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7 Most Common Mistakes on ACT Math & How to Avoid Them

Posted by Dora Seigel | Sep 3, 2016 8:00:00 AM

ACT Math

 

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I've tutored many students on the ACT Math section, and they often found it frustrating. Some struggled because they considered themselves better English students and felt overwhelmed by the content and pacing of ACT Math. Others found that even though they considered themselves strong math students, they had a hard time getting the score they wanted in the ACT Math section. But all these students typically made the same types of mistakes. 

In this article, I’ll go over the seven most common mistakes students make on the ACT Math section and how to avoid them.

 

Mistake #1: Skipping Steps

ACT Math questions can be very sneaky. Problems can appear at first glance deceptively easy because they only require you to know basic math topics

However, the ACT questions ask for you to apply this basic knowledge in unique ways and often require you to run through several steps to get to the correct answer. If you don’t write out these steps, you can easily end up with the wrong answer.  

For example, check out this ACT Math question:

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I’m going to admit that the first time I attempted this I got it wrong because I did not write down my steps! Hopefully, you’ll learn from my mistake. Together, we will write out the steps and get to the correct answer.

There are 4 questions with 3 possible answers, and only 1 of the 3 answer choices will be correct. Therefore, for each question, Elliott has a ${1}/{3}$ chance of answering correctly. Since there are 4 questions, Elliot’s chances of answering all 4 correctly at random are $({1}/{3})({1}/{3})({1}/{3})({1}/{3})$ which equals ${1}/{81}$, so the correct answer is E.

Initially, I tried to do this problem in my head without writing any steps down. Because I didn't write anything down, I mistakenly thought there were four possible answer choices for each question instead of three. Therefore, I got the wrong answer, ${1}/{256}$. Thankfully, my answer wasn't one of the answer choices, so I caught my mistake, but I would have missed the question otherwise. 

Don’t miss problems because you didn’t write out all of the steps. This is arguably the easiest mistake to fix. All you need to do is write out all your steps, and you’ll never accidentally miss a problem because you skipped a step! Learn from my silly mistake!

 

Mistake #2: Forgetting Formulas

The ACT doesn’t give you any formulas. However, you’ll need to use a lot of formulas to answer questions in the ACT Math section. You need to know these math formulas to answer the questions correctly. We’ve compiled a complete list of all the formulas you need to know for ACT Math.

You need to memorize these formulas. Create flashcards to help you memorize. I cannot stress enough how important memorizing formulas is. You’ll see at least 10 questions (out of 60) on the ACT Math section that you will not be able to answer without knowing formulas.

Check out this ACT Math question that you couldn’t answer without knowing the formula: 

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If you didn't have your trigonometry formulas memorized (SOHCAHTOA), you would have no idea how to answer this question. It's impossible to answer this question without knowing the formula for the tangent of an angle since that is the value you're trying to find.

If you remember your trigonometry formulas, you know that the tangent of an angle is the opposite/adjacent. For this question, you need to find the tangent of angle B. The adjacent side for angle B is 2, which means it is our denominator. This means we can eliminate answer choices H, J, and K.

However, you cannot find the final answer without also knowing the formula for the Pythagorean TheoremYou need to know the Pythagorean Theorem in order to find the measure of the missing side of the triangle, the opposite side to angle B. 

Using the Pythagorean Theorem, you can find this missing side measure.

$$a^2+b^2=c^2$$

$$a^2+2^2=5^2$$

$$a^2+4=25$$

$$a^2=21$$

$$a=√{21}$$

The opposite side will be $√{21}$, and we know that our adjacent side is 2.

The final answer is F, ${√{21}}/{2}$. 

 

Mistake #3: Not Understanding Functions 

Functions tend to be one of the hardest concepts, if not the hardest concept, for most students. Students are usually less familiar with algebraic and/or trigonometric functions than they are with other math concepts such as fractions and percentages. Some students have completely forgotten functions or never learned them in the first place. 

To master the ACT math section, you need to be a whiz at functions. See this ACT Math function question: 

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To answer this question, you need to know the rules of trigonometric functions and translations. You will not be able to answer this question without knowing these rules. You first need to use your knowledge of trigonometric functions to read the graph, and then, you need to apply your knowledge of translations rules to find the final answer. 

First, you need to be able to identify which function is $sin(x)$ and which is $sin(x+a)+b$ on the graph since they're not identified for you. If you know your trigonometric functions, you know that the y-intercept of $sin(x)$ is 0, meaning the graph of $sin(x)$ crosses through the origin. Therefore, the other function must be $sin(x+a)+b$.  

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Once you've correctly identified which function is which, you need to figure out how $y=sin(x)$ was changed to make $y=sin(x+a)+b$, which is where your translation knowledge comes in. Based on the given information in the question, you know the two have the same maximum values, meaning the amplitude was not changed. By looking at the graph you can tell $y=sin(x)$ was shifted to the left or right to make $y=sin(x+a)+b$, but it was not moved up or down.

Since there was no up or down movement, b must equal zero since any change in b would cause $y=sin(x)$ to move up or down. Therefore, the answer must be A, but let's check by figuring out what a should be. 

Because $y=sin(x)$ repeats itself infinitely, you can shift it either to the left or right to create the new function $y=sin(x+a)+0$. Therefore, $a$ could be positive or negative (for example, ${-3π}/{2}$ or ${π}/{2}$, but it could not equal zero, so A is the correct answer. 

If you've forgotten functions, then you need to review. You must review all math concepts that you’re rusty on in order to succeed on ACT Math. Lucky for you, we’ve written specific ACT Math content guides to help you study any individual ACT Math content area that you might be struggling with, from trigonometric functions to translationsratios to rotations, points to probabilities and much more.

