5 Tips on Tackling the SAT Subject Test: Math Level II
By Leo Lam
(ACT, SAT, SSAT, Math, Physics, MAT, STEP, TSA, English Builder tutor at The Edge Learning Center)
Many universities require students to submit two or three SAT Subject Test scores in addition to their ACT/SAT scores. Those students who plan to study STEM in the future will often choose to take the Math Level II test. The score range of this test is 200 to 800. Many top universities will only accept a score of 800 on this test. Math II is one of the most competitive subjects amongst the many offered by College Board: it is taken by the most number of students; more than a fifth of the students receive a “perfect” score of 800; and the average score is close to 700. Students who take the test for the first time find it overwhelming: not only does the test cover a wide range of topics, but it also asks them in unconventional ways. Even students who have done exemplarily well in their Math classes can find this test challenging at times. To help you achieve the higher score that you desire, here are some tips to follow when you take this test.
1. Time Management
Just like many of the standardized tests out there, the SAT Math II requires you to work out many questions in a limited amount of time. You will be given 1 hour to finish 50 questions; this works out to 72 seconds, or 1 minute 12 seconds, per question. However, you should not focus on the “per question” time frame. The test gets progressively harder, and this means that the time spent on the last 15 to 20 questions can be significantly longer than that spent on the first half of the test. You must move quickly at the beginning while maintaining your accuracy. You do not want to read a question blankly just to read it again. Underline the key information and consider its significance. Identify what exactly are you tasked to find. Apply all the values given in the question. If you end up omitting a given value from the question, ask yourself: what am I missing? The test makers know exactly what kinds of careless mistakes student often make, and they put them as trap answers. This means picking an answer choice without utilizing all the information given will most likely be incorrect (there are, of course, exceptions, but they are rare).
In other words: be vigilant, and spend appropriate amount of time based on the position of the question.
2. Choose Your Method Wisely
There are always different ways to solve a problem. In order to minimize the amount of time spent on a question, choosing an appropriate and effective method is extremely important. While many questions can be solved algebraically, there are times when graphing the problem using your graphic display calculator (GDC) will yield a result faster. Furthermore, because the entire test is multiple-choice, trying out the answers (back-solving) or making up values (picking numbers) can be more efficient than solving for the solution.
You can read more about the basic concepts of back-solving and picking numbers from James, one of our awesome Test Prep teachers here at The Edge. Below are few additional details to pay attention to for Math II:
i. The answer choices are often rounded solutions, not exact. This means back-solving will not guarantee the exact result. In that case, choose the answer choice that gives you the closest value. Here is an example:
If we try each answer choice, we would get:
A. cos(-1.00)=tan(-1.00) → 0.54030…=-1.55740…
B. cos(-0.52)=tan(-0.52) → 0.86781…=-0.57256…
C. cos(0.00)=tan(0.00) → 1=0
D. cos(0.52)=tan(0.52) → 0.86781…=0.57256…
E. cos(0.67)=tan(0.67) → 0.78382…=79225…
We can see that none of the equation is actually correct. However, answer choice E gives us the closest result, making it the correct solution.
ii. If there is more than one unknown in the question, make sure to pick numbers that follow all of the given conditions. Let’s take a look at the following example:
In this question, we are working with three different unknowns: a, x, and y. The first two equations give us the conditions. Thus, we need to work with values that satisfy these conditions. In this case, we will let a=2. Using a calculator, we can then find:
Using these values and plugging them into the answer choices, we get that:
Which is the correct answer.
iii. Be mindful of the values we pick, particularly when we are working with trigonometric equations. Use the proper value (radian vs. degree) according to the question. If you prefer working with one over the other, make sure to convert your answer at the end accordingly. Also, avoid special angles like multiples of 30°, 45°, 60°, or 90° ( in radians, respectively). These angles have special properties, and they may lead to unique results that are often used as trap answers.
