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Cheat Sheet

ACT Math For Dummies

From ACT Math For Dummies by Mark Zegarelli

Making sure you have a handle on algebra, geometry, and trigonometry is a solid start for success on the math section of the ACT. However, to boost your confidence — and your score — even higher, you should master some helpful test-taking strategies, as well as make sure you know how to translate word problems into equations and use sketches to figure out what a tricky-sounding question is really asking.

Test-Taking Strategies for the Math Portion of the ACT

The math portion of the ACT contains 60 questions, and you have 60 minutes to complete that part of the test. So you have roughly 1 minute per question. Every question you answer correctly is worth 1 point toward your raw score on the test. Employing some test-taking strategies can help ensure that you answer all the questions as best you can. The following sections provide some tips to keep in mind.

Remember: Not all ACT math questions are created equally. Generally speaking, the questions increase in difficulty as you proceed from Question 1 to Question 60. Here’s the general breakdown of difficulty:

  • Easy: Questions 1 through 20

  • Medium: Questions 21 through 40

  • Hard: Questions 41 through 60

Take two passes on the ACT Math test

To maximize your time and confidence, use the tried-and-true strategy of taking two passes over the ACT, particularly when working the math section. Here’s what to do for each of the passes:

  • Pass 1: Start with Question 1 and work your way forward, answering questions that look relatively quick and easy and jumping over those that look difficult or time-consuming.

  • Pass 2: After you’ve answered all the quick and easy questions, circle back to the first question you skipped over and work your way forward to the end again.

This test-taking strategy maximizes the number of questions you can answer with confidence. It also helps you save time for the tough questions, which usually take more than 1 minute to solve. And don’t forget that you get an average of 1 minute per question!

Every ACT math section includes a few questions that are practically begging for you to skip over them. For example, you may consider passing over questions that

  • Are very long and wordy.

  • Seem purposely confusing and don’t make a lot of sense even the second time you read them.

  • Have large or complicated numbers that involve long or difficult calculations.

Of course, not every problem with the preceding characteristics is as difficult as it looks. But as you run across problems like these, feel free to jump over them — even on Pass 2. If you have time at the end of the test, you can always try to pick off a few of these questions.

But if you’re going to skip questions, you may as well skip these hairy beasts. However, do try to fill in an answer for every question in the end. (See the upcoming section for details on how best to guess on the ACT.)

Guess wisely on the rest of the ACT test

On the ACT math test, you don’t lose points from your raw score when you fill in a wrong answer. So strategically you should fill in every answer, even if you have to make a wild guess.

Of course, you don’t want to guess on math questions that you may be able to answer correctly — especially among the test’s earlier questions, which tend to be easier. And keep in mind that an educated guess is always better than a wild guess. So whenever possible, rule out answers that you know are wrong. Keep track of these wrong answers by crossing them out in your test booklet.

Don’t guess at any answers while you’re still on the first pass (see the previous section, “Take two passes on the ACT Math test,” where I discuss tackling the test in two separate passes). Instead, begin guessing on your second pass of the test. At this point, if you can confidently rule out a couple of answers but don’t know how to proceed with a question, you can save time by guessing at the answer and moving on to the next question.

Keep track of the questions that you guess on. If you have time at the end of the math test — or if you have an unexpected brainstorm — you can revisit these questions and make a more educated guess.

Monitor your time closely, and when your 60 minutes of math are almost up, take a moment to guess at all the remaining answers — don’t leave any blank. With a bit of luck, you may pick up a few additional points on some of these questions.

Remember that the ACT is different from the SAT in one crucial respect:

On the ACT, no points are taken off for wrong answers.
On the SAT, 1/4 point is taken off for every wrong answer.

So, be sure to answer every question on the ACT, even if you have to guess.

Using Charts and Pictures to Answer ACT Math Questions

Some math problems are difficult to visualize, so sketching out a chart or picture of the given information can help you arrive at the correct answer when taking the math portion of the ACT. Here are some tips to keep in mind:

  • If you’re a visual person — an artist or a photographer, for example — start sketching sooner rather than later.

  • Your sketch doesn’t have to be perfect. Just seeing how the question looks on paper may help you out.

  • When you’ve got the beginnings of a sketch, step back from it and decide what kind of problem you’re trying to solve. For example, do you need arithmetic, algebra, or geometry to solve it?

Consider the following example question:

Jason likes to begin his workout with a run from his house to the gym. He runs 4 miles due west, then makes a left turn and runs 2 miles due south to arrive at the gym. Which of the following is the best approximation of the shortest distance from Jason’s house to the gym?

(A) 4.2 miles
(B) 4.5 miles
(C) 4.8 miles
(D) 5.2 miles
(E) 5.5 miles

At first reading, you may not see exactly what this question is asking. Making the following sketch helps put it into perspective:

image0-1.jpg

Now you can see that this problem is a geometry problem with a right triangle. You already know the lengths of the two legs, and you want to know the distance from the house to the gym, which is the hypotenuse. So use the Pythagorean theorem, as follows:

image1-1.jpg

Use your calculator to find that

image2-1.jpg

So the right answer is Choice (B).

Solving Math Word Problems on the ACT

A word problem (also called a story problem or a problem in a setting) gives you information in words rather than in just equations and numbers. To answer a math word problem on the ACT, you have to translate the provided information into one or more equations and then solve.

You can solve some word problems fairly easily. Jotting down the numbers in the problem can be useful to help get you focused and moving in the right direction. The following example word problem shows you how:

A charity is holding a lottery to raise money. A book of 20 tickets sells for $70.00, and a book of 50 tickets sells for $150.00. How much do you save on each ticket by buying a book of 50 tickets rather than a book of 20 tickets?

(A) $0.10
(B) $0.20
(C) $0.25
(D) $0.50
(E) $0.75

If you’re not immediately sure how to proceed, jot down the numbers in an orderly fashion:

Book of 50    $150    50
Book of 20    $70    20

This step only takes a moment and gets your brain moving. When you organize the information in this way, you may see that the next step involves division:

Book of 50    $150 ÷ 50 = $3.00
Book of 20    $70 ÷ 20 = $3.50

Now you can easily see that buying a book of 50 tickets saves $0.50 per ticket, so the correct answer is Choice (D).

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