sat iic questions

Test Preparation SAT Subject Test Preparation
1

<p>here are some questions im having trouble with (there are no explanations for them)</p>

<li>If P and Q are different points in a plane, the set of all points in the plane that are closer to P than to Q is</li>
</ol>

<p>a) the region of the plane on one side of a line
b) the interior of a square
c) a wedge-shaped region of the plane
d) the region of the plane bounded by a parabola
e) the interior of the circle</p>

<p>ive never seen anything about this before :(</p>

<p>What is the degree mesaure of the largest angle of a triangle that has sides of length 7,6, and 6</p>

<p>a)31.00
b)54.31
c)71.37
d)125.69
e)144.31</p>

<p>If Xo = 0 and Xn+1 = sq root of (6 + Xn) then X3 = </p>

<p>a) 2.449
b) 2.907
c) 2.984
d) 2.997
e) 3.162</p>

<p>If the magnitudes of vectors a and b are 5 and 12, resp. then the magnitude of vector (b-a) could NOT be</p>

<p>a) 5
b 7
c 10
d 12
e 17</p>

<p>an indirect proof of the statement “if x =2, then sq root of x is not a rational number” could begin with the assumption that </p>

<p>a x = sq root 2
b x2 = 2
c sq root x is rational
d sq root x is not rational
e x is nonnegative</p>

<p>which one of the following has an element that is less than any other element in the set?
I. the set of positive rational numbers
II. the set of positive rational numbers r such that r2 greater/equal to 2
III. the set of positive rational nubers r such that r2 greater than 4</p>

<p>a) None
b) I only
c) II only
d) III only
e) I and III</p>

<p>any help is appreciated! test on saturday</p>

2

<p>Hm, okay let's see.</p>

<p>Here are what I think are the answers.</p>

<ol>
<li>(A)</li>
</ol>

<p>Let line L be the perpendicular bisector of PQ. We realize that any point on L is equidistant from P and Q. So, we reason that all points past L is what we are interested in. This is a (half)-plane.</p>

<p>Next question: (C)</p>

<p>This is an isoceles triangle with a base of 7 and legs of 6. We can split the base in the middle, giving us two right triangles of base 3.5 and hypotenuse 6. We can take arcsin(3.5/60) to find half of the vertex angle. Multiplying by 2 gives the vertex angle. By Hinge Theorem, this must be the largest angle.</p>

<p>Next question: (C)</p>

<p>Easily done on a calculator. First just type in 0 and press Enter. Then, type sqrt(6 + Ans) and press Enter. This gives x1. Press Enter again. This gives x2. Again gives x3.</p>

<p>Next question: (A)</p>

<p>The smallest magnitude of the two vectors comes about if they are antiparallel to each other (180 degrees apart). The magnitude would then be 7, which is the smallest possible magnitude of the vector difference. Therefore, it cannot be 5.</p>

<p>Next question: (C)</p>

<p>We are given that this is an indirect proof, so it will most likely be a proof by contradiction (in fact, in Real Analysis, this is how this proof is constructed). So, the assumption should be proven false. We can assume (C) and at the end, we conclude, by showing a contradiction, that our initial assumption CANNOT be true.</p>

<p>(Btw, very highly unlikely that a question like this will appear on the test).</p>

<p>Next question: (A)</p>

<p>Hmm, interesting question. We know that a rational number is a number that can be expressed as a ratio of two integers. We can immediately cross off II because II is the set of all number greater than or equal to sqrt(2). Since sqrt(2) is obviously irrational, there is no one rational number that is justttttt above it. The same logic applies for III. There is no one rational number that is justtttt above 2. For I, we will have rational numbers of the form 1/x, where x is a very large number. Again, for every x that we choose, there will always be exist x + 1 which is greater than x. Thus, there is no single rational number that is smaller than any number in the set.</p>

<p>(Also very unlikely to appear on the test)</p>

<p>Where are these questions from, by the way?</p>

3

<p>these are from the 1998 collegeboard's "the real SAT IIs"</p>

<p>all the answers you gave were the correct ones, thanks!</p>

<p>can u explain hinge thrm to me please?
also for the last one, i don't understand what the question is asking for</p>

<p>thanks for the help!</p>

4

<p>A,C,C,A,C</p>

<p>I dont get the last question either :/</p>

5

<p>Okay, Hinge Theorem is very simple. In a triangle, the side with the biggest length will have the greatest angle. So, in this triangle, 7 is the largest side and will thus have the biggest angle.</p>

<p>So, for the last one:</p>

<p>We are asked to determine if any of these sets contains a unique element which is smaller than all the other elements. For example, consider the (ordered) set: {1,3,8,34,52,70}. In this set, 1 is obviously the smallest number in the set. </p>

<p>We define a rational number to be a number that can be expressed as p/q, where p and q are integers. So basically any fraction (1/2, 3/16, 42/234) as well as integers (2, 4, 3) are all rational numbers. </p>

<p>For the first set, we are given the set of rational numbers greater than 0. In order to minimize our number, we minimize the numerator and maximize the denominator. So, our numerator will be the smallest non-zero integer: 1. Our denominator should be a huge number. But for every big integer that we can think of, there still exists a number bigger than that; thus there is not one number that is biggest. In addition, 1/2 = -1/-2, so if our numerator is -1, our denominator will be the SMALLEST integer we can think of. Again, this is not unique. The same logic applies for the other two sets (refer to my first post, it should make more sense). </p>

<p>This is why none of the sets have a unique smallest number.</p>

6

<p>ok i get it now.
thats a weird one
thanks Rupac!</p>