ACT Preparing for Higher Math Practice

What the test measures

Preparing for Higher Math skills

Number and Quantity: know and comprehend the meaning of a number; use number properties and operations to compute; understand the relationships between integers and rational numbers; use ratios, proportions, and percentages to solve problems; use exponents, radicals, and integer exponents to solve problems; use absolute value to solve problems.
Algebra: understand and use the properties of operations; use linear equations and inequalities in one variable; use linear functions; find and interpret the slope and intercepts of a linear equation or function; use systems of equations and inequalities; use the properties of exponents and radicals; use rational expressions; solve quadratic equations; use polynomial expressions; use factored form of a polynomial to solve problems; understand and use complex numbers; use the properties of logarithms.
Functions: understand the concept of a function and use function notation; understand and determine the domain and range of a function; interpret and translate between algebraic, graphical, tabular, and verbal representations of functions; analyze, graph, and build functions; use recursive and explicit functions; use transformations of functions; use function composition; use inverse functions.
Geometry: identify and use geometric concepts and relationships; find the measure of angles and lengths; use properties of parallel and perpendicular lines; use properties of congruent and similar figures; use properties of polygons, circles, and three-dimensional figures; use coordinate geometry; apply trigonometric ratios and relationships; solve problems involving area, perimeter, volume, and surface area; use trigonometric ratios and relationships in right triangles.
Statistics and Probability: understand categorical and quantitative data; use and interpret data representations; calculate and interpret measures of center and spread; understand and apply the properties of probability; describe and interpret relationships between two variables; make inferences from sample data; use counting principles.

Standards basis

ACT College and Career Readiness Standards (Mathematics) — national

How the ACT reports it

ACT’s math test is built around the ACT Mathematics reporting categories and ACT College and Career Readiness Standards rather than a state-specific framework. The official description says these standards are empirically derived and are the focus of ACT assessments, with modeling counted across categories.

Blueprint & weighting

Preparing for Higher Math 57%–60% total; Number and Quantity 7%–10%; Algebra 12%–15%; Functions 12%–15%; Geometry 12%–15%; Statistics and Probability 8%–12%; Integrating Essential Skills 40%–43%; Modeling is reported throughout and overlaps other categories.

Official sources

ACT Description of Math Test
ACT College and Career Readiness Standards
ACT College and Career Readiness Standards Mathematics PDF

Practice by skill

Topics mapped to this domain

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8 free questions · 0/0 correct

Practice playeasy

A diving board may be used only when the pool depth is at least $10.0$ feet. The water is currently $8.4$ feet deep. What is the minimum increase needed in the water depth, in feet, so that the diving board may be used?

The depth must be at least $10.0$ feet. The minimum increase is $10.0 - 8.4 = 1.6\textsf{.}$

Practice playeasy

Solve for $x$ : $x + 5 = -3$ .

Subtract 5 from both sides: $x = -8$ .

Practice playeasy

What is $7 \times (-2)$ ?

Result: $-14$ .

Practice playeasy

A $\text{\char36}60$ shirt is on sale for $15\%$ off. What is the sale price?

Discount: $0.15 \times \text{\char36}60 = \text{\char36}9.0$ . Sale: $\text{\char36}60 - \text{\char36}9.0 = \text{\char36}51.0$ .

Practice playeasy

A customer buys a desk for $\text{\char36}250$ and pays $7\%$ sales tax on the purchase. How much is the sales tax, in dollars?

Tax $= 0.07 \times 250 = 17.50$ dollars.

Practice playmedium

Five identical printing presses can complete a job in $12$ hours. Working at the same rate, how many hours would it take $8$ of these presses to complete the same job?