Solidify your arithmetic, learn about variables and graphs, level up your algebra, and learn the essentials of geometry.

- Use number lines to visualize addition, subtraction, and negative numbers.
- Leverage equivalent fractions as a strategy to add and subtract fractions.
- Generalize previous understandings of multiplication and division to multiply and divide fractions.
- Interpret exponents as repeated multiplication and radicals as the opposite of exponents.
- Understand the relationship between fractional exponents and radicals.
- Apply the order of operations to evaluate arithmetic expressions.

- Convert between units of measurement and compute unit rates.
- Understand the relationship between whole, part, and percentage.

- Express a composite integer as the product of its prime factors.
- Leverage prime factorization as a strategy to compute greatest common factors and least common multiples.

- Understand the concept of a variable as a placeholder in a mathematical expression or verbal phrase.
- Create equations that describe relationships between quantities.
- Understand rules of algebra as a process of reasoning and use them to solve linear equations, inequalities, and systems.
- Relate the solutions of two-variable equations and inequalities to graphs in the coordinate plane.
- Set up and solve systems of linear equations in real-world modeling contexts.

- Leverage multiplication as a strategy to transform rational equations into linear equations.
- Extend knowledge of radicals and solving linear equations to handle cases when the variable is raised to a power.
- Relate absolute value to distance on the number line and apply this understanding to solve absolute value equations and inequalities.

- Leverage the distributive property and an understanding of like terms to manipulate polynomial expressions.
- Understand the relationship between multiplication and factoring and apply a systematic method to factor trinomials with leading coefficients.

- Identify, interpret, and build functions that model relationships between two quantities.
- Represent and reason about functions using formal notation.
- Visualize functions in the coordinate plane by graphing.

- Classify triangles and quadrilaterals based on their properties.
- Use geometric relationships to solve for unknown angle measures and side lengths.
- Compute area and perimeter of circles, triangles, and various types of quadrilaterals.
- Calculate side lengths and areas of special right triangles using geometric reasoning and the Pythagorean theorem.

1.

Fractions
41 topics

1.1. Adding and Subtracting Fractions and Whole Numbers

1.1.1. | Adding Fractions and Whole Numbers Using Models | |

1.1.2. | Adding Fractions and Whole Numbers | |

1.1.3. | Subtracting Fractions and Whole Numbers Using Models | |

1.1.4. | Subtracting Fractions and Whole Numbers |

1.2. Adding and Subtracting Fractions

1.2.1. | Least Common Multiples | |

1.2.2. | Least Common Denominators | |

1.2.3. | Comparing Fractions Using Common Denominators | |

1.2.4. | Adding Fractions With Unlike Denominators Using Models | |

1.2.5. | Subtracting Fractions With Unlike Denominators Using Models | |

1.2.6. | Adding Fractions With Unlike Denominators | |

1.2.7. | Subtracting Fractions With Unlike Denominators |

1.3. Adding and Subtracting Mixed Numbers

1.3.1. | Adding Mixed Numbers With Unlike Denominators | |

1.3.2. | Subtracting Mixed Numbers With Unlike Denominators | |

1.3.3. | Subtracting Mixed Numbers With Unlike Denominators Using Improper Fractions |