 

Mistake #4: Panicking at Unfamiliar Question Formats

The ACT sometimes asks questions in strange ways, which can scare a lot of students. I had many students who, even though they'd reviewed all of the math content areas, would read the question and rather than trying to figure it out would just freak out and give up. 

The question below is one that presents an unfamiliar question format. You’ll likely recognize it as an algebra question, and if you were asked to find the solutions for x (had you been given numerical values of m and n), you’d likely know how to answer that question. However, instead, this question tells you the value of x and asks you to figure out what m and n are.

Let’s work through this problem together: 

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If the only possible solution for x is -3, that means the given equation can also be represented as $(x-y)^2=0$. We need to figure out what y is in order to find out what m and n are.

If $(x-y)^2=0$, then you can separate it into $(x-y)(x-y)=0$. For this to be true, x-y has to equal 0.

$$x-y=0$$

The question told us that the only solution for x is -3, so we plug that in and solve:

$$-3-y=0$$

$$-y=3$$

$$y=-3$$

Now that we know the value of y, we plug it back into $(x-y)^2=0$ and then multiply and simplify to figure out what m and n are:

$$(x-(-3))^2=0$$

$$(x+3)^2=0$$

$$(x+3)(x+3)=0$$

$$x^2+3x+3x+9=0$$

$$x^2+6x+9=0$$

Therefore, $m=6$, so the answer is C.

There is no easy solution to this type of mistake. The only way to learn from this mistake is with practice. ACT Math questions are unlike the math questions you usually see in math class. They are much trickier.

I recommend taking as many practice ACT tests as you can in order to get used to the style of ACT math questions. You need to train yourself to be able to solve math questions in this new way.

 

Mistake #5: Solving for the Wrong Value

As I just said, ACT Math questions can be tricky. They are tricky not only because they ask you to apply basic skills in new ways but also because they sometimes phrase questions in weird, convoluted ways.

Although the ACT is often called the more straightforward test in comparison to the SAT (or at least in comparison to the old SAT), some ACT Math questions are far from straightforward. Take for example this question: 

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The question is basically asking how the surface area will change if you double the length, width and height. However, if you misread the question, you could easily jump to the incorrect conclusion that the surface area was doubled, and the answer is A.

Given the formula for surface area, $A=2lw+2lh+2wh$, if we double $l$, $w$, $h$, the new surface area would be

$$SA=2(2l)(2w)+2(2l)(2h)+2(2w)(2h)$$

$$SA=2(4lw)+2(4lh)+2(4h)$$

That can be written as

$$SA=4(2lw+2lh+2wh)$$

When that is compared to the original $SA=2lw+2lh+2wh$, you can see it’s 4 times the original, so the answer is B.

Take your time. I know you don’t have a lot of time on the ACT Math section, but you need to read each question completely and make sure that you know what you’re being asked. The ACT Math section will always throw you an answer choice that will seem correct if you misread the question. They are trying to tempt you to answer incorrectly. Don’t fall for it!

 

Mistake #6: Incorrectly Using Your Calculator

You need to be careful with your calculator. It’s a great tool, but to quote the Spiderman comics, “With great power comes great responsibility.” It’s very easy to feel rushed during the ACT Math questions, and, in your hurry to find the answer, you type the wrong number(s) into your calculator and, therefore, come to the wrong answer.

Now, this is typically one of the better mistakes to make on this list because if you type in the wrong number(s) you’ll likely find no matching answer in the ACT answer choices, and you’ll realize you made a mistake.

However, you don’t want to be making this mistake. Even if you catch your mistake because there is no matching answer choice, you’ve still cost yourself valuable time that you could have been using to answer another question. Take the time to check that you’ve copied the numbers into your calculator correctly.

 

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Type carefully!

 

Mistake #7: Not Pacing Yourself

With only 60 minutes to answer 60 questions, you need to learn to pace yourself. To determine your pacing, you need to first figure out your target score. The questions progress from easy to hard, so no matter what score you're aiming for always attempt the questions chronologically. 

If you're aiming for a score higher than 30, then you're going to need to answer all or almost all of the 60 questions. That means you must spend under 1 minute per question on the first 30 questions to save time for the harder end questions.

If you're aiming for a score below 30, then you can afford to skip some questions. Determine how many questions you need to answer to reach your score and then pace according to that amount of questions. For example, if you're aiming for 20, then you only need to get 32 math questions right. You can allow yourself a minute and a half per question, and you should attempt the first 40-45 questions and skip the hardest ones at the end. Simply choose a random letter and bubble that in for the ones you skip, since there is no penalty for guessing. 

I won’t go into detail because we have another great guide on how to stop running out of time on ACT Math and how to take advantage of the easy to hard question order.

However, I will say to truly master the pacing you need to take many practice tests under realistic conditions. Don’t give yourself even one extra minute on your practice tests because this can artificially inflate your score. Stick to 60 minutes for the ACT Math section.  

 

What’s Next?

Now that you know the most common mistakes on ACT Math, you might want to take a look at our specific ACT Math content guides to help you study any individual ACT Math content area that you might be struggling with, from ratios to rotations, points to probabilities.

Stuck on an ACT Math problem? We'll show you how to figure out when you're really stuck and what to do about it.

Want additional help with ACT Math? Don’t sweat it. We've compiled all our best free ACT Math guides into one ultimate ACT math study guide.

 

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Dora Seigel
About the Author

As an SAT/ACT tutor, Dora has guided many students to test prep success. She loves watching students succeed and is committed to helping you get there. Dora received a full-tuition merit based scholarship to University of Southern California. She graduated magna cum laude and scored in the 99th percentile on the ACT. She is also passionate about acting, writing, and photography.



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