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SAT Math Prep

The SAT Math Prep course is a mastery-based, performance-driven program designed to help students succeed on the SAT Math exam. This course is entirely practice-based and functions as an advanced performance-training environment. Students engage exclusively with high-fidelity SAT-style problems that mirror the structure, rigor, pacing, and cognitive demands of the official exam.

Enrollment in this course requires prior completion of our SAT Math Fundamentals course. The Fundamentals course provides the essential conceptual instruction and addresses over 120 critical "missing middle" topics that are not typically covered in standard curricula, yet are essential for high performance on the SAT exam. SAT Math Prep builds on that foundation by focusing exclusively on strategic execution, exam fluency, and sustained accuracy under authentic testing conditions.

Overview

Outcomes

Content

SAT Math Prep is organized around a hierarchical knowledge graph that reflects the full scope of SAT-tested mathematics: Algebra, Advanced Math, Geometry and Trigonometry, and Problem-Solving and Data Analysis.

Each topic is subdivided into structured knowledge points (KPs), with each KP containing progressively more sophisticated sub-skills. Students advance sequentially through these levels, demonstrating mastery before progressing. Advancement is mastery-based: students must meet defined performance thresholds before unlocking subsequent material.

The system continuously diagnoses areas of weakness and dynamically routes students through the knowledge graph to reinforce prerequisite skills. If a student struggles within a topic, the platform can automatically redirect them to the corresponding SAT Math Fundamentals topic for explicit instruction and scaffolded practice before returning them to exam-level problems. This ensures that conceptual gaps are repaired at their source, allowing students to resume performance training with confidence.

There is no fixed endpoint to this course. Students receive an estimated SAT score that updates with every task they complete, and they may continue refining speed, accuracy, and strategic decision-making until exam day, sharpening their performance through increasingly sophisticated problem sets that simulate authentic SAT conditions.

Upon successful completion of this course, students will have mastered the following:

Through sustained mastery-based practice, students will develop the ability to:

This course serves as the capstone performance phase of SAT preparation within the Math Academy system, transforming foundational knowledge into exam-ready fluency and confidence.

