ACT, Inc. is the non-profit organization that administers the ACT college admissions test. They are the only source for official, previously released exams. Practice tests from third-party publishers like Kaplan or McGraw-Hill are just approximations. Fortunately ACT makes freely available previously administered tests. This post addresses the 60 questions in the Math section from the 2015-2016 ACT. This post and the answer explanations on Piqosity were contributed by undergraduate students at Rice University as part of a project for their class BUSI 390.

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Hi there! If you’re here, then you are on your way to success in conquering the ACT. We hope this practice will guide the way you approach questions and help de-mystify the process of thinking in multiple steps to arrive at a solution. We are excited to help you along the way, and welcome, from Avery Landrum, Joan Liu, and Connie Shen!

General Strategies

1. For more complex problems, break down the question into smaller steps; this process makes you feel less overwhelmed and will help to eliminate careless mistakes.
2. Draw pictures when it gets confusing. Don’t be afraid to spend time organizing the picture of your thoughts, especially if it can prevent you from making silly mistakes and having to go back and figure out what’s wrong, which can take even more time.
3. Plug in the answer choices to quickly check your work. With questions that ask you to solve variables, this is a quick way to make sure you didn’t make a silly mistake.
4. Eliminate incorrect answer choices. You might not know the correct answer but chances are you can eliminate a few obviously wrong ones. Since you don’t get penalized for incorrect answers on the ACT (or the new SAT), eliminate as many choices as possible and make a guess!
5. Skip difficult questions and come back later. All the questions are worth the same number of points. So why not maximize your wins and get all the easy ones (for you) down first? :)

Tips on Concepts Featured in this 2013 Previously Released ACT Math

1. Break complex problems down into smaller steps.

If r=9, b=5, and g=-6, what does (r+b-g)*(b+g) equal?

1. 20
2. 19
3. 8
4. -8
5. -20

To solve this problem:

1. Plug in r=9, b=5, and g=-6 into the expression to obtain (9+5- (-6))*(5+(-6)).
2. This simplifies to (20)*(-1) = -20.

Quick Tip–  This question is fairly straightforward, just make sure to do your math correctly and not get confused by subtracting a negative number (two negatives make a positive!).

2. How to Combine Two Functions

Given f(x) = x – 1/x  and g(x) = 1/x, what is f(g(½)) ?

1. 3/2
2. 0
3. -2/3
4. -3/2
5. -3

To solve this problem:

1. We start with the inner function which is g(1/2). g(x) = 1/x, so g(1/2) = 1/ (1/2) = 2
2. Now we find f(2); f(x) = x – 1/x, so f(2) = 2 – 1/2 = 3/2

3. Memorizing terms in order to apply them in solving the question.

Q: What is the difference between the mean and the median of the set [3, 8, 10, 15] ?

1. 12
2. 9
3. 4
4. 1
5. 0

To solve this problem:

1. First, we need to find the mean, or average of the set. We calculate it by (3+8+10+15)/4 = 36/4 = 9
2. 2. Second, we need to find the mean, or middle number of the set. To do this, we need to take the average of the middle two terms (8 and 10) to find the mean. Doing the math: (8+10)/2 = 9, which is the mean

4. Solving Word Problems

A car accelerated from 88 feet per second (fps) to 220 fps in exactly 3 seconds. Assuming the acceleration was constant, what was the car’s acceleration, in feet per second per second, from 88 fps to 220 fps?

1. 102.67
2. 75.33
3. 44
4. 29.33
5. 1/44

To solve this question:

1. Know the formula for acceleration in this case is (End fps – Beg fps) time = acceleration.
2. Use the given information to solve for acceleration in the formula: (220-88)/3 = 44

Draw a visual when needed.

The sides of a square are 3 cm long. One vertex of the square is at (2,0) on a square coordinate grid marked in centimeter units. Which of the following points could also be a vertex of the square?

1. ( 5, 0)
2. ( 4, 1)
3. ( 1,−1)
4. ( 0, 1)
5. (−4, 0)

To solve this question:

1. Consider the possibilities for the other three vertices of the square. First think about the x-dimension by considering points 3 cm away from (2,0) on either side: (3, 0) to the right, and (-1, 0) to the left. Then think about the y-dimension: (2, 3) and (2, -3).
2. Use process of elimination to select the correct answer choice.

Good Luck!

We wish you the best of luck in your studies and on your official exam day! We remember when we were doing practice questions for the first time and felt so overwhelmed by all the material we needed to review. Just remember that you know more than you think you do, and focus on thinking through a problem rather than memorizing how to solve it. That way, one practice question will equip you in facing many other types, and you will be more prepared!

The key to success on the ACT or SAT is just practice, practice, and more practice. When we were studying for the ACT, we spent weeks just doing practice test after practice test. Make sure you learn from the mistakes on each practice test so the next one will be even better.

Not only does practicing ensure that you understand all the material covered in the exam, but it also gets you comfortable with the time limitations and overall setting of the exam. The last thing you want to do is use the actual exam as a trial run. Good luck, and we are confident that you will do well!

Let’s Practice

Through the link below, you’ll find a practice quiz that contains all 60 of the questions from the previously released 2013-2014 ACT. If you want to simulate a more realistic testing environment, limit yourself to the test-allowed 60 minutes. After you take the test, you’ll get instant results, answer explanations, and detailed analysis of your performance.

These questions are the property of ACT, Inc., but the answer explanations were provided by the students who authored this blog post. 