Back To Course

ACT Prep: Practice & Study Guide48 chapters | 407 lessons | 23 flashcard sets

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Jessica Bayliss*

If math isn't your strongest subject, tests like the ACT math exam can be daunting. Learn techniques to correctly answer questions on the ACT math exam even when you're not sure exactly how to solve them.

The **best way to boost your score** on the ACT math is to thoroughly review all of the math concepts and do lots of practice problems. Good preparation will help you answer questions quickly and correctly. However, there will probably be some questions that have you stumped - and that's okay. You're not expected to know everything.

Even if you're totally stumped, always leave a guess. Remember, there is no penalty for guessing, and you might just get the answer right and earn an extra point. Guessing should be your last resort, though, so in this lesson, we're going to go over two strategies you can use when you don't know how to solve a problem.

The ACT is a multiple-choice exam, and you can use that to your advantage. For many questions, you can **plug in the answer choices** to see which answer is correct. Let's look at a simple example to see how this works.

Solve 3*x* + 4 = 16 for *x*

A. 3

B. 4

C. 5

D. 6

E. 7

Let's say I didn't know how to solve this equation for *x*. Instead of struggling through the problem, I could plug in the answer choices to see which one works.

Let's start with choice A. I'll plug in 3 to get:

3(3) + 4 = 16

If I simplify this, I get:

9 + 4 = 16

or

13 = 16, which obviously is not true.

Choice A is incorrect, so let's move on to choice B. This time, I'll plug in 4. Now we have:

3(4) + 4 = 16

which simplifies to

12 + 4 = 16

or

16 = 16

This one's true!

*x*=4, which means choice B is the correct answer.

This strategy worked, but it can be time-consuming because you essentially have to eliminate 4 answer choices to find the one that is correct. I don't recommend using it for problems that you know how to solve. In the example we just saw, the problem was a simple linear equation problem. If you don't know how to solve that problem, you should practice because it will definitely appear multiple times on the exam. Save this strategy for trickier, more challenging problems.

You can't use this strategy for all types of problems. It works best for ones that ask you to solve for a variable, such as in the example we worked through.

You'll see several problems on the exam that ask you to work with variables. These can be difficult because they're abstract and can't be worked with a calculator. You can often make them simpler if you **substitute in real numbers for the variables**.

Let's look at an example to see how this works.

3*x* + 4 = 16 is equal to which of the following equations?

A. 4 = 16 + 3*x*

B. *x* + 4/3 = 16/3

C. *x* + 2 = 8

D. 3*x* + 12 = 48

E. *x* + 4 = 16/3

Looking at all of these equations is a little overwhelming, and you might be unsure of where to start. Instead of driving ourselves crazy reconfiguring this equation, let's sub in a real number for *x*.

In this case, the question contains a linear equation, so I can just solve for *x*.

I'll subtract 4 from both sides to get 3*x* = 12

And then divide by 3 on both sides to learn that *x* = 4.

Now, all I need to do is plug 4 into the answer choices until I see which one is true.

Let's start with choice A. When I plug in 4 I get:

4 = 16 + 3(4)

or

4 = 28

Definitely not true, so choice A is incorrect.

Let's try choice B.

4 + 4/3 = 16/3

Simplifying this equation involves some fraction arithmetic. Even if you though you may remember how to do fraction arithmetic, I recommend using your calculator to reduce the chance of careless mistakes. After plugging this into my calculator, I see that:

16/3 = 16/3.

That's true! Choice B is correct again.

This strategy generally works when you have variables in both the question and the answer choices. The key to using this strategy correctly is figuring out the restrictions on your variable.

In our example, *x* could only have one value, 4, and I knew that because linear equations only have one solution. I couldn't pick any number at random to plug in.

Let's look at one more example. It's a little more complicated.

The quantity *a* * *b* is always a positive real number when:

A. *a* is positive and *b* is negative

B. *b* is positive and *a* is negative

C. Both *a* and *b* are positive

D. Both *a* and *b* are negative

E. *a* and *b* are any real number

This problem is a bit of a puzzle. You have to think pretty abstractly to answer it, which can be particularly difficult when you're feeling rushed.

Fortunately, there are variables in both the question and the answer choices, so I can use the strategy to plug in actual numbers. In this case, I know that the product of *a* and *b* is a positive real number, which is any number above 0 all the way up to infinity. To make my life easy, I'm going to select a small number: let's say 10.