1.
Algebra
77 topics
1.1. Linear Expressions and Equations in One Variable
 1.1.1. Evaluating Expressions
1.1.2. Finding Equivalent Equations
1.1.3. Solving One-Step Addition Equations
1.1.4. Solving One-Step Multiplication Equations
1.1.5. Solving Multistep Linear Equations
1.1.6. Solving Equations by Combining Terms
1.1.7. Solving Equations With Fractional Coefficients
1.1.8. Solving Linear Equations Containing Binomials
1.1.9. Solving Linear Equations Containing Binomials by Factoring
1.1.10. Solving Linear Equations With Binomials on Both Sides
1.1.11. Manipulating Linear Equations Containing Binomials
1.2. Word Problems and Modeling
 1.2.1. Numerical Word Problems
1.2.2. Multistep Numerical Word Problems
1.2.3. Constructing Models With One-Variable Linear Equations
1.2.4. Modeling and Solving Problems Using Linear Equations
1.2.5. Linear Models Presented in Unsimplified Form
1.2.6. Modeling Geometry Problems Using Linear Equations
1.3. Two-Variable Linear Equations
 1.3.1. Solving Two-Variable Linear Models
1.3.2. Constructing Models With Two-Variable Linear Equations
1.3.3. Modeling Totals Using Two-Variable Linear Equations
1.3.4. Interpreting Two-Variable Linear Equations
1.3.5. Interpreting Coefficients of Two-Variable Linear Equations
1.4. Linear Functions
 1.4.1. Evaluating Linear Functions
1.4.2. Finding a Function Input for a Given Output
1.4.3. Linear Functions Containing Unknown Parameters
1.4.4. Working With Function Composition
1.5. Functions in Tabular Form
 1.5.1. Identifying Tables Corresponding to Linear Functions
1.5.2. Identifying Linear Functions Corresponding to Tables
1.5.3. Linear Functions as Tables in Applications
1.5.4. Analyzing Functions in Tabular Form
1.5.5. Function Tables Containing Unknown Parameters
1.6. Graphs of Linear Equations
 1.6.1. Interpreting Coefficients of Lines in Slope-Intercept Form
1.6.2. Finding Equations of Lines Using Slopes and Points
1.6.3. Graphs of Linear Equations in Slope-Intercept Form
1.6.4. Finding Intercepts of Lines in Slope-Intercept Form
1.6.5. Constructing and Analyzing Slope-Intercept Equations
1.6.6. Properties of Lines Given in Standard or General Form
1.6.7. Analyzing Linear Equations in General Form
1.6.8. Analyzing Linear Equations of Shifted Lines
1.6.9. Constructing Linear Functions Using Slope-Intercept Form
1.7. Parallel and Perpendicular Lines
 1.7.1. Parallel Lines
1.7.2. Slopes of Perpendicular Lines
1.7.3. Perpendicular Lines
1.8. Modeling With Linear Functions
 1.8.1. Modeling With Linear Functions
1.8.2. Constructing Models Using Linear Functions
1.8.3. Further Constructing Models Using Linear Functions
1.8.4. Interpreting Coefficients of Linear Functions in Context
1.8.5. Interpreting Graphs of Linear Functions
1.8.6. Modeling Using Slope-Intercept Form
1.9. Systems of Two-Variable Linear Equations
 1.9.1. Solving Simple Systems of Linear Equations
1.9.2. Identifying Structure in Systems of Linear Equations
1.9.3. Solving Systems of Equations Using Addition or Subtraction
1.9.4. Solving Systems of Equations Using Elimination
1.9.5. Modeling Word Problems With Systems of Linear Equations
1.9.6. Solving Problems With Systems of Linear Equations
1.9.7. Solving Problems With Systems of Linear Equations in Standard Form
1.9.8. The Intersection of Two Lines
1.9.9. The Relationship Between Systems of Linear Equations and Graphs
1.10. Linear Equations With Infinitely Many or No Solutions
 1.10.1. Determining the Number of Solutions to a Linear Equation
1.10.2. Linear Equations With Infinitely Many Solutions
1.10.3. Linear Equations With No Solutions
1.10.4. Determining the Number of Solutions to a Linear System
1.10.5. Linear Systems With Infinitely Many Solutions
1.10.6. Parametrizing Systems of Linear Equations
1.10.7. Linear Systems With No Solution
1.11. Linear Inequalities One Variable
