ACT Mathematics — multi-step percent, rate, mixture and measurement problems

About a fifth of the enhanced ACT mathematics section is Integrating Essential Skills, which ACT describes as rates and percentages, proportional relationships, area, surface area and volume, average and median, and expressing numbers in different ways — combined into chains of steps and applied in varied contexts. Modeling, the work of producing and interpreting models, is counted across the whole section. This material trains those multi-step problems, each written as a short real-world situation in US units.

The percent questions show why a 20 percent increase followed by a 20 percent decrease does not return to the start, take a percent of a percent of a school's students, and recover a price from a total that already includes sales tax, where dividing by 1.08 is right and subtracting 8 percent of the total is not. Rate problems follow: a mixture of two acid solutions solved by tracking the pure acid, two pipes filling a pool together by adding rates, the average speed of a round trip as total distance over total time, and the fuel cost of a trip through a chain of units.

Measurement and modeling close the set: the area of a room from a scale floor plan, the gallons needed to fill an aquarium to three fourths of its height with the conversion factor given, a weighted course grade, the score needed to raise an average, and the meaning of the growth factor in an exponential population model.

The material offers two formats. The quiz has twelve multiple-choice questions with four answer choices each, as on the enhanced ACT, and every explanation names the slip behind each wrong choice, so a miss tells you what to fix. The flashcards collect the rules and formulas worth knowing by heart.

The content is based on ACT's published description of the mathematics section (reporting categories and the topics listed for each). It is independent practice and is not produced or endorsed by ACT.

• Combine successive percent changes and reverse a percent increase
• Solve mixture and work-rate problems
• Use scale drawings and chains of unit conversions
• Compute weighted averages, average speeds and required scores
• Interpret the parameters of a model in context

Practice material written by Zestly, based on ACT's published description of the ACT mathematics section (act.org, Mathematics Test Description: Preparing for Higher Math — Integrating Essential Skills and Modeling). Formulas beyond the basics are given in the questions, as ACT states that recall of complex formulas is not required.