# ACT Math: Pacing & Strategy Overview

The ACT Math Test is always the second test and comes right after the English Test. It is always 60 minutes long and consists of 60 questions. Concepts tested include arithmetic, algebra, coordinate geometry, plane geometry, and (unfortunately) trigonometry. The math concepts get harder as you progress, so timing is an important part of the test. As you proceed, you must make sure not to spend more than 1-2 minutes on any single question.

Once you are in the middle of the section and begin to encounter more challenging concepts, make sure you don’t let any one question frustrate you or waste your time. You’ll need a little extra time to handle those challenging questions at the end, so make sure to move through the first third of the test quickly and confidently but don’t rush yourself.

If a question is taking you more than a minute, skip it and move on. You can always come back! If you run out of time at the end and don’t have time to come back to it, make sure to fill in something on your answer grid. There is no wrong answer penalty on the ACT, so you definitely want to make sure to answer every single question!

In terms of general strategy, when you read each Math question, don’t just automatically reach for the calculator and start crunching numbers. Sometimes taking a few extra seconds to consider the best approach to solve a problem will actually save you time in the long run. Many Math problems on the ACT can be solved in a few different ways and often one way will be much faster.

Be thoughtful and deliberate when reading each question stem. Look for patterns and shortcuts. If you are stuck on a problem and can’t find a way to approach it, study the answer choices. Eliminating four wrong answer choices is just as effective as finding the right answer! Also look for opportunities to use one of the following two strategies:

### Backsolving

Backsolving is an excellent strategy to use when there are numbers in the answer choices. Instead of setting up your own equation, assume each answer choice is correct. This is a great strategy to use when you are stuck because it lets you check your work as you go! Let’s look at an example:

Claire took a fifty-question algebra test and answered every question, scoring a 10. Her teacher calculated the score by subtracting the number correct from three times the number incorrect. How many questions did Claire answer correctly?

A. 30

B. 34

C. 36

D. 40

E. 42

Since this is a word problem and there are numbers in the answer choices, this question is a great candidate for Backsolving. Let’s start with answer choice (C) 36. Since the answer choices on the ACT are ranked from smallest to greatest, starting with answer choice (C) will help us eliminate three answers at once.

If Claire answered 36 correctly, then she must have answered 14 incorrectly (because it was a 50 question-test). Three times the number incorrect (14) = 42. We then subtract the number correct (36) to get a score of 6. However, the problem told us that her score was a 10. A 6 is too small, so we can eliminate choices (A), (B) and (C).

The next logical choice to try is (D). If she answered 40 correctly, then she must have answered 10 incorrectly. Three multiplied by 10 = 30. Then we subtract 30 from the number correct (40). Our answer is 10, which matches the score mentioned in the question stem, so we know we have our correct answer!

### Picking Numbers

Anytime you see variables in a question stem or in the answer choices, you can Pick Numbers. Let’s try an example question:

There are m students total in the classroom taking the ACT. n of those students will score above the 90% percentile. Which expression represents the number of students who will NOT score in the 90^{th} percentile?

- n (m – n)
- n + n
- m / n + n
- n (m – n) / n
- m x n

Here we have two variables: m and n. We can pick numbers for those variables as long as they make sense within the context of the word problem. We know that m must be a bigger number than n since m is the total number of students and n is a portion of that. Let’s say m = 4 and n = 2. I chose these numbers because they are low and easy to work with – remember that Picking Numbers should make the math simpler. Why pick 4,567 for m when we can pick 4?

If m = 4 and n = 2, we know that 2 students will NOT score in the 90^{th} percentile. Let’s plug in our picked numbers into the answer choices and see which once yields 2! The answer here is (D).

Start looking for opportunities to Backsolve and Pick Numbers when you practice and remember, the smart ACT Math test-taker excels in both time-management and strategy!