Chapter 1

Reviewing ACT Math Basics

IN THIS CHAPTER

Beginning with an overview of ACT math

Identifying four important steps to success

Studying the six math topics tested on the ACT

Figuring out what’s not tested

All across the United States — and especially in the Midwest, South, and Rocky Mountain states — high school juniors and seniors prepare for one of the most action-packed Saturdays of their lives. No, I don’t mean the prom, graduation day, or a really excellent date with someone their parents don’t know about and wouldn’t approve of if they did. No, they’re preparing for something even more fun than that: the ACT.

Well, okay, back on Earth, it turns out that at least some of this is true: It looks like you will be taking the ACT (which I figured out the moment you bought this book). In this chapter, I begin the work of helping you get ready for the most fun part of all: the 60-minute math test.

I start this chapter with a look at what’s on the math portion of the ACT. Then I provide a bit of advice about four general ways to improve your score. Finally, I list the six math topics that the ACT tests you on, including a breakdown of the specific skills within each topic that you should focus on to do well.

The chapter ends with a sigh of relief as you discover the math that you don’t need to worry about on the ACT. (However, the teacher of your current math class may still want you to know something about it, so don’t flush it from your memory just yet!)

Getting an Overview of ACT Math

The ACT contains five separate tests, which are always presented in this order:

1. English
2. Mathematics
3. Reading
4. Science
5. Writing (optional)

This book focuses exclusively on the second test, the ACT mathematics test. This math portion lasts for 60 fun-filled minutes and contains 60 questions. Generally speaking, questions appear roughly in order of difficulty.

The test is scored on a scale of 1 (lowest) to 36 (highest). As a rule of thumb, here’s how I think of ACT scores:

• A score of 20 is about average, just about equivalent to a 500 math score on the SAT.
• A score of 25 is a good, college-ready score, similar to a 600 math score on the SAT.
• A score of 30 (or above!) is a great score, on par with a 700 math score on the SAT.

On the ACT, test graders don’t take off points for wrong answers — that is, you won’t be penalized for guessing. So keep an eye on the time and, just before your time is up, fill in answers to all 60 questions. Make as many educated guesses as you can, of course. But even wild guessing won’t hurt your score, so fill in those answers before time’s up!

Taking Four Key Steps to ACT Math Success

I like to give the following four important pieces of advice to those students who want to improve their ACT math scores:

• Sharpen your basic math skills.
• Get comfortable using your calculator.
• Solidify your ACT-math-specific skills.
• Take practice tests under timed conditions.

In this section, I give you an overview of these four steps. The rest of the book is devoted, one way or another, to working on them.

Sharpening your basic math skills

By the basics, I mean the math calculations that precede pre-algebra. For example:

• Multiplication tables up to
• Adding, subtracting, multiplying, and dividing fractions
• Converting percents to decimals and vice versa
• Converting common percents, such as 10%, 20%, 25%, 50%, and 75%, to fractions and vice versa
• Working with negative numbers
• Knowing the order of operations (PEMDAS: parentheses, exponents, multiplication and division, addition and subtraction)

When I say know this stuff, I mean that you should know it stone cold — the way you know your own name. If you’re wasting precious time trying to remember or calculate , you’ll benefit greatly from investing just a few hours to work with a set of flash cards designed to help you strengthen these skills. In Chapter 3, I cover these topics to refresh your memory.

Getting comfortable with your calculator

You may already be well aware (and grateful!) that calculators are allowed on the ACT. Moreover, because virtually everyone will be using one, you should consider a calculator not just optional, but mandatory.

First off, if you’re like me, you probably use your phone as your go-to calculator. Additionally, you may use an online graphing calculator (my favorite one is at desmos.com) for help while working on your homework. Unfortunately, on the ACT, you can’t use your phone or any other device that gives you online access, so you need either a scientific calculator or a graphing calculator.

If you already own a good calculator and are reasonably adept at using it, just use this quick rule of thumb to make sure it’s up to speed: Check to see whether it can do trigonometric calculations like sin x. If it can, it’s probably just fine; if not, you need to think about an upgrade well before the ACT so you have time to practice with it.

In Chapter 2, I give you some specifics about your calculator. And for those of you who are considering or who already own a graphing calculator, I recommend TI-83 Plus Graphing Calculator For Dummies (Wiley) and TI-89 Graphing Calculator For Dummies (Wiley), which are both written by C. C. Edwards.

Solidifying your ACT-specific math skills

Studying for the ACT should be mostly a review of skills that are covered in your math classes. However, no matter how hard you work in your classes, the material you covered two or three years ago may not be fresh in your mind. So focused preparation for the ACT can really pay off.

Parts 2, 3, and 4 (Chapters 4 through 13) provide a detailed review of the math that shows up most on the ACT. You can work through dozens of example problems and answer 108 practice questions specifically related to those topics.

Taking practice tests under timed conditions

Time is money, and money changes everything. So it’s not surprising that time changes everything — especially on the ACT, where you have only 60 minutes to answer 60 math questions. Purposefully working under low-stakes time pressure adds a useful dimension to your study, especially as you get closer to your test date when the stakes will be higher.

Part 5 of this book — Chapters 14 through 17 — contains two complete practice tests (and answers!) for you to try out, plus access to a third test online. I recommend that you take them under real test conditions. In other words, take them in one hour with the calculator you plan to use on the test and no additional help. You may start out taking the first test as a benchmark before you begin working on the rest of the problems in the book. Or, if you prefer, save all three tests until you feel confident answering questions with no time pressure — then start the clock running and see how you do.

What Should You Study? Knowing What’s on the ACT

The ACT covers six overall topics in math: pre-algebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry, and trigonometry. In this section, I break down all these topics into manageable bits and discuss the individual skills included in each. Parts 2, 3, and 4 (Chapters 4 through 13) cover this material in depth, with plenty of example questions and practice problems.

Taking care of the basics in pre-algebra

Pre-algebra includes a variety of topics that prepare you for algebra. In this section, I discuss the specific pre-algebra skills that show up most on the ACT. And in Chapter 4, I focus on these types of questions, providing plenty of example questions and showing you how to answer them.

Basic arithmetic

You obviously need to know the four operations: addition, subtraction, multiplication, and division. You also want to feel comfortable working with negative numbers, fractions, and decimals. I cover some of this material in this book, but if you feel that you need a more thorough review, pick up Basic Math and Pre-Algebra For Dummies (Wiley) by yours truly.

Number sequences

A number sequence is a list of numbers arranged in a pattern. Here’s an example:

In this case, each number in the sequence is 3 greater than the number before it. An ACT question may ask you to find the next number or a missing number in a number sequence.

Factors and multiples

When one natural number is divisible by another, the smaller number is a factor of the greater number, and the greater number is a multiple of the smaller number. For example, 12 is divisible by 4, so

• 4 is a factor of 12.
• 12 is a multiple of 4.

To answer an ACT question, you may need to find all the factors of a number or the greatest common factor or the least common multiple among several numbers.

Fractions and Decimals

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