Need help on 2 SAT math problems

Test Preparation
1

<p>From Test # 7, Section 8 of the blue collegeboard book</p>

<h1>15 of that section. I cant really describe it cuz it's a cube with lines, so if anyone has a college board book with them, their help would be appreciated.</h1>

<p>16) If xy = 7 and x-y = 5, then (x^2)<em>y - x</em>(y^2) =</p>

<p>(A) 2
(B) 12
(C) 24
(D) 35
(E) 70</p>

<p>The answer is 35. I got this answer though by cheating. I solved the first 2 equations for y, plugged them into my TI , and found the intersection ( x=6.14 y= 1.14 ). Then I plugged in those numbers into the last equation and got 35. there has to be better way to do this. anyone have any ideas?</p>

<p><strong>edit</strong>* nevermind. I just noticed the distributive property at work</p>

2

<p>With #15 it is important to be able to visualize the relationship between the size of the triangle's angle and length of the hypotenuse. This question could just as easily be rephrased as: Which one of the triangles has the longest sides and hypotenuse? Triangle XDY does, because it's going the diagonal of the cube (which is the longest distance you can travel in a cube). Therefore, Angle XDY is the smallest angle because the triangle is stretched out, thus minimizing the size of its acute angles (keep in mind the perpendicular angle is the same in all of them). </p>

<p>*Another good way of looking at this problem is to know that in triangles, given two sides and two angles, the larger angle is *opposite the longer side. Which line running along the base of the cube is longest? YD because it's a diagonal. Therefore angle DXY is the largest acute angle and angle and angle XDY is the smallest acute angle. </p>

<h1>16 it looks like you figured it out. All you're doing is distributing the monomial over the binomial. The result is 5 * 7.</h1>

<p>NEVER do such a simple problem using your TI. Force yourself to think algabraically. I guarantee you there is not one question on the SAT that requires the use of TI's solver and graphing intersections. In the time it takes you to punch in all those keys, you can answer 10 questions. </p>

<p>Hope that helps,
Andre</p>

3

<p>thanks for all the help. 3D geometry is still a bit intimidating to me</p>