Mr. Cantlin's Math Tutoring

Any maths. Specializing in long-term preparation for the ACT.

ACT Tips

What the test means.
The current ACT is a fair test of math knowledge needed to start at a Precalculus or Calculus level at college. Yes, it is only a snapshot. But it is a meaningful one. A high score does not guarantee the student will do well in Calculus at college as it does not measure work ethic, social maturity, or ambition or perseverance. But a low score is a good indicator that the student is not prepared to take a rigorous college Calculus class. My experience and belief is that a student with good math ability can, through practice and hard work, get a great ACT score. The earlier this preparation starts, the better. I recommend starting in eighth or ninth grade. The key is not trying to teach to the test but to teach the core topics. If you learn them well enough, the test will take care of itself as it is a fair test and a good measure of math competency.

Memorization is Needed for Core Competency.
Somehow, over the last 30 years or so, educators, especially in math, have convinced themselves that memorization is bad and that it is an indication of bad teaching to require memorizing anything. False! There is no doubt it is hard work to memorize facts, and the work is unpopular with students. But it is very costly in terms of the student's core competence in math to pretend that you don't have to memorize anything. Here is the most glaring symptom based on my personal experience on working with advanced teens from local schools in and around Oneonta. They don't know their times tables. Not just some, I claim most of them don't. Yes, from the Seniors taking AP Calculus down to the Freshmen taking Algebra 1. They just don't know them. How do they get by? By "counting up" or, if they have time, by using a calculator. What do they know? They know how to fake it! They are experts at pretending they know their times table. In class, they only volunteer answering the questions for the ones they know. One-on-one, they will stall for time on the ones they don't know while they "count up". It would be an impressive feat if it was not the only thing impressive about the state of their times table knowledge. Of course, on a timed test like the ACT where the answers are carefully crafted to ensure common mistakes are trapped, there is a price to pay for not knowing your times tables. Back to memorization in general, name one important job that does not require a large amount of memorization before a person even begins to be considered competent in that job. Yet we are so adverse to requiring students to memorize math formulas and definitions that our best students, more often than not, are not skilled at memorizing facts. This is a place where some tough love is needed, both by parents and teachers. Memorization is a basic skill that can be improved by training and practice. It is a basic skill that the schools should not apologize for teaching and using. Failure to do so, is in my humble opinion, professional negligence.

What Should You Memorize for the ACT?
I made a list that is a good starting point! The PDF file that is linked to below has a list of "things to memorize" for the ACT. It has the answers attached so you can use it like a flashcard. Put one in your notebook, one in your room, one on the fridge :-). Study, rinse and repeat. Memory is repetition. Memory is repetition. I started to build this list when I started to tutor and it is a work in progress, but I have found I rarely need to update it because most students do not know even these few formulas and definitions. Knowing the items on this list certainly addresses some of the most glaring weaknesses I see in my student's knowledge of basic definitions and formulas. Many of the math questions on the ACT will present a basic knowledge question in a way that the student has never seen before. The intent is to see if the student can fall back on their knowledge of definitions and formulas to understand what the problem is really asking. If the knowledge is not there to fall back on...guessing is the only option left.
Click Here for "Things To Memorize" Worksheet" .

What Books Do You Recommend for the ACT?
The two books I recommend getting are "The Real ACT" for its practice questions because it is written by the company that makes the ACT and the questions all come from actual ACTs. This is a big plus as it is tough to get sample questions that are not too easy or too hard. The older version of this book is still valuable and very inexpensive if bought used. It has 3 complete practice tests with questions from actual ACTs. For topic reviews, i.e., reteaching yourself an ACT topic. I think the Barron's books are well written. Get a Barron's Math and Science Workbook for its great explanations of math topics. Don't buy new books, you can buy 4 or 5 good used ones for the price of a new one. I have purchased many and never been disappointed. Used ACT books are very inexpensive. Try Amazon for used books or my favorite: Better World Books. Don't write in your practice books. When you are done with your books, give them to a younger student or resell them on the used book market or better yet, donate them to your local public school library.

What Calculator Do You Recommend for the ACT?
All 60 questions on the ACT are designed to be done without a calculator. Repeat, all 60 questions on the ACT are designed to be done without a calculator. The most common symptom I see from a student that is under-prepared for the ACT is a gross overuse of the calculator. See my remarks above about times table and memorization problems that I know are widespread in Blount County. A well prepared student might not use a calculator at all, or only a few times during the test. That being said, the calculator you use should be one that is appropriate for the test, and one you are VERY familiar with. A graphing calculator, while allowed, is in my opinion is not the best choice as most students are not experts at using one and the "easy" functions can be harder to get to just because the calculator is more complicated. It can also trap you into wasting precious time getting deeper and deeper into the calculator instead of actually thinking about the problem. And the ~ $19 calculator I recommend, because it is newer technology than most graphing calculators used in school, does a few things that can be useful on the ACT, like simplifying radicals, better than the bulky and complicated graphing calculators. My current recommended calculator is the TI-36X Pro. The multiline display greatly improves accuracy and efficiency because you can see four lines of input. It is solar/battery operated, and is a good value. The way it shows fractions and scientific notation is particularly nice. It has a powerful and easy to use function/table maker very similar to a graphing calculators. Great features for the ACT are the way it shows exact values of simplified square roots and exact values of trigonometric functions. It does prime factorizations too. The ability to scroll up and see/use previous answers is very convenient. And the modern (TI calls it "mathprint") 4-line display beats my 10 year old TI-83 Plus graphing calculator hands down. It is perfect for the ACT. I strongly recommend that the calculator you use on the ACT is the same one you use every day. The worst thing to do is borrow some fancy calculator that is new to you for the test. I will help you master your calculator during tutoring.

