Our SAT Math Fundamentals course provides students with the core content knowledge required in the math section of the SAT exam. Filling in missing gaps is the first and most important step towards preparing for the exam as lacking any of these skills will be exposed and reflected in the student's score.

However, to achieve the best possible outcome, students must also dedicate time to a structured and intentional test preparation process, which we describe in this article on how to prepare for a standardized math test.

This course covers the core skills outlined in the SAT Math curriculum.

Students begin by taking a diagnostic assessment, which will identify their current knowledge frontier and any weaknesses in their foundational knowledge.

Once the student has completed the diagnostic assessment, our sophisticated algorithms will create a custom course that addresses any foundational weaknesses along with a plan for building on their existing strengths to attain the highest possible score.

The following data gives the composition of the SAT Math Fundamentals course against the traditional math sequence.

- Prealgebra: 39%
- Algebra I: 39%
- Geometry: 19%
- Algebra II: 3%

For example, 39% of the topics in the SAT Math Fundamentals course are from Prealgebra.

The data below describes the proportion of each high school course whose topics feature in SAT Math Fundamentals.

- Prealgebra: 90%
- Algebra I: 82%
- Geometry: 63%
- Algebra II: 9%

For example, a student who's completed SAT Math Fundamentals will have completed at least 90% of Prealgebra.

The following data gives the composition of the SAT Math Fundamentals course against the integrated sequence.

- Prealgebra: 39%
- Integrated Math I: 37%
- Integrated Math II: 24%

For example, 37% of the topics in the SAT Math Fundamentals course are from Integrated Math I.

The data below describes the proportion of each high school course whose topics feature in SAT Math Fundamentals.

- Prealgebra: 90%
- Integrated Math I: 81%
- Integrated Math II: 37%

For example, a student who's completed the SAT Math Fundamentals course will have completed at least 81% of Integrated Math I.

- Addition, subtraction, multiplication, and division with rational numbers, and solving real-world and mathematical problems involving these operations.
- Manipulating expressions involving exponents and radicals, fractional and negative exponents, and the rules of exponents and radicals.
- Applying the order of operations to evaluate complex expressions containing rational numbers, fractional and negative exponents, and radicals.
- Constructing, evaluating, simplifying, and factoring linear algebraic expressions.

- Solving one-step and multi-step linear equations, including cases involving rational expressions, cross-multiplication, unknown coefficients, and multiple variables.
- Using linear equations to model and solve real-world and mathematical problems.

- Graphing linear equations, calculating and describing a graph's key features.
- Working with slope-intercept, point-slope, and standard forms of straight line equations and determining properties of lines presented in these forms.
- Finding equations of parallel and perpendicular lines.
- Using two-variable equations to solve contextual problems, including problems involving speed, distance, time, and acceleration.
- Solving two-variable systems of linear equations using substitution and elimination, including cases with fractional and decimal coefficients, systems with no solutions or infinitely many solutions, and explaining how the solutions relate to the intersection of two lines.
- Using two-variable systems to model and solve contextual problems.

- Solving single-variable linear inequalities, compound inequalities, and systems of inequalities and graphing their solutions.
- Interval notation, including unions and intersections.
- Solving two-variable linear inequalities and systems of inequalities using a graphical method.
- Using single-variable and two-variable inequalities in real-world modeling contexts.

- Understanding and applying basic geometry concepts, including working with segments, angles, and their properties.
- Solve problems involving complementary, supplementary, corresponding, alternate, and consecutive angles.

- Solving problems with interior and exterior angles of triangles.
- Classifying triangles and applying the isosceles triangle theorem.
- Understanding and applying terminology related to geometry in three dimensions and identifying common three-dimensional shapes.

- Applying the ASA, SAS, AAS, SSS, and HL congruence criteria, and the AA, SSS, and SAS similarity criteria.
- Applying the midpoint and proportionality theorems.
- Solving problems related to polygon and solid similarity, including area and volume scale factors.