3. Rely on Your GDC
The College Board recommends the students to use a GDC (graphing calculator) when taking the Math Level II test. You can find the list of approved calculators here. Don’t even think about taking this test without at least a scientific calculator; approximately 20% of the questions require a calculator, and another 20% that will take too long if solved by hand.
Having a graphing calculator can significantly cut down on the amount of time needed to work out certain questions. However, this tool is only effective if used correctly. You can read about my tips on using a GDC here.
It is important that you are familiar with the functions of your graphing calculator for the test. The last thing you want is to spend 5 minutes finding the “log” function on your calculator. Here are some steps to take that will help reduce the time spent on a question:
i. Check whether you are in Degree or Radian mode, especially when dealing with trigonometric equations. Be able to change mode on the fly.
ii. If you want to see something from the graph, make sure you have the right window size. The question will likely provide a hint (or even the exact values) about where your answer should fall within. Set the window first to avoid graphing twice.
iii. Know where to find some uncommon symbols like i (imaginary numbers), ! (factorial), nCr(combination), nPr(permutation), (summation), or |x| (absolute value). There is no guarantee that you will need to use all of these symbols, but you need to be ready.
4. Focus on the Basics
There comes a point when you read the question and have no idea what is going on. You can’t even decide what method to use to solve the problem. So what do you do?
This is when you must focus on the information given, apply whatever knowledge you have learned, and try to proceed to as far as you can. As I mentioned at the beginning, the Math II test requires students to know a wide range of topics (Number and operations; Algebra and functions; Geometry and measurement; Data analysis, statistics, and probability), and often time the question can be presented in an unfamiliar way. However, the College Board will never require the students to apply knowledge or concepts that are beyond the scope of high school level mathematics: instead, a question masks the basic knowledge in a complex setting. Here is an example involving multi-variable function:
If f:(x,y)→ (x+2y,y) for every pair (x,y) in the plane, for what points (x,y) is it true that (x,y)→(x,y)?
A. The set of points (x,y) such that x=0
B. The set of points (x,y) such that y=0
C. The set of points (x,y) such that y=1
D. (0,0) only
E. (-1,1) only
At first, students may see that this is a function question because of the notation used. However, they may not understand how to proceed as the function is defined as coordinates instead of operations. But we don’t need to understand the mechanics behind this multi-input/multi-output function (which is actually a transformation) in order to find the answer. Focus on what we need to achieve: the input needs to be the same as the output. If we then separate the two coordinates and look at them individually, we get:
The first statement tells us that y must be 0, which means we can eliminate A, C, and E. Neither statement tells us anything about x, so choice D, which says x must also be 0, has a limitation that is not supported by our calculation. Therefore, the logical solution would be B.
In the end, break down an unfamiliar question into smaller parts. Apply your knowledge and see where it can take you.
5. Know When to Give Up
One misconception about the Math II test is that in order to get a “perfect” 800, you must get every question right. That is not the case at all. In fact, out of the 50 questions, students often need to get 43 or more correct answers in order to receive a score of 800. This means that it is strategically viable to skip questions that are too difficult or too lengthy to solve. This raw score (the amount of questions you correctly answered) does not get reported to the university. In other words, there is no difference between getting all 50 questions correct, or only getting 43 questions right but skipping 7.
And skip you should. The SAT Subject Tests all have a “penalty” system: a fraction of a point is subtracted from a wrong answer, while no point is deducted for an unanswered question. The amount deducted depends on the number of choices given in the question: 1/4 point for a five-choice question, 1/3 for a four-choice question, and 1/2 for a three-choice question. Since all questions on the Math II are five-choice questions, an incorrect answer will result in a quarter point penalty. If you are able to eliminate two or three choices, then you should take the chance and give it a guess. Otherwise, play safe and skip.
Leo’s Blog: Making Sense of Parabolas , A link between Math and Life, Fun! Facts about Factorials!, Decomplexifying Complex Numbers, Getting into the Top US Universities – ACT & SAT Exam Strategies (I), Getting into the Top US Universities – ACT & SAT Exam Strategies (II)
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