<p>Hello everyone ,
I'm a senior getting ready to retake the SAT on June 6th, since I got deferred for low SAT scores. I'm having some trouble with 4 Math problems from the Blue book "March 2005 test and beyond". They are all from the free response part... so here we go:</p>
<p>1) There is a picture of a circle, separated in 6 even parts, numbered from 1 to 6.
A player spins the arrow twice. The fraction a/b is formed, a is the number of the sector where the arrow stops after the 1st spin and b is the number of the sector where the arrow stops after the 2nd spin. On every spin, each of the numbered sectors has an equal probability of being the sector on which the arrow stops. What is the probability that the fraction a/b is greater than 1?</p>
<p>2) Exactly 4 actors try out for the 4 parts in a play. If each actor can perform any one part and no one will perform more than 1 part, how many different assignments of actors are possible?</p>
<p>3)Let the operations TRIANGLE and SQUARE be defined for all real numbers a and b as follows:
a TRIANGLE b = a +3b
a SQUARE b = a +4b</p>
<p>4) In the xy-coordinate plane, the graph of x=y^2 -4 intersects like l at (0,p) and (5,t). What is the greatest possible value of the slope of l ?</p>
<p>If 4 TRIANGLE (5y) = (5y) SQUARE 4, what is the value of y ?</p>
<p>Answers:
1) 15/36
2)24
3)1.2
4)1</p>
<p>3)Let the operations TRIANGLE and SQUARE be defined for all real numbers a and b as follows:
a TRIANGLE b = a +3b
a SQUARE b = a +4b
If 4 TRIANGLE (5y) = (5y) SQUARE 4, what is the value of y ?</p>
<p>Plug and chug:</p>
<h1>4triangle5y = 4+15y</h1>
<p>5ysquare4 = 5y + 16
4 + 15y = 5y + 16 10y=10, y=1</p>
<p>4) In the xy-coordinate plane, the graph of x=y^2 -4 intersects like l at (0,p) and (5,t). What is the greatest possible value of the slope of l ?</p>
<p>Find all values of P and T by plugging in the x coordinates.</p>
<p>so p can be -2 or 2, t can be -3 or 3. Then, to find the GREATEST slope, you do change in y / change in x by using the values :
3-(-2)/(5-0) = 1.</p>
<p>For 1:
Your fraction will either be equal to one, less than one, or greater than one.
First of all, there are 6*6 = 36 total possibilities. 6 of those possibilities will give you a fraction of value 1 - that is, landing on the same number both times. </p>
<p>Of the 30 remaining possibilities, exactly half of those will be greater than one, since their reciprocals will be less than one. Therefore, your answer is 15/36. </p>
<p>For 2:
Say the parts are called A, B, C, and D. For part A, you have four choices of actors. For part B, you now only have three choices, since one actor is fixed in role A. </p>
<p>Continue this to find 4<em>3</em>2*1 = 24.</p>
<p>Thank you so much, I didn't expect a response in such a short time, now I can continue taking the next test peacefully :)</p>
<p>I didn't get the explanation of 1...</p>