The ACT Math Prep course is a mastery-based, performance-driven program designed to help students achieve their highest possible score on the ACT Math exam. This course is entirely practice-based and functions as a specialized exam-training environment. Students engage with high-fidelity ACT-style problems and practice exams that closely mirror the structure, rigor, pacing, and cognitive demands of the official exam, developing the ability to perform accurately and efficiently under timed conditions.
Enrollment in this course requires prior completion of our ACT Math Fundamentals course. Students must complete ACT Math Fundamentals before being promoted to ACT Math Prep. The Fundamentals course provides the essential conceptual instruction and addresses gaps in foundational knowledge that could otherwise limit exam performance. ACT Math Prep builds on that foundation by focusing on strategic execution, exam fluency, efficient problem-solving, and sustained accuracy under authentic testing conditions.
ACT Math Prep is organized around a hierarchical knowledge graph encompassing six mathematical domains: Number & Quantity, Algebra, Functions, Geometry, Statistics & Probability, and Integrating Essential Skills. Together, these areas provide comprehensive practice across the mathematical concepts and problem types represented in the course's ACT preparation curriculum.
Number & Quantity includes exponents and radicals, number theory, complex numbers, matrices, and vectors. Students practice recognizing mathematical structures, simplifying expressions, applying numerical properties, and solving problems that require efficient symbolic manipulation and quantitative reasoning.
Algebra covers algebraic expressions, linear equations and inequalities, systems of equations, quadratic equations, polynomials, rational and radical equations, absolute value, and mathematical modeling. Practice emphasizes identifying efficient solution strategies, manipulating expressions accurately, and translating contextual problems into mathematical relationships.
Functions includes function notation and composition, linear and quadratic functions, exponential and logarithmic functions, polynomial and rational functions, sequences and series, and trigonometric functions. Students practice interpreting functions across algebraic, graphical, tabular, and contextual representations, recognizing important features, and selecting appropriate methods to solve problems.
Geometry covers lines, angles, polygons, congruence, similarity, right triangles, trigonometry, area, perimeter, circles, coordinate geometry, solid geometry, and conic sections. Students develop fluency in applying geometric relationships, interpreting diagrams, identifying relevant information, and solving multi-step problems efficiently.
Statistics & Probability includes measures of center and spread, data displays, probability, counting and combinatorics, and data modeling. Students practice interpreting statistical information, reasoning about uncertainty, calculating probabilities, and extracting relevant conclusions from tables, graphs, and contextual data.
Integrating Essential Skills reinforces arithmetic and number sense, ratios, rates, proportions, percentages, unit conversions, numerical word problems, basic statistics, and measurement geometry. This area ensures that foundational skills remain fluent and accessible when students encounter more complex questions under time pressure.
Practice is mastery-based and tailored to students' demonstrated performance rather than following a fixed unit-by-unit sequence. The system identifies weaknesses and provides targeted opportunities to strengthen the relevant skills. When a conceptual gap is exposed, students can return to ACT Math Fundamentals for instruction and reinforcement before resuming exam-level practice.
Timed practice and high-fidelity exam simulations help students develop effective pacing, maintain accuracy across varied problem types, and make sound decisions under pressure. Students can continue refining their speed, accuracy, and strategic execution as they prepare for exam day.
Upon successful completion of this course, students will have mastered the following:
This course serves as the capstone performance-training phase of ACT preparation within the Math Academy system, transforming foundational mathematical knowledge into exam-ready fluency, speed, accuracy, and confidence.
