ACT
ACT Math practice and prep course
Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability. Start with 300 free questions. The full course adds the lessons, the study guide, and practice tests.
Course outline
- How to Use This CourseThe ACT Math format, the six reporting categories, the recognition sheet, method choice, and a step-by-step routine for working through each chapter.10 questions
- Diagnostic TestA 45-question diagnostic sampling all six ACT Math categories, with full explanations and a skills map that tells you which chapters to study first.45 questions
- Real and Complex NumbersClassify rational and irrational numbers, cycle through powers of i, and add, multiply, and divide complex numbers, including when a quadratic has complex roots.30 questions
- Exponents and RadicalsApply the exponent rules, simplify and combine radicals, rationalize denominators, and solve radical and exponential equations while checking for extraneous roots.30 questions
- Vectors and MatricesAdd vectors and find magnitudes, then work with matrices: sums, scalar multiples, determinants, products, dimensions, and systems written as matrix equations.30 questions
- Part I ReviewA mixed review of Number and Quantity: complex numbers, exponents and radicals, vectors, and matrices, with no chapter labels.20 questions
- Linear Equations and SystemsSolve linear equations, inequalities, compound inequalities, and systems by substitution or elimination, and rearrange formulas.30 questions
- Quadratic EquationsSolve quadratics by factoring and the quadratic formula, use the discriminant, and find vertices and the sum and product of roots.30 questions
- Other Types of EquationsSolve polynomial equations by factoring, use the factor theorem, solve exponential equations with a common base, and check radical equations for extraneous roots.30 questions
- Absolute ValueSolve absolute value equations and inequalities, check extraneous solutions when a variable is outside the bars, and model tolerances.30 questions
- Part II ReviewA mixed review of Part II Algebra: linear equations and systems, quadratics, polynomial, exponential and radical equations, and absolute value.20 questions
- Function Notation and CompositionEvaluate functions, compose them in the right order, and find domain and range, including restrictions from roots, denominators, logarithms, and real-world context.34 questions
- Polynomial FunctionsFind rates of change, zeros, and end behavior of polynomials, and use the arithmetic-sequence formula to work with non-adjacent terms.30 questions
- Other Function FamiliesWork with rational functions and their asymptotes, evaluate logarithms, and model growth, decay, and geometric sequences with exponentials.30 questions
- Transformations and Piecewise FunctionsShift, reflect, and scale graphs by reading what happens inside and outside a function, build equations from descriptions, and evaluate piecewise functions.33 questions
- Inverse FunctionsUndo a function by swapping x and y, use domain and range swaps, and handle restricted domains and compositions with inverses.30 questions
- Sequences and SeriesSum arithmetic and geometric series with the right formula, read sigma notation, and avoid off-by-one errors in counting terms.30 questions
- LogarithmsCombine and split logarithms with the product, quotient and power rules, solve log and exponential equations, and reject invalid solutions.30 questions
- Part III ReviewA mixed review of the Functions topics in Part III, plus extra practice on series, logarithms, and basic trigonometry.26 questions
- Lines, Angles, and TrianglesUse angle relationships for parallel lines, triangles, exterior angles, and isosceles triangles, and apply the triangle inequality.30 questions
- Congruence and SimilarityTell similar from congruent figures, apply scale factors to lengths, perimeters, and areas, and choose the right congruence criterion.32 questions
- Right Triangles and TrigonometryUse the Pythagorean theorem, special right triangles, sine, cosine, tangent, and exact unit-circle values.30 questions
- Circles and Conic SectionsWork with circle equations, arcs, and tangents, then identify ellipses, hyperbolas, and parabolas and find their key features.35 questions
- Area and VolumeCompute areas and volumes of common shapes, build composite figures by adding and subtracting, and scale volumes of similar solids.31 questions
- Coordinate GeometryUse the distance and midpoint formulas, slope relationships, and grid-aligned bases to solve problems about points, lines, and triangles in the coordinate plane.30 questions
- Trigonometry Beyond Right TrianglesRewrite trig expressions with identities and solve non-right triangles with the Law of Sines and Law of Cosines.30 questions
