicular

CHAPTER 9: SYSTEMS OF EQUATIONS IN TWO VARIABLES

Unit 1: Solving Systems of Equations

By Graphing

By Addition

By Substitution

Unit 2: Word Problems with Systems of Equations

Number and Value Problems

CHAPTER 10: EXPONENTS & POLYNOMIALS

Unit 1: Exponent Rules

The Product Rule

The Power Rule

The Quotient Rule

Unit 2: Advanced Exponent Problems

Numerical Bases and Exponents of Zero

Unit 3: Multiplying Polynomials

The Distributive Property

F.O.I.L.

Advanced Problems

CHAPTER 11: FACTORING POLYNOMIALS

Unit 1: Greatest Common Factor

Rules for Finding the G.C.F.

Factoring Out the G.C.F.

Unit 2: Factoring Special Polynomials

Special Trinomials with Positive Constant

Special Trinomials with Negative Constant

Difference of Two Squares

Unit 3: Factoring Trinomials

Coefficient on x2 Term, Positive Constant

Coefficient on x2 Term, Negative Constant

Unit 4: Factoring Completely

Factoring Out G.C.F. as First Step

Unit 5: Solving Polynomial Equations by Factoring

Beginning Equations

Intermediate Equations

CHAPTER 12: RATIONAL EXPRESSIONS & EQUATIONS

Unit 1: Beginning Rational Expressions

Simplifying Rational Expressions

Multiplying and Dividing Rational Expressions

Unit 2: Advanced Rational Expressions

Adding Rational Expressions

Subtracting Rational Expressions

Unit 3: Solving Rational Equations

Beginning Rational Equations

CHAPTER 13: RADICAL EXPRESSIONS & EQUATIONS

Unit 1: Beginning Radical Expressions

Simplifying Radicals

Multiplying Radicals

Dividing Radicals

Unit 2: Advanced Radical Expressions

Addition and FOILing

Unit 3: Solving Radical Equations

Beginning Equations

CHAPTER 14: QUADRATIC EQUATIONS

Unit 1: Quadratic Equations and Graphing

Graphs of Quadratic Functions and Beginning Transformations

Graphs of Quadratic Functions and Advanced Transformations

Unit 2: Completing the Square

Square Rooting Both Sides

Beginning Completing The Square

Unit 3: The Quadratic Formula

Beginning Quadratic Formula

CHAPTER 15: RATIO & PROPORTION

Unit 1: Ratio

Introduction to Ratios

Equal Ratios

Unit 2: Proportion

Introduction to Proportion

Solving Proportions

Proportion

CHAPTER 16: SEGMENTS & ANGLES

Unit 1: Segments and Length

Segments, Rays, and Length

Segment Addition Postulate and Midpoint

Unit 2: Angles and Measure

Angles and Measure

Angle Addition Postulate and Angle Bisector

Unit 3: Angle Pairs

Complementary and Supplementary Angles (Part 1)