| 1.1.1. | Simplifying Integer Powers | |
| 1.1.2. | Simplifying Negative Exponents | |
| 1.1.3. | Applying Scientific Notation | |
| 1.1.4. | Simplifying Rational Exponents | |
| 1.1.5. | Evaluating Powers | |
| 1.1.6. | Reducing Radical Expressions | |
| 1.1.7. | Rewriting Radical Sums and Binomials | |
| 1.1.8. | Estimating Roots | |
| 1.1.9. | Identifying Characteristics of Powers | |
| 1.1.10. | Solving Exponential Equations |
| 1.2.1. | Finding a Greatest Common Factor | |
| 1.2.2. | Applying Divisibility Conditions | |
| 1.2.3. | Finding a Least Common Multiple | |
| 1.2.4. | Using Remainders | |
| 1.2.5. | Finding a Digit in a Repeating Decimal | |
| 1.2.6. | Comparing Repeating Decimals | |
| 1.2.7. | Using Prime Factorizations | |
| 1.2.8. | Identifying Prime Numbers | |
| 1.2.9. | Determining Parity | |
| 1.2.10. | Identifying Irrational Numbers | |
| 1.2.11. | Using Properties of Consecutive Integers | |
| 1.2.12. | Identifying True Statements About Integers |
| 1.3.1. | Simplifying Expressions With the Imaginary Unit | |
| 1.3.2. | Computing With Complex Numbers | |
| 1.3.3. | Multiplying Complex Numbers | |
| 1.3.4. | Using Complex Conjugates | |
| 1.3.5. | Dividing Complex Numbers |
| 1.4.1. | Combining Matrices | |
| 1.4.2. | Multiplying a Matrix by a Scalar | |
| 1.4.3. | Multiplying Matrices | |
| 1.4.4. | Finding Determinants | |
| 1.4.5. | Modeling With Matrix Products |
| 1.5.1. | Finding Components of a Vector | |
| 1.5.2. | Combining Vectors |
| 2.6.1. | Combining Like Terms | |
| 2.6.2. | Distributing Over Binomials | |
| 2.6.3. | Expanding Products of Binomials | |
| 2.6.4. | Expanding Powers of Binomials | |
| 2.6.5. | Factoring Algebraic Expressions | |
| 2.6.6. | Simplifying by Canceling Factors | |
| 2.6.7. | Evaluating Algebraic Expressions | |
| 2.6.8. | Applying Defined Operations | |
| 2.6.9. | Rewriting Expressions Using Relations |
| 2.7.1. | Solving Linear Equations | |
| 2.7.2. | Working Backward to Find an Unknown | |
| 2.7.3. | Solving Linear Equations With Parentheses | |
| 2.7.4. | Evaluating Expressions After Solving | |
| 2.7.5. | Solving Literal Equations | |
| 2.7.6. | Applying Linear Formulas | |
| 2.7.7. | Identifying Characteristics of Linear Equations |
| 2.8.1. | Solving Linear Inequalities | |
| 2.8.2. | Identifying Consequences of Inequalities | |
| 2.8.3. | Writing Linear Inequalities | |
| 2.8.4. | Finding a Threshold From a Linear Inequality | |
| 2.8.5. | Graphing Linear Inequalities | |
| 2.8.6. | Using Systems of Linear Inequalities |
| 2.9.1. | Solving Linear Systems | |
| 2.9.2. | Solving Systems by Elimination | |
| 2.9.3. | Determining How Many Solutions a System Has | |
| 2.9.4. | Modeling Word Problems With Systems | |
| 2.9.5. | Using a System Solution | |
| 2.9.6. | Solving Three-Variable Systems |
| 2.10.1. | Factoring Quadratic Expressions | |
| 2.10.2. | Using Factors of a Quadratic | |
| 2.10.3. | Solving Perfect Square Equations | |
| 2.10.4. | Solving Quadratic Equations by Factoring | |
| 2.10.5. | Applying the Quadratic Formula | |
| 2.10.6. | Using the Discriminant | |
| 2.10.7. | Applying Vieta's Formulas | |
| 2.10.8. | Modeling With Quadratic Equations |
| 2.11.1. | Expanding Binomial Powers | |
| 2.11.2. | Factoring Polynomials | |
| 2.11.3. | Solving Higher-Degree Equations |
| 2.12.1. | Simplifying Rational Expressions | |