1.4. Multiplying Fractions

1.4.1. | Multiplying Unit Fractions by Whole Numbers Using Models | |

1.4.2. | Multiplying Fractions by Whole Numbers Using Models | |

1.4.3. | Multiplying Fractions by Whole Numbers | |

1.4.4. | Multiplying Fractions by Whole Numbers: Word Problems | |

1.4.5. | Strategies to Simplify Whole Number and Fraction Multiplication | |

1.4.6. | Multiplying Mixed Numbers by Whole Numbers | |

1.4.7. | Multiplying Fractions by Unit Fractions Using Models | |

1.4.8. | Multiplying Fractions Using Models | |

1.4.9. | Multiplying Fractions | |

1.4.10. | Multiplying Fractions: Word Problems | |

1.4.11. | Multiplying Mixed Numbers by Fractions | |

1.4.12. | Multiplying Mixed Numbers | |

1.4.13. | Multiplying Mixed Numbers: Word Problems | |

1.4.14. | Connecting Fraction Multiplication and Area | |

1.4.15. | Finding Areas Using Fraction Multiplication |

1.5. Dividing Fractions

1.5.1. | Interpreting Fraction Division Using Area Models | |

1.5.2. | Dividing Whole Numbers by Unit Fractions Using Models | |

1.5.3. | Dividing Whole Numbers by Unit Fractions | |

1.5.4. | Dividing Unit Fractions by Whole Numbers Using Models | |

1.5.5. | Dividing Unit Fractions by Whole Numbers | |

1.5.6. | Reciprocals | |

1.5.7. | Dividing Whole Numbers by Fractions Using Models | |

1.5.8. | Dividing Whole Numbers by Fractions | |

1.5.9. | Dividing Fractions by Whole Numbers Using Models | |

1.5.10. | Dividing Fractions by Whole Numbers | |

1.5.11. | Dividing Fractions Using Models | |

1.5.12. | Dividing Fractions |

2.

Ratios & Percentages
28 topics

2.6. Ratios

2.6.1. | Introduction to Ratios | |

2.6.2. | Equivalent Ratios | |

2.6.3. | Writing Ratios Using Fractions | |

2.6.4. | Ratio Tables | |

2.6.5. | Graphing Ratios | |

2.6.6. | Unit Rates | |

2.6.7. | Solving Problems Using Unit Rates | |

2.6.8. | Speed as a Unit Rate |

2.7. Working With Units

2.7.1. | Units | |

2.7.2. | Units of Area and Volume | |

2.7.3. | Unit Conversions Using Base Units of Mass | |

2.7.4. | Two-Step Unit Conversions | |

2.7.5. | Unit Conversions Using Base Units of Length | |

2.7.6. | Unit Conversions Using Units of Time | |

2.7.7. | Converting Units of Area to Smaller Units | |

2.7.8. | Converting Units of Area to Larger Units | |

2.7.9. | Determining Units in Formulas | |

2.7.10. | Selecting Units for Rates of Change | |

2.7.11. | Degrees of Accuracy |

2.8. Percentages

2.8.1. | Understanding Percentages Using Models | |

2.8.2. | Converting Between Percentages and Fractions | |

2.8.3. | Converting Between Percentages and Decimals | |

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

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

2.8.6. | Finding a Percentage Given Two Numbers | |

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

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

2.8.9. | Percentage Increase, Decrease, and Error |

3.

The Number System
22 topics

3.9. Addition and Subtraction of Rational Numbers

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

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

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

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

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

3.9.6. | Adding a Negative Number | |

3.9.7. | Subtracting a Negative Number | |

3.9.8. | Additive Inverses of Numbers | |

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

3.9.10. | Absolute Value |

3.10. Multiplication and Division of Rational Numbers

3.10.1. | Multiplying Positive Numbers With Negative Numbers | |

3.10.2. | Multiplying Negative Numbers | |

3.10.3. | Dividing With Negative Numbers | |

3.10.4. | Dividing With Negative Decimals and Fractions | |

3.10.5. | Reciprocals of Rational Numbers | |

3.10.6. | Multiplying and Dividing With Zero | |

3.10.7. | Fractions of Fractions | |

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

3.11. Number Theory

3.11.1. | Prime and Composite Numbers | |

3.11.2. | Prime Factorization of Integers | |

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

3.11.4. | Finding Lowest Common Multiples Using Prime Factorization |

4.

