Math Questions

Test Preparation SAT Preparation
1

<p>I know these aren't the most difficult questions I just need an explanation as to why they are the answer</p>

<p>1)
If y=2^x, which of the following expressions is equivalent to 4^x - 2^x+1 for all positive integer values of x?</p>

<p>(A) 2y-2
(B) y^2
(C) y^2-y
(D) y^2 - 2y
(E) y^2+2y</p>

<p>2)
The length of equilateral triangle ABC above is 6. D, E and F are midpoints of AB, BC, and AC, respectively. A, B, and C are the centers of the circles that contain arcs DF (arc), DE (arc), and FE (arc), respectively. What is the perimeter of the shaded region?</p>

<p>(A) 9 - π/3
(B) 9
(C) 3π
(D) 4π - 3
(E) 9 + π/3</p>

<p>π is pi</p>

<p>3)</p>

<h2>x|0 | 1 | 2 |</h2>

<p>y|10 | a | b |</p>

<p>The values of x and y in the table above are related so that (y-1) is directly proportioanl to (x+1). What is the value of b - a</p>

<p>open ended</p>

<p>4)</p>

<p>Points Q, R, and S are on line L in that order, and point P is not on line L. If PQ = PS, which of the following must be true?</p>

<p>(A) PQ > PR
(B) PQ > QR
(C) PQ > QS
(D) PR > RS
(E) QR > RS</p>

<p>5)
The last one is a graph</p>

<p>The graph of the equations y = x^2 and y = k - x^2, where k is a constant, are shown above. If the length of AB is an integer, which of the following CANNOT be the value of k.</p>

<p>(A) 2
(B) 8
(C) 12
(D) 18
(E) 32</p>

<p>If you would like me to post the answers just say so, I know them I just need an explanation. Or if you need the section/question number and if you want to know the difficulty level.</p>

2

<p>In the future, please post page numbers. It’s much easier than typing it up and easier for us as well.</p>

<ol>
<li>Are you sure you copied it right? </li>
</ol>

<p>y = 2^x. y^2 = (2^x)^2 = 2^(2x)
4^x = (2^2)^x = 2^(2x)</p>

<p>4^x - 2^x+1 = y^2 - y + 1. That’s not a choice I see but it’s the correct answer IMO.</p>

<ol>
<li>I don’t know the shaded region :p. If it’s the inner “arc-triangle” in the center of the triangle, then the answer is C 3pi.</li>
</ol>

<p>BE, CE, and AD are radii of the circles. Since it’s equilateral, angles are 60 degrees and radii lengths are 3. The length of an arc s is s = r(theta), with theta in radians. so the perimiter is 3(pi/3) + 3(pi/3) + 3(pi/3) = 3pi.</p>

<ol>
<li>y -1 = k(x+1)</li>
</ol>

<p>Test (0,10). </p>

<p>10 - 1 = k(0 + 1)
k = 9</p>

<p>Test (1,a)</p>

<p>1 - 1 = 9(a + 1)
0 = 9(a +1)
a + 1 = 0
a = -1</p>

<p>Test (2,b)</p>

<p>2 - 1 = 9(b + 1)
1/9 = b + 1
b = 1/9 - 1 = -8/9</p>

<p>b - 1 = -8/9 - (-1) = 1/9</p>

<ol>
<li><p>A is correct. Tough to explain. Draw different cases. Here’s what I used:</p></li>
<li><p>Isoceles</p></li>
<li><p>Q, R close. S far away. </p></li>
<li><p>Q far away. R,S, close.</p></li>
<li><p>Please post the problem number. AB can be anything and I would like to see what they’re referring to.</p></li>
</ol>

3

<p>It is from the May 2009 QAS not the BB so I wasn’t sure if mattered if you knew the section number + problem number</p>

4

<ol>
<li>4^x - 2^x+1</li>
</ol>

<p>4^x = 2^(2x)= (2^x)^2 = y^2
and 2^x+1 equals 2^x*2^1 (or simply 2)
since 2^x= y,</p>

<p>the answer is y^2 - 2y, D</p>

<p>not sure if my explanation is clear, feel free to ask questions.</p>

5

<p>An0maly, you might wanna revise #3. You seem to have mixed up y and x when inputting in your second and third equations. I believe the answer should be 9.</p>

6

<p>Yeah, sorry, typo on 3. For 1 I didn’t realize he meant 2^(x+1). Long day =[</p>