Mathematics

Standards are provided for each Mathematics Test score range (except for the 1–12 range) along a score scale that is common to:

View or print the set of Mathematics Standards on two 8-1/2 x 11 pages (PDF).

  Score Range
13–15
Score Range
16–19
Score Range
20–23
Score Range
24–27
Score Range
28–32
Score Range
33–36
Basic Operations & Applications

Perform one-operation computation with whole numbers and decimals

Solve problems in one or two steps using whole numbers

Perform common conversions (e.g., inches to feet or hours to minutes)

Solve routine one-step arithmetic problems (using whole numbers, fractions, and decimals) such as single-step percent

Solve some routine two-step arithmetic problems

Solve routine two-step or three-step arithmetic problems involving concepts such as rate and proportion, tax added, percentage off, and computing with a given average Solve multistep arithmetic problems that involve planning or converting units of measure (e.g., feet per second to miles per hour) Solve word problems containing several rates, proportions, or percentages Solve complex arithmetic problems involving percent of increase or decrease and problems requiring integration of several concepts from pre-algebra and/or pre-geometry (e.g., comparing percentages or averages, using several ratios, and finding ratios in geometry settings)
Probability, Statistics, & Data Analysis

Calculate the average of a list of positive whole numbers

Perform a single computation using information from a table or chart

Calculate the average of a list of numbers

Calculate the average, given the number of data values and the sum of the data values

Read tables and graphs

Perform computations on data from tables and graphs

Use the relationship between the probability of an event and the probability of its complement

Calculate the missing data value, given the average and all data values but one

Translate from one representation of data to another (e.g., a bar graph to a circle graph)

Determine the probability of a simple event

Exhibit knowledge of simple counting techniques*

Calculate the average, given the frequency counts of all the data values

Manipulate data from tables and graphs

Compute straightforward probabilities for common situations

Use Venn diagrams in counting*

Calculate or use a weighted average

Interpret and use information from figures, tables, and graphs

Apply counting techniques

Compute a probability when the event and/or sample space are not given or obvious

Distinguish between mean, median, and mode for a list of numbers

Analyze and draw conclusions based on information from figures, tables, and graphs

Exhibit knowledge of conditional and joint probability

  Score Range
13–15
Score Range
16–19
Score Range
20–23
Score Range
24–27
Score Range
28–32*
Score Range
33–36†
Numbers: Concepts & Properties Recognize equivalent fractions and fractions in lowest terms Recognize one-digit factors of a number

Identify a digit's place value

Exhibit knowledge of elementary number concepts including rounding, the ordering of decimals, pattern identification, absolute value, primes, and greatest common factor

Find and use the least common multiple

Order fractions

Work with numerical factors

Work with scientific notation

Work with squares and square roots of numbers

Work problems involving positive integer exponents*

Work with cubes and cube roots of numbers*

Determine when an expression is undefined*

Exhibit some knowledge of the complex numbers†

Apply number properties involving prime factorization

Apply number properties involving even/odd numbers and factors/multiples

Apply number properties involving positive/negative numbers

Apply rules of exponents

Multiply two complex numbers†

Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions and numbers

Exhibit knowledge of logarithms and geometric sequences

Apply properties of complex numbers

Expressions, Equations, & Inequalities

Exhibit knowledge of basic expressions (e.g., identify an expression for a total as b + g)

Solve equations in the form x + a = b, where a and b are whole numbers or decimals

Substitute whole numbers for unknown quantities to evaluate expressions

Solve one-step equations having integer or decimal answers

Combine like terms (e.g., 2x + 5x)

Evaluate algebraic expressions by substituting integers for unknown quantities

Add and subtract simple algebraic expressions

Solve routine first-degree equations

Perform straightforward word-to-symbol translations

Multiply two binomials*

Solve real-world problems using first-degree equations

Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions)

Identify solutions to simple quadratic equations

Add, subtract, and multiply polynomials*

Factor simple quadratics (e.g., the difference of squares and perfect square trinomials)*