 1.11.1. Constructing Models With One-Variable Linear Inequalities
1.11.2. Modeling and Solving With One-Variable Linear Inequalities
1.11.3. Modeling and Solving Percentage Problems With One-Variable Linear Inequalities
1.11.4. Modeling and Solving With One-Variable Linear Inequalities: Advanced Cases
1.11.5. Compound Inequalities
1.11.6. Constructing Models With Compound Inequalities
1.12. Linear Inequalities in Two Variables
 1.12.1. Solutions of Two-Variable Linear Inequalities
1.12.2. Modeling With Two-Variable Linear Inequalities
1.12.3. Modeling and Solving Two-Variable Linear Inequalities
1.12.4. Systems of Two-Variable Inequalities
1.12.5. Modeling With Systems of Inequalities
1.12.6. Modeling and Solving Systems of Linear Inequalities
2.
Advanced Math
80 topics
2.13. Polynomial Expressions
 2.13.1. Adding Polynomials
2.13.2. Adding Polynomials Using the Distributive Law
2.13.3. Multiplying Binomials
2.13.4. Factoring Polynomials Using the GCF
2.13.5. Factoring Binomials Using Differences of Squares
2.13.6. Factoring Trinomials
2.13.7. Factoring Higher-Order Polynomials
2.14. Rational Expressions
 2.14.1. Simplifying Rational Expressions by Factoring
2.14.2. Simplifying Rational Expressions Using Polynomial Factorization
2.14.3. Adding Rational Expressions
2.14.4. Further Adding Rational Expressions
2.14.5. Fractions of Fractions
2.15. Exponential Expressions
 2.15.1. Exponential Expressions
2.15.2. Simplifying Exponential Expressions
2.15.3. Simplifying Exponential Expressions Using the Distributive Law
2.16. Quadratic Equations
 2.16.1. Perfect Square Quadratic Equations
2.16.2. Solving Quadratic Equations Using the Zero-Product Rule
2.16.3. Solving Quadratic Equations by Factoring
2.16.4. Solving Quadratic Equations With Leading Coefficients by Factoring
2.16.5. Solving Quadratic Equations Using the Quadratic Formula
2.16.6. Quadratic Equations With One Real Solution
2.16.7. Quadratic Equations With Two Real Solutions
2.16.8. Quadratic Equations With No Real Solutions
2.16.9. Counting Solutions to Quadratic Equations
2.16.10. Applying Vieta's Formulas
2.16.11. Solving Quadratic Equations With Unknown Parameters
2.17. Quadratic Functions
 2.17.1. Quadratic Functions
2.17.2. Graphs of Quadratic Functions
2.17.3. Determining Inputs of Quadratic Functions for Given Outputs
2.17.4. Finding Extreme Values of Quadratic Functions in Factored Form
2.17.5. Finding Extreme Values of Quadratic Functions in Vertex Form
2.17.6. Finding Extreme Values of Quadratic Functions in Standard Form
2.17.7. Using Standard and Factored Forms to Reason About Quadratic Functions
2.17.8. Using Symmetry to Reason About Quadratic Functions
2.17.9. Identifying Quadratic Functions From Tabular Data
2.18. Modeling With Quadratics
 2.18.1. Modeling Number Problems With Quadratic Equations
2.18.2. Modeling Geometry Problems With Quadratic Equations
2.18.3. Solving Border Problems With Quadratic Equations
2.18.4. Interpreting Quadratic Functions in Modeling Contexts
2.18.5. Interpreting Graphs of Quadratic Functions in Modeling Contexts
2.18.6. Modeling Planar Motion Using Quadratic Functions
2.19. Polynomials
 2.19.1. Elementary Cubic Functions
2.19.2. Higher-Degree Polynomials
2.19.3. Graphs of Higher-Degree Polynomials
2.19.4. Polynomial Transformations
2.19.5. Further Polynomial Transformations
2.19.6. Using the Factor Theorem to Reason About Polynomials
2.20. Exponential Functions
 2.20.1. Exponential Functions
2.20.2. Maxima and Minima of Exponential Functions
2.20.3. Exponential Functions Containing Unknown Parameters
2.20.4. Constructing Exponential Functions From Descriptions
2.20.5. Exponential Functions Expressed in Equivalent Forms
2.20.6. Transforming Exponential Functions
2.20.7. Identifying Exponential Functions From Tabular Data
2.21. Modeling With Exponential Functions
 2.21.1. Constructing Exponential Growth Models
