United States · ACTQ&A
MathsQ&A by dot point
A short Q&A bank for every United States Maths syllabus dot point. Each question and answer is drawn directly from our worked dot-point page, so you can scan key concepts before opening the long-form answer.
Algebra
- Solve exponential equations by matching bases and radical equations by isolating and squaring, checking for extraneous solutions (Algebra).3Q&A pairs
- 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).2Q&A pairs
- 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).2Q&A pairs
- Expand products of polynomials, factor by common factor, grouping and special patterns, and simplify polynomial and rational expressions (Algebra).3Q&A pairs
- Solve quadratic equations by factoring, the quadratic formula and square roots, and use the discriminant to count real solutions (Algebra).4Q&A pairs
- 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).2Q&A pairs
Format and Strategy
- 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.3Q&A pairs
- 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.2Q&A pairs
- 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.2Q&A pairs
- 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.2Q&A pairs
- 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.2Q&A pairs
Functions
- Interpret exponential functions for growth and decay, distinguish exponential from linear change, work with compound growth, and read basic logarithms as inverse exponents (Functions).2Q&A pairs
- Read and use function notation, evaluate functions including composition, and identify domain and range from rules and graphs (Functions).3Q&A pairs
- 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).2Q&A pairs
- 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).2Q&A pairs
- Identify arithmetic and geometric sequences, find a specified term using the explicit rule, and compute simple sums (Functions).3Q&A pairs
- 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).2Q&A pairs
Geometry
- Apply angle relationships (vertical, supplementary, parallel-line angles) and triangle properties (angle sum, exterior angle, isosceles and the triangle inequality) to find unknowns (Geometry).2Q&A pairs
- 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).2Q&A pairs
- 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).3Q&A pairs
- Apply the distance, midpoint and slope formulas, identify parallel and perpendicular lines, and analyse figures placed in the coordinate plane (Geometry).2Q&A pairs
- 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).2Q&A pairs
- Identify similar and congruent figures, use proportional corresponding sides and equal corresponding angles, and apply scale factors to lengths, areas and volumes (Geometry).2Q&A pairs
Number and Quantity
- 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).2Q&A pairs
- 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).2Q&A pairs
- 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).2Q&A pairs
- Classify numbers within the real number system, work with absolute value, and add, subtract, multiply and simplify complex numbers using (Number and Quantity).3Q&A pairs
- Add, subtract and scalar-multiply vectors and matrices, find a vector's magnitude, and multiply small matrices (Number and Quantity).2Q&A pairs
Statistics and Probability
- Count outcomes with the fundamental counting principle, and distinguish permutations (order matters) from combinations (order does not matter) (Statistics and Probability).2Q&A pairs
- 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).2Q&A pairs
- 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).2Q&A pairs
- 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).2Q&A pairs
- 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).2Q&A pairs