| 2.12.2. | Combining Rational Expressions | |
| 2.12.3. | Identifying Characteristics of Rational Expressions | |
| 2.12.4. | Solving Proportions | |
| 2.12.5. | Solving Rational Equations | |
| 2.12.6. | Solving Square-Root Equations | |
| 2.12.7. | Isolating Variables From Powers | |
| 2.12.8. | Identifying Characteristics of Radical Expressions | |
| 2.12.9. | Identifying Characteristics of Absolute Values | |
| 2.12.10. | Solving Absolute Value Equations | |
| 2.12.11. | Determining Absolute-Value Solution Sets | |
| 2.12.12. | Solving Absolute Value Inequalities |
| 2.13.1. | Writing Rate and Earnings Models | |
| 2.13.2. | Writing Structural Linear Models | |
| 2.13.3. | Writing Quantity and Spending Models | |
| 2.13.4. | Expressing Related Quantities | |
| 2.13.5. | Writing Linear Models From Data | |
| 2.13.6. | Using a Given Algebraic Model | |
| 2.13.7. | Modeling Perimeter Problems | |
| 2.13.8. | Modeling Cost Problems | |
| 2.13.9. | Modeling Related-Quantity Problems | |
| 2.13.10. | Modeling Mixture Problems | |
| 2.13.11. | Equating Linear Models | |
| 2.13.12. | Modeling With Nonlinear Equations |
| 3.14.1. | Evaluating a Function | |
| 3.14.2. | Evaluating a Function in Context | |
| 3.14.3. | Evaluating a Multivariable Function | |
| 3.14.4. | Performing Operations on Functions | |
| 3.14.5. | Evaluating Function Compositions | |
| 3.14.6. | Composing Functions Algebraically | |
| 3.14.7. | Finding an Inverse Function | |
| 3.14.8. | Identifying Characteristics of Functions |
| 3.15.1. | Writing Function Rules From Data | |
| 3.15.2. | Matching Functions to Representations | |
| 3.15.3. | Determining Rates of Change | |
| 3.15.4. | Determining Function Outputs | |
| 3.15.5. | Finding Extreme Values of Quadratics | |
| 3.15.6. | Locating Points on a Parabola | |
| 3.15.7. | Transforming Quadratic Functions |
| 3.16.1. | Evaluating Exponential Functions | |
| 3.16.2. | Constructing Exponential Models | |
| 3.16.3. | Identifying Features of Exponential Functions | |
| 3.16.4. | Solving Exponential Equations | |
| 3.16.5. | Evaluating Logarithms | |
| 3.16.6. | Applying Logarithm Properties | |
| 3.16.7. | Relating Exponential and Logarithmic Forms | |
| 3.16.8. | Solving Logarithmic Equations | |
| 3.16.9. | Identifying Features of Logarithmic Functions |
| 3.17.1. | Determining Domain From an Equation | |
| 3.17.2. | Reading Domain From a Graph | |
| 3.17.3. | Finding Asymptotes of a Rational Function | |
| 3.17.4. | Finding Points and Zeros of a Function | |
| 3.17.5. | Describing Behavior of a Function Graph | |
| 3.17.6. | Determining the Range of a Function | |
| 3.17.7. | Translating Function Graphs Vertically | |
| 3.17.8. | Translating Horizontally and Reflecting Graphs | |
| 3.17.9. | Matching a Graph to an Equation | |
| 3.17.10. | Interpreting Piecewise Graphs |
| 3.18.1. | Working With Arithmetic Sequences | |
| 3.18.2. | Finding a Term of a Geometric Sequence | |
| 3.18.3. | Writing an Explicit Formula for a Sequence | |
| 3.18.4. | Computing Terms of a Recursive Sequence | |
| 3.18.5. | Summing an Arithmetic Series | |
| 3.18.6. | Summing Geometric and Other Series |
| 3.19.1. | Converting Angle Measures | |
| 3.19.2. | Finding Points in Standard Position | |
| 3.19.3. | Using the Pythagorean Identity | |
| 3.19.4. | Finding Cosine From Sine | |
