Confusing Math Questions Helppp!!!??

Test Preparation SAT Preparation
1

<p>(They might not be hard for you guys but i got a tad confused)</p>

<p>So I started reviewing over some practice test carefully and in my math section
I came across a couple problems which I do not know either how to get the answer or why the answer is different than what I thought it to be.Help me please =) !
[Please do not scrutinize me for not knowing the answer] </p>

<p>The Questions are as following and are found in the CB's The SAT Preparation Booklet for 2008-2009:</p>

<p>1)What is the greatest possible area of a triangle with one side of length 7 and another side of length 10?
A)17 B)34 C)35 D)70 E)140 {now i know its 35 but why?} </p>

<p>[Section 6 #5 in actual booklet It has a circle incribe with 2 triangle i cant draw it here but ill post the questions anyway]</p>

<p>2)In the figure above, triangle ABC is inscribed in the circle with center O and diameter AC. If AB = AO what is the degree measure of triangle ABO ?
A)15 B)30 C)45 D)60 E)90 (It says C but idk how any ideas ?)</p>

<p>(again theres like 3 segments which make 3 angle that meet at a certain point. Hopefully you guys will recognize it. I cant draw it but heres the question Section 6 # 7 btw)</p>

<p>3) In the figure above, segment AB, segment CD,& segment EF intersect at P. If r=90, s=50, t=60, u=45, and w=50, what is the value of x?
A045 B)50 C)65 D)75 E) Cannot e determined by info given</p>

<p>4) If 6<|x-3|<7 and x<0, what is one possible value of |x|? (i guess like 3.1 and the answer was any number greater than 3 but less than 4 so i got it right but how?)(Section 6 #16)</p>

<p>5)What is the product of the smallest prime number that is greater than 50 and the greatest prime number that is less than 50? (Section 6 #17)</p>

<p>(number line) -8 a b c d e f 10</p>

<p>6) On the number line above, the tick marks are equally spaced and their coordinates are shown. Of these coordinates, which has the smallest positive value? (Section 8 #5)
A)a B)b C)c D)d E)e</p>

<p>7) Two spheres, one with radius 7 and one with radius 4, are tangent to each other. If P is any point on one sphere and Q is any point on the other sphere, what is the maximum possible length of segment PQ?
A)7 B)11 C)14 D)18 E)22</p>

<p>I cant illustrate these problem i think the image is needed but they are on Section 8 numbers 9,12,& 14. If anyone knows them please let me know.</p>

<p>8) Let @x be defined as x + 1\x for all nonzero integer x. If @x= t, where t is n integer, which of the following is a possible value of t ?
A)1 B)0 C)-1 D)-2 E)-3</p>

<p>Those are it again there in the booklet mostly every receives and hopefully you guys can help me understand the answers to these questions.</p>

<p>thanks !</p>

2

<p>for the first one its greatest possible area comes as a right triangle, </p>

<p>for the others can you provide a page number, if so than I can aid you, I can’t really picture the triangles while looking at my computer here haha</p>

3

<p>for 4- x clearly has to be any number below -3 however above -4 since subtracting three from a number in that range will give you -6.xxx & the absolute value will be between 6&7 </p>

<p>5- just find the greatest prime below 50 & the least above it 47&53 respectively & multiply them together (2491) </p>

<p>6- the answer should be C, just think since there are 5 numbers between -8 & 10 the numbers have to be slightly greater than 3 units apart, so just see how many it will take to get past 0 from -8 (3 of them) </p>

<p>7- there diameters are 8 & 14 respectively so the maximum distance is the far edge of each of these spanning the 14 and 8 , 14+8=22 </p>

<p>8- what do you mean by n integer? (i think you mean an? not perfectly certain though)</p>

<p>so if you can provide the page number for any I haven’t answered, and explain n integer I can help with the rest</p>

4

<ol>
<li> You know the 3rd side (“x”) of the triangle is such that 3 < x < 17 </li>
</ol>

<p>But we’re trying to find the maximum area of the triangle; there are several ways you could go about this (Heron’s Formula, Law of Cosines, etc), but I think the easiest way is to use the answer choices. You know it must be at least 35 because if 7 and 10 are the legs of a right triangle the area is 35. You should also be able to visualize (if you can’t you could use Law of Cosines/Heron’s/Triangle Area Formula) the triangle, doing so you should see that there is no possible length (x < 17) for which the area can be 70, thus it must be C) 35.</p>

5

<p>Theyre found in the sat preparation booklet from 08-09 pages are 65, 67, 74-76.</p>

<p>And sorry its an* interger</p>

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<p>heres a link to it</p>

<p><a href=“College Board - SAT, AP, College Search and Admission Tools”>College Board - SAT, AP, College Search and Admission Tools;

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<p>Spratley’s suggestion about using the Law of Cosines provides an obvious result - if you understand the Law of Cosines. By calculating triangle area as b*h/2 and choosing either side to be the base, the task of maximizing area is reduced to the task of maximizing height - which occurs in a right triangle (for area 35).</p>

<p>In the figure above, triangle ABC is inscribed in the circle with center O and diameter AC. If AB = AO what is the degree measure of triangle ABO ?
A)15 B)30 C)45 D)60 E)90 (It says C but idk how any ideas ?)</p>

<p>There are several ways to do this problem. AO = BO becasuse they are both radii. Since AB = AO, triangle ABO is an equilateral triangle (with angle ABO = 60 degrees, not 45).</p>

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<p>Thanks I can see that clearer now. Any idea on the others ?</p>

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<p>5)What is the product of the smallest prime number that is greater than 50 and the greatest prime number that is less than 50? (Section 6 #17)</p>

<p>You will need to recognize 47 and 53 as the target primes. 47 and 53 can be multiplied as
(50-3)(50+3) = 50^2 - 3^2 = 2500-9 = 2491.</p>

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<p>8) Let @x be defined as x + 1/x for all nonzero integer x. If @x= t, where t is an integer, which of the following is a possible value of t ?
A)1 B)0 C)-1 D)-2 E)-3</p>

<p>If t is an integer, it has no fractional part, so 1/x must not yield a fraction. x=1 or -1 are the only x for which this is true, so t = -1 + 1/-1 = -2 (x=1 yields t=2, but that answer is not a choice).</p>