Calling Out All Math Geniuses !!

Test Preparation
1

<p>So I've gone through some math sections in the blue book and i need some clarifications regarding some problems. I beg you to help me understand these problems. And I will reallly really really appreciate it if you do. Here they are:</p>

<p>(All from blue book...if a new 1 came out its not the new one)</p>

<p>pg397 # 7</p>

<p>pg398-99 #'s 11,12,13,&16 </p>

<p>pg400 # 19</p>

<p>pg408 #5 pg406 #7 </p>

<p>pg411 #13,&14
pg412 #17 & 18</p>

<p>pg427 #16
pg460 #4
pg462 #14 pg 463 #15 pg464 #19 </p>

<p>pg473 # 8
pg 475 #15 & 16</p>

<p>Especially pg 476 17 & 18</p>

<p>pg488 #5</p>

<p>pg490 #11 &12</p>

<p>pg 491 #15</p>

<p>pg521 # 14 pg522 # 15 </p>

<p>pg 523 # 20
pg532 # 6 & 8</p>

<p>pg534 #14
pg535 #16</p>

<p>pg549 # 6 & 9</p>

<p>pg551 #'s15 17</p>

<p>pg 584 # 9 12</p>

<p>pg 585 # 16</p>

<p>pg 586 # 18 pg587 19, 20</p>

<p>pg 595 # 4 (i got E)</p>

<p>pg 596 # 8</p>

<p>pg599 # 17 & 18</p>

<p>pg 612 # 6</p>

<p>pg 515 #s 15 & 16</p>

<p>and finally pg653 # 3,5 AND pg 656 # 12 AND pg 657 's 17 & 18 -___-</p>

2

<p>That’s quite a few questions. Have you checked here?
<a href=“http://talk.collegeconfidential.com/sat-preparation/339734-consolidated-list-original-blue-book-math-solutions.html[/url]”>http://talk.collegeconfidential.com/sat-preparation/339734-consolidated-list-original-blue-book-math-solutions.html&lt;/a&gt;&lt;/p&gt;

3

<p>Yes I did most of them are not there and the ones that are really don’t help me understand and their clogged with a whole bunch of other stuff</p>

<p>. So possibly if you can take the time between today and tomorrow to help I would really appreciate it. Like a lot !! A wholeeee LOT !!!</p>

4

<p>you should post the actual questions. A lot of people who are able to help you have taken the SAT many years ago and do not have “the blue book” available</p>

5

<p>[Khan</a> Academy](<a href=“http://www.khanacademy.org/sat.jsp]Khan”>http://www.khanacademy.org/sat.jsp)</p>

<p>This has all the answers and explanations for the blue book problems.</p>

6

<p>pg.397 #7
The answer is D. The question states that rstv = 1 and stuv = 0. You know that u = 0 because when the variable u was introduced into the equation, the solution became 0.</p>

<p>pg. 398 #11
The answer is C. Since the circumference of the whole circle is 36 pi, you know that the diameter of the smaller semicircles is the radius of the bigger circle. Use the equation 2(pi)r = 36 pi to find the diameter of the smaller circles. After that you find out that the diameter of the semicircles is 18. Since there are two semicircles, you can think of it as one full circle and therefore use the equation (pi)d to find the answer, which is 18 pi.</p>

<p>pg. 398 #12
The answer is C. No matter what number you choose for a and b, the answer is constant because it is a linear function. If a = 0, b must = 48 and you get 48. If a = 23, b must = 35 and you still get the answer of 48.</p>

<p>pg. 398 #13
The answer is A. There are only four distinct numbers to this sequence. The numbers are 3, 5, -5, and -3. Since there are 55 terms in the sequence, you can divide 55 by 4(the four distinct numbers you have) to get a remainder of 3. Since you end on -3, count to the right three and you get -5 as your answer.</p>

<p>pg. 400 #19
The answer is C. The question states that machine B accepts bottles that contain fluid ounces that are greater than 11 7/8 and less than 12 1/8. Eliminate A and B because they have an equal sign. After look through each answer choice. Since n-12 is in an absolute value, you will get two inequalities at the end. Choice C for example, you would get n - 12 < 1/8 and n-12 > -1/8.</p>

