Your Comprehensive Guide to the ACT

Math

You need to know a lot of information to be able to answer every question on the ACT Math section. Fortunately, most of the actual math you need to know you've learned by the time you finish Algebra 2. The rest, which is not much, can easily be learned. What makes it easy is that the breadth of the subject is very narrow on the ACT, thus one need not learn the full scope and understanding. Let me explain: trigonometry in school takes quite a while to learn; you need to learn the theory of angles, what trig functions mean and what they're actually used for, various Pythagorean identities, etc. On the ACT however, there are only so many types of questions, including trig questions. Three types specifically, finding a missing side of a triangle, finding the value of a trig function on the unit circle, and what sine and cosine transformations look like on the X-Y coordinate plane. Each of these types of questions are extremely repetitive; so much so that you can follow the same steps to answer them whenever they appear. It's always the same.

Math Topics

Essentially, you need to know how to do basic algebra, how to handle ratios, percentages, exponents, scientific notation, coordinate geometry, plane geometry (including various geometry formulas), function notation, trigonometry, and various infrequently tested topics. These include matrices, imaginary numbers, logarithms and 3d spatial reasoning. These will usually appear as later, and thus more difficult, questions and are used to limit too many high scores.

Math Test-Taking Strategies

Good test takers learn how to get the right answer without doing the math, especially when they don't know how to do the math. The overarching philosophy to make this section far easier is to always seek to turn abstract problems into concrete ones. Often times, a question will ask you to do manipulations on quantities that they won't give you. "Sarah increased her long jump distance by 20%, and then by 10%." However, no initial long-jump distance is ever given. Here is where you can simply use your own number. Abstract to concrete. Many questions ask you to simplify an equation and find the answer choice that is its equivalent. You know that here you can easily use a simple number to substitute in for the variable in the equation and turn the problem from one requiring advanced algebra to one that only requires basic arithmetic. When you see answers that are all numbers, especially in increasing or decreasing order, you know that you can work backwards, and, instead of trying to solve a difficult math problem, plug in answers for a simple plug and chug process.

Here's an example of what I mean. Let's take a look at this typical ACT Math problem. This is a TYPE of problem, specifically an Exponents problem. One of only so many types of problems, I teach this as a type and teach the easy steps to the right answer. I'm going to demonstrate two easy ways to arrive at the right answer. 

Ok, so how do we handle this? It seems rather complicated, but really, if you know the steps and understand the right strategies, it's simple. One, the easy math way: we've learned simple steps to handle any exponent problem so we know that when you raise exponents to a power, you multiply. So we know that both term's exponent will be 12 (3x4 and 4x3). Then we know that when you combine terms, the exponents stay the same. Thus the right answer has to have 12 as an exponent. Thus the answer must be (d). No further work need be done. You've saved so much time by NOT fully expanding the problem and avoided opportunities to make mistakes. 

Okay, two, let's say you've completely forgotten all of the above, you freak out. Then you can fall back on the easy Test Taking Strategies we've learned. You grab your calculator, you say x=2 and then you plug in (2*2^3)^4 and (2*2^4)^3. You get some number, here 98,304. You use your calculator and plug in x=2 into each answer until you get to (d) and also get 98,304. You're done and you got the right answer. Easy.