<p>Can you guys help me understand these questions so that next time I see the same type I can solve them?</p>
<p>Blue Book Page 313
18. For all positive values of x the function f is defined by f(x)=x^3-x^-2. Of the following, which is the best approximation of f(x) values of x greater than 1000?
answer is x^3</p>
<p>I don't understand why it is x^3....</p>
<p>Please help, I have a serious problem trying to understand this question!</p>
<p>BB2 page 367
3. There are graphs in this question, so only ppl with the Blue Book ed 2 can help me =(
Answer is C.
What does it mean by f(x)=f(-x)??</p>
<ol>
<li>A class has twice as many boys as girls. the students in the class stand in one line, with a girl at the front of the line. Which of the following must be true?
A. The last person is a girl
B. The last person is a boy
C. There are more girls than boys
D There are at least 2 girls standing next to each other.
E There are at least 2 boys standing next to each other.</li>
</ol>
<p>Answer is E. I guessed E because there are more boys, so it is more likely for 2 boys to stand together, but is there a "proper" way for this question?</p>
<p>Page 369 Q8
There is a graph in this question, but I will still put the question here:
The figure above shows a portion of the graph of the function f. If f(x+5)=f(x) for all values of x, then f(x)=0 for how many different values of x between 0 and 12? </p>
<ol>
<li>It is basically asking “how does the function look for very large values of x?” x^-2 = 1/(x^2). As x increases, 1/x^2 decreases. For very large values, it is negligible and the graph represents the graph of x^3</li>
</ol>
<p>P. 367</p>
<ol>
<li>I have original BB and the question is “For which of the following graphs of f does f(x) = f(-x) for all values of x shown?” I am assuming this is the question you’re talking about.</li>
</ol>
<p>It’s basically asking “which function is even?” An even function is symmetric about the y axis. In essence, it’s saying “out of the graphs here, which one is made so that if you plug in a number and plug in it’s opposite, i.e. negative, will you get the same values?”</p>
<p>C is the only one like that. D can be even but we don’t know if f(2) = f(-2) since it’s not shown, so it’s not right.</p>
<ol>
<li>Make it simple by quantifying the variable. There are 4 boys and 2 girl in the class. Test each condition for your small class and you’ll see that only E can be correct. You could try 2/1 or 6/3 for confirmation, but it’s usually not necessary past the 3rd one.</li>
</ol>
<p>p. 369</p>
<ol>
<li>B</li>
</ol>
<p>It’s telling you that the function repeats every 5 units. For example, f(11) = f(6 +5) = f(6) = f(1 + 5) = f(1). f(x) =0 only 4 times between [0,5], so it is zero 8 times between [0,10]. From [10,12], the graph is the same as [0,2], so there is 1 more zero for 9 zeros in total.</p>
<p>f(11) is selected randomly by An0maly and it is just an example to tell you that the graph is repeating every 5 units,that’s the point. Between 1~5,you can count there are 4 intersections on x axis, which means all the x values for f(x)=0 between 1~5,then you will know there are another 4 between6~10, then 10~12, there are 2 units but one intersection. sum up and you will get 4+4+1=9, the answer.</p>
<p>I’m having trouble with another question in the blue book (I checked the explanation on the website but I still don’t understand why they did it that way).</p>
<p>Page 486
16. On a square gameboard that is divided into n rows of n squares each, k of these squares lie along the boundary of the gameboard. Which of the following is a possible value for k?
a) 10
b) 25
c) 34
d) 42
e) 52
The first way I did this problem was to make up squares that had the same number of rows as squares per row. Then I started counting the squares along the boundary for each square as it got bigger by dimension. I reached the 7x7 square which has 7 squares in each row and 7 rows. This means that it has 25 squares along the boundary. So I chose B.</p>
<p>But the answer was E) 52 and I still don’t get it.</p>
<ol>
<li>If t and k are positive integers in the inequalities above and t > k, what is the value of t?