- Calculating perimeters and areas of polygons in the plane.
- Applying the distance and midpoint formulas.
- Solving problems related to the surface area and volume of three-dimensional figures, including cubes, rectangular solids, pyramids, cylinders, cones, and spheres.

- Circle fundamentals: interiors and exteriors of circles, circular arcs, sectors, and segments.
- Calculating circumferences and areas of circles and circular sectors.
- Solving problems involving tangent lines to circles.
- Working with radians, including converting between radians and degrees and using radians to calculate arc lengths and areas of sectors.
- Equations of circles in the coordinate plane, including techniques for determining properties of circles from their algebraic equations.

- The Pythagorean theorem and its converse.
- The 45-45-90 and 30-60-90 special right triangles.
- Using trigonometric ratios to calculate side lengths and angle measures in right triangles.
- Using the special trigonometric ratios and the relationship between sine and cosine in terms of cofunctions.
- Modeling and solving real-world problems using trigonometry.

- Functions essentials, including representations of functions, the vertical line test, domain, range, global and local extrema, roots, end-behavior, increasing and decreasing functions, piecewise functions, and inverse functions in simple cases.

- Applying the rules of absolute value and solving simple absolute value equations.
- Sketching absolute value functions, including cases with translations, stretches, reflections, and composite transformations.
- Determining roots of transformed absolute value functions.

- Polynomial fundamentals, including simplifying, adding, subtracting, multiplying, and factoring polynomials.
- Techniques for solving quadratic equations, including applying the zero product rule, completing the square, and the quadratic formula.
- Finding the discriminant of a quadratic equation and solving related problems.
- Performing graph transformations of simple quadratic curves, including cases with translations, stretches, reflections, and composite transformations.
- Finding the axis of symmetry and roots of a general quadratic function and plotting their graphs.
- Solving nonlinear systems of equations involving quadratic functions and lines.
- Using quadratic functions to model real-world situations, such as vertical motion, revenue, cost, and profit functions.
- Factoring higher-order polynomials using greatest common factors, differences of squares, and grouping, and solving polynomial equations using these techniques.

- Exponential expressions and equations, including modeling exponential growth and decay situations in context.
- The domain, range, intercepts, asymptotes, roots, and end behavior of exponential functions.
- Using exponential functions to model and solve real-world problems.

- Adding, subtracting, multiplying, dividing, and simplifying rational expressions, and solving rational equations.
- Simplifying radical expressions and solving radical equations.

- Solving real-world and mathematical problems involving ratios, percentages, unit rates, and proportional relationships, including modeling and solving real-world and mathematical problems.
- Determining units in formulas, including rates of change, working with standard and non-standard units.
- Performing unit conversions using algebraic techniques, including converting between units of area and volume.

- Summarizing and representing data through concepts such as centrality, spread, skew, and outliers and using frequency tables, dot plots, box plots, and histograms to visualize data and interpret distributions.
- Using scatter plots to identify trends in bivariate data, estimating trend lines, interpreting trend line coefficients in context, understanding the correlation coefficient, and matching data with an appropriate regression model.
- Probability: single and compound events, Venn diagrams, conditional probability, and independent events.

1.

