Study on the flyACTMathematics
ACT
Mathematics — ACT topics
- 34 topics
- 45 questions on the paper
- 50 minutes
- 1718 practice questions in the app
- Free
The ACT Mathematics section is split into 34 topics, from Real number system and number properties to Counting, combinations, and permutations. The paper gives it 45 questions in 50 minutes. The app holds 1718 practice questions across these topics.
What the section covers
| Topic | Share of the section | In the app |
|---|---|---|
| Real number system and number propertiesPrimes, factors, multiples, GCF/LCM · Even/odd and positive/negative properties · Rational vs. irrational (π, √n) · Absolute value and distance on the number line | ≈3% | 61 questions |
| Integer and rational exponentsExponent rules and simplification · Rational (fractional) exponents ↔ radicals · Scientific notation and powers of 10 | — | 41 questions |
| Radicals and rootsSimplifying square and cube roots · Operating with radical expressions | ≈5% | 41 questions |
| Complex numbersPowers of i and simplification · Adding, subtracting, multiplying complex numbers · Properties of the complex number system | ≈3% | 47 questions |
| Vectors and matricesVectors: magnitude, direction, addition, scalar multiplication · Matrices: add/subtract/scalar multiply, and multiply matrices | ≈2% | 49 questions |
| Fractions, decimals, and operationsOperations and order of operations · Fraction ↔ decimal ↔ percent conversion · Comparing and ordering (number line, ordering fractions) | ≈3% | 54 questions |
| Percents and percent changePercent of / is-of basics · Percent increase and decrease · Multi-step percent in context (tax, discount, successive change) | — | 43 questions |
| Ratios, rates, and proportional relationshipsRatios and proportions · Unit rates and unit conversion (derived units, ft/sec → mi/hr) · Scale factor and similar-figure proportion · Direct vs. inverse variation | ≈6% | 68 questions |
| Linear equations and expressions in one variableSimplify and evaluate expressions (like terms, substitution) · Solve multi-step linear equations · Translate words to symbols and solve in context | ≈2% | 61 questions |
| Inequalities (linear and compound)Solving linear inequalities, including reversing the sign · Compound inequalities and number-line graphs · Absolute value inequalities | — | 47 questions |
| Systems of equationsSolve by substitution and elimination · Set up and solve a system from a word problem | ≈5% | 49 questions |
| Polynomial expressions and factoringAdd, subtract, multiply polynomials (incl. binomials/FOIL) · Factoring (GCF, difference of squares, trinomials) · Polynomial roots and the remainder theorem | ≈8% | 60 questions |
| Quadratic equationsSolve by factoring / zero-product property · Quadratic formula and completing the square · Interpret roots and number of solutions | ≈2% | 46 questions |
| Radical and rational equationsRadical equations and extraneous solutions · Rational equations and when an expression is undefined | — | 38 questions |
| Exponential relationshipsExponential growth and decay models · Solving exponential equations with a common base | — | 49 questions |
| Function notation and evaluating functionsEvaluate f(x) at a value · Interpret function notation in context · Composite functions f(g(x)) | ≈6% | 66 questions |
| Linear functions and graphsSlope and rate of change · Writing and matching linear equations to graphs · Interpreting a linear model (starting value + amount per unit) | ≈2% | 40 questions |
| Quadratic and polynomial functionsParabola features (vertex, axis, intercepts) · Standard/vertex/factored form and graph matching · Polynomial behavior and roots | ≈2% | 42 questions |
| Radical and rational functionsDomain and range · Vertical asymptotes and undefined points | ≈1% | 38 questions |
| Piecewise functions | ≈1% | 46 questions |
| Exponential and logarithmic functionsExponential functions and their graphs · Logarithms: definition, evaluation, basic properties | ≈2% | 45 questions |
| Key features and transformations of graphsVertical and horizontal translations · Reflections and stretches · Reading key features (intercepts, max/min, increasing/decreasing) | ≈1% | 54 questions |
| Lines, angles, and polygonsParallel lines and transversals · Angle sums (triangle, polygon, 90/180/360) · Perimeter and area of polygons and composite figures · Lines of symmetry | ≈5% | 59 questions |
| Triangles — congruence, similarity, Pythagorean theoremTriangle area, perimeter, and basic properties · Pythagorean theorem and triples · Special right triangles (30-60-90, 45-45-90) · Similarity, congruence, and scale factor | ≈6% | 62 questions |
| Circles — arcs, sectors, angles, equationsCircumference and area · Arcs, sectors, and angle relationships · Equation of a circle (center and radius) | ≈5% | 61 questions |
| Surface area and volume of solidsVolume of prisms, cylinders, cones, spheres · Surface area and derived measures (find one measure from another) | ≈1% | 38 questions |
| Coordinate geometry — distance, midpoint, slope, line equationsSlope, distance, and midpoint · Equations of lines, parallel and perpendicular · Graphing and matching lines and inequalities · Transformations of points (translate, reflect, rotate) | ≈3% | 66 questions |
| Conic sections | ≈1% | 36 questions |
| Right-triangle trigonometry and trig functionsSOH-CAH-TOA and solving right triangles · The unit circle · Graphs of trig functions · Basic identities and trig equations | ≈5% | 61 questions |
| Measures of center and spreadMean, median, mode, range · Working backwards from an average (missing value, frequency counts) · Weighted average | ≈6% | 59 questions |
| Data collection methods and study design | — | 40 questions |
| Bivariate data and relationships (scatterplots, correlation)Scatterplots, trend, and line of best fit · Two-way frequency tables and translating between representations | ≈1% | 45 questions |
| Probability and sample spacesSimple probability and complements · Compound events (and / or / not) · Independent vs. dependent, conditional probability · Geometric probability | ≈9% | 61 questions |
| Counting, combinations, and permutationsFundamental counting principle and Venn-diagram counting · Permutations vs. combinations | ≈1% | 45 questions |
Shares are approximate: the topic mix of the Mathematics questions on real ACT papers.
How it is scored
Counts toward the ACT composite (1–36). How ACT scores work
Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.
Other ACT sections
Harder than the exam: ACT Challenge · Competition-style problems
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