Solve first-degree inequalities that do not require reversing the inequality sign*

Manipulate expressions and equations

Write expressions, equations, and inequalities for common algebra settings

Solve linear inequalities that require reversing the inequality sign

Solve absolute value equations

Solve quadratic equations

Find solutions to systems of linear equations

Write expressions that require planning and/or manipulating to accurately model a situation

Write equations and inequalities that require planning, manipulating, and/or solving

Solve simple absolute value inequalities

  Score Range
13–15
Score Range
16–19
Score Range
20–23
Score Range
24–27
Score Range
28–32*
Score Range
33–36†
Graphical Representations Identify the location of a point with a positive coordinate on the number line Locate points on the number line and in the first quadrant

Locate points in the coordinate plane

Comprehend the concept of length on the number line*

Exhibit knowledge of slope*

Identify the graph of a linear inequality on the number line*

Determine the slope of a line from points or equations*

Match linear graphs with their equations*

Find the midpoint of a line segment*

Interpret and use information from graphs in the coordinate plane

Match number line graphs with solution sets of linear inequalities

Use the distance formula

Use properties of parallel and perpendicular lines to determine an equation of a line or coordinates of a point

Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle)†

Match number line graphs with solution sets of simple quadratic inequalities

Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax2 + c

Solve problems integrating multiple algebraic and/or geometric concepts

Analyze and draw conclusions based on information from graphs in the coordinate plane

  Score Range
13–15
Score Range
16–19
Score Range
20–23
Score Range
24–27
Score Range
28–32*
Score Range
33–36†
Properties of Plane Figures   Exhibit some knowledge of the angles associated with parallel lines

Find the measure of an angle using properties of parallel lines

Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90°, 180°, and 360°)

Use several angle properties to find an unknown angle measure

Recognize Pythagorean triples*

Use properties of isosceles triangles*

Apply properties of 30°-60°-90°, 45°-45°-90°, similar, and congruent triangles

Use the Pythagorean theorem

Draw conclusions based on a set of conditions

Solve multistep geometry problems that involve integrating concepts, planning, visualization, and/or making connections with other content areas

Use relationships among angles, arcs, and distances in a circle

Measurement Estimate or calculate the length of a line segment based on other lengths given on a geometric figure

Compute the perimeter of polygons when all side lengths are given

Compute the area of rectangles when whole number dimensions are given

Compute the area and perimeter of triangles and rectangles in simple problems

Use geometric formulas when all necessary information is given

Compute the area of triangles and rectangles when one or more additional simple steps are required

Compute the area and circumference of circles after identifying necessary information

Compute the perimeter of simple composite geometric figures with unknown side lengths*

Use relationships involving area, perimeter, and volume of geometric figures to compute another measure

Use scale factors to determine the magnitude of a size change

Compute the area of composite geometric figures when planning or visualization is required

Functions†    

Evaluate quadratic functions, expressed in function notation, at integer values†

Evaluate polynomial functions, expressed in function notation, at integer values†

Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths†

Evaluate composite functions at integer values†

Apply basic trigonometric ratios to solve right-triangle problems†

Write an expression for the composite of two simple functions†

Use trigonometric concepts and basic identities to solve problems†

Exhibit knowledge of unit circle trigonometry†

Match graphs of basic trigonometric functions with their equations†

Ideas for Progress
Score Range
1–12
Ideas for Progress
Score Range
13–15
Ideas for Progress
Score Range
16–19
Ideas for Progress
Score Range
20–23
Ideas for Progress
Score Range
24–27
Ideas for Progress
Score Range
28–32
 

Notes:

  • Students who score in the 1–12 range are most likely beginning to develop the knowledge and skills assessed in the other ranges.
  • Standards followed by an asterisk (*) apply to the PLAN and ACT Mathematics Tests only.
  • Standards followed by a dagger (†) apply to the ACT Mathematics Test only.
  • Standards for the 28–32 range are specific to PLAN and the ACT while the Standards for the 33–36 range pertain to the ACT only.
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