United States · ACTSyllabus
Maths syllabus, dot point by dot point
Every dot point in the United States Mathssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.8, Anthropic's latest AI.
Algebra
Module overview →- How do you solve exponential and radical equations on the ACT, and how do you avoid extraneous solutions?Solve exponential equations by matching bases and radical equations by isolating and squaring, checking for extraneous solutions (Algebra).10 min answer →
- How do you manipulate algebraic expressions and find the equation of a line in the coordinate plane on the ACT?Evaluate and rearrange algebraic expressions, solve literal equations for a variable, and find the slope and equation of a line in the coordinate plane (Algebra).10 min answer →
- How do you solve linear equations and inequalities, including those with variables on both sides, on the ACT?Solve linear equations and inequalities in one variable, including multi-step and variables-on-both-sides cases, and remember to flip the inequality when multiplying or dividing by a negative (Algebra).10 min answer →
- How do you expand, factor and simplify polynomial expressions on the ACT?Expand products of polynomials, factor by common factor, grouping and special patterns, and simplify polynomial and rational expressions (Algebra).10 min answer →
- How do you solve quadratic equations on the ACT by factoring, the quadratic formula, and the discriminant?Solve quadratic equations by factoring, the quadratic formula and square roots, and use the discriminant to count real solutions (Algebra).11 min answer →
- How do you solve a system of two linear equations on the ACT by substitution or elimination?Solve systems of two linear equations by substitution and elimination, interpret the solution as an intersection point, and recognise systems with no solution or infinitely many solutions (Algebra).10 min answer →
Format and Strategy
Module overview →- What is the ACT calculator policy, and how do you use a calculator well on the Math test?Apply the ACT calculator policy (calculator permitted throughout, some models prohibited) and use a calculator strategically to save time without losing accuracy or setup understanding.9 min answer →
- What is the current format of the ACT Mathematics test, and what changed when the enhanced ACT replaced the legacy version?Describe the enhanced ACT Mathematics format: about 45 questions in 50 minutes with four answer choices, a permitted calculator throughout, a 1 to 36 score, and how it differs from the legacy 60-question, 60-minute test.9 min answer →
- What is the Integrating Essential Skills reporting category, and how do you handle its multi-step word problems?Explain the Integrating Essential Skills reporting category (about 40 to 43 percent of the test) and solve its multi-step problems that combine rates, proportions, percentages, averages, area and measurement in real contexts.10 min answer →
- What is the Modeling reporting category on the ACT Math test, and how do you produce and interpret a model?Explain the Modeling reporting category (a cross-cutting score) and produce, interpret, evaluate and improve mathematical models that translate a real situation into equations, expressions or graphs.9 min answer →
- How do you pace the ACT Math test, guess well, and understand how the 1 to 36 score is produced?Pace the ACT Math test at about 67 seconds per question, use elimination and the no-penalty rule to guess every remaining question, and understand how raw scores convert to the 1 to 36 scale and the Composite.9 min answer →
Functions
Module overview →- How do you interpret exponential growth and decay, distinguish them from linear change, and read logarithms on the ACT?Interpret exponential functions for growth and decay, distinguish exponential from linear change, work with compound growth, and read basic logarithms as inverse exponents (Functions).11 min answer →
- How do you read function notation, evaluate functions, and find domain and range on the ACT?Read and use function notation, evaluate functions including composition, and identify domain and range from rules and graphs (Functions).10 min answer →
- How do you interpret linear functions, slope as a rate of change, and build a linear model on the ACT?Interpret a linear function's slope as a rate of change and its intercept as a starting value, build linear models, and read slope from points, tables and graphs (Functions).10 min answer →
- How do you read a quadratic function's graph, including its vertex, intercepts and axis of symmetry, on the ACT?Read a parabola from the three forms of a quadratic, find the vertex, axis of symmetry, intercepts and direction of opening, and identify maximum or minimum values (Functions).11 min answer →
- How do you work with arithmetic and geometric sequences on the ACT, including finding a term and a sum?Identify arithmetic and geometric sequences, find a specified term using the explicit rule, and compute simple sums (Functions).10 min answer →