If you need a graphing calculator for school and the ACT, for AP Calculus for example, I recommend the Casio Prizm fx-CG10. It is less expensive than comparable TI graphing calculators, and, is much easier to learn and use. It does not have a CAS (computer algebra system) and therefore is allowed on the ACT. It is also perfect for AP Calculus, a graphing calculator is required for the AP Calculus exam. You are allowed two calculators at the ACT, you can only use one at a time, so you could bring the TI36x Pro as your main one and use the Casio if you had a math emergency of some kind on a particular question. The ACT is designed so every problem can be done without a calculator and the best prepared students will not use one at all, or at most for one or two problems. The weakest students begin playing on their calculators like a piano keyboard on question 1 and continue to do so for the entire test, of course these students do not typically score as college ready. That being said, the calculator you do bring should be one that is appropriate for the job and one you know very well.

Mr. C.'s Recommended ACT calculator, the TI-36X Pro

Mr. C.'s Recommended ACT graphing calculator, the NumWorks Graphing Calculator

Order the Test Results.
Usually after three of the ACT tests in a given school year (the September (changed from December), April, and June tests) the ACT lets you purchase (~$30) your test results. For math this is something I strongly encourage you to do every time you get the chance because you can see where you made your mistakes. Of course, buying your results and not examining the questions and your responses carefully is a waste of money. But if you carefully break down what your mistakes were, it is a targeted way to focus your practice. Please do this whether you tutor with me or not. It is a real opportunity to improve and should not be overlooked. Of course, if you are tutoring with me, I would be very pleased and anxious to go over the results with you. There is no better way, in my opinion, of deciding what topics you need to study and practice. Place this order at the time you register for the test so you have the best chance of getting them before the next test. The April results will probably not get to you before the June test, but you will have all summer to go over them!
Ordering a Copy of Your Test Questions and Answers.

Don't Worry About Speed, Worry About Knowing the Topics
Yes, there are 60 problems to do in 60 minutes and the time is what makes it a tough test i.e., a fair measure of what you know. And you do have to manage your time, your practice should help you tell when your "1 minute" is up for the problem you are on and you have to decide if you should move on or not. But the biggest mistake I see among students that score less than they should based on their knowledge is to rush through the questions they find easy. This is a poor investment of your time since it increases, sometimes greatly, your chance of missing a problem you know how to do. Usually by a sign error or basic arithmetic mistake. And the time you save may end up being spent on a problem you don't know how to do. So take enough time to make sure you get the ones you know how to do right. Do not try to do the whole problem using mental math, slow down and write enough down to do it right. Use parentheses for substituting. You do not have to practice going faster, the more you know the faster you will naturally go. Students that have a good grasp of the underlying topics, and that have practiced enough to be good managers of their time, rarely use a calculator and rarely have trouble finishing with time to spare. Most beginning students will tell you the questions go from easiest to hardest. But they really go from Pre-algebra to Algebra 2 and within those topics, the questions are for the most part as easy at the end as they are at the beginning. For example, once you have covered transforming functions thoroughly, and have covered all of the topics, an early question on transforming a linear function is no more difficult and takes no more time than a question near the end about transforming a sine or cosine function. Here is another example. Have you ever watched a professional plumber change a faucet? I can do it, but it might take me several hours with a lot of that time spent going back and forth to get the right parts, tools, a mop, towels (don't ask). Whereas a good plumber has the knowledge to look like he or she is working slowly, and takes five minutes to do the job well with no leaks. The plumber's knowledge naturally improves the speed at which the job can be done. The point is, the more you know the faster you go!

There Is No Science Test
There is too much of a variety in the science classes taken by 9th to 11th graders across the U.S. for the ACT to put together a comprehensive science test. Would you test physics? Many high school students, unfortunately, don't take it. Chemistry? Biology? So what is the science test? First off, it is only 35 minutes. What does that tell you about its depth? Second, in my opinion, unlike the math test which is a fair test of math competency, it has almost nothing to do with measuring a student's knowledge of science. The description of the test is fluffed up tremendously. What it is, in my terms, is a technical reading comprehension test. You are given several sets of information, usually seven. These are completely independent of each other. Each set will involve evaluating a narrative and almost always has a graph, table, or both. You only have about five minutes to digest the information and answer the five or six questions related to it. There are essentially no calculations involved, they don't even allow calculators. When you practice, if you take say 15 minutes to thoroughly understand the information presented, the questions turn out to be really, really easy. SO the only thing that is hard about it is learning how to digest the information in say four minutes. Once you can do that you can answer all the questions related to it in one minute, they are not hard questions, you will agree after practicing. Do it six more times and voila, you just aced the "science" exam. It is not, in my opinion, a science test and should not be called a science test. I think it should be called a "technical speed reading test". The students who are good readers, and who have a quick grasp of graphs and tables of information will naturally do well on this test. What you call something is important. If you skim the test, it looks like a science test. But it is not. All the knowledge you need, with the exception of some basic common sense science knowledge, is contained in the narrative, table, or graphs. But I would bet the farm that administrators and school boards use the results to evaluate whether their "science" programs and teachers are doing the jobs. What a mistake, they might as well use a "Magic 8 Ball" to make their decisions. Nevertheless, it says "Science Test" so that is what it will be; "You may rely on it." Bottom line, I think the science test is easy to prepare for and by going over a few practice tests in detail I think I can give a student confidence in their ability to do well on this section of the ACT.

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