Beatfreaks Official SAT Math Section Help Thread

Test Preparation SAT Preparation
1

<p>Doesn't need to be stickied or anything but I need help with 26 Math questions =p. I thought it make sense for me to post it all in one thread instead of making 26 threads. Also, I will post any other Math questions I have trouble with here, in the future. Thank you guys!</p>

<p>So since 26 is A LOT and I don't want to burden anyone, I'm just going to post 6 at time. After every 6 are answered, then I'll post the next 6. I would REALLY appreciate your help guys. My Math SAT score is 550, but as I keep practicing, I keep getting the same score or lower (I even dipped to 470 at one point). I REALLY need to get this score up to the 600+ range. All and any help would be appreciated. Thanks again.</p>

<p>College Board Blue Book Edition 2:</p>

<h1>18, P.400</h1>

<p>x | -1 | 0 | 1 |
f(x) | 1/8| 1/2| 2|</p>

<p>(^ That's supposed to be a table.)</p>

<p>The table above shows some values for the function f. If f(x) = ka^x for some constants k and a, what is the value of a?
Answer: 4</p>

<h1>7, P.415</h1>

<p>The two sides of a triangle each have length 5. All of the following could be the length of the third side EXCEPT
Answer: 10 (Other choices, 1,3,4,radical 50)</p>

<h1>11, P.417</h1>

<p>Samantha is packing for a trip. Of the towels in the closet, 6 are brown. She will randomly pick one of the towels to pack. If the probablity is 2/5 that the towel she will pick is brown, how many towels are in the closet?
Answer: 15</p>

<h1>14, P.417</h1>

<p>Each term of a certain sequence is greater than the term before it. The difference between any two consectuive terms is in the sequence is always the same number. If the 3rd and 6th terms of the sequence are 17 and 77, respectively, what is the 8th term?
Answer: 117</p>

<h1>16, P. 418</h1>

<p>A four digit integer, WXYZ, in which W, X, Y and Z each represent a different digit, is formed according to the following rules.</p>

<ol>
<li> X = W + Y + Z</li>
<li> W = Y + 1</li>
<li> Z = W -5</li>
</ol>

<p>What is the four digit number?
Answer: 5940</p>

<h1>11, P.423</h1>

<p>A cube has 2 faces painted black and the following faces painted white. The total area of the white faces is 64 sq in. What is the volume of the cube, in cubic inches?
Answer: 64</p>

<p>Explanations/Break downs to these questions will be HEAVILY appreciated.</p>

2

<p>Question one:</p>

<p>Since it’s a function, just take each pair and plug it in, eventually forming a system that can be solved for a and k. Fortunately, the (0,.5) pair makes for an easy solution. </p>

<p>.5=ka^0, so a=1 (properties of exponents), therefore:</p>

<p>k=.5</p>

<p>Plug the first pair and k into the function:</p>

<p>(1/8) = (.5)(a)^-1 </p>

<p>Get rid of the negative exponent by making a^-1 the fraction 1/a, so:</p>

<p>(1/8) = .5/a >>> (1/8)a=.5 >>> a=4</p>

3

<p>Question two:</p>

<p>No side of a triangle can have a length greater than or equal to twice that that of any other side. Therefore, 10 is the answer (5x2).</p>

4

<p>Question three:</p>

<p>This problem can be solved using a proportion, where x is the number of total towels.</p>

<p>(6/x) = (2/5)</p>

<p>Cross multiply and solve x for 15.</p>

5

<p>Question four:</p>

<p>Let x equal the difference between each term. There are three x’s between the 3rd and 6th terms. Therefore, the total difference between those two terms is 3x. </p>

<p>The difference between the terms is 77-17=60. Therefore, 3x=60. x=20</p>

<p>There are two x’s between the 6th and 8th terms. 2x=2(20)=40.</p>

<p>Add this to the 6th term and get 40+77=117</p>

6

<p>Isnt it 2 x’s between each? </p>

<p>X,X,17 (3rd term), x,x,77(6th term), x, 117(8th term).</p>

<p>Ahhh this question confuses me.</p>

7

<p>Question five:</p>

<p>Because W=Y+1, you can substitute Y+1 for W in the last equation to get Z=Y-4.</p>

<p>Substitute Y+1 into the first equation for W, and substitute Y-4 into the first equation for Z. You should get X=3Y-3.</p>

<p>Because X is the sum of the other numbers, we know that X has the greatest value. In order to get a reasonable value for X, Y must either be 3 (in which case X=6) or 4 (in which case x=9). However, because Z=W-5, we know that X must be larger than 6. </p>

<p>Therefore, X is 9 and Y must be 4. Substitute 4 for Y in the second equation and find W to be 5. Substitute 5 for W into the last equation and find Z to be 0.</p>

<p>Thus, W=5, X=9, Y=4, Z=0</p>

<p>5940</p>

8

<p>@ Post #6,</p>

<p>x represents the difference between each term, not just any given term. One makes three jumps (or additions of x) in order to get from the third term to the sixth term.</p>

