Hello mathamatics, my old friend.
I have been, intermittenly anyway, bitching about having to do those unnecessary SAT IIs. For those of you who don't know, UCLA requires three SAT IIs, or two SAT IIs if there is a writing section in the SAT I taken. I took the new SAT I, so there was a writing section (I have also taken the old SAT I three times, but that's another story). This means that I have to take two SAT IIs to enroll in UCLA.
Except I'm not going to UCLA, but rather am going to go to the Barrett Honors College at ASU. The BHC and ASU as a whole don't require SAT IIs.
This means I'm taking two SAT IIs on the off chance that I decide to go to UCLA instead, because I don't like the BHC... except that if I were to take up their offer, I would have had to allready gotten sick of the BHC, and I can't really do that until I go to ASU. Thus, if I were to need two SAT IIs, it would be next year, and unlikely at that.
Thus I call them unnecessary. And, in the classic opposition-defiant disorder way, have avoided studying for them like the plague.
Not that plague avoidance is not a immovable force, as shown by death rates. However, my mother is an unstoppable force. Unstoppable force + not-quite-immovable will? Mother prevails. But ODD(I must be calling it a wrong name - that's almost as bad an acronym as "Youth For Understanding"(YFU) or "Moderate Breadth Attention Deficit Disorder") means I try anyway, like a salmon going up the Niagara Falls.
Yesterday I studied Biology (Eco). It was kinda fun. I knew all the stuff that went on inside a human body, because I took Bio 3 (Human bio - duh), but I wasn't that used to all the stuff outside of humans. Photosynthesis, for one. I guess this is what I get for skipping most of highschool. But it was cool stuff - I've always been fascinated by how the human body works... I think this stems from my medical training, various maladies, and natural curiousity about everything. (I might note that I'm fascinated by just about everything.) I took a mock test this morning.
Most of today has been studying for my Math IIC SAT II. I haven't touched mathematics since I got a B in Calc 1 back in... 2004. Long time, no math. I'm as rusty as steel wool left in a sauna for a year.
So it's no surprise that math really struck me: It's so wonderfully logical. I must have missed math or something, as I got this warm familiar feeling. Lovely. I was, however, badly out of practice. So badly, in fact, that I had pretty much forgotten Trig. Most of the other stuff came right back, but I must have not used trig much. I studied it for quite some time. Rather useful stuff, but it turns out that I can't relearn trig in an afternoon. Tough cookies. I hate memorisation anyway, and there is no way in hell that I'm going to re-memorise those identities. Last time in trig, I used my knowledge of what they all did, and some in-test proofs, to know it/derive it all. Not this time.
I also took a mock Math IIC test tonight. It was all going pretty good - I knew most the stuff, save for trig, which I made educated guesses at. But there was one problem, the last problem, that bugged the hell out of me when I checked the answer.
Question: What is the greatest number of intersections possible between a parabola and a circle?
I assume they mean just a single curve parabola, adjusted up or down. Right? Well then it's six possible intersections. That's right, Kaplan, six intersections. Not four, like you have in that crummy answer of yours, with that simple diagram.
Now, I suppose that some of you are scratching your heads. Please note that even with just a single curve parabola, adjusted up or down(in this case down), can get six intersections. Infinite intersections would be possible if I were allowed to make that many curves, but I am just dealing with one here.
How? What happens if you increase the (even) exponent on X? Well, the sides get steeper, and the domain of -1 < x < 1 gets closer and closer to 0. Pretty soon, it looks like a |_| rather than a U. That's how you get six.
If you don't believe me, graph these:
Circle: x^2 + y^2 = 4 (circle of radius two, centered on th origin)
Parabola: y = x^90 - 1.91
I trust that you can put those into your puny little graphing calculators, graph both, and see what I mean. I reccomend a window of 2 in every direction, but zoom liberally.
It doesn't ave to be those exact equations, but they make it outright visible on my calculator. Now I'll have some fun with my rusty knowledge of trig (I'm typing this on my own, non-web computer, so I can't get to my beloved Wikipedia):
Assuming that the ideal (as exponent --> infinity) parabola is a pure right angle mess, I'll screw around to test the boundaries:
In the circle I'm using, the radius is 2. Scaled down, I'll change it into the everlovin' unit circle. That puts the walls of my ideal parabola at 1/2, and I'll tilt the parabola over so they're at y = 1/2 and y = -1/2. Since it's symetrical over the x-axis, I'll just consider the positive half.
I can do this one in my head - in the ideal parabola, it only has to be shifted down by more than (3^(1/2))/2 (god that looks better on paper) to have six intersections. Obviously it can't be shifted down to the point of reaching the bottom.
