Actual SAT Math 2 questions - I need help and clarifications. There are 8 qns

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1

<p>1) If P and Q are different points in a plane, the set if all points, the set of all points in this plane that are close to P than to Q is
a) The region of the plane on one side of a line</p>

<p>I guessed the answer, but why???</p>

<p>2) In a certain experiment, there is a 0.2 probability that any thermometer used in error by more than 1 deg C. If 4 thermometers are used, what is the probability that all of them are in error by more than 1 deg C.
a) .0016
b) .0081
c) .16
d) .25
e) .8</p>

<p>3) The magnitudes of vectors a and b are 5 and 12 respectively, then the magnitude of vector (b-a) could not be</p>

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

<p>4) For all theta, sin (theta) + sin (- theta) + cos (theta) + cos (- theta) = </p>

<p>a) 0
b) 2
c) 2 sin theta
d) 2 cos theta
e) 2 (sin theta+ cos theta)</p>

<p>5) The radius of the base of a right circular cone is 6 and the radius of the parallel cross section is 4. If the distance between the base and the cross section is 8, what is the height of the cone</p>

<p>a) 11
b) 13 1/3
c) 16
d) 20
e) 24</p>

<p>6) An indirect proof of the statement “If x=2, then sq.rt of x is not a rational number could begin with the assumption that</p>

<p>a) X = Sq. rt 2
b) x.x = 2
c) sq. rt of x is rational
d) sq. rt of x is not rational
e) x is nonnegative</p>

<p>7) How many ways can 10 people be divided into two groups, one with 7 people and the other with 3 people</p>

<p>a) 120
b) 210
c) 240
d) 5040
e) 14400</p>

<p>8) Which of the following has an element that is less than any other element is that set?</p>

<p>I) The set of positive rational numbers
II) The set of positive rational numbers r such that r.r >= 2
III) The set of positive rational numbers r such that r.r >= 2</p>

<p>A) None
B) I only
C) II only
D) III only
E) I and III</p>

<p>Thanks so much. Please share some of the actual tough Math 2 qns from practice tests.</p>

2

<p>for #6, the answer is C. Since we all know (without proof) that the sqrt of 2 is irrational, an indirect proof would assume that it is rational, and then show that there’s a contradiction (therefore it is irrational).</p>

3

<p>Small correction:</p>

<p>8) Which of the following has an element that is less than any other element is that set?</p>

<p>I) The set of positive rational numbers
II) The set of positive rational numbers r such that r.r >= 2
III) The set of positive rational numbers r such that r.r >= 4</p>

<p>A) None
B) I only
C) II only
D) III only
E) I and III</p>

4

<h1>4 is d) 2cos theta (I’ll replace theta with x in my explanation)</h1>

<p>There are 2 identities (known as negative-angle identities) that you need to know to solve this:</p>

<p>sin (-x) = -sin (x)
cos (-x) = cos (x)</p>

<p>These can be either committed to memory, or you can even reason it out by picking an arbitrary angle for x (personally, I use pi/2):</p>

<p>sin (-pi/2) = sin (3pi/2) = -1 = -sin (pi/2)</p>

<p>AND</p>

<p>cos (-pi/2) = cos (3pi/2) = 0 = cos (pi/2)</p>

5

<h1>2: If there’s a 0.2 probability that one thermometer is off by more than 1 C, then the probability of all four being like that is (0.2)^4 = .0016.</h1>

<h1>3: Triangle Inequality: the sum of the lengths of two sides of a triangle must be greater than the third side…both 5 and 7 don’t work, but we’re talking about vectors, so degenerate triangles are allowed (i.e. straight line), so 7 works. so 5.</h1>

<h1>5: Let x be the height from the tip of the cone until the parallel cross section. Then by similarity 4/6 = x/x+8. It naturally follows that x = 16, and the height is 24.</h1>

<h1>7: Effectively you’re just choosing 3 people. 10C3 = 120.</h1>

<h1>8: I’m not sure I understand the question entirely, actually. I’ll leave it to someone else.</h1>

6

<p>^ #3 is about vectors, not triangles. I would think that <b> - <a> would just be b - a, which would be 7. Still, I am assuming that these vectors are placed along the x or y axis (though placing them at any angle would probably yield the same result, if they were placed at the SAME angle).</a></b></p><b><a>
</a></b>