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Tackling Pre-Algebra on the ACT Math Test

Pre-algebra and arithmetic are the fundamental mathematics tested on the ACT Math test. Out of 60 questions, about 10 of them will be pre-algebra concepts. You’ll be required 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.

Here’s an example of a Pre-Algebra question in the word problem format:

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%. The correct answer is (E).

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.

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