Exponents & Radicals
32 topics

4.12. Exponents

4.12.1. | Introduction to Exponents | |

4.12.2. | Evaluating Exponents | |

4.12.3. | Evaluating Larger Exponents | |

4.12.4. | Evaluating Exponents With Fractional Bases | |

4.12.5. | Evaluating Exponents With Decimal Bases | |

4.12.6. | Evaluating Whole Number Expressions Containing Exponents | |

4.12.7. | Squaring Rational Numbers | |

4.12.8. | Cubing Rational Numbers | |

4.12.9. | Exponents With Rational Bases | |

4.12.10. | The Zeroth Power | |

4.12.11. | Powers of Negative One | |

4.12.12. | Negative Exponents |

4.13. The Rules of Exponents

4.13.1. | The Product Rule for Exponents | |

4.13.2. | The Quotient Rule for Exponents | |

4.13.3. | The Power Rule for Exponents | |

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

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

4.13.6. | Combining the Rules of Exponents |

4.14. Order of Operations

4.14.1. | Evaluating Rational Number Expressions Without Exponents | |

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

4.14.3. | Evaluating Rational Number Expressions With Integer Exponents |

4.15. Radicals

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

4.15.2. | Squaring a Square Root | |

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

4.15.4. | Surds | |

4.15.5. | Simplifying Expressions With Surds | |

4.15.6. | Evaluating Numerical Expressions Containing Radicals | |

4.15.7. | Adding and Subtracting Radicals | |

4.15.8. | Rationalizing Denominators |

4.16. The Rules of Radicals

4.16.1. | Radicals as Fractional Exponents | |

4.16.2. | The Product Rule for Radicals | |

4.16.3. | The Quotient Rule for Radicals |

6.

Equations & Inequalities
49 topics

6.17. Algebraic Expressions

6.17.1. | Introduction to Algebraic Expressions | |

6.17.2. | Constructing Algebraic Expressions | |

6.17.3. | Evaluating Linear Expressions | |

6.17.4. | Evaluating Rational Expressions | |

6.17.5. | Identifying Terms in Linear Expressions | |

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

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

6.18. Simplifying Linear Expressions

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

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

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

6.18.4. | The Distributive Law With Three Terms | |

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

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

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

6.18.8. | Simplifying Linear Expressions Containing Fractions | |

6.18.9. | Factoring Linear Expressions |

6.19. Solving One-Step Linear Equations

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

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

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

6.20. Solving Multi-Step Linear Equations

6.20.1. | Solving Two-Step Equations | |

6.20.2. | Solving Linear Equations With Fractional Coefficients | |

6.20.3. | Solving Linear Equations With Decimal Coefficients | |

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

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

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

6.20.7. | Solving Two-Variable Equations | |

6.20.8. | Equations With Many Solutions and No Solutions | |

6.20.9. | Solving Linear Equations With Unknown Coefficients | |

6.20.10. | Solving Linear Equations With Unknown Coefficients by Factoring | |

6.20.11. | Solving Many-Variable Equations |

6.21. Modeling With Linear Equations

6.21.1. | Interpreting Linear Expressions | |

6.21.2. | Modeling With Linear Equations |

6.22. Solving Linear Inequalities

6.22.1. | Inequalities | |

6.22.2. | Compound Inequalities | |

6.22.3. | Verifying Solutions of Linear Inequalities | |

6.22.4. | Solving One-Step Linear Inequalities | |

6.22.5. | Solving Two-Step Inequalities | |

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

6.22.7. | Further Solving Linear Inequalities | |

6.22.8. | Solving Compound Inequalities | |

6.22.9. | Interval Notation | |

6.22.10. | Unbounded Intervals | |

6.22.11. | Unions of Intervals | |

6.22.12. | Intersections of Intervals | |

6.22.13. | Compound OR Inequalities | |

6.22.14. | Compound AND Inequalities |

6.23. Nonlinear Equations

6.23.1. | Solving Equations Using the Square Root Method | |

6.23.2. | Solving Equations With Odd Exponents Using the Nth Root Method | |

6.23.3. | Solving Equations With Even Exponents Using the Nth Root Method |

7.