Preliminaries
61 topics

1.1. Addition and Subtraction of Rational Numbers

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

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

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

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

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

1.1.6. | Adding a Negative Number | |

1.1.7. | Subtracting a Negative Number | |

1.1.8. | Additive Inverses of Numbers | |

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

1.2. Multiplication and Division of Rational Numbers

1.2.1. | Multiplying Positive Numbers With Negative Numbers | |

1.2.2. | Multiplying Negative Numbers | |

1.2.3. | Dividing With Negative Numbers | |

1.2.4. | Equivalent Fractions With Negative Numbers | |

1.2.5. | Dividing With Negative Decimals and Fractions | |

1.2.6. | Reciprocals of Rational Numbers | |

1.2.7. | Multiplying and Dividing With Zero | |

1.2.8. | Fractions of Fractions | |

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

1.3. Exponents

1.3.1. | Squaring Rational Numbers | |

1.3.2. | Cubing Rational Numbers | |

1.3.3. | Exponents With Rational Bases | |

1.3.4. | The Zeroth Power | |

1.3.5. | Powers of Negative One | |

1.3.6. | Negative Exponents | |

1.3.7. | The Product Rule for Exponents | |

1.3.8. | The Quotient Rule for Exponents | |

1.3.9. | The Power Rule for Exponents | |

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

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

1.3.12. | Combining the Rules of Exponents |

1.4. Radicals

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

1.4.2. | Squaring a Square Root | |

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

1.4.4. | Surds | |

1.4.5. | Simplifying Expressions With Surds | |

1.4.6. | Evaluating Numerical Expressions Containing Radicals | |

1.4.7. | Adding and Subtracting Radicals | |

1.4.8. | Rationalizing Denominators | |

1.4.9. | Radicals as Fractional Exponents | |

1.4.10. | The Product Rule for Radicals | |

1.4.11. | The Quotient Rule for Radicals |

1.5. Order of Operations

1.5.1. | Evaluating Rational Number Expressions Without Exponents | |

1.5.2. | Evaluating Expressions With Positive Integer Exponents | |

1.5.3. | Evaluating Expressions With Integer Exponents |

1.6. Algebraic Expressions

1.6.1. | Introduction to Algebraic Expressions | |

1.6.2. | Constructing Algebraic Expressions | |

1.6.3. | Evaluating Linear Expressions | |

1.6.4. | Evaluating Rational Expressions | |

1.6.5. | Identifying Terms in Linear Expressions | |

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

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

1.7. Simplifying Linear Expressions

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

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

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

1.7.4. | The Distributive Law With Three Terms | |

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

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

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

1.7.8. | Simplifying Linear Expressions Containing Fractions | |

1.7.9. | Factoring Numerical Expressions | |

1.7.10. | Factoring Linear Expressions |

2.

Algebra - Linear Equations in One Variable
20 topics

2.8. Solving Linear Equations

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

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

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

2.8.4. | Solving Two-Step Equations | |

2.8.5. | Solving Linear Equations With Fractional Coefficients | |

2.8.6. | Solving Linear Equations With Decimal Coefficients | |

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

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

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

2.8.10. | Solving Two-Variable Equations | |

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

2.8.12. | Solving Linear Equations With Unknown Coefficients | |

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

2.8.14. | Solving Linear Inequalities With Unknown Parameters | |

2.8.15. | Solving Many-Variable Equations |

2.9. Modeling With Linear Equations

2.9.1. | Interpreting Linear Expressions | |

2.9.2. | Modeling With Linear Equations | |

2.9.3. | Consecutive Integer Problems | |

2.9.4. | Speed, Distance, Time Problems | |

2.9.5. | Further Speed, Distance, Time Problems |

3.

Algebra - Linear Equations in Two Variables
33 topics

3.10. Graphs of Linear Equations

3.10.1. | The Cartesian Coordinate System | |

3.10.2. | Distances Between Points in the Coordinate Plane | |

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

3.10.4. | Graphing Linear Equations | |

3.10.5. | Horizontal and Vertical Lines | |

3.10.6. | Calculating Slopes of Straight Lines | |

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

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

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

3.10.10. | Equations of Lines in Standard Form | |

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

3.10.12. | Parallel Lines in the Coordinate Plane | |

3.10.13. | Finding the Equation of a Parallel Line | |

3.10.14. | Perpendicular Lines in the Coordinate Plane | |

3.10.15. | Finding Equations of Perpendicular Lines |

3.11. Modeling With Two-Variable Linear Equations

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

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

3.11.3. | Analyzing and Interpreting Graphs of Linear Equations | |

3.11.4. | Distance-Time Graphs | |

3.11.5. | Calculating Acceleration From a Speed-Time Graph | |

3.11.6. | Calculating Distance From a Speed-Time Graph |

3.12. Systems of Equations

3.12.1. | Introduction to Systems of Linear Equations | |

3.12.2. | Solving Systems of Equations by Substitution | |

3.12.3. | Introduction to the Elimination Method | |

3.12.4. | Solving Systems of Linear Equations Using Elimination: One Transformation | |

3.12.5. | Solving Systems of Linear Equations Using Elimination: Two Transformations | |

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

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

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

3.12.9. | Calculating the Intersection of Two Lines | |

3.12.10. | Modeling Number Problems Using Systems of Linear Equations | |

3.12.11. | Modeling Coin Problems Using Systems of Linear Equations | |

3.12.12. | Solving Systems of Nonlinear Equations Using Graphs |

4.