| 3.19.5. | Applying Quotient and Angle Identities | |
| 3.19.6. | Identifying Equivalent Trig Representations | |
| 3.19.7. | Finding Amplitude, Period, and Range | |
| 3.19.8. | Matching and Transforming Trig Graphs | |
| 3.19.9. | Finding Triangle Area Using Sine | |
| 3.19.10. | Using the Law of Sines | |
| 3.19.11. | Using the Law of Cosines | |
| 3.19.12. | Solving Trig Equations and Inequalities |
| 4.20.1. | Finding Lengths on a Line | |
| 4.20.2. | Finding Angles Formed by Intersecting Lines | |
| 4.20.3. | Finding Reflex and Divided Angles | |
| 4.20.4. | Problem-Solving With Intersecting Lines | |
| 4.20.5. | Solving Angle Bisector Problems | |
| 4.20.6. | Finding Angles With Parallel Lines | |
| 4.20.7. | Problem-Solving With Parallel Lines | |
| 4.20.8. | Finding Interior Angles of Triangles | |
| 4.20.9. | Finding Exterior Angles of Triangles | |
| 4.20.10. | Finding Angles in Isosceles Triangles | |
| 4.20.11. | Problem-Solving With Isosceles Triangles | |
| 4.20.12. | Relating Sides to Opposite Angles | |
| 4.20.13. | Applying the Triangle Inequality | |
| 4.20.14. | Classifying Triangles | |
| 4.20.15. | Identifying Angle and Shape Properties | |
| 4.20.16. | Finding Interior Angles of Polygons | |
| 4.20.17. | Finding Angles in Parallelograms | |
| 4.20.18. | Finding Lengths With Parallel Sides | |
| 4.20.19. | Finding Lengths in Regular Polygons |
| 4.21.1. | Translating and Reflecting a Point | |
| 4.21.2. | Applying a Rigid Motion | |
| 4.21.3. | Dilating a Figure | |
| 4.21.4. | Identifying Corresponding Parts Under Congruence | |
| 4.21.5. | Using Corresponding Parts Under Similarity | |
| 4.21.6. | Finding Corresponding Lengths in Similar Figures | |
| 4.21.7. | Using Scale Factors in Similar Figures | |
| 4.21.8. | Finding Lengths Using Parallel Lines | |
| 4.21.9. | Finding Areas of Similar Figures |
| 4.22.1. | Applying the Pythagorean Theorem | |
| 4.22.2. | Modeling Situations Using the Pythagorean Theorem | |
| 4.22.3. | Finding Diagonals and Perimeters With the Pythagorean Theorem | |
| 4.22.4. | Finding Lengths in Figures With the Pythagorean Theorem | |
| 4.22.5. | Finding Altitudes and Areas With the Pythagorean Theorem | |
| 4.22.6. | Checking and Applying Pythagorean Relationships | |
| 4.22.7. | Problem-Solving With Special Triangles | |
| 4.22.8. | Finding Trigonometric Ratios | |
| 4.22.9. | Finding a Trigonometric Ratio From Other Ratios | |
| 4.22.10. | Using Cofunction Relationships | |
| 4.22.11. | Finding a Side From a Trigonometric Ratio | |
| 4.22.12. | Finding a Length From an Angle Measure | |
| 4.22.13. | Writing an Inverse-Trigonometric Expression |
| 4.23.1. | Finding Areas of Composite Rectilinear Figures | |
| 4.23.2. | Finding Areas of Divided Rectangles | |
| 4.23.3. | Finding Perimeters of Figures | |
| 4.23.4. | Using a Given Perimeter | |
| 4.23.5. | Finding Areas of Quadrilaterals | |
| 4.23.6. | Finding Areas of Triangles | |
| 4.23.7. | Finding Shaded Areas With Circles | |
| 4.23.8. | Comparing Areas of Figures | |
| 4.23.9. | Finding Areas of Nested Regions | |
| 4.23.10. | Finding a Length From Area |
| 4.24.1. | Finding Areas Involving Circles | |
| 4.24.2. | Finding the Circumference of a Circle | |
| 4.24.3. | Finding Distance Along a Circle | |
| 4.24.4. | Comparing Areas of Circles | |
| 4.24.5. | Finding Arc Measure | |