<p>pg. 411 #13
The answer is 3. The question gives the graph of the function g and the equation of the function h. The question also gives the value of x. Since the value of x is 1, look at the x axis and find 1 and find the y value that corresponds with the x value. Since the equation is h(x) = g(2x) + 2, if you plug in 1 for x, you will get g(2) + 2. You will find that 2 on the x axis will correspond with 1 on the y axis. So g(2) is 1. 1 + 2 = 3.</p>

<p>pg. 411 #14
The answer is 24. Since there are four actors and four parts assigned, the answer is 4!. 4<em>3</em>2*1 = 24.</p>

<p>pg 412 #17
The answer is 1. The question provides you with two coordinates, (0,p) and (5,t). If you plug in both coordinates to the equation, you can get four different possible choices. If we plug in (0,p), we will have 0=p^2 -4. Then you can get p=+/- 2. If you plug in (5,t), you will get 5 = t^2 -4. Then t = +/- 3. The equation of the slope of the two coordinates is (t-p)/(5). Since you want the greatest possible slope, you want t to equal the greatest possible positive value and p to equal the lowest possible negative value. So, t = 3 and p = -2. Then if you plug in those values into the equation you will get 5/5 or 1.</p>

<p>These are all i could do for now, because you have too many questions lol.</p>

7

<p>Here we go again…
pg. 427 #16
The answer is D. Since Set Z is every number inside Set X and Set Y except for the common members, it is x+y-2k. Set X contains x members and Set Y contains y members. Also, there would be two times the common members because there is a set of common members in Set X and another set of common members in Set Y, therefore 2k. An example would be Set X {1, 2, k} Set Y {k, 4, 5}. K is in both sets, so there are 2 k’s instead of only 1.</p>

<p>pg. 460 #4
The answer is E. You just need to visualize this image carefully. You can eliminate A and B because that wouldn’t make a rectangular prism. Just draw an image of the rectangular prism that is flattened. The height is 2, the length is 4, and the width is 3. Can’t really explain this clearly.</p>

<p>pg. 462 #14
The answer is D. Visualize the diagram as a square. You can draw an imaginary line on the side that is missing the line. Since a square has equal sides, the imaginary line would have a length of 6 also. Also, since every angle is a right angle in a square, you find out that the triangle is equilateral. To find out the angles just find the compliment of 30, which is 60. Once that is done, you know that an equilateral triangle has equal sides, therefore making the two other sides each have a length of 6. If you add up all five sides, you will have an answer of 30.</p>

<p>pg. 463 #15
The answer is C. The greatest prime factor of 38 is 19 and the greatest prime factor of 100 is 5. If you add those two together you get your answer of 24.</p>

<p>pg. 464 #19
The answer is A. Since this diagram is a section of a circle, you would need to find out the circumference of the whole circle. Since 30 is 1/12 of 360, the circumference of the whole circle would be 6 pi times 12, which is 72 pi. After doing the 2 pi r equation to find out the radius (36), you use the area formula to find out that the area of the circle is 1296 pi. Then you can divide the area by 12, because the section of the circle is 1/12 of the whole circle. Then you get your answer of 108 pi.</p>

<p>pg. 473 #8
The answer is E. For the bottom two triangles, you know that the unknown angles are 180-a-b. For the top triangle, the unknown angle is 180-b-c. Since you are finding c in terms of a and b, you must isolate c. Since all three unknown angles are supplementary, the sum of the unknown angles equal 180. so 180 =3(180)-2a-3b-c. After you subtract 180 from the left hand side and add c you will get c = 360-2a-3b.</p>

<p>pg. 475 #15
The answer is 1/2. The question tells the the height and the base of both triangles. For the smaller triangle, the base is PT and the height is SV. PT has a value of 3 and SV is equal to QV-QS, or 3-1, which is equal to 2. Area of a triangle is (1/2)bh so (1/2)(PT)(SV) = (1/2)(3)(2) = 3. For the bigger triangle, the base is PR and the height is QV. QV = 3 and PR = 4. Once again use the area formula and you get 6. Since the question is asking for the fraction of area PST/area PQR, plug in the area and you get 1/2 as your answer.</p>