Algebra - Linear Inequalities
20 topics

4.13. Linear Inequalities

4.13.1. | Inequalities | |

4.13.2. | Compound Inequalities | |

4.13.3. | Verifying Solutions of Linear Inequalities | |

4.13.4. | Solving One-Step Linear Inequalities | |

4.13.5. | Solving Two-Step Inequalities | |

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

4.13.7. | Further Solving Linear Inequalities | |

4.13.8. | Solving Compound Inequalities | |

4.13.9. | Interval Notation | |

4.13.10. | Unbounded Intervals | |

4.13.11. | Unions of Intervals | |

4.13.12. | Intersections of Intervals | |

4.13.13. | Introduction to Modeling With Inequalities | |

4.13.14. | Modeling With One-Step Inequalities | |

4.13.15. | Modeling With Two-Step Inequalities |

4.14. Two-Variable Linear Inequalities

4.14.1. | Graphing Strict Two-Variable Linear Inequalities | |

4.14.2. | Graphing Non-Strict Two-Variable Linear Inequalities | |

4.14.3. | Further Graphing of Two-Variable Linear Inequalities | |

4.14.4. | Solving Systems of Linear Inequalities | |

4.14.5. | Modeling With Two-Variable Linear Inequalities |

5.

Geometry - Points, Lines, & Angles
25 topics

5.15. Introduction to Geometry

5.15.1. | Units of Area and Volume | |

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

5.15.3. | Parallel and Perpendicular Lines | |

5.15.4. | Measures of Segments | |

5.15.5. | Congruent Segments | |

5.15.6. | Midpoints | |

5.15.7. | Collinear Points | |

5.15.8. | The Segment Addition Postulate |

5.16. Angles

5.16.1. | Angles and Measures of Angles | |

5.16.2. | Connecting Angles and Circles | |

5.16.3. | Measuring Angles Using a Protractor | |

5.16.4. | Sums of Angles | |

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

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

5.16.7. | Congruent Angles | |

5.16.8. | Vertical Angles | |

5.16.9. | Solving Problems With Angles |

5.17. Advanced Angles

5.17.1. | Complementary Angles | |

5.17.2. | Supplementary Angles | |

5.17.3. | Corresponding Angles | |

5.17.4. | Alternate Angles | |

5.17.5. | Consecutive Angles | |

5.17.6. | Angle Criteria for Parallel Lines | |

5.17.7. | Angle Bisectors | |

5.17.8. | Segment Bisectors |

6.

Geometry - Polygons & Solids
16 topics

6.18. Triangles

6.18.1. | Interior Angles of Triangles | |

6.18.2. | Exterior Angles of Triangles | |

6.18.3. | Problem Solving With Angles of Triangles | |

6.18.4. | Classifying Triangles | |

6.18.5. | The Isosceles Triangle Theorem | |

6.18.6. | Heights of Triangles |

6.19. Polygons

6.19.1. | Polygons | |

6.19.2. | Interior Angles of Polygons | |

6.19.3. | Exterior Angles of Polygons | |

6.19.4. | Congruent Polygons | |

6.19.5. | Regular Polygons | |

6.19.6. | Properties of Rectangles and Squares |

6.20. Solid Geometry

6.20.1. | Identifying Three-Dimensional Shapes | |

6.20.2. | Faces, Vertices, and Edges of Polyhedrons | |

6.20.3. | Nets of Polyhedrons | |

6.20.4. | Finding Surface Areas Using Nets |

7.

