Help Needed from the Math Buffs!!

Test Preparation
1

<p>I took the PSAT and PLAN this year (I'm a sophomore) and even though I did really well on the reading and writing, I did pretty badly (relative to how I could do) on the math sections...66 on the PSAT and 28 on the PLAN. Well, they sent me my test booklets and I'm examining the questions I missed. The PSAT website offers explanations of the questions, but they don't explain them very well, and the PLAN doesn't offer any (that I know of). </p>

<p>I'd really appreciate it if someone could help explain the following questions and how to solve them. I know for some of them I could just use guess and
check, but I'd really like to understand the math behind them, especially in the sequence questions. I took algebra II over the summer so I could do pre-calc honors this year, and we went through the sequences and series chapter really fast, so I don't really remember much:</p>

<p>Sequence I: 2, 4, 6, 8, . . .
Sequence II: 1/64, 1/32, 1/16, 1/8, . . .</p>

<p>In sequence I above, the first term is 2 and every term after the first is 2 greater than the previous term. In sequence II, the first term is 1/64 and every term after the first is 2 times the previous term. What is the least positive integer n for which the nth term of sequence II is greater than the nth term of sequence I?</p>

<p>a) 8
b) 12
c) 14
d) 20
e) 24</p>

<p>If m is a positive integer and m = 12r, which of the following must be true? </p>

<p>I. r is positive
II. r is an integer
III. m is an even integer</p>

<p>a) I only
b) II only
c) III only
d) I and II only
e) I, II, III</p>

<p>If 2x < 3 and 3x > 4, what is one possible value of x? (it's a grid-in question)</p>

<p>(I know this question could be done easily using guess and check but I really need to understand sequences) Summer Olympics are numbered sequentially with Roman numerals. The same is true of another popular athletic event, the Super Bowl. The XXVII Summer Olympics and Super Bowl XXXIV both took place in the year 2000. The Super Bowl has taken place once a year since 1967. The Summer Olympics have taken place at 4-year intervals during that time. In what year were there Summer Olympics and a Super Bowl with the same number? (Note: XXVII = 27 and XXXIV = 34)</p>

<p>f) 1972
g) 1976
h) 1984
j) 1992
k) There was no year when this happened.</p>

<p>The pyramid shown below has a height of 48 inches and a base that is a
rectangle with an area of 108 square inches. A plane parallel to the base intersects the pyramid to form a rectangle with an area of 12 square inches.
What is the distance, in inches, between the 2 rectangles? (I realize this might be easier to understand if you had the picture...) </p>

<p>f) 16
g) 24
h) 27
j) 32
k) 42 2/3</p>

<p>Start with the line y = 3/2x + 6 in the standard (x,y) coordinate plane. Rotate this line clockwise 90 degrees about the origin. Which of the following is the y-intercept of the new line?</p>

<p>f) 0
g) 2
h) 4
j) 6
k) 9</p>

<p>One of the following graphs in the standard (x,y) coordinate plane is the graph of | x | + | y | = 1 for all coordinate pairs where x and y have the same sign. Which graph is it?</p>

<p>Okay, I can't show you the graphs, obviously...but how would I graph this on my TI-83 plus to figure out what it looks like? I'm not sure how to put it in slope intercept form. </p>

<p>That's all, folks. Thanks so much! If any math folks need help with any critical reading or writing questions (PSAT, PLAN, ACT or SAT), I'd be glad to help.</p>

2

<p>For the first one, find equations for each sequence. For sequence 1, you start out with 2 and increase by 2 so f(n)=2+2(n-1). For the second sequence, you are multiplying by 2 each time, so g(n)=2^(n-1)<em>(1/64). Set the two equations equal to each other and solve for n:
2+2n-2=2^(n-1)</em>(1/64)
2n=2^n/128
256n=2^n
n=11.526937
That is the point where the two values are equal; since n has to be an integer (you cant have a fraction of a term), n=12 is where the second is greater than the first. B</p>

3

<p>For the second one, I is the only one true; rearranging gives r=m/12--a positive divided by a positive will always give a positive; m/12 does not have to be an integer (try m=7, for instance); m does not have to be an integer, as r could be irrational, for example (12pi does not equal an integer). A.</p>

<p>If m is a positive integer and m = 12r, which of the following must be true?</p>

<p>I. r is positive
II. r is an integer
III. m is an even integer</p>

<p>a) I only
b) II only
c) III only
d) I and II only
e) I, II, III</p>

4

<p>For the third: let n be the event number where the two events had the same number. You know that the Super Bowl started in 1967, while the Olympics started in 1896 (27 olympics, so 26 not including 2000, so 2000-26*4=1896). Make an equation: since they both happened in the same year, 1896+4n=1967+n; solving for n gives n=23.666 repeating. Since this is not a whole number, there was no year that this happened. K.</p>

5

<p>Fourth: Draw a triangle that is a cross section of the pyramid (cutting the square in half through its sides, all the way up to the top of the pyramid). You can assume that the base is a square (can't really explain why, but you can), so the base of the triangle is sqrt(108)=6sqrt(3). You are trying to find where the base would be 12, so you are trying to find a line on this triangle parallel to the base of the triangle that is equal to sqrt(12)=2sqrt(3). What you have now are similar triangles, one with base 6sqrt3 and height 48 and another with base 2sqrt 3 and height x. 6sqrt3/2sqrt3=48/x, so x=16. Now, the distance between the two planes is the distance between 48 and 16, or 48-16=32. J.</p>

6

<p>Fifth: graph the equation on the graphing calculator. You will see that the y intercept is at 6 and the x intercept is at -4. What happens when you rotate the graph 90 degrees clockwise is that your positive y axis becomes your positive x axis, the negative x axis becomes the postive y axis, and so on. You'll notice that the line intersects the original negative x axis 4 thingys out; therefore, the new y intercept will be 4. H.</p>

7

<p>for the one with m and r, towerpumpkin, you said "m does not have to be an integer," but the question says "if m is a positive integer." just pointing that out because wouldn't that change the answer to d?</p>

8

<p>You are right that it says integer, but that choice still doesn't work. For example, let r=13/12. m would then equal 13--an integer, but not an even. The answer is still A.</p>