ACT Preparing for Higher Math Practice

ACT Preparing for Higher Math. Practice it free.

This category encompasses the mathematical skills and concepts students typically need to know to be prepared for entry-level college mathematics courses; questions focus on concepts and skills used broadly across fields and foundational to the other categories. This All grades reporting domain maps to 176 practice skills and 8 representative questions from the playable bank.

All grades / ACT college-admissions test (skills typically acquired through beginning of grade 12)PHM176 mapped skills

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

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 clinic recorded customer wait times, in minutes, for $16$ visits. The frequency table shows the results.
$\begin{array}{c|c} \text{Wait time (min)} & \text{Number of customers} \\ \hline 2 & 2 \\ 5 & 3 \\ 8 & 2 \\ 11 & 6 \\ 14 & 3 \end{array}$

What is the median wait time?

Expand to $16$ wait times: $2, 2, 5, 5, 5, 8, 8, 11, 11, 11, 11, 11, 11, 14, 14, 14$ . The $8$ th and $9$ th values are both $11$ , so the median is $11$ minutes.

Practice playeasy

Four small data sets are listed below. Which set has the least standard deviation?

Set A: $7, 9, 11, 13$
Set B: $8, 10, 10, 12$
Set C: $5, 10, 10, 15$
Set D: $6, 9, 11, 14$

Set B has mean $10$ with two values at the mean and the others only two units away, giving the smallest standard deviation, about $1.4$ . Sets A, C, and D spread farther from their means.

Practice playeasy

The distances, in miles, run on seven days are $6\textsf{,}$ $8\textsf{,}$ $12\textsf{,}$ $9\textsf{,}$ $14\textsf{,}$ $7\textsf{,}$ and $14\textsf{.}$ Which data set has the same mean?

The original mean is $\dfrac{6 + 8 + 12 + 9 + 14 + 7 + 14}{7} = 10$ . The set $4\textsf{,}$ $6\textsf{,}$ $8\textsf{,}$ $10\textsf{,}$ $12\textsf{,}$ $14\textsf{,}$ $16$ also has mean $10$ , so the means match.

Practice playeasy

Five afternoon temperatures, in degrees Fahrenheit, are $64\textsf{,}$ $78\textsf{,}$ $72\textsf{,}$ $60\textsf{,}$ and $66\textsf{.}$ Which data set has the same median?

In order, the original values have middle value $66$ , so the median is $66$ . The set $61\textsf{,}$ $65\textsf{,}$ $66\textsf{,}$ $77\textsf{,}$ $81$ also has median $66$ , so the medians match.

Practice playeasy

On four science quizzes, Priya earned scores of $85$ , $92$ , $78$ , and $88$ . On a fifth quiz, her score was $x$ . The mean score on all five quizzes is $87$ . What is the value of $x$ ?

Five quizzes with a mean of $87$ total $5 \times 87 = 435$ . Since $85 + 92 + 78 + 88 = 343$ , $x = 435 - 343 = 92$ .

ACT Preparing for Higher Math. Practice it free.

Preparing for Higher Math skills

Topics mapped to this domain

Interpreting at least and at most

Solving one- and two-step linear equations

Integer operations

Central Measures from Tally Charts (ACT)

Compare standard deviation of data sets (ACT)

Comparing means

Comparing medians

Find score from mean

Mean change from data set edits

Mean from a data list

Measures of center and variability

Median from a data list

8 free questions · 0/0 correct

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