Two-Variable Equations
22 topics

7.24. Graphs of Linear Equations

7.24.1. | The Cartesian Coordinate System | |

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

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

7.24.4. | Graphing Linear Equations | |

7.24.5. | Horizontal and Vertical Lines | |

7.24.6. | Calculating Slopes of Straight Lines | |

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

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

7.24.9. | Equations of Lines in Point-Slope Form | |

7.24.10. | Equations of Lines in Standard Form | |

7.24.11. | Determining Properties of Lines Given in Standard Form |

7.25. Modeling With Two-Variable Linear Equations

7.25.1. | Modeling With Linear Equations in Two Variables | |

7.25.2. | Further Modeling With Linear Equations in Two Variables | |

7.25.3. | Analyzing and Interpreting Graphs of Linear Equations |

7.26. Systems of Linear Equations

7.26.1. | Introduction to Systems of Linear Equations | |

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

7.26.3. | Solving Systems of Two Linear Equations Using Elimination | |

7.26.4. | Systems of Linear Equations With Fractional Coefficients | |

7.26.5. | Systems of Linear Equations With Decimal Coefficients | |

7.26.6. | Solving Systems of Nonlinear Equations Using Graphs | |

7.26.7. | Systems of Equations With No Solutions and Infinitely Many Solutions | |

7.26.8. | Calculating the Intersection of Two Lines |

8.

Radical & Rational Expressions
16 topics

8.27. Radical Expressions

8.27.1. | Writing Radical Expressions Using Fractional Exponents | |

8.27.2. | The Square Root of a Perfect Square With Algebraic Expressions | |

8.27.3. | The Square Root of a Perfect Square With Domain Restrictions | |

8.27.4. | The Cube Root of a Perfect Cube With Algebraic Expressions | |

8.27.5. | Simplifying Square Root Expressions Using the Product Rule | |

8.27.6. | Combining Radical Expressions Using the Product Rule | |

8.27.7. | Evaluating Algebraic Radical Expressions | |

8.27.8. | Adding and Subtracting Radical Expressions |

8.28. Rational Expressions

8.28.1. | Equivalent Expressions With Fractions | |

8.28.2. | Simplifying Rational Expressions | |

8.28.3. | Simplifying Rational Expressions by Factoring | |

8.28.4. | Splitting Rational Expressions Into Separate Terms |

8.29. Rational Equations

8.29.1. | Solving Rational Equations Containing One Fractional Term | |

8.29.2. | Solving Rational Equations Using Cross-Multiplication | |

8.29.3. | Solving Rational Equations Containing Binomials Using Cross-Multiplication | |

8.29.4. | Solving Rational Equations Using the Flip Method |

9.

Functions
12 topics

9.30. Functions

9.30.1. | Introduction to Functions | |

9.30.2. | Visual Representations of Functions | |

9.30.3. | Graphs of Functions | |

9.30.4. | The Domain of a Function | |

9.30.5. | Global Extrema of Functions | |

9.30.6. | End Behavior of Functions | |

9.30.7. | The Range of a Function | |

9.30.8. | The Range of a Function: Advanced Cases | |

9.30.9. | The Roots of a Function | |

9.30.10. | Increasing and Decreasing Functions | |

9.30.11. | Piecewise Functions | |

9.30.12. | Modeling With Linear Functions |

10.

Absolute Value
7 topics

10.31. Absolute Value Expressions, Equations & Inequalities

10.31.1. | Absolute Value Expressions | |

10.31.2. | Rules of Absolute Value | |

10.31.3. | Further Rules of Absolute Value | |

10.31.4. | Absolute Value Equations | |

10.31.5. | Further Absolute Value Equations | |

10.31.6. | Absolute Value Inequalities | |

10.31.7. | Absolute Value Graphs |

11.

Exponential Functions
17 topics

11.32. Rules of Exponents

11.32.1. | The Product Rule for Exponents With Algebraic Expressions | |

11.32.2. | The Quotient Rule for Exponents With Algebraic Expressions | |

11.32.3. | The Power Rule for Exponents With Algebraic Expressions | |

11.32.4. | The Power of Product Rule With Algebraic Expressions | |

11.32.5. | The Power of Quotient Rule With Algebraic Expressions |

11.33. Exponential Expressions and Equations

11.33.1. | Solving Exponential Equations with Integer Solutions | |

11.33.2. | Creating Exponential Growth Expressions | |

11.33.3. | Creating Exponential Decay Expressions |

11.34. Exponential Functions

11.34.1. | Exponential Functions | |

11.34.2. | Modeling Exponential Growth With Functions | |

11.34.3. | Interpreting Exponential Growth | |

11.34.4. | Solving Exponential Growth Problems | |

11.34.5. | Modeling Exponential Decay With Functions | |

11.34.6. | Interpreting Exponential Decay | |

11.34.7. | Solving Exponential Decay Problems | |

11.34.8. | Graphing Exponential Growth Functions | |

11.34.9. | Graphing Exponential Decay Functions |

12.

