<p>Hello everyone,</p>
<p>I'm assuming that if you're reading this, you're no doubt panicking about the upcoming math II subject tests that's just a few days away. Well have no fear, because this guide will hopefully provide some last minute advice for getting that coveted, immaculate, perfect score of an 800! After seeing user sjsharks, among many others, offer their invaluable advice over a few of the available tests, I decided to make a guide myself, and hope that it can help some of you get your desired scores! </p>
<p>In case you're wondering if I'm even qualified to write this guide, I recently received an 800 on the official test, as well as 800's in several of the various practice tests. And no, I haven't been deriving equations since I could first walk, nor did I qualify for USAMO as a freshman in high school - I'm just your run-of-the-mill math student who's here to offer their tips on how to succeed on this test.</p>
<p>So let's get started.</p>
<p><strong><em>Number 1: Your experience</em></strong></p>
<p>First and foremost, It's critical that you are at least finishing up a precalculus-level course or higher before taking this test. There is simply too much higher level math material covered on this subject test to take it after learning by review, and it'll be much more difficult than it needs to be. If you're in higher math and simply need to glance over some shaky precal concepts, that's perfectly fine, just grab a review book and refresh yourself over some of the basics. You'd be surprised at what you forget after immersing yourself in the world of Calculus.</p>
<p><strong><em>Number 2: Your calculator and you</em></strong></p>
<p>During the math II test, you're allowed one and only one lifeline: your graphing calculator. While some people dismiss the importance of it, I'm here to tell you that it will without a doubt be your best friend at test time, and might even save you from a few of the trickier questions.
I recommend a ti-84 graphing calculator, as it is simple, easy to use, and fully capable of solving most of the questions on the test by itself. Know how it works, know the shortcuts, and know how to fix it if you mess something up. Use fresh batteries. Make sure the buttons work. And most importantly, be familiar with the various functions that you can use, especially those under the "math" library. </p>
<h1>Major tip one - MAKE GOOD USE OF YOUR CALCULATOR. DON'T UNDERESTIMATE IT.</h1>
<p><strong><em>Number 3: How to attack this test</em></strong></p>
<p>I'm sure what I'm about to say will meet with a lot of disagreement, and for good reason. It really won't make much sense. We've been taught our whole life to see math in one specific way, and I'm here to disregard that entirely.</p>
<h1>Major tip two - SOLVE THE PROBLEMS HOWEVER YOU CAN, NO MATTER WHAT; THINK OUTSIDE OF THE BOX.</h1>
<p>This is not a test of conceptual knowledge. It's a test of your problem-solving skill. You don't need to know every single formula that's ever been created, nor do you need to fully understand why you use what method you use. Almost every problem out there can be solved with brute force, shortcuts, or just plain common sense, and you shouldn't be afraid to use these methods whenever you can. Math taught us since the beginning that we should know why we do things, but this is not the time for that. </p>
<p>Don't underestimate the ability to bullcrap your way to an answer!</p>
<p>Example problem:
During the first two hours of a 300-mile trip, a car is driven at an average speed of k miles per hour. At what average speed, in miles per hour, must the car be driven for the rest of the distance if the trip takes 4 more hours?
