Math: "hard" questions

Test Preparation SAT Preparation
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<p>I'm scoring in the high 600-700 range on the math portions (from practice tests in the blue book) after practicing a lot for about a month to avoid careless mistakes. I usually get all of the easy and medium (first 16 or so for example for section 2) questions correct. Now my concern is generally with the last few problems. </p>

<p>Any tips or tricks? Do you omit hard ones when you feel your chances are slim for getting it right? Plug in answers? Sometimes that works, but i find it's usually more difficult than that. </p>

<p>Any advice is appreciated. I'm taking the sat on 3/12. But I have 2 more chances to take it. Over summer I will be working on this too so a long term study plan is welcome too.</p>

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<p>Here are some things I posted in another thread that you may find useful:</p>

<p>Here are a few tips for breaking through that sticking point:</p>

<p>Short term:</p>

<p>(1) Make sure you know as many basic SAT specific strategies as possible. As a simple example, if you find yourself performing a lot of algebra, then you’re probably not doing things the most efficient way. Learning just a few extra strategies will help you save time on earlier questions so that you have extra time for those few that are giving you trouble.</p>

<p>(2) Don’t just solve problems. Try to really understand them. After you do a problem can you explain to another student how to do it? Can you explain why that method works. Understanding the problems a little deeper will help increase your level of mathematical maturity which will eventually lead to a higher score.</p>

<p>(3) Spend some extra time practicing those hard problems that show up towards the end of each section. Try to solve these problems multiple ways, and once again, try to understand why your methods work.</p>

<p>Long term:</p>

<p>Pick up a more advanced math book, and work through it very slowly on your own. The topic doesn’t matter - what matters is that you’re attempting to solve difficult math problems on your own. Knowing more math will not help you, but the process of learning new math on your own will increase your level of mathematical maturity. This can potentially raise your score. </p>

<p>Students that are doing well in AP Calculus will generally perform better in SAT Math. This has nothing to do with the amount of math they know. The reason is that AP Calculus requires more advanced reasoning and problem solving skills. Anyone taking AP Calculus that is performing fairly well will have a higher level of mathematical maturity than students in lower level math courses.</p>

<p>I should stress the following: studying advanced mathematics does not increase your SAT Math score - it increases your potential to score higher. Most students have the potential to score between 70 and 130 points higher in Math on their SAT from their PSAT (this is a rough estimate based on starting scores between 400 and 550 - higher starting scores are tougher to improve). If this is enough for you, then just learn some SAT specific strategies, practice problems at a level that is slightly above what you can currently do, and keep redoing them until you can get them right on your own.</p>

<p>If you want your score to go up more substantially, or if you want to hit that 800, then you absolutely must increase your mathematical potential. This means getting a deeper understanding of mathematics in general. Here is an excerpt directly from my SAT Math book with the 3 primary ways to raise mathematical maturity:</p>

<ol>
<li><p>Do SAT math problems. If you can currently only solve Level 1 geometry problems, and a month from now you can solve Level 2 geometry problems, then guess what—you’ve increased your level of mathematical maturity. So keep doing SAT problems a level above your current ability until the day of the test. If you only have about 3 months before your test, then this is the method you should employ most, if not exclusively.</p></li>
<li><p>Learn some mathematics by yourself. This may seem contrary to what has already been stated—but it’s not. Knowing more mathematics will probably not raise your score very much, especially if the math is handfed to you. But the process of learning mathematics will increase your mathematical maturity. What kind of math should you learn? It doesn’t matter! Pick something you find the most enjoyable, and try to learn it on your own. If you get stuck, then ask for help—but developing the skill to learn math yourself will definitely increase your mathematical maturity. This strategy is more long term and you should consider it if you have 6 months or more before your SAT exam.</p></li>
<li><p>Attempt difficult math problems. There are lots of challenging math problems out there that only require the math that you already know. There are math magazines, websites, and books full of problems. Pick a few and struggle with them. Just trying difficult problems and developing strategies will increase your mathematical maturity, even if you never solve a single one on your own.</p></li>
</ol>

<p>end of excerpt</p>

<p>I just want to stress one last thing. Raising your mathematical maturity does not necessarily equate to getting a higher score on the SAT. For this to happen, you absolutely must practice SAT problems. The main point is that if you decide to work on your level of mathematical maturity, make sure that this is in addition to direct preparation for the SAT. It should not be a substitute for it.</p>

<p>This advise is all based on my 10 years of experience as an SAT Math tutor. I hope this is helpful for those of you trying to hit that 800. Best of luck everyone!</p>

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<p>

This is a huge controversy in the prep world. I say you should. Plenty of people say you shouldn’t. Both sides use the same basis for their arguments: the SAT’s scoring system. I guess what it really comes down to is whether you’re good at eliminating WRONG answers or not (On a geometry question, for example, some very simple guesstimating can usually help you eliminate at least one wrong answer if the diagram is drawn to scale;in that case, I say you should absolutely guess), and what kind of score you’re shooting for (if you want an 800, you have no choice but to guess if you’re stymied; leaving one blank will probably eliminate you from the running). Also, it depends on how often you’re stumped. 2 guesses on the SAT is basically the same as 2 blanks if they’re wrong (assuming you got everything else right). 3 guesses, if they’re all wrong, will hurt your score.</p>