Geometry - Congruence & Similarity
13 topics

7.21. Congruence

7.21.1. | The ASA Congruence Criterion | |

7.21.2. | The AAS Congruence Criterion | |

7.21.3. | The SAS Congruence Criterion | |

7.21.4. | The SSS Congruence Criterion | |

7.21.5. | The HL Congruence Criterion |

7.22. Similarity

7.22.1. | Similarity and Similar Polygons | |

7.22.2. | Side Lengths and Angle Measures of Similar Polygons | |

7.22.3. | Areas of Similar Polygons | |

7.22.4. | The AA Similarity Criterion | |

7.22.5. | The SSS Similarity Criterion | |

7.22.6. | The SAS Similarity Criterion | |

7.22.7. | The Midpoint Theorem | |

7.22.8. | The Triangle Proportionality Theorem |

8.

Geometry - Length, Area & Volume
19 topics

8.23. Perimeter & Area of Plane Figures

8.23.1. | The Perimeter of a Polygon | |

8.23.2. | Areas of Rectangles and Squares | |

8.23.3. | Areas of Parallelograms | |

8.23.4. | Areas of Triangles | |

8.23.5. | Areas of Trapezoids | |

8.23.6. | Areas and Perimeters of Composite Shapes | |

8.23.7. | The Area Between Two Shapes |

8.24. Coordinate Geometry

8.24.1. | Midpoints in the Coordinate Plane | |

8.24.2. | The Distance Formula | |

8.24.3. | Calculating Perimeters in the Plane | |

8.24.4. | Calculating Areas of Rectangles in the Plane |

8.25. Surface Area and Volume

8.25.1. | Surface Areas of Cubes | |

8.25.2. | Surface Areas of Rectangular Solids | |

8.25.3. | Volumes of Rectangular Solids | |

8.25.4. | Volumes of Cylinders | |

8.25.5. | Volumes of Spheres | |

8.25.6. | Slant Heights of Right Cones | |

8.25.7. | Volumes of Right Cones | |

8.25.8. | Volumes of Pyramids |

9.

Geometry - Circles
19 topics

9.26. Circles

9.26.1. | Circles | |

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

9.26.3. | The Circumference of a Circle | |

9.26.4. | Areas of Circles | |

9.26.5. | Central Angles and Arcs | |

9.26.6. | Calculating Arc Lengths of Circular Sectors | |

9.26.7. | Calculating Areas of Circular Sectors | |

9.26.8. | Further Calculating Areas of Sectors | |

9.26.9. | Problem Solving With Circles | |

9.26.10. | Tangent Lines to Circles |

9.27. Circles in the Coordinate Plane

9.27.1. | Circles in the Coordinate Plane | |

9.27.2. | Equations of Circles Centered at the Origin | |

9.27.3. | Equations of Circles | |

9.27.4. | Determining Properties of Circles by Completing the Square | |

9.27.5. | Calculating Circle Intercepts | |

9.27.6. | Intersections of Circles with Lines |

9.28. Radians

9.28.1. | Introduction to Radians | |

9.28.2. | Calculating Arc Length Using Radians | |

9.28.3. | Calculating Areas of Sectors Using Radians |

10.

Trigonometry
19 topics

10.29. Right Triangles

10.29.1. | The Pythagorean Theorem | |

10.29.2. | The 45-45-90 Triangle | |

10.29.3. | The 30-60-90 Triangle | |

10.29.4. | The Area of a 45-45-90 Triangle | |

10.29.5. | The Area of a 30-60-90 Triangle | |

10.29.6. | The Area of an Equilateral Triangle | |

10.29.7. | Diagonals of Squares |

10.30. Trigonometry

10.30.1. | Angles and Sides in Right Triangles | |

10.30.2. | The Trigonometric Ratios | |

10.30.3. | Calculating Trigonometric Ratios Using the Pythagorean Theorem | |

10.30.4. | Calculating Side Lengths of Right Triangles Using Trigonometry | |

10.30.5. | Calculating Angles in Right Triangles Using Trigonometry | |

10.30.6. | Modeling With Trigonometry | |

10.30.7. | The Reciprocal Trigonometric Ratios | |

10.30.8. | Trigonometric Ratios in Similar Right Triangles | |

10.30.9. | Trigonometric Functions of Complementary Angles | |

10.30.10. | Special Trigonometric Ratios | |

10.30.11. | Calculating the Area of a Right Triangle Using Trigonometry | |

10.30.12. | Solving Multiple Right Triangles Using Trigonometry |

11.