a) (k/2) - 75
b) 75 - (k/2)
c) (1/75) - (2/k)
d) (2/k) - (1/75)
e) 75 - k</p>
<p>At first, I had no idea how to conceptually or "correctly" solve this problem. That's just not my strong point, and I don't doubt that some of you feel the same way. So when all else failed, I used the best strategy available to bullcrapping problems where you're stumped, shown below.</p>
<h1>Major tip three - PICK A TEST VARIABLE, PLUG IT IN, AND USE THAT TO WORK YOUR WAY TO THE ANSWER.</h1>
<p>For the problem above, we know that there is a given variable, k, which is the average speed a car drove in 2 hours. We will pick an arbitrary number (in this case 60) and work from there. Plugged into the givens, we see that at 60 mph for 2 hours, the car will drive 120 miles. Given that we must drive 300 total miles, we can use a little math to find that in the remaining 4 hours, we must drive 180 more miles, for a grand total of 45 mph average speed. Knowing all this, we can plug our test variable into our given answer choices and find what works!</p>
<p>To save time, the correct answer is (b). Plug in the test variable of 60 mph to see that 75 - (60/2) is 45, which is precisely the answer that we were looking for. Armed with only the most basic math functions, we were thus able to solve a problem that might otherwise have taken much longer to figure out through conceptual understanding. This strategy is absolutely critical; Don't be afraid to use it!</p>
<p>Also remember that your calculator can do most of the problems for you. Don't remember how to find the zeroes of a function? Stick it in the graph and find them. Don't even know what the determinant of a matrix is? Let your calculator know it for you. The calculator will be your biggest asset in bs'ing answers on this test, so make sure that you use it to its full potential.</p>
<p><strong><em>Number 4: Background knowledge</em></strong></p>
<p>While I advocate the extreme importance of solving problems however you can, it is vital that you have at least some basic knowledge of key facts and formulas for the test. I'll give you what I believe to be the most important formulas, but this list is far from complete.</p>
<p>Distance formulas: both 2d and 3d, these are life-saving formulas that can be applied in a lot of problems to get to the answer; You must know these!
distance</a> formula</p>
<p>Quadratic formula: This is a universally recommended formula that if you haven't already memorized backwards and forwards, should learn right away!
The</a> Quadratic Formula Explained</p>
<p>Series formulas: I'm fairly confident that you'll see some form of these on the test, so don't miss the opportunity to get these questions right when you can! Memorize both arithmetic and geometric series.
Arithmetic</a> Sequences and Series
Geometric</a> Sequences and Series</p>
<p>Trigonometry: Arguably one of the biggest aspects of the test. These, while they can often be solved with your calculator alone, are extremely important to understand if you expect to solve the more involved questions involving trig. Not necessary to memorize, but be familiar with them.
Table</a> of Trigonometric Identities</p>
<p>Logarithms: Always present in some shape or form, you can expect to see some logs on the test, so be sure to brush up on the shortcuts to get these freebie questions!
RULES</a> OF LOGARITHMS</p>
<p>Again, this list is open to any and all additions by users, and I strongly recommend that you review many precalculus and algebra concepts in order to prepare for this test.</p>
<p><strong><em>Number 5: Preparation</em></strong></p>
<p>In the end, there's only one way to truly prepare for this test: practice! It's the only way to know what you're capable of, what you're great at, and what you need to work on.</p>
<p>As far as practice materials go, I personally recommend Barrons for extremely difficult tests that really test your thinking ability. A good rule of thumb is to take these practice tests and add 100 points to get your expected score on the real deal. For more realistic tests, Princeton's is a good choice, and I can't speak much for the other books, so if any users have insight about this, feel free to share it. </p>
<p>I'd advise that you consistently practice solving problems in the coming weeks before the test, and make sure to fully understand any mistakes you make, so that you don't repeat them on the actual test.</p>
<p><strong><em>Number 6: THE TEST</em></strong></p>
<p>Finally, it's time to sit down for a grueling, nerve-shattering hour and take this blasted test.
If you're reading this moments before you walk into the testing building, just remember these last minute tips:</p>
<ul>
<li><p>Stay calm. In the end, it's just a test. It won't change your life.</p></li>
<li><p>Make sure you have everything you need, ESPECIALLY A CALCULATOR.</p></li>
<li><p>Don't get hung up on a question. You can miss about 6 and get an 800. If you're stuck, move on.</p></li>
</ul>
<p>And most importantly,</p>
<ul>
<li>ATTACK THE PROBLEMS, AND SOLVE THEM BY ANY MEANS NECESSARY. You don't get points for eloquently describing a rigorous proof explaining your answer. Plug and chug, stick it in a graph, who cares. Just solve it. Think abstractly.</li>
</ul>
<p>Good luck to all of you taking this test, hope this helps. If you have questions, feel free to ask, and if you have further advice, feel free to share!</p>