Advanced SAT Math Strategies for those that want an 800 in math

Test Preparation SAT Preparation
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<p>Fwiw, the Joseph problem is not an average speed problem. It is a simple proportion problem. There is no need for d for distance here. The proportions are GIVEN and all that is needed is to establish that 30 = 2/5 of the total time. </p>

<p>2/5 * 180 = 72.</p>

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<p>Let’s get back to Permutations and Combinations for a bit. Here’s a quck review of what we talked about so far:</p>

<p>A permutation is an arrangement. A combination is a subset of a particular set containing a specific number of elements.</p>

<p>For example, the permutations of {1, 2, 3} taken 2 at a time are 12, 21, 13, 31, 23, and 32. The combinations of {1, 2, 3} taken 2 at a time are 12, 13, and 23.</p>

<p>Note that 12 and 21 represent the same combination, but different permutations. In fact, in general, each combination corresponds to a list of permutations. There are always more permutations than combinations. </p>

<p>To compute the number of permutations or combinations, you can </p>

<p>(a) simply list them and count.
(b) use the nPr and nCr functions in your graphing calculator.</p>

<p>Try this example:</p>

<p>Compute the number of permutations and combinations of elements from the set {a, b, c, d} taken (a) 2 at a time, and (b) 4 at a time. </p>

<p>Compute these numbers in 2 different ways:</p>

<p>(1) By using the nPr and nCr functions in your graphing calculator.
(2) By listing all of them and counting.</p>

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<p>About how hard does the SAT math section get? Like, what level… all the way to Calculus, and how tricky is it? I took it a while back, but didn’t score as highly as I hoped, so any tips, or ways not to get tripped up?</p>

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<p>^ I’m fairly certain it only covers up to Geometry. No Trigonometry whatsoever.</p>

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<p>Ok. I think it’s time for another advanced strategy. I call the following formula the “Fence Post Formula.”</p>

<p>Description: The number of integers from a to b, inclusive, is b-a+1. </p>

<p>For example, let’s count the number of integers from 5 to 12, inclusive. They are 5, 6, 7, 8, 9, 10, 11, 12, and we see that there are 8 of them. Now 12 – 5 = 7 which is not the correct amount, but 12 – 5 + 1 = 8 which is the correct amount.</p>

<p>If you ever happen to forget this little formula test it out on a small list of numbers as I just did. But it’s nice to have this one committed to memory so that it is there for you when you need it.</p>

<p>Note that if you put up a fence that is 10 feet long, and put up fence-posts every foot, then there are 10 – 0 + 1 = 11 fence-posts.</p>

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<p>Here are a couple of examples where you may find the fence-post formula useful:</p>

<p>(1) How many numbers between 72 and 356 can be expressed as 5x+3, where x is an integer?</p>

<p>(2) Set X contains only the integers 0 through 180 inclusive. If a number is selected at random from X, what is the probability that the number selected will be greater than the median of the numbers in X?</p>

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<p>Is number 1 57?
and is number 2, just 1/2?</p>

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<p>Dr Steve ,
I am really disappointed in your book !!
I bought it before January test and My math score was supposed to increase to 800 but instead of that , my score decreased and when I sent to you , you didn’t even dare to reply !!
Now,I am going to take the june test and i hope that i get the 800 !!</p>

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<p>@Ashley</p>

<p>I’m afraid that I never received a message from you regarding your score. Did you send it to my email or somewhere else?</p>

<p>The only discussion I have had with you that I can remember is in this thread from January where we discussed one of my problems and you seemed to really like the book: <a href=“http://talk.collegeconfidential.com/sat-preparation/1443404-math-dr-steve-warners-book-2.html[/url]”>http://talk.collegeconfidential.com/sat-preparation/1443404-math-dr-steve-warners-book-2.html&lt;/a&gt;&lt;/p&gt;

<p>As far as your score goes, what was your starting score, and what did it decrease to? If you provide me with some specifics, I can help you determine what you should be focusing on for he June test.</p>

<p>If you were unhappy with one of my products I will make sure that you get a refund or provide you with something else. Send me an email or pm and we will figure out what would be best for you.</p>

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<p>@Remi</p>

<p>Yes - the first one is 57.</p>

<p>The second one is not right. Let’s do a simpler example and see if you can find your mistake:</p>

<p>Set X contains only the integers 0 through 2 inclusive. If a number is selected at random from X, what is the probability that the number selected will be greater than the median of the numbers in X? </p>

<p>The total here is 3 and the median is 1. So there is 1 integer greater than the median. Therefore the desired probability is 1/3.</p>

<p>Now see if you can solve the harder one above.</p>

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<p>Thanks for your concern :)</p>

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@DrSteve

For your permutation and combination question:

Of Permutations of set { a, b, c, d} taken 2 at a time: I got 12

Of Permutations taken 4 at a time: I got 24

Of Combinations taken 2 at a time: I got 6

Of Combinations taken 4 at a time: I got 1

Are those right?

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@DrSteve

ntegers 0 through 180 inclusive. If a number is selected at random from X, what is the probability that the number selected will be greater than the median of the numbers in X?
What was the actual answer to this problem?

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@salt123 X = {0, 1, 2, …, 180}

There are 181 numbers in X (not 180), and the median is 90. The numbers greater than the median of X are {91, 92, …, 180}, or 90 numbers. The probability is 90/181.

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A couple of notes about MiTer’s solution (which is completely correct):

  1. The answer needs to be gridded in as a decimal since the fraction would take up too many slots and it cannot be reduced.
  2. It’s not necessary here but you can formally use the fence-post formula to compute both the numerator and denominator.
  3. This type of question is unlikely to appear on the new SAT based upon the college board’s released sample questions.
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@ThatSpellingGuy111 Those are correct.

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Would you recommend these strategies for the new SAT? My daughter got. 640 on the math part of the October PSAT without studying. She has since reviewed some of her older math, she is in AP Calc currently. Would these strategies help her for the new SAT? Also, what about your beginning and intermediate lessons?
These are her scores from the recent ACT: Mathematics 26
  Pre-Algebra/Elem. Algebra 15
  Algebra/Coord. Geometry 12

  Plane Geometry/Trig. 14
Thanks for your advice. Her reading and writing scores are much higher so she wants to bring her math up to those levels.

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The strategies in this thread I would usually teach only to students that are at about a 700 or above. I suspect that Xiggi’s formula will still be useful to know for the new SAT. Counting problems will not be on the new SAT, so you can disregard anything about permutations and combinations. In general I have gotten rid of some advanced strategies that were useful for the old SAT and replaced them with new ones. Most of the basic and intermediate strategies I teach are still the same, but they are now being used for different types of problems.

Based on your daughter’s PSAT score it seems that with some prep she may do much better in math on the SAT than the ACT. I would guess this is due to the fact that she has been exposed to Precalculus recently.