<p>pg.475 #16
The answer is 2 or 7. h(x) = 14 + (x^2/4) and h(2m) = 9m. You need to plug in 2m into x. So your equation would be 9m = 14 + ((2m)^2/4) which is also 9m = 14+m^2 if you subtract 9m, you will get m^2 -9m + 14. Factor out this equation and you will get (m-7)(m-2) = 0. Solve for m and you get 7 or 2.</p>

<p>pg. 476 #17
The answer is 149. There are 10 clocks of type A, 5 clocks of type B, and 3 clocks of type C. First, find out the number of chimes each clock emits and multiply the chimes by the number of clocks of each type. Type A chimes n times on the nth hour. Since the time is from 7:15 to 8:45, type A chimes 8 times. Type A also chimes on the half hour, so it would chime at 7:30 and at 8:30. That is 2 times. 8 + 2 = 10. Since there are 10 clocks of type A, multiply 10 by 10. Write down that type A clocks chime 100 times. Type B only chimes n times on the nth hour, so type B would chime 8 times. Multiply that by 5 and you get 40. Type C chimes one on the hour and once on the half hour. That would mean that type C chimes on 7:30 8:00 and 8:30, which is 3 times. Multiply that by 3 and you get 9. 100+40+9 = 149.</p>

<p>pg. 476 #18
The answer is 72. Since the colored box cannot be at either end. There are only four possible choices on one end and three possible choices on the other end because boxes cannot be repeated. With that information you will get 4 _ _ _ 3. Since you lose two boxes, you have only three possible choices for one spot, two possible choices for another spot and 1 possible choice for the last spot. 4 3 2 1 3. Multiply those numbers together to get 72 as your answer.</p>

<p>pg. 488 #5
The answer is C. For this question you just need to look at the graph closely. The question is asking what value is y if x = 5. Look for x = 5 and then look for the y coordinate that corresponds with the x value. The line is at between 4 and 2 and therefore is at 3.</p>

<p>pg. 490 #11
The answer is A. Since a and c are negative constants, you know the parabola opens down and it has a negative y intercept. C determines the y intercept and a determines the direction a parabola opens.</p>

<p>pg. 490 #12
The answer is B. If you think about this question carefully, you will know that the length of PR is 2BC. Since PQ and QR is symmetric to AB and CD respectfully, you know that the length of the line segments will not change wherever you place point Q. If you place point Q in the middle of BC, both PQ and QR is equal to BC. Since BC is 4, you can find the answer by using the equation 2BC. 2(4) = 8.</p>

<p>pg. 491 #15
The answer is C. The question tells you that the triangle is a right triangle and the lengths of the sides are consecutive EVEN integers. Since x is the shortest leg of the triangle, the other leg of the triangle is x+2 and the hypotenuse is x+4. If you use the pythagorean theorem, you get the answer x^2 + (x+2)^2 = (x+4)^2.</p>

<p>pg. 521 #14
The answer is A. The question tells you that the both x and y are positive integers, which means that the minimum value of both variables is 1. If you plug 1 into the equation 2x + 3y < 6, you get 5<6. If you increase any of the variables by 1, you will invalidate the inequality. Therefore, there is only one possible ordered pair.</p>

<p>pg. 522 #15
The answer is C. From the diagram you know that triangle ABC is isosceles and triangle DEF is equilateral. In triangle ABC, the lengths of AB and BC are equal and the perimeter of the triangle is 21. In triangle DEF, all lengths are the same and the perimeter is 15. 21-15 = 6.</p>

<p>pg. 523 #20
The answer is C. Since the remainder of 15 must be 3, you know that a multiple of the factors must be 12. In this case, 1, 2, 3, 4, 6, and 12 has a multiple of 12. There are a few values that do not agree with this problem. 1, 2, and 3 are not possible because they provide different remainders. Only 4, 6, and 12 are possible choices and therefore you have 3 possible choices.</p>

<p>I will probably continue this tomorrow.</p>

8

<p>thanks a bunch !!</p>

9

<p>pg. 532 #6
The answer is D. In this question you need to isolate the variable m. In order to do that, just divide m^2 on both sides and the equation will be 10k^-1 = 100m^-1. After that, divide both sides by 100 and you will be left with (1/10)k^-1 = m^-1. Since the question is asking for m^-1 in terms of k, you can leave the equation as it is and simplify the left hand side. k^-1 is also 1/k and (1/k)(1/10) = 1/10k</p>