Now, I want to look at the answer choices and play with different values of *a* and *b* to see which ones will let me reach ten.

Let's start with choice A.

*a* is positive and *b* is negative

Let's say *a* is positive 5 and *b* is -2

5 * -2 = -10

Negative 10, not positive, so choice A is incorrect.

Let's try choice B.

*b* is positive and *a* is negative

This time, let's say *a* = -5 and *b* = 2, so we have:

-5 * 2 = -10

Another negative number, so choice B is incorrect.

Let's try choice C - both *a* and *b* are positive

Let's say *a* = 5 and *b* = 2

5 * 2 = 10

A positive number! C is correct!

When you're doing this on the actual test, I recommend checking all the answer choices to confirm that you haven't made a careless mistake. Also, avoid using 0 or 1 when plugging in numbers because 0 and 1 can yield confusing results.

Let's review the two strategies you can use when you're stumped by a problem on the ACT math.

First, use the answer choices. By plugging in the answer choices, you can often find the correct answer. But remember, this is usually only faster if you don't know how to solve the problem.

Second, substitute in real numbers. Don't let variables confuse you. If you see variables in both the question and answer choices, you can substitute real numbers in for them.

Finally, if you still don't know how to solve the problem, guess and move on. Don't let yourself get bogged down on a difficult problem. It's better to take your best guess and move on.

After watching this lesson, you should be able to demonstrate three strategies for when you're stuck on a math problem during the ACT exam.

To unlock this lesson you must be a Study.com Member.

Create your account

Already a member? Log In

BackDid you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
3 in chapter 10 of the course:

Back To Course

ACT Prep: Practice & Study Guide48 chapters | 407 lessons | 23 flashcard sets

- College 101: College Prep & Retail Business Lite
- Recruiting & Managing the Multigenerational Workforce
- CTEL 1, 2, 3 Combined Exam (031/032/033): Study Guide & Practice
- MoGEA Science & Social Studies Subtest: Study Guide & Practice
- CSET Physical Education (129/130/131): Study Guide & Practice
- ICAS Science - Paper J Flashcards
- PSAT - Reading Test Flashcards
- NES Family & Consumer Sciences (310) Flashcards
- UExcel Bioethics - Philosophical Issues Flashcards
- TECEP College Algebra Flashcards
- How To Pass The Elementary Algebra Accuplacer
- Accuplacer Tips
- How to Study for the Accuplacer
- HESI Test Cost
- Study.com ASWB Scholarship: Application Form & Information
- ACCUPLACER Prep Product Comparison
- Accuplacer Test Locations

- Strategies for Teaching Semantics to ESOL Students
- Applying Morphology to ESOL Instruction
- Jim Crow Laws in To Kill a Mockingbird
- Teaching ELL Students Narrative Writing
- Sorting Algorithm Comparison: Strengths & Weaknesses
- Practical Application: Writing Job Interview Questions
- Calculate the Intrinsic Value of a Firm
- Practical Application for Software Engineering: Component-Level Design
- Quiz & Worksheet - Language Objective for ESL Students
- Quiz & Worksheet - Victorian Architecture
- Quiz & Worksheet - Origins of the Muslim-Hindu Conflict
- Quiz & Worksheet - Choosing Grade-Appropriate Texts
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies

- Middle School US History Curriculum Resource & Lesson Plans
- Computing: Skills Development & Training
- Intro to Economics
- AP Physics 1 Textbook
- Quantitative Analysis for Teachers: Professional Development
- Michigan Merit Exam - Math: Linear Regression
- Forms & Characteristics of Government
- Quiz & Worksheet - The National Labor Relations Act
- Quiz & Worksheet - Effective Leadership Qualities
- Quiz & Worksheet - Classroom Applications for Jigsaw Activities
- Quiz & Worksheet - Methods for Positive Classroom Management
- Quiz & Worksheet - Modulus in Math

- Algebraic Rule: Definition & Concept
- Allele Frequency: Definition, Calculation & Example
- Memoir Lesson Plan
- SAT Chemistry Test: Content, Format & Scoring
- How to Set Up a Class and Invite Students in Your Study.com Virtual Classroom
- 8th Grade Persuasive Writing Prompts
- Parts of a Book Lesson Plan
- How to Prepare for the GMAT
- Where Can I Find Free SAT Prep Classes?
- Online Training Courses with Certificates
- What is the PSAT 8/9? - Information, Structure & Scoring
- How Much Does the GRE Test Cost?

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject