Math CHALLENGE...Post the hardest math SAT I questions you can find..

Test Preparation
141

<p>How many sets of 10 can be taken if you have 10 identical blue towels and 10 unique red towels?</p>

<p>Just felt that too many explanations in #43 diluted the idea, plus one detail was plain wrong.
Let's try again, leaving extra explanations in #43.</p>

<p>We can rephrase a question:
+++++++++++++++++++++++++++
How many sets of towels selected from 10 numbered red towels are there, if a set can consist of any number of towels -
from 0 (empty set; in old question form, it means all 10 out of 10 are blues) </p>

<h1>to 10 (old form: full red set - no blues).</h1>

<p>Let's make a table with towels' numbers on top, and place 1’s in columns for the towels included in a set and 0’s for those that are not.</p>

<h2>Each row will represent a binary number, and they will go in ascending order</h2>

<h2>1 2 3 4 5 6 7 8 9 10</h2>

<p>0 0 0 0 0 0 0 0 0 0 = decimal 0
0 0 0 0 0 0 0 0 0 1 = decimal 1
0 0 0 0 0 0 0 0 1 0 = decimal 2
0 0 0 0 0 0 0 0 1 1 = decimal 3
0 0 0 0 0 0 0 1 0 0 = decimal 4
0 0 0 0 0 0 0 1 0 1 = decimal 5
0 0 0 0 0 0 0 1 1 0 = decimal 6
0 0 0 0 0 0 0 1 1 1 = decimal 7
0 0 0 0 0 0 1 0 0 0 = decimal 8</p>

<p>So on …</p>

<p>The last number in this table will be 1 1 1 1 1 1 1 1 1.
There are as many possible sets of towels as rows in the table.</p>

<p>Total number of rows is 1 more then the last number
(we start counting from 0).
1 1 1 1 1 1 1 1 1 1 + 1 = 1 0 0 0 0 0 0 0 0 0 0 = 2^10 in decimal.
2^10 = 1024.
That's the answer.</p>

142

<p>At a dispute club session 20% of its members were involved in an arguing training: each of them had one sparring with every other member of that group.
If there were 21 verbal scuffles, how many members are in the club?</p>

143

<p>X1 and X2 are the roots of
x^2 - pqx + p + q = 0.
+++++++++++++++</p>

<p>Find 1/(X1)^2 + 1/(X2)^2</p>

144

<p>35 members.</p>

<p>21 * 2! = 42 = 7*6 </p>

<p>So 7 = .2x</p>

<p>x = 35</p>

145

<p>in response to gcf101, what you have to do do is start from the answer until you get to the question. :) you'll see. if u can't work from the question to the answer, use reverse logic</p>

146

<p>Sum of the roots: -b/a=pq
Product of roots: c/a=p+q</p>

<p>1/(X1)^2 + 1/(X2)^2=((X1)^2+(X2)^2)/((X1)(X2))^2</p>

<p>Solve the top:
(X1)^2+(X2)^2= (X1+X2)^2-2(X1)(X2)=(pq)^2-2(p+q)
bottom:
((X1)(X2))^2=(p+q)^2</p>

<p>1/(X1)^2 + 1/(X2)^2=((pq)^2-2(p+q))/(p+q)^2</p>

147

<p>If a ball is thrown straight up at a certain speed, its height h, in feet, after t seconds is given by the formula h = 48t - 16t^2.
How many feet will the ball fly in one second through the air, starting one second after it is thrown?</p>

148

<p>0 ft.</p>

<p>f(1)=32
f(2)=32
Change in h=0 ft.</p>

149

<p>Here's a question where the wording gets you.</p>

<p>If c is the number of cats and d is the number of dogs, what equation is equivalent to the statement "There are 3 fewer than 4 timess as many dogs as cats?"</p>

150

<p>At t = 1.5s, it reaches a height of 36 ft...</p>

151

<p>gcf101, are you asking for distance or displacement? Displacement is 0 but distance is 8 feet.</p>

152

<p>I quoted this question from my memory, trying to preserve its murky wording.
The correct answer was 8 feet - the distance.
If you replace "straight up" with "45 deg...", there is no uncertainty.</p>

<p>It's a good, but extreme practice question. True SAT phrasing can be tricky, but not ambigious.
Objections?</p>

153

<p>How do you get the answer to that one?</p>

154

<p>That's heavy stuff, man.
You can look it up in Thomas/Finney Calculus 9th ed., p.395 (length of the curve y=f(x) from a to b).</p>

<p>This could be of interest too (but of no use to your question):
<a href="http://mathforum.org/dr.math/faq/formulas/faq.ellipse.html%5B/url%5D"&gt;http://mathforum.org/dr.math/faq/formulas/faq.ellipse.html&lt;/a&gt;&lt;/p>

155

<p>"If c is the number of cats and d is the number of dogs, what equation is equivalent to the statement "There are 3 fewer than 4 timess as many dogs as cats?""</p>

<p>d - 3 = 4c</p>

156

<p>i think it's...........
4c-3=d
am i right or wrong? please tell us the correct answer!</p>

157

<p>But it's not really finding the length of the curve. It's just interpreting the function (and its graph, if you want to). The function shows that at t = 1.5s, the ball reaches its maximum height of 36 ft. You stated that the ball was thrown STRAIGHT UP --- so there is no need to calculate the length of the curve, etc. It started and ended the time interval of analysis (1 to 2 s) at 32 ft...so, it went straight up 4 ft, then fell back down 4 ft again. Combined, it moved 8 ft totally in 1 second.</p>

158

<p>this is the one that screwed me over on the actual SAT...</p>

<p>"how many right angles are formed by the edges of a cube?"</p>

<p>i didnt know whether to consider right angles made by the vertex of 3 edges or not. i dont know if that even makes sense....ah well, it would be nice to figure it out.</p>

159

<p>duneguy, you are correct. It is 4c - 3 = d or 4c = d + 3</p>

160

<p>That was actually on the SAT?</p>

<p>Yikes. I'll try it:
The definition of an edge is where 2 faces meet. So, count everyplace two faces meet.
The bases of the cube make 4 right angles each, one with each face they meet, total of 8.
each face makes 4 right angles which each other face when they meet at an edge. 4 x 4 = 16
You would not count the right angles made by vertices of 3 edges, as those are vertices, not edges.
I'd say it's 24.</p>