2.21.2. Constructing Exponential Decay Models
2.21.3. Determining Unknown Parameters in Exponential Models
2.21.4. Calculating Unknown Times in Exponential Models
2.21.5. Converting Units of Time in Exponential Models
2.21.6. Interpreting Exponential Models
2.22. Nonlinear Equations and Functions
 2.22.1. Absolute Value Equations
2.22.2. Rational Equations
2.22.3. Radical Equations
2.22.4. Equations Containing Multiple Radicals
2.22.5. Absolute Value Functions
2.22.6. Rational Functions
2.23. Multivariable Equations
 2.23.1. Solving Multivariable Equations
2.23.2. Further Multivariable Equations
2.23.3. Solving Multivariable Rational Equations
2.23.4. Solving Multivariable Nonlinear Equations
2.24. Interpreting Graphs
 2.24.1. Identifying Intercepts of Functions From Graphs
2.24.2. Identifying Graph Properties in Modeling Contexts
2.24.3. Interpreting Graph Properties in Modeling Contexts
2.25. Systems of Nonlinear Equations
 2.25.1. Solving Constant-Quadratic Systems of Equations
2.25.2. Solving Linear-Quadratic Systems of Equations
2.25.3. Solving Challenging Linear-Quadratic Systems of Equations
2.25.4. Exploiting Structure to Solve Nonlinear Systems of Equations
2.25.5. Linear-Quadratic Systems With One Solution
2.25.6. Linear-Quadratic Systems With Zero or Two Solutions
2.25.7. Other Systems of Nonlinear Equations
3.
Geometry and Trigonometry
60 topics
3.26. Lines, Angles, and Triangles
 3.26.1. Corresponding Angles
3.26.2. Consecutive Angles
3.26.3. Vertical Angles
3.26.4. Problem-Solving With Corresponding Angles
3.26.5. Interior Angles of Triangles
3.26.6. Interior Angles of Special Triangles
3.26.7. Exterior Angles of Triangles
3.26.8. Solving Problems With Multiple Triangles
3.26.9. Interior and Exterior Angles in Connected Triangles
3.27. Area and Perimeter
 3.27.1. Areas of Rectangles and Squares
3.27.2. Perimeters of Squares, Rectangles, and Triangles
3.27.3. Calculating Areas in the Coordinate Plane
3.27.4. Constructing Functions Representing Area and Perimeter
3.28. Right Triangles
 3.28.1. Areas of Right Triangles
3.28.2. The Pythagorean Theorem
3.28.3. Modeling Situations Using the Pythagorean Theorem
3.28.4. Problem-Solving With Isosceles Right Triangles
3.28.5. Problem-Solving With Special Triangles
3.28.6. Further Problem-Solving With Special Triangles
3.28.7. Solving Right Triangle Problems by Manipulating Radicals
3.29. Circles
 3.29.1. Radians
3.29.2. Arc Lengths of Sectors
3.29.3. Areas and Circumferences of Circles
3.29.4. Isosceles Triangles Formed Within Circles
3.29.5. Tangent Lines to Circles
3.29.6. Bisectors of Chords
3.30. Circles in the Coordinate Plane
 3.30.1. The Canonical Equation of a Circle
3.30.2. Canonical Equations of Transformed Circles
3.30.3. General Equations of Circles in the Coordinate Plane
3.30.4. Solving Problems Involving the Canonical Equation of a Circle
3.31. Inscribed Shapes
 3.31.1. Solving Problems Involving Inscribed Squares
3.31.2. Solving Problems Involving Inscribed Circles
3.31.3. Solving Problems Involving Circles Inscribed in Equilateral Triangles
3.31.4. Solving Problems Involving Equilateral Triangles Inscribed in Circles
3.32. Surface Area and Volume
 3.32.1. Volumes of Right Rectangular Prisms
3.32.2. Surface Areas of Right Rectangular Prisms
3.32.3. Volumes and Surface Areas of Cubes
3.32.4. Volumes of Cylinders
3.32.5. Volumes of Cylinders: Word Problems
3.32.6. Volumes of Spheres
3.32.7. Volumes of Cones
3.32.8. Volumes of Composite Solids
3.32.9. Constructing Functions Representing Surface Area and Volume
3.32.10. Surface Areas of Combined Rectangular Prisms
3.33. Congruence and Similarity
 3.33.1. Congruent Triangles
3.33.2. Finding Corresponding Angles in Similar Shapes
3.33.3. Finding Corresponding Lengths in Similar Shapes
3.33.4. Solving Problems With Similar Triangles
3.33.5. Solving Problems With Embedded Right Triangles
