ACT Math study guide
ACT Math · Work through your exam, one topic at a time.
The ACT is a college admissions test; ACT reports that more than 2 million students take it each year, that 100% of U.S. colleges accept it, and that it has been trusted for 60+ years. The ACT Math study guide has 5 sections and about 1,653 words.
01Number and Quantity
Number and Quantity on the ACT is mostly arithmetic in disguise: converting between fractions, decimals, and percents; setting up ratios and proportions; applying integer exponent rules and radical rules; reading scientific notation; evaluating absolute value; and doing simple arithmetic with complex numbers, where i^2 = -1 . You should also be fluent with factors, multiples, prime factorization, and the sign rules for products and quotients.
328 words, about 2 min02Algebra
Algebra questions ask you to manipulate expressions and solve equations and inequalities. Expect linear equations and inequalities in one and two variables, slope and intercepts, systems of two equations (substitution, elimination, and the conditions for zero or infinitely many solutions), polynomial arithmetic and factoring, quadratic equations solved by factoring or the quadratic formula, the discriminant, rational expressions, and translation of word problems into equations.
351 words, about 2 min03Functions
Functions questions test the idea of a rule that assigns exactly one output to each input. You need function notation, domain and range, composition, inverses, transformations of graphs, and the behavior of the main families: linear, quadratic, polynomial, exponential, rational, radical, and logarithmic.
340 words, about 2 min04Geometry
Geometry on the ACT covers angle relationships, triangle properties (angle sum, isosceles, congruence, similarity), the Pythagorean theorem and special right triangles, perimeter and area of polygons and circles, arc length and sector area, volume and surface area of solids, coordinate geometry (distance, midpoint, slope, parallel and perpendicular lines), transformations, and right-triangle trigonometry including degree–radian conversion. Inscribed versus central angles: an inscribed angle is half the central angle that subtends the same arc.
309 words, about 2 min05Statistics and Probability
This domain tests summary statistics (mean, median, mode, range, and the meaning of standard deviation), reading data displays such as tables, histograms, box plots, and scatterplots, basic probability for single and compound events, counting with the multiplication principle and with permutations versus combinations, conditional probability, expected value, and the logic of sampling and study design. Median with an even number of values is the average of the two middle values after sorting - and sorting is required first.
325 words, about 2 min