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What are some of the best resources and drills that one can use to take students from good to great scores on the SAT especially in math section.

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    $\begingroup$ I think one great resource is practice tests. Otherwise, I reiterate from my comment here the suggestion of Purple Math. $\endgroup$
    – Benjamin Dickman
    Commented Feb 15, 2015 at 9:51

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As far as drills go - I've made the observation that calculators are a detriment in many situations. When I am with a student who takes 30 seconds on a calculator to do a bit of simple math that I can do in my head almost instantly, I try to encourage them to learn to do mental math. Yes, calculators are allowed on the SAT, much to my chagrin, but if their use is a 30 second delay, after 30 questions, there are 15 wasted minutes. Minutes than can be used to answer more questions or go back and check work.

I'd suggest a review of the 12x12 multiplication table. When it dropped to 10x10, I don't know, but when I went to school, it was 12x12 and we liked it.

Next, there are techniques to look at the choices of answers and cross out 2 or even 3 of the 4 that are not candidates. For example, 2 equations, 2 unknowns. I've seen practice exams where the choices are easy to put back into the equations, and brute force elimination in seconds instead of actually solving the problem. For some problems, the answers are each an order of magnitude different. Why stop to multiply 2.879 by 3.265 when only only number is in the 9-10 range?

When it comes to learning the process, I respect "show all work" and will explain to students that they lost points because they didn't do just that, even though they have a correct answer. (again note, I am not the teacher, just helping after the fact). But on the SATs, it's the opposite. It's an enemy to be beaten, and the pedagogical rules don't apply. Every trick, whether to save time or eliminate incorrect answers, should be used.

Update to the "no trig" comment - this question is in CK-12's SAT Flex Prep Book.

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To solve exactly, the trig functions are needed. But. If angle A were 45$^\circ$, I'd know the base was 6, and the sides each $3\sqrt{2}$. That's about 14.4. With only one answer greater than 14.4, The answer D is obvious. And, in my opinion, avoids the not so small risk that the calculator is set to radians.

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    $\begingroup$ +1 i definitely agree with everything you said esp about wasting time using calculator on simple arithmetic, however i do think that calculator can speed things up, depending on the situation, for instance solving a system of equations, it is very easy to graph them and hit the "Find Intersection" (i know it is not literally a button but most modern calcs have this ability) and get the answer in about ten seconds as opposed to a few minutes to do it by hand $\endgroup$
    – celeriko
    Commented May 10, 2015 at 18:10
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    $\begingroup$ Of course. I am talking about the use of the calculator that makes me cringe, not the use where it's simply needed. The Tan of 35 degrees, the log of some random number, etc. I appreciate the comment, and upvote. $\endgroup$
    – JTP - Apologise to Monica
    Commented May 10, 2015 at 18:37
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    $\begingroup$ I agree with @celeriko that efficient calculator use is absolutely crucial. For instance, I would advise all but the strongest students to solve an equation like 2^x + 2^x + 2^x + 2^x = 2^7 using either "solver" or "solve by graphing" on the graphing calculator. $\endgroup$
    – Frank Newman
    Commented May 10, 2015 at 20:49
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    $\begingroup$ Note to @JoeTaxpayer that trig and logs are not currently covered on the SAT Math. They are on the SAT Math Subject test, though. $\endgroup$
    – Frank Newman
    Commented May 10, 2015 at 20:50
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    $\begingroup$ Frank Newman wrote: For instance, I would advise all but the strongest students to solve an equation like 2^x + 2^x + 2^x + 2^x = 2^7 using either "solver" or "solve by graphing" on the graphing calculator. Interesting. I would have thought this would cry out $4 \cdot 2^x = 2^7$ and $2^{x+2} = 2^7$ even for not so strong students. But perhaps not in these days when well over 50% of all students are taking either the SAT or ACT. (It was about 15% of my high school graduating class, but that was in another era in a rural location.) $\endgroup$
    – Dave L Renfro
    Commented May 11, 2015 at 16:44
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I agree with @BenjaminDickman that practice tests are crucial. It stands to reason that the most realistic practice tests will be the ones made available by the company who writes the actual SAT, CollegeBoard. This book has ten full-length practice tests:

The Official SAT Study Guide Second Edition

Warning: this book will be most useful before CollegeBoard makes major changes to the SAT in 2016.

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