3.33.6. Further Problem-Solving With Embedded Right Triangles
3.33.7. Identifying Information Needed to Determine Similarity
3.33.8. Relating Length and Area in Similar Shapes
3.33.9. Length, Surface Area, and Volume in Similar Solids
3.34. Trigonometry
 3.34.1. Trigonometric Ratios in Right Triangles
3.34.2. Calculating Lengths and Areas Using Trigonometry
3.34.3. Calculating Trigonometric Ratios Using the Pythagorean Theorem
3.34.4. Cofunction Relationships and Identities
3.34.5. Relations Between Trigonometric Ratios in Similar Right Triangles
3.34.6. Problem-Solving Using Trigonometric Ratios in Similar Right Triangles
3.34.7. Trigonometric Ratios of Large Special Angles
4.
Problem-Solving and Data Analysis
67 topics
4.35. Sampling and Surveys
 4.35.1. Sampling Bias and Validity
4.35.2. Estimation From Proportions and Samples
4.35.3. Interpreting Survey Data
4.35.4. Margin of Error
4.35.5. Interpreting Margin of Error
4.36. Measures of Centrality
 4.36.1. The Mean of a Dataset
4.36.2. The Median of a Dataset
4.36.3. Comparing Measures of Center
4.36.4. The Relationship Between Means and Sums
4.36.5. Finding Unknown Observations From Centrality Measures
4.37. Representing Data
 4.37.1. Tabular Datasets
4.37.2. Frequency Tables
4.37.3. Bar Graphs
4.37.4. Box Plots
4.37.5. Measuring Centrality From Frequency Tables
4.37.6. Bounding Statistical Metrics
4.38. Comparing Data
 4.38.1. Comparing Data Sets
4.38.2. Comparing Data Sets Presented Visually
4.38.3. Comparing Centrality Measures From Frequency Tables
4.38.4. Comparing Centrality Measures With Symmetric Datasets
4.38.5. Comparing Statistical Effects of Data Change
4.38.6. Effects of Additional Data on Centrality Measures
4.39. Probability
 4.39.1. Simple Probabilities in Real-World Contexts
4.39.2. Calculating Probabilities From Datasets
4.39.3. Calculating Probabilities From Frequency Tables
4.39.4. Simple Probabilities From Two-Way Frequency Tables
4.39.5. Conditional Probabilities From Two-Way Frequency Tables
4.39.6. Calculating Conditional Probabilities
4.40. Linear Regression
 4.40.1. Making Predictions Using Best-Fit Lines
4.40.2. The Slope of a Best-Fit Line
4.40.3. Identifying Best-Fit Lines
4.40.4. Best-Fit Lines With Compressed Axes
4.40.5. Analyzing Residuals of Best-Fit Lines
4.40.6. Transformations of Best-Fit Lines
4.41. Nonlinear Data Models
 4.41.1. Interpreting Data Plots
4.41.2. Interpreting Time-Series Graphs
4.41.3. Average Rate of Change From Data Plots
4.41.4. Linear vs. Exponential Models
4.41.5. Quadratic vs. Exponential Models
4.42. Percentages
 4.42.1. Finding Parts of Numbers From Percentages
4.42.2. Expressing Ratios of Numbers as Percentages
4.42.3. Finding Percentages Represented by Variables
4.42.4. Finding Totals From Percentages
4.42.5. Applying Percentages in Succession
4.43. Percentage Change
 4.43.1. Expressing Percentage Change Using Decimals
4.43.2. Calculating Percentage Change
4.43.3. Applying Percentage Change
4.43.4. Finding Original Values From Percentage Change
4.43.5. Applying Successive Percentage Changes
4.43.6. Further Successive Percentage Changes
4.43.7. Multistep Percentage Problems
4.44. Unit Conversions
 4.44.1. Unit Conversions to Smaller Units of Length
4.44.2. Unit Conversions to Larger Units of Length
4.44.3. Unit Conversions Between Units of Mass and Volume
4.44.4. Two-Step Unit Conversions
4.44.5. Unit Conversions Between Mixed Units
4.44.6. Converting Between Mixed Units Containing Squares
4.45. Ratios, Rates and Proportional Relationships
 4.45.1. Ratios
4.45.2. Applying Ratios
4.45.3. Working With Ratios in Various Settings
4.45.4. Rate Problems
4.45.5. Multistep Rate Problems
4.45.6. Speed Problems
4.45.7. Algebraic Expressions With Rates and Ratios
4.45.8. Solving Equations Describing Proportional Relationships
4.45.9. Calculating Density
4.45.10. Descriptions of Physical Phenomena