ACT WorkKeys Applied Math is built in levels. Every question is written to one level from 3 to 7, and the test puts them in order, so the first questions are Level 3 and the last are Level 7. The levels are cumulative: a Level 5 question can use any skill from Levels 3 and 4, plus the new Level 5 skills. This page walks through what each level adds, with one short worked example for each, so you can see where your skills stand and what to study next.

This page is independent practice information and is not affiliated with ACT. The level descriptions below follow ACT’s published skill lists for Applied Math.

Applied Math at a glance

Item	Details
Questions	34, with a few unscored tryout questions mixed in
Time	55 minutes
Choices	5 per question
Calculator	Allowed; the online test has an on-screen calculator
Formula sheet	Provided, with conversions and shape formulas
Scored questions by level	About 6 at Level 3, 6 at Level 4, 7 at Level 5, 6 at Level 6 and 6 at Level 7

The level counts come from the test blueprint in ACT’s technical manual, which describes 31 scored questions per form. By skill, the blueprint has about 6 questions on basic operations, 4 on fractions, 5 on percents, ratios and proportions, 5 on unit conversions, 3 on geometry and 8 on applied reasoning, spread across problems about quantities, money, time and measurement.

What changes as the levels rise

Two things change as you move up: the math gets harder, and so does the setup, from numbers given in the order you use them to problems with extra, missing or implied information.

Level	How the problem is written	Typical math
3	Short, in logical order, no extra information	One operation, money and time
4	Information may be out of order or extra; may include a simple chart	One or two operations, averages, simple ratios and fractions
5	Several steps of logic and calculation	Conversions, mixed units, perimeter and area, percents
6	Considerable setup from words to math	Reverse percents, multi-step conversions, rates, volume of boxes
7	Unusual format, incomplete or implied information	Fraction ratios, cylinders, cones and spheres, weighted averages

Level 3

Level 3 problems translate directly into one calculation. You add or subtract (including negative numbers), or multiply and divide positive numbers. You also change familiar fractions to decimals (¹⁄₂ = 0.5, ¹⁄₄ = 0.25), change decimals to percents, use familiar money and time conversions such as 1 hour = 60 minutes, and total several prices and make change.

Example. You are a cashier. A customer buys items for \(6.75 and \)8.40 and pays with a \(20 bill. The total is \)15.15, so the change is \(20.00 - \)15.15 = $4.85.

Level 4

Level 4 adds one or two operations, and the setup gets a little harder: the information may be out of order or include extra numbers, and it may come in a simple chart, diagram or graph. New skills include finding the average (mean) of whole numbers or decimals, working with simple ratios, proportions and rates (such as miles per hour), adding common fractions, decimals or percents, adding or subtracting fractions with the same denominator, and multiplying a mixed number by a whole number or decimal.

Example. You cut 4 shelves, each 2 ¹⁄₄ feet long, from a board. The shelves use 4 x 2 ¹⁄₄ = 9 feet of board.

Level 5

Level 5 problems take several steps, such as totaling an order and then figuring the sales tax. You decide which information, calculations and conversions to use. New skills include adding and subtracting fractions with unlike denominators, converting units within or between systems when the conversion is given (in the problem or on the formula sheet), working with mixed units such as feet and inches or hours and minutes, finding the best deal with one or two steps, finding the perimeter, circumference or area of basic shapes, and using a percent for a discount, markup or tax. You may also be asked to find where a mistake was made, such as the wrong line on an invoice.

Example. A room is 12 feet by 15 feet, and flooring is sold by the square yard. The area is 12 x 15 = 180 square feet. With 9 square feet in a square yard, that is 180 / 9 = 20 square yards.

Level 6

Level 6 needs considerable translation from words to math and multi-step calculations. New skills include reverse percentages (finding the original amount when you know the amount after a percent was added or taken off), conversions that take several steps, explaining why a mistake happened, choosing the best deal from a group and then using the result, finding an area when you must rearrange a formula or convert units first, the volume of rectangular solids, and production rates such as units per hour over a shift. You may also have to pick the equation that matches a situation.

Example. A customer’s total of \(64.80 includes 8% tax. The price before tax is \)64.80 / 1.08 = \(60.00. Taking 8% off the total (\)59.62) is the classic wrong answer, because the tax was figured on the lower price.

Level 7

Level 7 problems may be written in an unusual way, and information may be incomplete or implied, so you have to make an assumption to solve them. New skills include ratios, rates and proportions where at least one quantity is a fraction, conversions with fractions, mixed numbers, decimals or percents, the volume of cylinders, cones and spheres, comparing value with percent difference or unit cost, and basic statistics such as a weighted average or what spread and tolerance mean. You may also have to find the reason for a mistake.

Example. A cylindrical drum has a radius of 1 foot and a height of 3 feet. Its volume is 3.14 x 1 x 1 x 3 = 9.42 cubic feet. With 1,728 cubic inches in a cubic foot and 231 cubic inches in a gallon, it holds 9.42 x 1,728 / 231 = about 70.5 gallons.

The formula sheet and calculator

You do not need to memorize conversions or shape formulas: the Applied Math formula sheet lists them, from distance, volume and temperature conversions to the volume of a cylinder, cone or sphere. ACT’s directions say to use 3.14 for pi, since a calculator’s pi key may give an answer that does not match the choices. See the full Applied Math formula sheet for every line.

How to study by level

• Find your ceiling. Work questions in level order and note where you start to miss. Study that level first, since the levels build on each other.
• Practice setup, not just arithmetic. From Level 5 up, most misses come from using the wrong numbers or skipping a step.
• Learn the common traps. Forgetting to convert inches to feet, using the diameter instead of the radius, averaging averages, and taking a percent off a total that already includes it.
• Know what level you need. Your NCRC level is set by your lowest of the three scores; see the NCRC certificate levels and how scores and levels relate.

To work through examples at every level, try the Applied Math practice questions, which run three questions at each level from 3 to 7. For the full picture of all three tests, see the WorkKeys test guide.

Keep practicing

Our three timed Applied Math practice tests each have 34 questions in 55 minutes, in level order from Level 3 to Level 7, with the formula sheet and an on-screen calculator beside every question, an explanation for every answer and an estimated level when you finish. Start from the home page.