9

<p>^^^^Ahhh I get you. Gosh, these tricks are awful!</p>

<p>Anywho, thanks again for your detailed explanations. I understand them more effeciently.</p>

10

<p>Question six:</p>

<p>A cube has six sides. If two are black, then four are white. The total area of the white region is 64. Therefore, 64/4=16; each white face (and any face because it’s a cube) has an area of 16 in^2.</p>

<p>The area of a square (which is what each face is because it’s a cube) is the square of each side. Let x represent a side length of one of the squares. x^2=16. x=4</p>

<p>Because we’re dealing with a cube, x also represents the edge lengths of the cube. The volume of a cube is found by taking the third power (“cubing”) the edge length. x^3=V, so (4^3)=V. V=64</p>

<p>64 in^3</p>

11

<p>I’ll take the next six now. :D</p>

12

<p>Next 6:</p>

<h1>10, P. 422</h1>

<p>If k=x/3 and x isn’t 0, what does 3x equal in terms of k?
Answer: 9k</p>

<h1>15, P.424</h1>

<p>If the length of a rectangle is increased by 30% and the width of the same rectangle is decreased by 30%, what is the effect on the area of the rectangle?
Answer: It is decreased by 9%</p>

<h1>19, P.457</h1>

<p>In the xy-cooridnate plane, lines l and q are perpendicular. If line l contains the points (0,0) and (2,1) and line q contains the points (2,1) and (0,t), what is the value of t?
Answer: 3</p>

<h1>20, P.457</h1>

<p>The square x is equal to 4 times the square of y. If x is 1 more than twice y, what is the value of x?
Answer: 1/2</p>

<h1>8, P.465</h1>

<p>Meredith has a red hat, a blue hat, and a white hat. She also has thrree sweaters-one red, one blue, and one white-and three pairs of jeans-one red, one blue, and one white. meredith wantsd to wear a red, white and blue outfit consisting of one hat, one sweater, and one pair of jeans. How many different possibilities does she have?
Answer: 6</p>

<h1>12, P.467</h1>

<p>If 3x+y/y = 6/5, what is the value of x/y?
Answer: 1/15</p>

<p>And Silverturtle, this equation is for you: Silverturtle=Awesomeness!</p>

13

<p>Question one:</p>

<p>k=x/3. Solve for x and get x=3k. Multiply by three on both sides to get 3x=9k. </p>

<p>9k</p>

14

<p>Question two:</p>

<p>Plug in any numbers for the length and width. For ease of calculation, I’ll pick 100.</p>

<p>L=(100)(1.30)=130</p>

<p>W=(100)(.70)=70</p>

<p>The new area is (130)(70)= 9,100. Old area is 100^2=10,000.</p>

<p>Decrease of 9%.</p>

15

<p>Are you sure question three’s answer is 3? I keep getting 5.</p>

16

<p>I’ll skip it for now. Question four: </p>

<p>The given equations are x^2=4(y^2) and x=2y+1.</p>

<p>Plug 2y+1 in for x and get (2y+1)^2=4(y^2)</p>

<p>Foil the binomial on the left side and get 4y^2+4y +1=4y^2)</p>

<p>The 4y^2 terms cancel out and we have 4y+1=0. Solve for y and get -1/4.</p>

<p>Plug back into the second equation given. x=(2)(-1/4)+1=1/2</p>

<p>x=1/2</p>

17

<p>Question five: </p>

<p>There are three possible choices for the first group. Because one color has now been chosen, there are two choices for the second group. There is only one selection for the third group because two colors have already been chosen. </p>

<p>Multiply the possible combinations from each group for the total number. T=(3)(2)(1)=6</p>

<p>You could have also solved it by using factorial: 3!=6.</p>

18

<p>Question six:</p>

<p>(3x+y)/y=(6/5)</p>

<p>Write it as a proportion on your paper in order to better visualize. If you cross multiply, you will get 15x+5y=6y. Solve for 15x and get 15x=y. Therefore, 15=y/x. </p>

<p>Take the reciprocal of both sides in order to get x/y=1/15.</p>

19

<p>Here was my process for question three:</p>

<p>The slopes of two perpendicular lines are opposite reciprocals of one another. So let’s calculate the slope for line l. Let m equal slope and the points be (a,b) and (c,d).</p>

<p>For line l’s points of (0,0) and (2,1), m=(d-b)/(c-a), so m=(1-0)/(2-0)=1/2</p>

<p>The opposite reciprocal 1/2 is -2. Therefore, line q’s slope is -2. </p>

<p>For line q’s points of (2,1) and (0,t), m=(d-b)/(c-a), so -2=(t-1)/(0-2). 4=t-1, so t=5.</p>

<p>5 </p>

<p>I’m not sure why I’m getting a different answer.</p>

20

<p>just saying thank you for putting it in one thread lol</p>