Advanced Algebra - Functions
18 topics

11.31. Functions

11.31.1. | Introduction to Functions | |

11.31.2. | Visual Representations of Functions | |

11.31.3. | Graphs of Functions | |

11.31.4. | The Domain of a Function | |

11.31.5. | The Vertical Line Test | |

11.31.6. | Global Extrema of Functions | |

11.31.7. | Local Extrema of Functions | |

11.31.8. | End Behavior of Functions | |

11.31.9. | The Range of a Function | |

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

11.31.11. | The Roots of a Function | |

11.31.12. | Increasing and Decreasing Functions | |

11.31.13. | Piecewise Functions | |

11.31.14. | Modeling With Linear Functions | |

11.31.15. | The Arithmetic of Functions | |

11.31.16. | Function Composition | |

11.31.17. | Describing Function Composition | |

11.31.18. | Introduction to Inverse Functions |

12.

Advanced Algebra - Absolute Value
10 topics

12.32. Absolute Value Expressions and Equations

12.32.1. | Absolute Value Expressions | |

12.32.2. | Rules of Absolute Value | |

12.32.3. | Further Rules of Absolute Value | |

12.32.4. | Absolute Value Equations | |

12.32.5. | Further Absolute Value Equations |

12.33. Absolute Value Functions

12.33.1. | Absolute Value Graphs | |

12.33.2. | Vertical Reflections of Absolute Value Graphs | |

12.33.3. | Stretches of Absolute Value Graphs | |

12.33.4. | Combining Transformations of Absolute Value Graphs | |

12.33.5. | Roots of Absolute Value Functions |

13.

Advanced Algebra - Polynomials
57 topics

13.34. Polynomials

13.34.1. | Introduction to Polynomials | |

13.34.2. | The Degree of a Polynomial | |

13.34.3. | Simplifying Polynomials | |

13.34.4. | The Distributive Law for Polynomials | |

13.34.5. | Adding and Subtracting Polynomials | |

13.34.6. | Monomials, Binomials and Trinomials | |

13.34.7. | Multiplying Binomials | |

13.34.8. | Multiplying Polynomials | |

13.34.9. | Squaring Binomials | |

13.34.10. | The Difference of Squares Formula |

13.35. Factoring Polynomials

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

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

13.35.3. | Factoring Perfect Square Trinomials | |

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

13.35.5. | Factoring Differences of Squares | |

13.35.6. | Factoring Trinomials | |

13.35.7. | Factoring Trinomials Using Common Factors | |

13.35.8. | Factoring Trinomials With Leading Coefficients | |

13.35.9. | Further Factoring Trinomials With Leading Coefficients |

13.36. Quadratic Equations

13.36.1. | Introduction to Quadratic Equations | |

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

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

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

13.36.5. | Solving Perfect Square Quadratic Equations | |

13.36.6. | Perfect Square Quadratic Equations with One or No Solutions | |

13.36.7. | The Zero Product Rule for Solving Quadratic Equations | |

13.36.8. | Solving Quadratic Equations Using a Difference of Squares | |

13.36.9. | Solving Quadratic Equations with No Constant Term | |

13.36.10. | Solving Quadratic Equations by Factoring | |

13.36.11. | Solving Quadratic Equations with Leading Coefficients by Factoring | |

13.36.12. | Completing the Square | |

13.36.13. | Completing the Square With Odd Linear Terms | |

13.36.14. | Completing the Square With Leading Coefficients | |

13.36.15. | Solving Quadratic Equations by Completing the Square | |

13.36.16. | Solving Quadratic Equations With Leading Coefficients by Completing the Square | |