Vocabulary

Given Lines are Parallel

CHAPTER 17: GEOMETRIC FIGURES IN TWO-AND THREE-DIMENSIONS

Unit 1: Triangles and Quadrilaterals

Vocabulary and Triangle Sum Theorem

Quadrilaterals

Unit 2: Polygons and Angles

Vocabulary

Sum of Interior and Exterior Angles

Regular Polygons

Unit 3: Circles

Circles

Unit 4: Three-Dimensional Figures

Classifying 3-Dimensional Figures

Nets

CHAPTER 18: MEASUREMENT

Unit 1: Perimeter and Circumference

Perimeter

Circumference

Word Problems

Unit 2: Area

Area of Squares and Rectangles

Area of Triangles

Area of Parallelograms and Trapezoids

Area of a Circle

Word Problems

Unit 3: Surface Area and Volume

Surface Area

Volume of Prisms and Pyramids

Volume of Cylinders, Spheres, and Cones

Word Problems

Unit 4: The Pythagorean Theorem

Pythagorean Theorem

Pythagorean Triples

CHAPTER 19: NEGATIVE & RATIONAL EXPONENTS

Unit 1: Simplifying Expressions with Negative Exponents

Negative Exponents

Negative Exponent Rules

Multiplying and Dividing with Negative Exponents

Unit 2: Operations with Scientific Notation

Multiplying and Dividing Scientific Notation

Unit 3: Rational Exponents and Radical Expressions

Rational Exponents

Fractional Exponents

Writing Radicals in Exponential Form

CHAPTER 1: EVALUATING EXPRESSIONS

Unit 1: Introduction to Variables, Exponents, and Properties

Exponents

Variables

Field Properties

Unit 2: Integers

Graphing and Writing Integers

Comparing Integers

Opposites and Absolute Value

Addition and Subtraction

Multiplication and Division

Unit 3: Order of Operations and Evaluating Algebraic Expressions

Order of Operations

Evaluation

Unit 4: Operations with Rational Numbers

Least Common Multiple

Addition and Subtraction

Multiplication and Division

Unit 5: Expressions with Absolute Value

Integers

CHAPTER 2: DECIMALS & SCIENTIFIC NOTATION

Unit 1: Scientific Notation

Powers of Ten

Converting from Scientific to Standard Notation

Converting from Standard to Scientific Notation

Unit 2: Rational and Irrational Numbers

Terminating and Repeating Decimals

Determining if a Number is Rational or Irrational

CHAPTER 3: SOLVING LINEAR EQUATIONS IN ONE VARIABLE

Unit 1: Simplifying Algebraic Expressions

Combining Like Terms

Distributive Property

Distributive / Like Terms

Unit 2: Beginning Equations

One-Step Equations

Two-Step Equations

Equations with Fractions

Unit 3: Multi-Step Equations

Equations Involving Distributive

Variable on Both Sides

Variable on Both Sides / Fractions

Variable on Both Sides / Distributive

Unit 4: Formulas

Beginning Formulas

Advanced Formulas

CHAPTER 4: WORD PROBLEMS

Unit 1: Modeling Expressions and Equations

Translating English to Algebra

Modeling Two-Step Equations

Unit 2: Solving Word Problems

Number Problems

Geometry Problems

Value Problems

CHAPTER 5: INEQUALITIES, ABSOLUTE VALUE, FUNCTIONS, & GRAPHING

Unit 1: Linear Inequalities in One Variable

Solving and Graphing Inequalities

Combined Inequalities

Advanced Inequality Problems

Unit 2: Absolute Value

Absolute Value Equations

Absolute Value Inequalities

Unit 3: Functions

The Coordinate System

Domain and Range

Definition of a Function

Function and Arrow Notation

Unit 4: Graphing

Graphing within a Given Domain

Graphing Lines

The Intercept Method

Graphing Inequalities in Two Variables

CHAPTER 6: LINEAR EQUATIONS IN TWO VARIABLES

Unit 1: Slope

Using the Graph of a Line to Find Slope

Using Slope to Graph a Line

Using Coordinates to Find Slope

Unit 2: Slope-Intercept Form

Using Slope-Intercept Form to Graph a Line

Converting to Slope-Intercept Form and Graphing

Unit 3: Writing Equations in Slope-Intercept Form

Using Tables and Slope-Intercept Form

Unit 4: Point-Slope and Standard Forms

Standard Form

The Point-Slope Formula

Given Two Points

Parallel and Perpendicular

Unit 5: Direct Variation and Applications of Linear Functions

Direct Variation

Applications of Direct Variation and Linear Functions

CHAPTER 7: SYSTEMS OF EQUATIONS

Unit 1: Solving Systems of Equations

By Graphing

By Addition

By Substitution

Advanced Systems

Unit 2: Word Problems

Number and Value Problems

CHAPTER 8: EXPONENTS & POLYNOMIALS

Unit 1: Exponent Rules

The Product Rule

The Power Rule

The Quotient Rule

Unit 2: Advanced Exponents

Numerical Bases and Exponents of Zero

Combining Exponent Rules

Unit 3: Multiplying Polynomials

The Distributive Property

F.O.I.L.

Advanced Problems

CHAPTER 9: FACTORING

Unit 1: Greatest Common Factor

Rules for Finding the G.C.F.

Factoring Out the G.C.F.