| 4.24.6. | Finding Arc Length | |
| 4.24.7. | Finding Angles in Circles | |
| 4.24.8. | Problem-Solving With Circle Lengths |
| 4.25.1. | Finding the Midpoint of a Segment | |
| 4.25.2. | Finding a Point Dividing a Segment | |
| 4.25.3. | Finding the Distance Between Points | |
| 4.25.4. | Finding Slope From Two Points | |
| 4.25.5. | Finding Slope From an Equation | |
| 4.25.6. | Comparing and Reading Slopes | |
| 4.25.7. | Interpreting Slope and Its Changes | |
| 4.25.8. | Using Slopes of Parallel Lines | |
| 4.25.9. | Using Slopes of Perpendicular Lines | |
| 4.25.10. | Writing the Equation of a Line | |
| 4.25.11. | Finding a Point on a Line | |
| 4.25.12. | Writing the Equation of a Circle | |
| 4.25.13. | Problem-Solving With Circles | |
| 4.25.14. | Further Problem-Solving With Circles | |
| 4.25.15. | Finding Area in the Coordinate Plane | |
| 4.25.16. | Placing Figures in the Coordinate Plane | |
| 4.25.17. | Locating Points in the Coordinate Plane |
| 4.26.1. | Finding Volumes of Prisms and Cylinders | |
| 4.26.2. | Finding Volumes of Pyramids, Cones, and Spheres | |
| 4.26.3. | Finding a Dimension From Volume | |
| 4.26.4. | Finding the Surface Area of a Solid | |
| 4.26.5. | Converting Volume in Context | |
| 4.26.6. | Applying Volume Scale Factors | |
| 4.26.7. | Packing Congruent Solids | |
| 4.26.8. | Identifying Features of a Solid |
| 4.27.1. | Writing Ellipse Equations | |
| 4.27.2. | Finding Features of an Ellipse | |
| 4.27.3. | Working With Hyperbolas | |
| 4.27.4. | Analyzing Intersections of Conics |
| 5.28.1. | Finding a Weighted Mean | |
| 5.28.2. | Finding a Median From Frequencies | |
| 5.28.3. | Comparing Measures of Center | |
| 5.28.4. | Finding How a Data Change Affects a Mean | |
| 5.28.5. | Using Means and Sums | |
| 5.28.6. | Determining Effects of Changing Data | |
| 5.28.7. | Finding Unknown Values From Center Measures | |
| 5.28.8. | Comparing Measures of Spread |
| 5.29.1. | Reading Two-Way Tables | |
| 5.29.2. | Reading Category Tables | |
| 5.29.3. | Reading Bar Graphs | |
| 5.29.4. | Working With Circle Graphs | |
| 5.29.5. | Reading Frequency Distributions | |
| 5.29.6. | Reasoning About Data Displays | |
| 5.29.7. | Reading Trend Graphs |
| 5.30.1. | Finding a Simple Probability | |
| 5.30.2. | Solving for a Count Given a Probability | |
| 5.30.3. | Working With Event Relationships | |
| 5.30.4. | Finding a Union With Overlap | |
| 5.30.5. | Finding a Probability From a Two-Way Table | |
| 5.30.6. | Finding a Conditional Probability From a Table | |
| 5.30.7. | Finding a Conditional Probability | |
| 5.30.8. | Applying a Conditional Probability | |
| 5.30.9. | Multiplying Independent Probabilities | |
| 5.30.10. | Finding a Without-Replacement Probability | |
| 5.30.11. | Problem-Solving With Dependent Selections | |
| 5.30.12. | Finding a Probability of an Arrangement | |
| 5.30.13. | Finding a Probability From a Sample Space | |
| 5.30.14. | Finding a Geometric Probability | |
| 5.30.15. | Computing an Expected Value | |
| 5.30.16. | Problem-Solving With Expected Value |
| 5.31.1. | Counting Independent Choices | |
| 5.31.2. | Counting Character Codes | |
| 5.31.3. | Counting Permutations | |
| 5.31.4. | Counting Combinations | |
| 5.31.5. | Counting Overlapping Sets | |
| 5.31.6. | Identifying Possible Set Sizes |