- How do shifts, reflections and stretches transform the graph of a function on the ACT?Apply vertical and horizontal shifts, reflections and stretches to the graph of a function, and read a transformed function's equation from its parent (Functions).10 min answer →
Geometry
Module overview →- How do you use angle relationships and triangle properties to find unknown angles and sides on the ACT?Apply angle relationships (vertical, supplementary, parallel-line angles) and triangle properties (angle sum, exterior angle, isosceles and the triangle inequality) to find unknowns (Geometry).10 min answer →
- How do you compute area, perimeter, surface area and volume of common shapes and solids on the ACT?Compute the perimeter and area of triangles, rectangles, parallelograms, trapezoids and circles, and the surface area and volume of prisms, cylinders and other common solids (Geometry, Integrating Essential Skills).11 min answer →
- How do you use circle formulas and the equation of a circle on the ACT?Apply circle formulas for circumference, area, arc length and sector area, and use the standard equation of a circle to find its centre and radius (Geometry).10 min answer →
- How do you use the distance, midpoint and slope formulas in the coordinate plane on the ACT?Apply the distance, midpoint and slope formulas, identify parallel and perpendicular lines, and analyse figures placed in the coordinate plane (Geometry).10 min answer →
- How do you use the Pythagorean theorem and SOH-CAH-TOA to solve right triangles on the ACT?Apply the Pythagorean theorem, the special right triangles, and the sine, cosine and tangent ratios (SOH-CAH-TOA) to find sides and angles of right triangles (Geometry).11 min answer →
- How do you use similarity and congruence, including proportional sides and scale factors, on the ACT?Identify similar and congruent figures, use proportional corresponding sides and equal corresponding angles, and apply scale factors to lengths, areas and volumes (Geometry).10 min answer →
Number and Quantity
Module overview →- How do you apply the laws of exponents, simplify roots, and work with scientific notation on the ACT?Apply integer and rational exponent laws, simplify and operate with square and higher roots, and convert and compute with numbers in scientific notation (Number and Quantity).11 min answer →
- How do you compute percentages, percent change, and reverse percentages on the ACT?Compute a percentage of a number, percent increase and decrease, successive and reverse percentages, and simple interest in real contexts (Number and Quantity, Integrating Essential Skills).10 min answer →
- How do you set up and solve ratio, proportion and rate problems on the ACT?Set up and solve ratios, proportions and rates, including unit rates, scaling, direct and inverse variation, and unit conversion (Number and Quantity, Integrating Essential Skills).10 min answer →
- How do you classify real numbers and perform basic operations with complex numbers on the ACT?Classify numbers within the real number system, work with absolute value, and add, subtract, multiply and simplify complex numbers using (Number and Quantity).10 min answer →
- How do you perform basic vector and matrix operations on the ACT?Add, subtract and scalar-multiply vectors and matrices, find a vector's magnitude, and multiply small matrices (Number and Quantity).10 min answer →
Statistics and Probability
Module overview →- How do you count arrangements and selections using the counting principle, permutations and combinations on the ACT?Count outcomes with the fundamental counting principle, and distinguish permutations (order matters) from combinations (order does not matter) (Statistics and Probability).10 min answer →
- How do you read and interpret tables, bar graphs, histograms and other data displays on the ACT?Read and interpret data from tables, bar graphs, line graphs, histograms, pie charts and box plots, and compute statistics or probabilities from a display (Statistics and Probability, Integrating Essential Skills).10 min answer →
- How do you compute and interpret the mean, median, mode and range of a data set on the ACT?Compute the mean, median, mode and range of a data set, find a missing value given a target mean, and interpret which measure of centre best describes data (Statistics and Probability).10 min answer →
- How do you compute the probability of simple and compound events on the ACT?Compute the probability of single events, complements, and compound events using the addition and multiplication rules, including independent and mutually exclusive events (Statistics and Probability).10 min answer →
- How do you compute a weighted average and the expected value of a random outcome on the ACT?Compute weighted averages (such as a course grade from weighted components) and the expected value of a random variable as a probability-weighted sum (Statistics and Probability).10 min answer →