Unit 2: Factoring Special Polynomials

Special Trinomials with Positive Constant

Special Trinomials with Negative Constant

Difference of Two Squares

Unit 3: Factoring Trinomials

Coefficient on x2 Term, Positive Constant

Coefficient on x2 Term, Negative Constant

Unit 4: Factoring by Grouping

Basic Technique

Advanced Strategies

Unit 5: Factoring Completely

Factoring Out G.C.F. as First Step

Factoring Difference of Two Squares as Last Step

Unit 6: Polynomial Equations

Beginning Equations

Intermediate Equations

CHAPTER 10: RATIONAL EXPRESSIONS & EQUATIONS

Unit 1: Beginning Rational Expressions

Simplifying Rational Expressions

Multiplying and Dividing Rational Expressions

Unit 2: Advanced Rational Expressions

Adding Rational Expressions

Subtracting Rational Expressions

Complex Fractions

Unit 3: Rational Equations

Beginning Rational Equations

Advanced Rational Equations

Unit 4: Inverse Variation

Inverse Variation

CHAPTER 11: RADICAL EXPRESSIONS & EQUATIONS

Unit 1: Beginning Radical Expressions

Simplifying Radicals

Multiplying Radicals

Dividing Radicals

Unit 2: Advanced Radical Expressions

Addition and FOILing

Advanced Division

Unit 3: Radical Equations

Beginning Equations

Advanced Equations

CHAPTER 12: QUADRATIC EQUATIONS

Unit 1: Completing the Square

Square Rooting Both Sides

Beginning Completing The Square

Advanced Completing The Square

Unit 2: The Quadratic Formula

Beginning Quadratic Formula

CHAPTER 13: IMAGINARY & COMPLEX NUMBERS

Unit 1: Imaginary Numbers

Beginning Imaginary Numbers

Advanced Imaginary Numbers

Unit 2: Complex Numbers

Beginning Complex Numbers

Advanced Complex Numbers

CHAPTER 14: QUADRATIC FUNCTIONS

Unit 1: Quadratic Equations in Vertex Form

Understanding y - k = a(x - h)2 Form

Graphing Quadratic Equations in y - k = a(x - h)2 Form

Writing Quadratic Equations in y - k = a(x - h)2 Form

Unit 2: Quadratic Functions and Graphing

Graphing Quadratic Functions

The Sum and Product of Roots Formula

Writing Quadratic Functions

CHAPTER 15: INTRODUCTION TO GEOMETRY

Unit 1: Basic Figures

Points, Lines, Planes, and Space

Segments, Rays, and Length

Segment Addition Postulate and Midpoint

Angles and Measure

Angle Addition Postulate and Angle Bisector

Unit 2: Reasoning

Inductive vs. Deductive Reasoning

Conditional Statements

Unit 3: Beginning Proofs

Properties

Algebra Proofs with Properties

Geometry Proofs with Midpoints and Angle Bisectors

CHAPTER 16: ANGLE PAIRS & PERPENDICULAR LINES

Unit 1: Angle Pairs

Complementary and Supplementary Angles (Part 1)