<p>It also comes down, honestly, to personal comfort. You should probably experiment with both ways, and see which one feels good to you. The author of the 2nd post linked below suggests marking every question you guessed on during a practice test, and then scoring your test with those answers in and with those answers as blanks, and seeing which you like better. That’s a great idea! </p>

<p>My opinion:
[PWN</a> the SAT: “When should I guess on the SAT?”](<a href=“http://blog.■■■■■■■■■■■■■/2011/02/when-should-i-guess-on-sat.html]PWN”>http://blog.■■■■■■■■■■■■■/2011/02/when-should-i-guess-on-sat.html)</p>

<p>Dissenting opinion:
[Guessing</a> on the SAT | Test-taking Strategy | Increase Your SAT Score](<a href=“http://increaseyoursatscore.com/guessing-on-the-sat/22/]Guessing”>http://increaseyoursatscore.com/guessing-on-the-sat/22/)</p>

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<p>My personal philosophy on guessing multiple choice questions is this. If you can eliminate even one answer choice you should take the guess. </p>

<p>This is the advice that I would give to a random student that I have never worked with. It is also my “lazy” answer. If as a student you just follow this guideline, then you’ll more or less be fine. But if I’m working with an individual student I may change this strategy based on how that specific student operates.</p>

<p>As far as I can tell PWN’s “five second rule” seems pretty convincing to me as well. One thing to be cautious of. On “hard” questions (questions appearing later in the section), intuition often fails since the questions are designed to trick you. So be careful about guessing the one that “seems best” unless you have a pretty good understanding of the problem (a strategy that I call “quasi-elimination” is designed to prevent this kind of mistake).</p>

<p>All in all, I think there are several philosophies that are all ok. The best thing that you can do is take the time to see which one works best for you, or the one with which you are most comfortable. Once you choose a philosophy, stick with it. You don’t want to waste time during the exam switching back and forth between guessing strategies.</p>

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<p>Realizing where the “lazy” recommendation originated from might make one wonder about its value. The College Board? The mostly ineffective SAT Prep factories? Clueless but well-meaning high school faculty? </p>

<p>The reality is that guessing delivers a positive outcome for a much smaller number of students that one might expect. Why? Having to guess on easy to medium questions is a sign of poor preparation. On harder questions, are we supposed to accept that student who cannot arrive at the correct answer should be able to correctly pick … the incorrect answer? </p>

<p>All in all, guessing should be the weapon of last resort. And one best avoided by most students.</p>

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<p>^ While I am definitely in the “if you spend time on it, answer it” camp, I agree that too much guessing is a sign of insufficient preparation. The question “Should I guess?” misses the point. The proper question is: which questions should I be spending time on? And the anwser is: develop a plan based on your score goal which your track record tells you is reasonable. For MOST test-takers (though perhaps not most on this forum – but maybe them too) that means being highly selective about even attempting the hardest questions. If you follow that plan, you only end up having to guess occasionally.</p>

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<p>Thanks for the responses everyone.</p>

<p>PWNtheSAT: thanks again. your blog is awesome. just bookmarked it!</p>

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<p>@ghuskies: Glad you’re finding it helpful!</p>

<p>I work mostly with kids who are high scorers (as is ghuskies based on the first post in this thread). My guessing rule reflects as much. I agree with the folks on here that if you’re guessing on anything but the hardest questions, you’re ill-prepared and it doesn’t bode well for your score. </p>

<p>DrSteve made a great point, too, which anyone considering hiring a tutor should take to heart: that a good tutor fine-tunes his advice to every student he has. There are general guidelines, of course, but I find myself constructing slightly different sets of rules for each kid I work with.</p>

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<p>I would like to add one more point about the “if you spend time on it, answer it” rule. I first assigned that rule to a student who, in a typical 20 question section, was seeing a mixture of omits, rights and wrongs, evenly jumbled from mabye #6 to the end, scoring about a 500. She went up 100 points after we switched her approach. The pressure of the SAT causes many students to give up on a problem before their subconscious has time to “see” the solution. I don’t tell kids to count how many choices they have eliminated, I don’t tell them to count how many times they used the letter C. I just say go slower and if you work on it, answer it. If as a result of this policy, a particular student never gets to questions 18, 19 and 20, that’s probably for the better.</p>

<p>I’m not sure that I would call this process “guessing”. Is there another name for what to call it when you grid in a bubble with less than 100% confidence? It is definitely important to have a tolerance for less than 100% confidence! I feel that students tend to forget about all of the times when a less than 100% confident answer turned out to be right. Like the old baseball saying, speaking of cheap hits, swinging bunts and the like: they are all line drives in the box score.</p>

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<p>Right, it’s much more learning to pull the trigger than straight-up guessing. I sometimes give students 30 seconds per question left blank when we’re going over a test to look again, and give me an answer. I’d say 70% of the time, they give me the correct one. Even more frequently when it’s a blank before say, #17. Had they spent 30 more seconds on the question at the time, they probably would have answered it correctly. </p>

<p>Getting kids to “guess” is, as you’re saying, sometimes just about forcing them to answer questions they should always answer, and making that uncertainty and fear of what really is a miniscule penalty a little less daunting.</p>

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<p>Just spent some time practicing from the BB and consciously read each question. Guess who got #20 right? </p>

<p>Happy dance!!</p>