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ACT College and Career Readiness Standards - Mathematics · ACT 2023
Number & Quantity
Perform a single computation using whole numbers and decimals.
Understand and use the concepts of factors and multiples.
Work with fractions, including addition, subtraction, multiplication, and division.
Convert between fractions, decimals, and percents.
Understand and use ratios, proportions, and rates to solve problems.
Work with integers and rational numbers, including operations and ordering.
Understand and apply properties of exponents and scientific notation.
Understand and work with absolute value.
Work with complex numbers, including operations.
Understand and use vectors and matrices.
Algebra
Solve routine one-step arithmetic problems using positive whole numbers.
Substitute values into simple algebraic expressions.
Solve linear equations and inequalities in one variable.
Manipulate and evaluate algebraic expressions, including polynomials and rational expressions.
Solve systems of linear equations in two variables.
Solve quadratic equations by factoring, completing the square, or using the quadratic formula.
Work with and solve problems involving arithmetic and geometric sequences and series.
Solve more complex equations, including those involving absolute value, radicals, and rational expressions.
Understand and use properties of logarithms.
Functions
Understand basic function concepts, including domain, range, and function notation.
Evaluate functions for given input values.
Interpret and use graphs of functions, including identifying key features like intercepts, slope, and maximum/minimum values.
Understand and work with linear functions, including slope-intercept form and point-slope form.
Understand and work with quadratic functions, including their graphs (parabolas) and properties.
Understand and work with exponential and logarithmic functions.
Understand and work with trigonometric functions, including their graphs, properties, and applications.
Understand transformations of functions (translations, reflections, stretches/compressions).
Combine functions using arithmetic operations and composition.
Geometry
Understand and use properties of points, lines, angles, and planes.
Work with properties of triangles, including angle sum, side-angle relationships, and the Pythagorean theorem.
Work with properties of quadrilaterals and other polygons.
Understand and use concepts of perimeter, area, and volume for various 2D and 3D shapes.
Work with circles, including properties of radii, diameters, chords, tangents, and secants; circumference and area.
Understand and apply concepts of similarity and congruence.
Use coordinate geometry, including distance formula, midpoint formula, and slope of a line.
Understand and apply basic trigonometric ratios (sine, cosine, tangent) in right triangles.
Work with transformations in the coordinate plane (translations, rotations, reflections, dilations).
Statistics & Probability
Collect, organize, display, and interpret data using tables, charts, and graphs (e.g., bar graphs, line graphs, pie charts, stem-and-leaf plots, scatterplots).
Calculate and interpret measures of central tendency (mean, median, mode) and spread (range, standard deviation).
Understand and apply basic probability concepts, including calculating probabilities of simple and compound events.
Use counting principles (e.g., permutations, combinations) to determine the number of outcomes.
Interpret and draw conclusions from statistical data, including recognizing patterns and trends.
Understand concepts of conditional probability and independence of events.
Understand and use probability distributions.
Make inferences about a population based on sample data.
Integrating Essential Skills: This category measures how well you can synthesize and apply your knowledge and skills to solve more complex problems. The questions ask you to address concepts such as rates and percentages, proportional relationships, area, surface area, and volume, average and median, and expressing numbers in different ways. Solve nonroutine problems that involve combining skills in chains of reasoning or applying skills in new contexts.
Solve problems involving rates, ratios, and percentages in various contexts.
Apply proportional reasoning to solve multi-step problems.
Solve problems involving area, surface area, and volume of composite shapes.
Calculate and compare averages and medians in complex data sets.
Convert between and use different representations of numbers (e.g., fractions, decimals, percents, scientific notation).
Solve non-routine problems that require combining multiple mathematical concepts or skills.
Apply mathematical skills in new or unfamiliar contexts.
Develop and use chains of reasoning to solve multi-step problems.
Modeling: This category represents all questions that involve producing, interpreting, understanding, evaluating, and improving models. Each question is also counted in other appropriate reporting categories. This category is an overall measure of how well you use modeling skills across mathematical topics.
Create and use mathematical models to represent real-world situations (e.g., using algebraic expressions, equations, functions, geometric shapes, or statistical representations).
Interpret mathematical models in the context of the situation they represent.
Evaluate the appropriateness and limitations of mathematical models.
Use models to make predictions and draw conclusions about real-world phenomena.
Improve or refine mathematical models based on new information or by comparing model predictions with actual outcomes.