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Minh Nguyen

ACT Pre-Algebra Study Guide

Pre-algebra consists of the math you learned back in middle school. If you did well in math during that time, then you can quickly skim through this guide to make sure you know the basics. If not, no worries! It’ll probably be much easier to get it this time around.

Even though this stuff may seem basic, keep in mind not to confuse simple with easy. The ACT will test your ability to figure out multi-step problems, weed through wordy paragraphs, and determine how to quickly solve questions without making silly errors.
Pre-Algebra Study Guide -magoosh

ACT Pre-Algebra Topics

Number Problems

These consist of general word problems that don’t really test you on a particular math skill. The hard part is not doing the actual math but figuring out what to do. Here you’ll find it very useful first figure out what the question is asking for, and then going back and reading the paragraph carefully.

Multiples, Factors, and Primes

This is where you may need to do some brushing up on your definitions in order to dust off the rust. Knowing how to find the LCM, GCF, and how to do prime factorization are important skills in your toolkit.

Percents, Fractions, and Decimals

Make sure you remember how to do basic math operations with percents, fractions, and decimals. Yes, you have a calculator, but it’s going to do you no good if you input the wrong numbers or put the decimal at the wrong spot. Be very diligent about knowing how to figure out percentages, because that’s one big area that the ACT test makers can try to trick you on.

Proportions and Ratios

They are pretty much like fractions, except that proportions and ratios tell you two or more parts of a whole (whereas a fraction only tells you one part out of a whole). The key is knowing how to convert ratios into fractions and vice-versa.

Absolute Value

The absolute value of a number is its magnitude, regardless of sign.

Exponents and Roots

An exponent is a number that is to be multiplied by itself a certain number of times. Roots are the opposite of exponents. Taking a root of an exponent returns that number to its original value.

Mean, Median, and Mode

These are all ways of describing a set of numbers. The mean and median find the “middle” of a set, while the mode tells you the number that occurs most often.


Probability questions can get complicated very quickly, but fortunately, the ACT doesn’t go very deep when it comes to this topic. You just need to know how to express probability as a fraction, decimal, or a percent.

Study Plan

Depending on how comfortable you are with math, you may not need to review the actual pre-algebra skills. The important thing is to be able to read through a problem and know what the ACT is testing you on. Once you start to recognize the patterns in the wording of the questions, it becomes much easier to know what action to take and what information to discard.

Start out by going through ACT practice problems and think about each step as you go. Circle key words, phrases, and cross out info you don’t need. After you get comfortable with that, gradually work up to speed. Remember to time yourself to make sure you are averaging under one minute per problem.

About Minh Nguyen

Minh's passion for helping students succeed grew during his time as a career counselor at the University of California, Irvine. Now, he's helping students all over the world by spilling SAT/ACT secrets through blog posts on Magoosh. When he's not busy tutoring or writing, he enjoys playing guitar, traveling, and talking about himself in third-person.

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