- Geometric TransformationsApply the coordinate rules for reflections, rotations, translations, and dilations, and track area under a scale factor.30 questions
- Circle TheoremsUse inscribed and central angles, tangents, chords, and secants, and match each figure to the right circle relationship.30 questions
- Geometric Reasoning and ConstructionsWork with converses, inverses, contrapositives, counterexamples, two-column proofs, and compass-and-straightedge constructions.26 questions
- Part IV ReviewMixed Geometry review across all ten Part IV chapters, plus extra practice on transformations, trigonometry, circles, and reasoning.32 questions
- Center and SpreadMean, median, mode, range, IQR, standard deviation, weighted means, and how skew and outliers change them.34 questions
- Study Design and SamplingSampling methods and bias, observational studies versus experiments, and reading two-way tables with joint, marginal, and conditional proportions.30 questions
- Two-Variable Data and ModelsLines of best fit, residuals, slope and intercept in context, correlation versus causation, and judging whether a model fits.33 questions
- ProbabilityCount outcomes, choose between the addition and multiplication rules, handle conditional probability, combinations, permutations, and expected value.30 questions
- Normal Distributions and Z-ScoresUse the 68-95-99.7 rule and z-scores to place values in a normal distribution and to compare scores from different tests.30 questions
- Statistical InferenceInterpret margins of error, check whether a claimed value is plausible, and understand sample size, sampling variability, and simulation.30 questions
- Part V ReviewA mixed review of all of Part V: center and spread, sampling, two-variable data, probability, normal distributions, and inference.28 questions
- Rates, Percentages, and ProportionsUnit rates, percent change versus percentage points, reversing a percent change, and direct and inverse proportions in word problems.30 questions
- Measurement and Unit ConversionConvert lengths, areas, volumes, and compound rates without dropping a factor, including squared and cubed units.30 questions
- Averages in ContextMissing-value averages, weighted averages, combined groups, and average speed as total distance over total time.30 questions
- Multi-Step ProblemsChain percent changes, scaling, rates, averages, and unit conversions, and carry each problem through to its final step.30 questions
- Part VI ReviewA mixed, unlabeled review of rates and percents, unit conversion, averages, and multi-step problems from Part VI.20 questions
- Calculator Routes and BacksolvingChoose between hand, handheld, Desmos, and hybrid routes, and use backsolving, plugging in, and estimating to beat the four answer choices.12 questions
- Archetypes and the Error LedgerA field guide to recurring ACT Math question forms and the specific mistakes each answer choice is built to catch.Lesson
- Practice: Choosing a RouteForty quick drills on picking hand, handheld, Desmos, or hybrid as the fastest reliable way to attack each kind of ACT Math situation.40 questions
- Mixed Challenge PracticeSixty mixed ACT Math problems that blend algebra, functions, geometry, statistics, and everyday quantitative skills without telling you which method to use.60 questions
- Final Skills CheckFourteen questions, each built to isolate one failure mechanism such as the wrong requested object, a sign flip, a unit slip, or an extraneous root.14 questions
- PacingDiagnose where ACT Math time leaks, decide when to leave a question, and review a timed section with a 10-question, 12-minute drill.10 questions
- Test Day and ReferencePlan your calculator, Desmos, scratch work, and checklists for ACT Math test day, then review the key relationships in one compact reference.Lesson
- Full-Length Benchmark TestA 45-question, 50-minute full-length ACT Math benchmark covering all reporting categories, with full solutions.45 questions
- Additional Practice Test 1A second 45-question, 50-minute full-length ACT Math form that rises in difficulty, with worked solutions.45 questions
- Additional Practice Test 2A 45-question, 50-minute ACT Math stress drill that practices recovery from expensive early items, with extra geometry, trigonometry, and visual interpretation.45 questions
- Geometry and Trigonometry Timed PracticeA 20-question, 22-minute timed set weighted toward similarity, trigonometry, circles, transformations, and measurement, with a method for diagnosing each missed question.20 questions
- Statistics and Probability Timed PracticeA 20-question, 22-minute timed set on center and spread, normal distributions, study design, margin of error, probability, bivariate models, and percent chains.20 questions