I help students preparing for the Math section of the ACT. I want to share with you a few impressions on the test itself, and some issues I’ve seen in my tutoring experience.
One of the first things I notice is that many of the problems are not anything like the problems most students see at their schools. Let me show you what I mean with one example I particularly like (Oh, my! Do you like the questions?).
In the real numbers, what is the solution of the equation \(8^{2x + 1} = 4^{1-x}\)?
You may say: What? How am I supposed to know? I haven’t seen that kind of equations yet!
Now, I’ll quickly tell you one way to solving it. Recall your powers of \(2\): \(2^1 = 2, 2^2 = 4, 2^3 = 8\). Bring to mind the laws of exponents: \[8^{2x + 1} = (2^3)^{2x+1} = 2^{3(2x+1)} = 2^{6x+3}.\] Similarly, \[4^{1-x} = (2^2)^{1-x} = 2^{2(1-x)} = 2^{2-2x}.\]
Now, you can compare the exponents of both expressions, and you realize that what you need to do is to solve the equation \(6x+3 = 2-2x\), which you may already now how to solve. The solution is \(x = -1/8\). Why they didn’t just write “Solve the equation \(6x+3 = 2-2x\)”? That’s because ACT (and SAT) is testing your understanding of the concepts and not only your computational abilities. Many people can solve linear equations if they are taught the recipe. But not that many can see problems like this one and realize that there are two key concepts to grasp for this problem: laws of exponents and solving linear equations.
That’s one of the reasons that I emphasize understanding of the concepts while I prepare students to take standardized tests.
Another thing that I want to show you with the example above is that in order to know what is the correct answer I don’t need an answer sheet. If you perform your computations correctly, you can be sure that you have the correct answer. I was surprised when one of the students I was tutoring said: how can you know what’s the correct answer if you don’t have the answer sheet? You too can be sure about the correct answer if you understand the math you’re performing.
A final thought that I want to share is that reaching the level of understanding needed for the test takes time. It doesn’t come in a few weeks of preparation. Math is slow, very slow. Don’t get discouraged if there’s something you’re not understanding. Be persistent, and look for some guiding. If you know that you’ll take one of these tests, start well ahead of time: months, or even years before your deadline. You can do it! But you need to be prepared. Another reason to prepare well ahead of time is that it takes a lot of practice being able to solve a significant amount of the questions under 60 minutes.
If you want some one-to-one help preparing for your test, don’t hesitate to get in touch!