<p>pg. 532 #8
The answer is C. Whenever you see these function questions, know that the number or variable inside the function is the x value. For example, f(5) means find the y value for the x value of 5. In this problem it shows you that f(b) = f(3) which means that both x values of b and 3 have the same y values. In the graph look find 3 on the x axis and find the y coordinate that corresponds with it. You find that f(3) = f(-1)</p>

<p>pg. 534 #14
The answer is 70. The question gives you a lot of givens, such as perpendicular lines, but the most important given is that LN and LM are equal. If LN and LM are equal, triangle LMN is isosceles. The diagram also shows that the angle made with line t and line segment LM is 125. Find the supplement of 125 and you find that angle LMN is 55. Since triangle LMN is isosceles the other base angle, LNM, is also 55. Then you can find the remaining angle, NLM, which is 70. Since you know that the angle made by line l and line segment LM is 90, find the supplement of the angles. 180 = 70 + 90 + y. Using this equation, you find out that angle KLN is 20. Every triangle has 180 degrees, so with that information you can find out x. 180 = 90+20+x. x = 70.</p>

<p>pg. 535 #16
The answer is 3. Use the information of the question to make an equation. Know that percentages are always out of a hundred. Since the equation tells you 125 percent, do 125/100, which is equal to 1.25. The equation is a+2b = 1.25(4b), a+2b=5b,a=3b. After that divide both sides by b to get a/b = 3.</p>

<p>pg. 549 #6
The answer is B. Once again, this is a function problem. The value inside the function is the x value and the whole function equates to the y value. Since the question tells you the y value, you need to find the x value. On the graph find 1 on the y axis and you see that there are a number of x values that correspond with the y value. The answer must be between -1 and 0. Only choice B, -0.5, is between -1 and 0.</p>

<p>pg. 549 #9
The answer is D. The equation tells you that the height must not be lower than 30 inches and must not exceed 50 inches. 30<h<50. Without even solving the inequalities, you know that there must be 40 in the equation, with a deviation of 10. Using that information the only possible choice is D.</p>

<p>pg. 551 #15
The answer is A. In the graph you can infer that the the line of best fit will be a constant. Although the hamsters received more training, their time did not improve and was similar to the times when the hamsters received less training. The only possible answer choice is A because that is a straight line.</p>

<p>I’m out of time and ill finish this later. You should focus on learning the rules of functions.</p>

10

<p>I assume you meant number 16 instead of 17.
pg. 551 #16
The answer is E. For this question look at the rectangle as a whole. Since the left hand side shows 2L and the right hand side shows 3W, you find out that W=(2/3)L. Since the whole rectangle is used to fill another rectangle with 12L units long and 10L units wide, you need to convert the W of the original rectangle to L. The length of the original rectangle would be 2L and the width would be (5/3)L. Since the pattern needs to cover a larger rectangle, there needs to be 6 rows and columns to fill it. 6<em>2L = 12L and (5/3)L</em>6=10L. There are 6 rows and 6 columns so 6<em>6=36. Also, there are five other rectangles inside the original rectangle so 36</em>5=180.</p>

<p>pg.584 #9
The answer is A. For these types of questions the simplest way to find the answer is to plug in numbers for each answer choice. If you use choice A for example, if you plug in (0,1), you get 1=0^2 +1. Beware, some plug-ins might be valid for more than one answer choice so you must use a few other numbers.</p>

<p>pg. 584 #12
The answer is D. The question gives you both a cube with edges of 4 cm and a rectangular prism with dimensions of 20cm, 24cm, and 32cm. Since 4cm goes into all of those numbers, just divide the dimensions by 4. You will get 5, 6, and 8. Just multiply those numbers together to get 240.</p>

<p>pg. 585 #16
The answer is B. Since both quarter circles have a radius of 1, you know that they are congruent. Also, since the radius is 1, you find the length of the radius to be 2 and the width to be 1. To find the area of the shaded region, you must subtract the area of both quarter circles from the area of the rectangle. The area of the rectangle is 2. Also, since there are two congruent quarter circles, it is equivalent to a semicircle. To find the area of the semicircle use the area of a circle formula and divide the result by 2. pi(1)^2 = pi. Area of semicircle = pi/2. Area of shaded area = Area of rectangle - Area of semicircle
Area of shaded area = 2 - pi/2</p>

