ACT Math
All ACT Math topics
The official ACT math taxonomy, with subtopics and a count of practice items in each. Click any topic to drill it.
The ACT doesn't pull questions from a vague pool of "math problems." Every item is written against a specific subtopic in a published taxonomy, and the test form is balanced so each topic shows up in roughly the same proportion every time. That's why drilling by topic works: if you're missing 3 out of 4 questions on linear systems, the test guarantees you'll see linear systems again on test day. Fix the topic, fix your score.
Below is the complete list of topics and subtopics covered by the ACT math section, with the number of practice questions we've filed in each. The rough percentages reflect the ACT's published content distribution.
Pre-Algebra
24% of test 56 practice questions
Pre-Algebra covers operations on whole numbers, fractions, decimals, integers, and rational numbers; ratios and percentages; basic statistics; and elementary probability.
Fractions, decimals, and integers
Operations on fractions, decimals, and integer arithmetic.
Ratios, proportions, and percentages
Setting up proportions and percent computations.
Mean, median, mode, and range
Measures of center and spread on small data sets.
Elementary probability
Counting outcomes and computing simple probabilities.
Elementary Algebra
17% of test 56 practice questions
Elementary Algebra covers solving single-variable linear equations and inequalities, basic polynomial operations, and substitution into algebraic expressions.
Single-variable linear equations
Solving ax + b = c and similar equations.
Polynomial addition and multiplication
Adding, subtracting, and multiplying polynomials including FOIL.
Substitution and evaluation
Plugging values into an expression and simplifying.
Absolute value equations and inequalities
Solving |expression| = k and |expression| < k.
Intermediate Algebra
15% of test 56 practice questions
Intermediate Algebra covers quadratic and polynomial equations, rational expressions, radicals, exponents, and basic function notation.
Quadratic equations
Solving quadratics by factoring or formula.
Function notation and composition
Evaluating f(x), composing f(g(x)), and inverse functions.
Arithmetic and geometric sequences
Finding the nth term of arithmetic and geometric sequences.
Systems of equations and matrices
Solving 2-by-2 systems and basic matrix arithmetic.
Coordinate Geometry
15% of test 56 practice questions
Coordinate Geometry covers lines and slopes, distance and midpoint, parallel and perpendicular lines, the equation of a circle, and an introduction to conic sections.
Lines, slopes, and intercepts
Slope, point-slope form, and parallel/perpendicular lines.
Distance and midpoint
Distance and midpoint between two points.
Circles in the coordinate plane
Standard equation, center, and radius of a circle.
Introduction to conics
Recognizing parabolas, ellipses, and hyperbolas from equations.
Plane Geometry
23% of test 56 practice questions
Plane Geometry covers triangles, polygons, circles, parallel lines and angles, areas and perimeters, and basic three-dimensional figures.
Triangles and the Pythagorean theorem
Right triangles, similar triangles, and triangle inequalities.
Polygons, perimeter, and area
Quadrilaterals, regular polygons, and area formulas.
Circles, arcs, and chords
Circumference, area, arcs, sectors, and inscribed angles.
Three-dimensional figures
Volume and surface area of prisms, cylinders, and cones.
Trigonometry
7% of test 56 practice questions
Trigonometry covers right-triangle trigonometry, the unit circle, basic trig identities, and graphs of trig functions.
Right triangle trigonometry
Sine, cosine, and tangent of right triangle angles.
The unit circle and special angles
Sine and cosine values at 0°, 30°, 45°, 60°, and 90°.
Basic trig identities
sin²θ + cos²θ = 1 and tan = sin/cos.
Graphs of sine and cosine
Amplitude, period, and phase shift.
Why drill by topic instead of by full test?
Mixed-topic practice has its place — it builds endurance, simulates pacing, and exposes weak spots. But once you've identified those weak spots, mixed practice is one of the slowest ways to fix them. If algebraic translation problems are eating your score, doing one of them every twenty minutes inside a full test won't drill the pattern into your hands. Doing fifteen of them in a row will. That's what the topic pages on this site are for.
Recommended sequence
For most students we suggest working topics in this rough order: linear equations, then linear systems, then ratios and percents, then quadratic functions, then geometry, then everything else. The early topics show up everywhere on the test — including inside questions whose surface category is something else — so locking them down early pays compounding returns.