Polynomials
19 topics

12.35. Polynomials

12.35.1. | Introduction to Polynomials | |

12.35.2. | The Degree of a Polynomial | |

12.35.3. | Simplifying Polynomials | |

12.35.4. | The Distributive Law for Polynomials | |

12.35.5. | Adding and Subtracting Polynomials | |

12.35.6. | Monomials, Binomials and Trinomials | |

12.35.7. | Multiplying Binomials | |

12.35.8. | Multiplying Polynomials | |

12.35.9. | Squaring Binomials | |

12.35.10. | Expanding Binomials Using Pascal's Triangle | |

12.35.11. | The Difference of Squares Formula |

12.36. Factoring Polynomials

12.36.1. | The Greatest Common Factor of Two Monomials | |

12.36.2. | Factoring Simple Polynomials Using Greatest Common Factors | |

12.36.3. | Factoring Perfect Square Trinomials | |

12.36.4. | Factoring Perfect Square Trinomials With Leading Coefficients | |

12.36.5. | Factoring Differences of Squares | |

12.36.6. | Factoring Trinomials | |

12.36.7. | Factoring Trinomials Using Common Factors | |

12.36.8. | Factoring Trinomials With Leading Coefficients |

13.

Geometry Fundamentals
23 topics

13.37. Introduction to Geometry

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

13.37.2. | Parallel and Perpendicular Lines | |

13.37.3. | Measures of Segments | |

13.37.4. | Congruent Segments | |

13.37.5. | Midpoints | |

13.37.6. | Collinear Points | |

13.37.7. | The Segment Addition Postulate |

13.38. Angles

13.38.1. | Angles and Measures of Angles | |

13.38.2. | Measuring Angles Using a Protractor | |

13.38.3. | Sums of Angles | |

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

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

13.38.6. | Congruent Angles | |

13.38.7. | Vertical Angles | |

13.38.8. | Solving Problems With Angles |

13.39. Advanced Angles

13.39.1. | Complementary Angles | |

13.39.2. | Supplementary Angles | |

13.39.3. | Parallel Lines and Transversals | |

13.39.4. | Perpendicular Lines and Bisectors |

13.40. Circles

13.40.1. | Introduction to Circles | |

13.40.2. | Arcs, Segments, and Sectors of Circles | |

13.40.3. | The Circumference of a Circle | |

13.40.4. | Areas of Circles |

14.

Polygons
20 topics

14.41. Triangles

14.41.1. | Interior Angles of Triangles | |

14.41.2. | Exterior Angles of Triangles | |

14.41.3. | Classifying Triangles | |

14.41.4. | The Triangle Inequality | |

14.41.5. | The Isosceles Triangle Theorem | |

14.41.6. | Heights of Triangles | |

14.41.7. | The Pythagorean Theorem | |

14.41.8. | The 45-45-90 Triangle | |

14.41.9. | The 30-60-90 Triangle |

14.42. Polygons

14.42.1. | Polygons | |

14.42.2. | Interior Angles of Polygons | |

14.42.3. | Exterior Angles of Polygons | |

14.42.4. | Congruent Polygons | |

14.42.5. | Regular Polygons | |

14.42.6. | The Perimeter of a Polygon | |

14.42.7. | Classifying Quadrilaterals | |

14.42.8. | Properties of Rectangles and Squares |

14.43. Area and Perimeter

14.43.1. | Areas of Rectangles and Squares | |

14.43.2. | Areas of Triangles | |

14.43.3. | Areas of Trapezoids |