Barron's Math II Tough Problems

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1

<p>Just a few that I really can't seem to get:</p>

<p>1) The circumference of a circle X^2+y^2-10y-36=0 is:
Answer is ~49</p>

<p>2) At the end of a meeting, all participants shook hands with another. Twenty right handshakes total were exchanged. How many people were at the meeting?
Answer is 8.</p>

<p>3) How many different ways can the letters in the word" MINIMUM" be rearranged?
Answer: they want you to do 7!/(2!3!) to get 420 for some reason...</p>

<p>Oh and quick question. My diagnostic test scored a 710 (35 raw, finished in just under an hour), and I scored a 700 on the first practice test (34 raw, took an extra 5-10 minutes). How accurate are these scores? I'm aiming for an 800 on the actual test.</p>

2

<p>1) Complete the square in “y”: x^2 + (y-5)^2 = 36 + 25 = 61
Since 61 = r^2, r = sqrt(61), and the circumference is 2<em>pi</em>r = 49</p>

<p>2) Let there be “n” people at the meeting. Since each person shook hands with every other person, n(n-1) handshakes took place. However, since A shaking hands with B is the same as B shaking hands with A, n(n-1)/2 unique handshakes took place. Just solve the equation:
n(n-1)/2 = 20 ===> n^2 -n - 40 = 0</p>

<p>However, this equation doesn’t give an integer, so I feel you copied the problem wrong, or I made a stupid mistake and am missing something.</p>

<p>3) There are 7 letters in MINIMUM, so there are 7! ways of arranging them. However, since I is repeated twice, and M is repeated 3 times, we divide by 2! and 3! to cancel out repeats. Thus, 7!/(3! * 2!) = 420.</p>

3

<ol>
<li><p>Complete the square to get x^2 + (y-5)^2 - 25 - 36 = 0, x^2 + (y-5)^2 = 61 = r^2. The circumference is 2sqrt(61)*pi. Not exactly 49, but I think they rounded.</p></li>
<li><p>Is that supposed to be “twenty eight?”
Basically, given n people in the room, there are nC2 = n(n-1)/2 ways to choose any two people, order irrelevant. Since every pair of people shake hands, we have n(n-2)/2 = 28, or n = 8.</p></li>
<li><p>Ah, yes you can’t simply say the number of ways is 7!. There are two I’s and three M’s in MINIMUM. You have to divide by 2! to account for the duplicate I’s, and 3! for the M’s.</p></li>
</ol>

4

<p>^^ Thanks! That should’ve read “twenty eight handshakes.” Any idea how a 710 and a 700 compare to the real test?</p>

5

<p>I never used Barron’s so I can’t say. Might be better to look at raw score.</p>

6

<p>For question 1, which chapter does the book teach you how to answer that question? </p>

<p>I am looking at the book right now and I can’t find anything about circles</p>

7

<p>The first problem’s more about completing the square. I would check sections on conics, if there are any.</p>

8

<p>Just remember when presented with an ellipse equation not in standard form, complete the square to get it there.</p>