Vertical Angles

Unit 2: Perpendicular Lines

Problems Involving Perpendicular Lines

Theorems Involving Perpendicular Lines

CHAPTER 17: PARALLEL LINES & POLYGONS

Unit 1: Parallel Lines

Vocabulary

Given Lines are Parallel

Unit 2: Angles of a Triangle

Vocabulary and Triangle Sum Theorem

Algebra Problems

Word Problems and Exterior Angle Theorem

Unit 3: Polygons

Vocabulary

Sum of Interior and Exterior Angles

Regular Polygons

CHAPTER 18: TRIANGLES & CONGRUENCE

Unit 1: Beginning Concepts

Congruent Figures

Proving Triangles are Congruent by SSS, SAS, and ASA

Unit 2: Advanced Concepts

Isosceles Triangle Theorems

Proving Triangles are Congruent by AAS and HL

Medians, Altitudes, and Perpendicular Bisectors

CHAPTER 19: QUADRILATERALS

Unit 1: Properties of Parallelograms

Properties of Parallelograms

Proving a Quadrilateral is a Parallelogram

More Parallel Line Theorems

Unit 2: Special Parallelograms and Other Quadrilaterals

Rectangles, Rhombuses, and Squares

Trapezoids

CHAPTER 20: SIMILARITY

Unit 1: Ratio and Proportion

Ratio

Proportion

Unit 2: Similar Polygons

Properties of Similar Polygons

Angle-Angle Similarity Postulate

Word Problems

Unit 3: Similarity Theorems

SSS and SAS Similarity Theorems

Triangle Proportionality and Triangle Angle-Bisector Theorems

CHAPTER 21: RIGHT TRIANGLES

Unit 1: The Pythagorean Theorem

The Pythagorean Theorem

Word Problems

Converse of the Pythagorean Theorem

Unit 2: Special Right Triangles

30-60-90 and 45-45-90 degree Triangles (Part I)

Unit 3: Right Triangle Trigonometry

Sine, Cosine, and Tangent (Part I)

Sine, Cosine, and Tangent (Part II)

Word Problems

CHAPTER 22: CIRCLES

Unit 1: Vocabulary and Tangents

Vocabulary

Tangents

Unit 2: Arcs, Chords, and Central Angles

Arcs and Central Angles

Beginning Arcs and Chords

Unit 3: Angles and Segments

Inscribed Angles

Angles Formed by Chords, Secants, and Tangents

Unit 4: Segment Lengths

Theorems and Beginning Problems

CHAPTER 23: AREA

Unit 1: Area of Rectangles, Squares, and Parallelograms

Area of Rectangles and Squares (Part I)

Area of Rectangles and Squares (Part II)

Area of Parallelograms

Unit 2: Area of Triangles, Rhombuses, and Trapezoids

Area of Triangles

Area of Rhombuses

Area of Trapezoids

Unit 3: Area of Regular Polygons and Circles

Area of Regular Polygons

Area and Circumference of Circles

CHAPTER 24: VOLUME & SURFACE AREA

Unit 1: Prisms

Vocabulary, Formulas, and Right Rectangular Prisms

Advanced Right Prisms

Unit 2: Pyramids

Vocabulary, Formulas, and Regular Square Pyramids

Advanced Regular Pyramids

Unit 3: Cylinders, Cones, and Spheres

Cylinders and Cones

Spheres

CHAPTER 25: PROBABILITY AND COUNTING

Unit 1: Probability

Simple Probability

Probability of Independent Events

Probability of Dependent Events

Unit 2: Counting Methods

Tree Diagrams and the Counting Principle

Permutations

Combinations

CHAPTER 26: COORDINATE GEOMETRY

Unit 1: Segments in the Coordinate Plane

Distance Formula

Midpoint Formula

Unit 2: Circles in the Coordinate Plane

Equation of a Circle

CHAPTER 27: NEGATIVE & RATIONAL EXPONENTS

Unit 1: Simplifying Expressions with Negative Exponents

Negative Exponents

Negative Exponent Rules

Multiplying and Dividing with Negative Exponents

Unit 2: Operations with Scientific Notation

Multiplying and Dividing Scientific Notation

Unit 3: Rational Exponents and Radical Expressions

Rational Exponents

Fractional Exponents

Writing Radicals in Exponential Form

Unit 4: Equations with Rational Exponents and Simplifying with Radical Exponents

Solving Equations with Rational Exponents

Radical Exponents

CHAPTER 28: COMPOSITE FUNCTIONS & INVERSES

Unit 1: Composite Functions

Composite Functions: f(g(x)) and g(f(x))

Unit 2: Inverses

Inverse Relations

Inverse Functions

CHAPTER 29: LOGARITHMS & EXPONENTIAL FUNCTIONS

Unit 1: Introduction to Logarithms

Logarithms and Logarithmic Functions

Solving Logarithmic Equations

Unit 2: Properties of Logarithms

Logarithm Rules and Properties

Evaluating Logarithms by Condensing or Expanding

Solving Advanced Log Equations

Unit 3: Evaluating Logarithms with a Calculator

Log Calculator Problems

Unit 4: Exponential Equations and Logarithms

Exponential Equations and Change of Base Formula

Exponential Growth and Decay

Half Life Formula and Doubling Time Formula

Unit 5: The Natural Logarithm

Natural Logarithms

Solving Natural Logarithm Equations with ln and e