Parabola(revised for ideals): x^a + b where a --> infinity and -(3^(1/2)) > b > -2
Circle: x^2 + y^2 = 4
Good? Silly Kaplan people.
Except I'm not going to UCLA, but rather am going to go to the Barrett Honors College at ASU. The BHC and ASU as a whole don't require SAT IIs.
This means I'm taking two SAT IIs on the off chance that I decide to go to UCLA instead, because I don't like the BHC... except that if I were to take up their offer, I would have had to allready gotten sick of the BHC, and I can't really do that until I go to ASU. Thus, if I were to need two SAT IIs, it would be next year, and unlikely at that.
Thus I call them unnecessary. And, in the classic opposition-defiant disorder way, have avoided studying for them like the plague.
Not that plague avoidance is not a immovable force, as shown by death rates. However, my mother is an unstoppable force. Unstoppable force + not-quite-immovable will? Mother prevails. But ODD(I must be calling it a wrong name - that's almost as bad an acronym as "Youth For Understanding"(YFU) or "Moderate Breadth Attention Deficit Disorder") means I try anyway, like a salmon going up the Niagara Falls.
Yesterday I studied Biology (Eco). It was kinda fun. I knew all the stuff that went on inside a human body, because I took Bio 3 (Human bio - duh), but I wasn't that used to all the stuff outside of humans. Photosynthesis, for one. I guess this is what I get for skipping most of highschool. But it was cool stuff - I've always been fascinated by how the human body works... I think this stems from my medical training, various maladies, and natural curiousity about everything. (I might note that I'm fascinated by just about everything.) I took a mock test this morning.
Most of today has been studying for my Math IIC SAT II. I haven't touched mathematics since I got a B in Calc 1 back in... 2004. Long time, no math. I'm as rusty as steel wool left in a sauna for a year.
So it's no surprise that math really struck me: It's so wonderfully logical. I must have missed math or something, as I got this warm familiar feeling. Lovely. I was, however, badly out of practice. So badly, in fact, that I had pretty much forgotten Trig. Most of the other stuff came right back, but I must have not used trig much. I studied it for quite some time. Rather useful stuff, but it turns out that I can't relearn trig in an afternoon. Tough cookies. I hate memorisation anyway, and there is no way in hell that I'm going to re-memorise those identities. Last time in trig, I used my knowledge of what they all did, and some in-test proofs, to know it/derive it all. Not this time.
I also took a mock Math IIC test tonight. It was all going pretty good - I knew most the stuff, save for trig, which I made educated guesses at. But there was one problem, the last problem, that bugged the hell out of me when I checked the answer.
Question: What is the greatest number of intersections possible between a parabola and a circle?
I assume they mean just a single curve parabola, adjusted up or down. Right? Well then it's six possible intersections. That's right, Kaplan, six intersections. Not four, like you have in that crummy answer of yours, with that simple diagram.
Now, I suppose that some of you are scratching your heads. Please note that even with just a single curve parabola, adjusted up or down(in this case down), can get six intersections. Infinite intersections would be possible if I were allowed to make that many curves, but I am just dealing with one here.
How? What happens if you increase the (even) exponent on X? Well, the sides get steeper, and the domain of -1 < x < 1 gets closer and closer to 0. Pretty soon, it looks like a |_| rather than a U. That's how you get six.
If you don't believe me, graph these:
Circle: x^2 + y^2 = 4 (circle of radius two, centered on th origin)
Parabola: y = x^90 - 1.91
I trust that you can put those into your puny little graphing calculators, graph both, and see what I mean. I reccomend a window of 2 in every direction, but zoom liberally.
It doesn't ave to be those exact equations, but they make it outright visible on my calculator. Now I'll have some fun with my rusty knowledge of trig (I'm typing this on my own, non-web computer, so I can't get to my beloved Wikipedia):
Assuming that the ideal (as exponent --> infinity) parabola is a pure right angle mess, I'll screw around to test the boundaries:
In the circle I'm using, the radius is 2. Scaled down, I'll change it into the everlovin' unit circle. That puts the walls of my ideal parabola at 1/2, and I'll tilt the parabola over so they're at y = 1/2 and y = -1/2. Since it's symetrical over the x-axis, I'll just consider the positive half.
I can do this one in my head - in the ideal parabola, it only has to be shifted down by more than (3^(1/2))/2 (god that looks better on paper) to have six intersections. Obviously it can't be shifted down to the point of reaching the bottom.
Parabola(revised for ideals): x^a + b where a --> infinity and -(3^(1/2)) > b > -2
Circle: x^2 + y^2 = 4
Good? Silly Kaplan people.