<p>pg. 586 #18
The answer is B. There are many givens for this equation. From the givens, you figure out that triangle ABC is isosceles, triangle DEF is equilateral, angle ABC is 30, and angle BDE is 50. Since triangle DEF is equilateral every angle is 60. Since triangle ABC is isosceles, both base angles are 75. Base angles = (180-ABC)/2. With that information you can evaluate the measure of angle ADF. Angle ADF = 180-angle BDE-angle EDF.
Angle ADF = 180-50-60=70. To find angle DFA, you need to subtract the two other angles from 180. Angle DFA = 180-angle ADF-angle FAD. Angle DFA=180-70-75=35.</p>

<p>pg. 587 #19
The answer is A. To find the answer just cross multiply each of the answer choices and you will see that only choice A is different from the other choices. For every other choice you will get af=cb, but for choice A you will get ac=fb.</p>

<p>pg. 587 #20
The answer is E. I’m not sure if I could explain this clearly. For choice I, the expression would equal ab-b. To make this equal 1, you would need a to be 1 so it does not interfere with b. Since a is 1, it does not matter what value b is and therefore is b-b=0.
For choice II, the equation would be (a+b)b-b =ab+b^2-b, or b^2 +(a-1)b. Since there is an addition and no subtraction, the result will never be 0.
For choice III, the expression is a(a+b)-(a+b)=a^2+ab-a-b, or a^2-a-(a-1)b. To make the answer 0, you need to make b=0. To do that, a must be 1. 1^2-1-(1-1)b. 1-1-(0)b=1-1=0.</p>

<p>pg. 595 #4
The answer is E. I’m not sure if you’re asking for an explanation for this problem. To find the answer you just need to find a number that is one more than a square. In this case, 7^2+1=50, 49+1=50, 50=50.</p>

<p>pg. 596 #8
I can’t seem to figure this question out.</p>

<p>pg. 599 #17
The answer is 8. The question is asking you to figure out the number of line segments that will not lie on the edge of the figure while connecting V to the other vertices. If you look at the diagram, you see that there are only 3 vertices that connect to V using an edge. Since there are 11 other vertices other than V, just do 11-3 to get 8 as your answer.</p>

<p>pg. 599 #18
The answer is 16. The important givens are that Points A and C are on the graph y=px^3 and that the area of ABCD is 4. Since both points A and C are on the graph, you know that the rectangle must be symmetric on both the x and y axis. Therefore, b=-a, c=-d. Also, since the question gives you the x values, you can find the width of the rectangle. (1/2)-(-1/2)=1. Since the area of the rectangle is 4, you can find the length of the rectangle by using the area formula. 4=1h, h=4. Also, because the rectangle is symmetric you need to divide the length of the rectangle by 2. +/- 2 is your y value. To find the value of p, you need to plug in a point that is both on the graph and on the rectangle. For example (1/2, 2). y=px^3, 2=p(1/2)^3, 2=p(1/8), p=16.</p>

<p>pg. 612 #6
The answer is A. To answer the problem, you need to know the basics of parallel lines that are cut by a transversal line. The few basics are corresponding angles, supplementary angles and transverse angles. u and s are transverse angles and therefore are congruent. r and u are corresponding angles and therefore congruent. t and u are supplements so they add up to 180. Using these basics, and the givens, you find out that r=u=s. 50=50=50. Also since u and t are supplements, 180=50+t, t=130. With that information you can find out the answer by adding s,t, and u. 50+50+130 = 230.</p>

<p>I am assuming you meant pg. 615
pg. 615 #15
The answer is B. To find the answer, you must first find the unmarked angle in terms of n. Also, know that both unmarked angles are congruent because they are transverse angles. The unmarked angles would be 180-n. Ignore one of the triangles and work with the other one first because you know they are congruent. To find out the marked angles, use the formula 180=angle1+angle2+angle3. 180=x+y+180-n, 0=x+y-n, n=x+y, where x+y are the marked angles. Since you know that both angles are congruent, just multiply the equation by two. 2n = 2x+2y.</p>

