The levels of standards on the ACT that reflect a proficiency with operations and applications revolve around complexity. Students who receive a 13 to 15 on the math section demonstrate that they can do simple, one-step operations such as subtraction or division with whole numbers, decimals and percents. Higher scores reflect an ability to tackle more complicated problems. A score of 33 to 36 goes to a student who can use complex arithmetic to solve multistep problems that include several pre-algebra and pre-geometry concepts at the same time, such as percent increases and ratios.
Many statistical problems on the ACT ask students to interpret graphs and charts. To achieve a score between 13 and the lower 20s, students must generally be able to read and note information from a table and do simple computations with it. They also should be able to calculate basic measures of central tendency, such as the average of a set of numbers. Scores above 20 start to indicate an ability to work backward from an average to the data that created it. Scores in this range also reflect probability skills. Scores in the upper 20s and 30s go to students who can work with joint and conditional probability as well as calculate the median and mode for a set of data.
The ACT tests a wide range of concepts when it comes to numbers. Students with a score in the 13 to 15 range show that they can reduce fractions and identify equivalent fractions. Those with a score from 16 to 19 can find one-digit factors and recognize place values of digits. Scores from 20 to 23 reflect an understanding of several concepts, including rounding, decimals, absolute value, primes and greatest common factor. If students can order fractions, work with scientific notation, solve roots and cubes, understand the meaning of a complex number and identify when an expression is undefined, they should score in the 24 to 28 range. To score into the 30s, students need to be able to work with algorithmic or series geometric concepts, conduct operations on complex numbers and apply algebraic properties to number concepts.
The highest ACT standards for equations involve creating equations and expressions to model situations as well as setting up and solving absolute value inequalities. Mid-range scores require students to model simple, pre-algebra situations such as rate/distance or proportion problems. Students that fall in this range also can work with polynomials and solve simple quadratic equations. If students can solve only very simple equations such as X + 3 = 10, they will meet the standards for a score of 13 to 15.
Students who manage a 13 to 19 on the math section of the ACT might be able only to graph on a number line and possibly identify points in the first quadrant of a coordinate plane. Those with a score in the 20s demonstrate that they can work with slope and other aspects of graphing linear equations. To get a score in the upper 20s or 30s, students need to show that they can graph inequalities, circles and parabolas. Furthermore, they need to be able to interpret and use information from a variety of graphs on the coordinate plane and identify transformations of graphs based on their equations.
No standards for plane figure understanding exist until the 16 to 19 score range, for which students must have some basic understanding of the angles involved in parallel lines. To receive a score in the 20s, students have to be able to use properties of parallel lines, isosceles triangles, vertical angles, supplementary angles, complementary angles and angle sum theorems to find unknown angles. Those who can make calculations involving special right triangles and the Pythagorean theorem should score in the 28 to 32 range. If they can integrate several concepts at once, as well as work with arcs and circles, they will meet the standard for the highest scores.
In preparation for college-level math, students need not only to understand geometric figures but be able to work with them in real-life situations. A score of 13 to 19 demonstrates that a student can calculate lengths and find areas and perimeters using whole numbers. A higher score indicates that he can find measurements of circle parts, apply geometric formulas and solve problems with multiple steps. To merit a score in the 30s, a student has to show that she can work with composite figures when visualization is required and use scale factors to figure out the magnitude of a change.