| 5.32.1. | Estimating a Population Mean | |
| 5.32.2. | Estimating a Population From a Sample Proportion | |
| 5.32.3. | Judging Evidence From a Sample | |
| 5.32.4. | Identifying a Model Type | |
| 5.32.5. | Applying the Empirical Rule | |
| 5.32.6. | Fitting a Linear Model to Data | |
| 5.32.7. | Using a Linear Model |
| 6.33.1. | Evaluating Absolute-Value Expressions | |
| 6.33.2. | Evaluating Numeric Expressions | |
| 6.33.3. | Evaluating Factorials and Quotients | |
| 6.33.4. | Comparing Signed Number Changes | |
| 6.33.5. | Computing Integer Amounts in Context | |
| 6.33.6. | Identifying Place Value and Properties | |
| 6.33.7. | Adding Fractions | |
| 6.33.8. | Subtracting Fractions | |
| 6.33.9. | Multiplying Fractions | |
| 6.33.10. | Dividing With Fractions | |
| 6.33.11. | Finding a Midpoint Between Fractions | |
| 6.33.12. | Locating Numbers on a Number Line | |
| 6.33.13. | Ordering Rational Numbers | |
| 6.33.14. | Estimating Square Roots |
| 6.34.1. | Partitioning a Total in a Given Ratio | |
| 6.34.2. | Finding a Whole From a Ratio | |
| 6.34.3. | Composing Chained Ratios | |
| 6.34.4. | Comparing Ratios | |
| 6.34.5. | Applying Proportions | |
| 6.34.6. | Finding a Unit Rate | |
| 6.34.7. | Solving Fuel Mileage Problems | |
| 6.34.8. | Working With a Rate of Change | |
| 6.34.9. | Finding Distance at Constant Speed | |
| 6.34.10. | Finding Position or Travel Time | |
| 6.34.11. | Finding an Average Speed | |
| 6.34.12. | Solving Multi-Leg Speed Problems | |
| 6.34.13. | Combining Rates |
| 6.35.1. | Finding a Percent of a Number | |
| 6.35.2. | Expressing a Ratio as a Percent | |
| 6.35.3. | Finding a Total From a Percent | |
| 6.35.4. | Applying a Percent Change | |
| 6.35.5. | Taking Successive Percents | |
| 6.35.6. | Applying Successive Percent Changes | |
| 6.35.7. | Finding a Percent in a Mixture |
| 6.36.1. | Computing With Mixed Units | |
| 6.36.2. | Converting a Measurement | |
| 6.36.3. | Applying Conversion Factors | |
| 6.36.4. | Converting a Rate |
| 6.37.1. | Computing a Total From Unit Prices | |
| 6.37.2. | Finding a Total From Repeated Amounts | |
| 6.37.3. | Computing a Cost From a Unit Rate | |
| 6.37.4. | Finding a Remaining Amount | |
| 6.37.5. | Comparing Two Totals | |
| 6.37.6. | Finding a Net Cost or Profit | |
| 6.37.7. | Computing Overtime Pay | |
| 6.37.8. | Finding a Unit Amount | |
| 6.37.9. | Finding a Fractional Part of a Whole | |
| 6.37.10. | Applying Successive Fractions | |
| 6.37.11. | Packing Into Whole Groups | |
| 6.37.12. | Finding Counts From Waste and Limits | |
| 6.37.13. | Combining Segments of a Trip | |
| 6.37.14. | Identifying a Necessary Conclusion |
| 6.38.1. | Finding a Mean | |
| 6.38.2. | Finding a Median | |
| 6.38.3. | Finding a Value From a Mean | |
| 6.38.4. | Finding a Difference of Center Measures |
| 6.39.1. | Finding the Area of a Rectangle | |
| 6.39.2. | Finding the Area of a Square | |
| 6.39.3. | Finding the Area of a Triangle | |
| 6.39.4. | Finding a Side From Equal Areas | |
| 6.39.5. | Combining Rectangle Areas | |
| 6.39.6. | Finding a Shaded Fractional Area | |
| 6.39.7. | Finding the Perimeter of a Rectangle | |
| 6.39.8. | Finding the Perimeter of a Square | |
| 6.39.9. | Finding the Volume of a Rectangular Prism | |
| 6.39.10. | Scaling a Rectangular Prism Volume | |
| 6.39.11. | Counting Packed Rectangular Units |