<p>pg. 615 #16
The answer is C. In order to answer this question you must first figure out the value of the second term in terms of t. Since each term is 3 greater than 1/3 the preceding term, the second term is (1/3)t+3=(t/3)+3=(t/3)+(9/3)=(t+9)/3. The question is asking for the ratio of the second term to the first term, it is second term/first term.
((t+9)/3)/t=((t+9)/3)*(1/t)=(t+9)/3t.</p>

<p>pg. 653 #3
The answer is B. Since x > 8, y must be less than 22. Choice A is not necessarily true because if x is 32, y can equal -2. The question never stated whether x or y is positive. Choice C is never true because x is greater than 8 and not equal to 8. Therefore, y can never be 22. Choice D is wrong because x+y would exceed 30. Choice E is wrong because once again, the question never stated whether x or y is positive. X can be greater than 30 and y can be less than 0.</p>

<p>pg. 653 #5
The answer is D. The answer is fairly simple. The question asks which term is equal to 8+(26-1)9. You know that 8 is the first term, and that each term after the first is found by adding 9 to the term preceding it. The equation shows that this number is 25 terms after the first term, therefore, the 26th term.</p>

<p>pg. 656 #12
The answer is 3. There are a few important givens in the question such as, point Q and R, the perimeter of the rectangle, and the coordinates of P and S. You know that QR=PS and QP=RS because the figure is a rectangle. Also, since P is (-1,0) and S is (1,0), PS=2=QR. Since the perimeter of PQRS is 10, use the equation
Perimeter of rectangle = 2l+2w. 10=2l+2(2), 6=2l, l=3.
With this information you know that the coordinate of R is (1,3) and the coordinate of Q is (-1,3). Plug in either the coordinate of R or Q into the equation of the parabola and solve for a.
3=a(1)^2, 3=1a, a=3.</p>

<p>pg. 657 #17
The answer is 8. For these types of questions, I find it easier to plug in numbers for the variables. Another method is that since the prime numbers are multiplied, some of the factors of n must be the original prime numbers. So far, we have 1, p, r, s, and n as the factors. Another fact is that some factors of n are product of two of the prime numbers. In this case, pr, ps, and rs would be factors. Therefore, in the end we have 8 different factors of n.
1, p, r, s, pr, ps, rs, n</p>

11

<p>Finally, the last question took awhile.
pg. 657 #18
The answer is 70. There are a lot of givens that are essential for this equation, such as the initial height. Lets start with the beginning of the question. When the time=0, the initial height is 6, which means that h(0)=6. Since the equation is h(t)= c - (d - 4t)^2, you get 6=c-(d-4(0))^2, 6=c-(d-0)^2, 6=c-d^2. Write down 6=c-d^2 because it is essential for the next few steps. In the next part, the question tells you that the ball reached the maximum of 106 feet at time = 2.5.
106 = c - (d^2 - 8dt - 16t^2), 106 = c - d^2 + 8dt - 16t^2.
Since c-d^2=6, you can substitute that value.
106 = 6 + 8dt - 16t^2.
Now plug in t to get, 106 = 6 + 8(2.5)d - 16(2.5)^2, 106 = 6 + 20d - 100, 106=20d-94
20d=200, d=10. Now that you have the value of the constant d, you can finish the question. Keep in mind that constants do not change. Finally the last part of the question asks for the height in feet of the ball at time t=1.
h(1) = c - (d^2 - 8dt + 16t^2), h(1) = c - d^2 + 8dt -16t^2. Once again, substitute c-d^2 for 6.
h(1) = 6+8dt-16t^2. At this point, substitute the remaining variables with the values you evaluated before. d=10 and t=1
h(1)=6+8(10)(1)-16(1)^2, 6+80-16, 86-16, 70
Therefore, h(1)=70.</p>

<p>I hope that these answers helped and hopefully weren’t ambiguous. After finishing all the problems that you needed help on, I believe that you should work more on functions, as it seems like it is your weak point. Also, I think that you should spend some time on word problems. Some tips that I would give is to study some tactics from test prep books, as it is helpful in some ways. Also, remember to check the ends of the questions, because CB likes to trick people. An example is finding x+4 instead of x. Good luck.</p>