13.36.17. | The Quadratic Formula | |

13.36.18. | The Discriminant of a Quadratic Equation |

13.37. Quadratic Functions

13.37.1. | Graphing Elementary Quadratic Functions | |

13.37.2. | Vertical Reflections of Quadratic Functions | |

13.37.3. | Graphs of General Quadratic Functions | |

13.37.4. | Roots of Quadratic Functions | |

13.37.5. | The Discriminant of a Quadratic Function | |

13.37.6. | The Axis of Symmetry of a Parabola | |

13.37.7. | The Average of the Roots Formula | |

13.37.8. | The Vertex Form of a Parabola | |

13.37.9. | Writing the Equation of a Parabola in Vertex Form | |

13.37.10. | Finding Intersections of Lines and Quadratic Functions |

13.38. Modeling With Quadratic Functions

13.38.1. | Modeling Downwards Vertical Motion | |

13.38.2. | Modeling Upwards Vertical Motion | |

13.38.3. | Vertical Motion | |

13.38.4. | Revenue, Cost, and Profit Functions |

13.39. Polynomial Expressions & Equations

13.39.1. | Factoring Polynomials Using the GCF | |

13.39.2. | Factoring Higher-Order Polynomials as a Difference of Squares | |

13.39.3. | Factoring Cubic Expressions by Grouping | |

13.39.4. | Determining the Roots of Polynomials | |

13.39.5. | Solving Polynomial Equations Using the GCF | |

13.39.6. | Solving Cubic Equations by Grouping |

14.

Advanced Algebra - Exponential Equations & Functions
25 topics

14.40. Exponential Expressions & Equations

14.40.1. | Writing Radical Expressions Using Fractional Exponents | |

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

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

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

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

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

14.40.7. | Combining the Rules of Exponents With Algebraic Expressions | |

14.40.8. | Solving Exponential Equations | |

14.40.9. | Solving Exponential Equations with Fractional Solutions | |

14.40.10. | Creating Exponential Growth Expressions | |

14.40.11. | Creating Exponential Decay Expressions |

14.41. Exponential Functions

14.41.1. | Exponential Functions | |

14.41.2. | Modeling Exponential Growth With Functions | |

14.41.3. | Interpreting Exponential Growth | |

14.41.4. | Solving Exponential Growth Problems | |

14.41.5. | Modeling Exponential Decay With Functions | |

14.41.6. | Interpreting Exponential Decay | |

14.41.7. | Solving Exponential Decay Problems | |

14.41.8. | Linear vs. Exponential Growth and Decay | |

14.41.9. | Linear vs. Exponential Growth and Decay Models |

14.42. Graphs of Exponential Functions

14.42.1. | Graphing Exponential Growth Functions | |

14.42.2. | Graphing Exponential Decay Functions | |

14.42.3. | Vertical Translations of Exponential Growth Functions | |

14.42.4. | Vertical Translations of Exponential Decay Functions | |

14.42.5. | Interpreting Graphs of Exponential Functions |

15.

Advanced Algebra - Rational and Radical Equations
22 topics

15.43. Rational Expressions

15.43.1. | Equivalent Expressions With Fractions | |

15.43.2. | Simplifying Rational Expressions | |

15.43.3. | Simplifying Rational Expressions by Factoring | |

15.43.4. | Simplifying Rational Expressions Using Polynomial Factorization | |

15.43.5. | Splitting Rational Expressions Into Separate Terms | |

15.43.6. | Adding and Subtracting Rational Expressions | |

15.43.7. | Adding Rational Expressions With No Common Factors in the Denominator | |

15.43.8. | Multiplying Rational Expressions | |

15.43.9. | Dividing Rational Expressions |

15.44. Rational Equations

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

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

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

15.44.4. | Solving Rational Equations Using the Flip Method |

15.45. Radical Expressions

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

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

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

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

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

15.45.6. | Simplifying Square Root Expressions Using the Quotient Rule | |

15.45.7. | Evaluating Algebraic Radical Expressions | |

15.45.8. | Adding and Subtracting Radical Expressions | |

15.45.9. | Solving Radical Equations |

16.

