act math pre-algebra study guide

pre-algebra and arithmetic are the fundamental mathematics tested on the act math test. out of 60 questions, about 10 of them will test pre-algebra concepts. you’ll need to understand the basics of fractions, decimals, roots, integers, ratios, proportions, and basic number properties to solve these questions.

you’ll also need to solve simple algebraic expressions and equations. an algebraic expression is a mathematical statement which often uses constants and variables. for example: 5y + 10. an algebraic equation contains an equals sign, such as 5y + 10 = 100. the math actually involved in pre-algebra questions will be fairly simple: addition, subtraction, multiplication, and division.

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. what we’ll do in this post is give you a quick overview of topics you’ll encounter, put them to the test with practice problems, then wrap up with a study plan to perfect those skills!
 

 

act math 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

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.

pre-algebra act math practice problems

ready to see those concepts in action? here’s an example of a pre-algebra word problem:

a polling firm is making a circle graph to illustrate the results of their recent poll of voters about the upcoming mayoral election. 25% of voters support kendra willard; 20% support steve jacobson; 15% support amber tarkington; and 10% support harry fink. the remaining voters either expressed no preference or supported other candidates. these voters will be grouped together into the category “other response.” what will be the degree measure of the other response sector?

1. 216
2. 120
3. 108
4. 54
5. 30

though this might seem intimidating because it’s a word problem, notice how easy that math involved is! all we have to do is add up the percentages for the supporters of the various named candidates: 25% + 20% + 15% + 10% = 70%. this means that the other responses sector must represent the remaining 30%. here’s the tricky part: since the question is looking for the degree measure of this portion, 30% of 360 degrees in a circle is 108 degrees. the correct answer is choice three, 108.

here’s a slightly more challenging question:

a and b are reciprocals (when multiplied together their product is 1). if a < -1, then b must be which of the following?

1. b > 1
2. 0 > b
3. 0 < b < 1
4. 0 > b > -1
5. 0 > b < -1

the easiest way to solve this is to plug in numbers. since a < -1, let’s choose numbers to look for a pattern:

let’s try a = -1, since that is the upper limit.
-1 x b = 1
b = -1

let’s try a = -2
-2 x b = 1
b = -1/2

now try a = -3
-3 x b = 1
b = -1/3

we can see a pattern emerging: as a decreases in value, b increases slightly and slowly approaches (but will never reach) 0. therefore b must be between 0 and -1—answer choice four.

act math pre-algebra 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 math section 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.