A)1
B)2
C)3
D)4
E)5
Answer is C, 3.</li>
</ol>
<p>Page 519</p>
<ol>
<li>Any 2 points determine a line. If there are 6 points in a plane, no 3 of which lie on the same line, how many lines are determined by pairs of these 6 points?
A)15
B)18
C)20
D)30
E)36</li>
</ol>
<p>A) 1 is not possible because t>k and k has to be a positive integer.
B) 2 is not possible because then k would have to be 1 and 2+1 is not > 4.
C) Works
D) 4 is not possible because then k would have to be 3,2, or1 and none of the combinations satisfy t^2-k^2<6
E) 5 Same error as in D)</p>
<p>2) Draw like a hexagonal shape with 6 points. Then you can make only 15 lines. Each point can make 5 lines with the other points and then we divide the lines we counted twice. 6*5/2 = 15</p>
<ol>
<li>In the rectangle ABCD, point E is the midpoint of BC. If the area of the quadrilateral ABED is 2/3, what is the area of rectangle ABCD?</li>
</ol>
<p>I’ve got another problem, if you can, please help!</p>
<ol>
<li>When the number w is multiplied by 4, the result is the same as when 4 is added to w. What is the value of 3w ?
(A) 3/4
(B) 1
(C) 4/3
(D) 3
(E) 4
answer is E</li>
</ol>
<ol>
<li>A class has twice as many boys as girls. the students in the class stand in one line, with a girl at the front of the line. Which of the following must be true?
A. The last person is a girl. **Potentially true, you could place a girl anywhere. But it is equally true that the last person could be a boy. So this is false. **
B. The last person is a boy **Other way around of A. **
C. There are more girls than boys ** You have twice as many boys as girls. False. **
D There are at least 2 girls standing next to each other. While true since it didn’t say that you couldn’t pair each girl with each other, they can be evenly matched with a boy as well.
E There are at least 2 boys standing next to each other. **Definitely. No matter how you do the combinations, this will hold. So this is true because you could manipulate D. **</li>
</ol>
<p>I wrote them as combinations because it was easier for me to visualize in a line. Also, would be a waste of space here to list them in a line.</p>
<p>Thanks a lot for all of those detailed explanations guys! </p>
<p>Sorry, I really don’t understand how to do this one. I tried making that expression into a difference of squares expression and found that 2x2y≥25 but dont know what to do after.</p>
<ol>
<li>If 0 ≤ x ≤ y and (x + y)^2 − (x − y)^2 ≥ 25, what
is the least possible value of y ?</li>
</ol>
<p>@dwarfwarri: I remember someone else did explain this problem in other topic.
The easiest way to solve this problem, I think, is to use your graph calculator
From (x + y)^2 − (x − y)^2 ≥ 25 => y≥ 25/(4x) (x#0)
and 0 ≤ x ≤ y</p>
<p>The ORANGE area in this graph represents all possible values of y so that y≥ 25/(4x) and 0 < x ≤ y.</p>
<p>The least possible value of y is where two lines y = x and y = 25/4x intercept each other, as shown in the graph.
And to find the coordinate: x = 25/4x => x = +/- 5/2 but x > 0 => x = y = 5/2</p>
<p>CalDud,
It makes no sense in Math. Where did you get those equations?
To get the result is easy. And you may say that it’s enough to beat SAT Math. Fair enough.
Anyway, I just want to explain for him how to get those equations.</p>
<p>Guys, where did you get the y=x equation from? I understand that you got the y=25/4x equation from simplifying the equation in the question, but where you find y=x ? Please help I’m confused.</p>
<p>Each of the following inequalities is true for some
values of x EXCEPT</p>
<p>(A) x < x^2 x^3
(B) x < x^3 < x^2
(C) x^2 < x^3 < x
(D) x^3 < x < x^2
(E) x^3 < x^2 < x</p>
<p>Why can’t E be a correct answer too? if you put in negative number for x, it isn’t true because (-x)^2 is not smaller than x, though the first part is correct…please help!</p>
![http://img258.imageshack.us/i/graph1b.jpg]Imageshack](http://img258.imageshack.us/i/graph1b.jpg%5DImageshack){kind=link}