Problem Solving - Ratios & Percentages
35 topics

16.46. Ratios

16.46.1. | Introduction to Ratios | |

16.46.2. | Equivalent Ratios | |

16.46.3. | Writing Ratios Using Fractions | |

16.46.4. | Working With Equivalent Ratios | |

16.46.5. | More on Equivalent Ratios | |

16.46.6. | Ratio Tables | |

16.46.7. | Graphing Ratios |

16.47. Unit Rates

16.47.1. | Unit Rates | |

16.47.2. | Solving Problems Using Unit Rates | |

16.47.3. | Speed as a Unit Rate | |

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

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

16.48. Proportional Relationships

16.48.1. | Understanding Proportional Relationships Using Tables | |

16.48.2. | Understanding Proportional Relationships Using Graphs | |

16.48.3. | Understanding Proportional Relationships From Descriptions | |

16.48.4. | Modeling with Direct Variation |

16.49. Percentages

16.49.1. | Understanding Percentages Using Models | |

16.49.2. | Converting Between Percentages and Fractions | |

16.49.3. | Converting Between Percentages and Decimals | |

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

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

16.49.6. | Finding a Percentage Given Two Numbers | |

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

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

16.49.9. | Percentage Increase, Decrease, and Error |

16.50. Units

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

16.50.2. | Two-Step Unit Conversions | |

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

16.50.4. | Unit Conversions Using Units of Time | |

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

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

16.50.7. | Determining Units in Formulas | |

16.50.8. | Selecting Units for Rates of Change | |

16.50.9. | Converting Between Mixed Units | |

16.50.10. | Degrees of Accuracy |

17.

Data Analysis - Statistics & Probability
42 topics

17.51. Summarizing Data

17.51.1. | Introduction to Statistics | |

17.51.2. | The Mean of a Data Set | |

17.51.3. | The Median of a Data Set | |

17.51.4. | The Mode of a Data Set | |

17.51.5. | Range, Quartiles and Interquartile Range | |

17.51.6. | Mean Absolute Deviation | |

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

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

17.51.9. | Outliers | |

17.51.10. | Removing Outliers |

17.52. Representing Data

17.52.1. | Frequency Tables | |

17.52.2. | Dot Plots | |

17.52.3. | Measuring Centrality Using Dot Plots | |

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

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

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

17.52.7. | Box Plots | |

17.52.8. | Histograms | |

17.52.9. | Comparing Measures of Center | |

17.52.10. | Comparing Measures of Spread |

17.53. Correlation

17.53.1. | Scatter Plots | |

17.53.2. | Trend Lines | |

17.53.3. | Making Predictions Using Trend Lines | |

17.53.4. | Interpreting Trend Line Coefficients | |

17.53.5. | Linear Correlation | |

17.53.6. | Selecting a Regression Model |

17.54. Introduction to Probability

17.54.1. | Sets | |

17.54.2. | Probability From Experimental Data | |

17.54.3. | Sample Spaces and Events in Probability | |

17.54.4. | Single Events in Probability | |

17.54.5. | The Complement of an Event | |

17.54.6. | Venn Diagrams in Probability | |

17.54.7. | Geometric Probability |

17.55. Compound Events in Probability

17.55.1. | The Union of Sets | |

17.55.2. | The Intersection of Sets | |

17.55.3. | Compound Events in Probability From Experimental Data | |

17.55.4. | Computing Probabilities for Compound Events Using Venn Diagrams | |

17.55.5. | Computing Probabilities of Events Containing Complements Using Venn Diagrams | |

17.55.6. | Conditional Probabilities From Venn Diagrams | |

17.55.7. | Conditional Probabilities From Tables | |

17.55.8. | The Multiplication Law for Conditional Probability | |

17.55.9. | Independent Events |