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ACT Prep: Practice & Study Guide43 chapters | 347 lessons

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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.

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