Further your understanding of arithmetic and geometry, learn about variables, and solve linear equations, inequalities, and systems.

- Understand exponents as repeated multiplication and radicals as the opposite of exponents.
- Simplify arithmetic expressions involving radicals and exponents using the order of operations.
- Understand the relationship between fractional exponents and radicals.

- Use geometric relationships to solve for unknown angle measures and side lengths.
- Compute area and perimeter of various types of quadrilaterals.

- Understand the concept of a variable as a placeholder in a mathematical expression or verbal phrase.
- Understand rules of algebra as a process of reasoning and use them to solve linear equations, inequalities, and systems.
- Visualize linear equations by graphing.

- Use proportions and rates of change to solve real-world problems.
- Summarize, represent, and interpret real-world data using statistical measures and graphical visualizations.

1.

Ratios & Percentages
24 topics

1.1. Ratios

1.1.1. | Introduction to Ratios | |

1.1.2. | Equivalent Ratios | |

1.1.3. | Writing Ratios Using Fractions | |

1.1.4. | Working With Equivalent Ratios | |

1.1.5. | More on Equivalent Ratios | |

1.1.6. | Ratio Tables | |

1.1.7. | Graphing Ratios |

1.2. Unit Rates

1.2.1. | Unit Rates | |

1.2.2. | Solving Problems Using Unit Rates | |

1.2.3. | Speed as a Unit Rate | |

1.2.4. | Calculating Unit Rates Associated With Ratios of Fractions | |

1.2.5. | Solving Unit Rate Problems Using Ratios of Fractions |

1.3. Proportional Relationships

1.3.1. | Understanding Proportional Relationships Using Tables | |

1.3.2. | Understanding Proportional Relationships Using Graphs | |

1.3.3. | Understanding Proportional Relationships From Descriptions |

1.4. Percentages

1.4.1. | Understanding Percentages Using Models | |

1.4.2. | Converting Between Percentages and Fractions | |

1.4.3. | Converting Between Percentages and Decimals | |

1.4.4. | Finding Part of a Number Given a Whole and a Percentage | |

1.4.5. | Finding Part of a Number Given a Whole and a Percentage: Word Problems | |

1.4.6. | Finding a Percentage Given Two Numbers | |

1.4.7. | Finding a Percentage Given Two Numbers: Word Problems | |

1.4.8. | Finding a Total Given a Part and a Percentage | |

1.4.9. | Percentage Increase, Decrease, and Error |

2.

The Number System
25 topics

2.5. Addition and Subtraction of Rational Numbers

2.5.1. | Subtracting a Positive Number From a Smaller Positive Number | |

2.5.2. | Subtracting a Positive Number From a Negative Number | |

2.5.3. | Subtracting a Positive Fraction From a Smaller Fraction | |

2.5.4. | Subtracting a Positive Decimal From a Smaller Decimal | |

2.5.5. | Adding a Positive Number to a Negative Number | |

2.5.6. | Adding a Negative Number | |

2.5.7. | Subtracting a Negative Number | |

2.5.8. | Additive Inverses of Numbers | |

2.5.9. | Solving Problems Using Addition and Subtraction of Rational Numbers |

2.6. Multiplication and Division of Rational Numbers

2.6.1. | Multiplying Positive Numbers With Negative Numbers | |

2.6.2. | Multiplying Negative Numbers | |

2.6.3. | Dividing With Negative Numbers | |

2.6.4. | Equivalent Fractions With Negative Numbers | |

2.6.5. | Dividing With Negative Decimals and Fractions | |

2.6.6. | Reciprocals of Rational Numbers | |

2.6.7. | Multiplying and Dividing With Zero | |

2.6.8. | Fractions of Fractions | |

2.6.9. | Solving Problems Using the Four Operations on Rational Numbers |

2.7. Number Theory

2.7.1. | Natural Numbers, Integers, and Rational Numbers | |

2.7.2. | Prime and Composite Numbers | |

2.7.3. | Prime Factorization of Integers | |

2.7.4. | Finding Greatest Common Factors Using Prime Factorization | |

2.7.5. | Finding Lowest Common Multiples Using Prime Factorization | |

2.7.6. | Divisibility of Integers | |

2.7.7. | Divisibility of Integers by 3, 9 and 6 |

3.

Exponents & Radicals
35 topics

3.8. Exponents

3.8.1. | Squaring Rational Numbers | |

3.8.2. | Cubing Rational Numbers | |

3.8.3. | Exponents With Rational Bases | |

3.8.4. | The Zeroth Power | |

3.8.5. | Powers of Negative One | |

3.8.6. | Negative Exponents |

3.9. The Rules of Exponents

3.9.1. | The Product Rule for Exponents | |

3.9.2. | The Quotient Rule for Exponents | |

3.9.3. | The Power Rule for Exponents | |

3.9.4. | The Power of Product Rule for Exponents | |

3.9.5. | The Power of Quotient Rule for Exponents | |

3.9.6. | Combining the Rules of Exponents |

3.10. Scientific Notation

3.10.1. | Writing Numbers in Scientific Notation | |

3.10.2. | Converting Scientific Notation to Standard Notation | |

3.10.3. | Comparing Numbers in Scientific Notation | |

3.10.4. | Addition and Subtraction in Scientific Notation | |

3.10.5. | Addition in Scientific Notation With Different Powers of Ten | |

3.10.6. | Subtraction in Scientific Notation With Different Powers of Ten | |

3.10.7. | Further Addition in Scientific Notation With Different Powers of Ten | |

3.10.8. | Multiplying Numbers in Scientific Notation | |

3.10.9. | Dividing Numbers in Scientific Notation |

3.11. Order of Operations

3.11.1. | Evaluating Rational Number Expressions Without Exponents | |

3.11.2. | Evaluating Rational Number Expressions With Positive Integer Exponents | |

3.11.3. | Evaluating Rational Number Expressions With Integer Exponents |

3.12. Radicals

3.12.1. | The Square Root of a Perfect Square | |

3.12.2. | Squaring a Square Root | |

3.12.3. | The Cube Root of a Perfect Cube | |

3.12.4. | Surds | |

3.12.5. | Simplifying Expressions With Surds | |

3.12.6. | Evaluating Numerical Expressions Containing Radicals | |

3.12.7. | Adding and Subtracting Radicals | |

3.12.8. | Rationalizing Denominators |

3.13. The Rules of Radicals

3.13.1. | Radicals as Fractional Exponents | |

3.13.2. | The Product Rule for Radicals | |

3.13.3. | The Quotient Rule for Radicals |

4.

Algebraic Expressions
17 topics

4.14. Algebraic Expressions

4.14.1. | Introduction to Algebraic Expressions | |

4.14.2. | Constructing Algebraic Expressions | |

4.14.3. | Evaluating Linear Expressions | |

4.14.4. | Evaluating Rational Expressions | |

4.14.5. | Identifying Terms in Linear Expressions | |

4.14.6. | Identifying Coefficients and Constants in Linear Expressions | |

4.14.7. | The Greatest Common Factor of Two Linear Expressions |

4.15. Simplifying Linear Expressions

4.15.1. | Identifying Like Terms in a Linear Expression | |

4.15.2. | Collecting Like Terms in a Linear Expression | |

4.15.3. | Applying the Distributive Law With Linear Expressions | |

4.15.4. | The Distributive Law With Three Terms | |

4.15.5. | Distributing the Negative Sign in a Linear Expression | |

4.15.6. | Simplifying Linear Expressions Using the Distributive Law | |

4.15.7. | Simplifying Linear Expressions When a Group of Terms Is Subtracted | |

4.15.8. | Simplifying Linear Expressions Containing Fractions | |

4.15.9. | Factoring Numerical Expressions | |

4.15.10. | Factoring Linear Expressions |

5.

Equations & Inequalities
28 topics

5.16. Solving One-Step Linear Equations

5.16.1. | Solving Linear Equations by Trial and Error | |

5.16.2. | Solving One-Step Addition and Subtraction Equations | |

5.16.3. | Solving One-Step Multiplication and Division Equations |

5.17. Solving Multi-Step Linear Equations

5.17.1. | Solving Two-Step Equations | |

5.17.2. | Solving Linear Equations With Fractional Coefficients | |

5.17.3. | Solving Linear Equations With Decimal Coefficients | |

5.17.4. | Solving Linear Equations With Variables on Both Sides | |

5.17.5. | Solving Linear Equations by Clearing a Rational Expression | |

5.17.6. | Solving Linear Equations Using Cross-Multiplication | |

5.17.7. | Solving Two-Variable Equations | |

5.17.8. | Equations With Many Solutions and No Solutions |

5.18. Solving Linear Inequalities

5.18.1. | Inequalities | |

5.18.2. | Compound Inequalities | |

5.18.3. | Verifying Solutions of Linear Inequalities | |

5.18.4. | Solving One-Step Linear Inequalities | |

5.18.5. | Solving Two-Step Inequalities | |

5.18.6. | Representing Solutions to Inequalities on Number Lines | |

5.18.7. | Further Solving Linear Inequalities |

5.19. Graphs of Linear Equations

5.19.1. | The Cartesian Coordinate System | |

5.19.2. | The Distance Between Two Points in the Coordinate Plane | |

5.19.3. | Two-Variable Linear Equations and Their Solutions | |

5.19.4. | Graphing Linear Equations | |

5.19.5. | Horizontal and Vertical Lines | |

5.19.6. | Calculating Slopes of Straight Lines | |

5.19.7. | Equations of Lines in Slope-Intercept Form | |

5.19.8. | Finding Properties of Lines Given in Slope-Intercept Form |

5.20. Systems of Equations

5.20.1. | Introduction to Systems of Linear Equations | |

5.20.2. | Solving Systems of Two Linear Equations Using Substitution |

6.

Geometry
47 topics

6.21. Introduction to Geometry

6.21.1. | Units of Area and Volume | |

6.21.2. | Points, Lines, Rays, and Segments | |

6.21.3. | Parallel and Perpendicular Lines | |

6.21.4. | Measures of Segments | |

6.21.5. | Congruent Segments | |

6.21.6. | Midpoints | |

6.21.7. | Collinear Points | |

6.21.8. | The Segment Addition Postulate |

6.22. Angles

6.22.1. | Angles and Measures of Angles | |

6.22.2. | Connecting Angles and Circles | |

6.22.3. | Measuring Angles Using a Protractor | |

6.22.4. | Sums of Angles | |

6.22.5. | Right, Straight, Full, and Null Angles | |

6.22.6. | Acute, Obtuse, and Reflex Angles | |

6.22.7. | Congruent Angles | |

6.22.8. | Vertical Angles | |

6.22.9. | Solving Problems With Angles |

6.23. Advanced Angles

6.23.1. | Complementary Angles | |

6.23.2. | Supplementary Angles | |

6.23.3. | Corresponding Angles | |

6.23.4. | Alternate Angles | |

6.23.5. | Consecutive Angles | |

6.23.6. | Angle Criteria for Parallel Lines | |

6.23.7. | Angle Bisectors | |

6.23.8. | Perpendicular Lines and Bisectors |

6.24. Triangles

6.24.1. | Interior Angles of Triangles | |

6.24.2. | Exterior Angles of Triangles | |

6.24.3. | Problem Solving With Angles of Triangles | |

6.24.4. | Classifying Triangles | |

6.24.5. | The Triangle Inequality | |

6.24.6. | The Isosceles Triangle Theorem | |

6.24.7. | Heights of Triangles |

6.25. Polygons

6.25.1. | Polygons | |

6.25.2. | Interior Angles of Polygons | |

6.25.3. | Exterior Angles of Polygons | |

6.25.4. | Congruent Polygons | |

6.25.5. | Regular Polygons | |

6.25.6. | The Perimeter of a Polygon |

6.26. Quadrilaterals

6.26.1. | Classifying Quadrilaterals | |

6.26.2. | Properties of Rectangles and Squares | |

6.26.3. | Properties of Trapezoids |

6.27. Area and Perimeter

6.27.1. | Areas of Rectangles and Squares | |

6.27.2. | Areas of Parallelograms | |

6.27.3. | Areas of Triangles | |

6.27.4. | Areas of Trapezoids | |

6.27.5. | Areas and Perimeters of Composite Shapes | |

6.27.6. | The Area Between Two Shapes |

7.

Statistics
20 topics

7.28. Summarizing Data

7.28.1. | Introduction to Statistics | |

7.28.2. | The Mean of a Data Set | |

7.28.3. | The Median of a Data Set | |

7.28.4. | The Mode of a Data Set | |

7.28.5. | Range, Quartiles and Interquartile Range | |

7.28.6. | Mean Absolute Deviation | |

7.28.7. | Comparing Data Sets Using Measures of Centrality | |

7.28.8. | Comparing Data Sets Using Measures of Spread | |

7.28.9. | Outliers | |

7.28.10. | Removing Outliers |

7.29. Representing Data

7.29.1. | Frequency Tables | |

7.29.2. | Dot Plots | |

7.29.3. | Measuring Centrality Using Dot Plots | |

7.29.4. | Measuring Range and MAD From Dot Plots | |

7.29.5. | Measuring Quartiles and IQR From Dot Plots | |

7.29.6. | Interpreting Shapes of Distributions Using Dot Plots | |

7.29.7. | Box Plots | |

7.29.8. | Histograms | |

7.29.9. | Comparing Measures of Center | |

7.29.10. | Comparing Measures of Spread |