UIL B 2012

[FabensMath]

Don't know if these were asked, so if they were you can give me the link. Thanks!

31. If a triangle has two sides of lengths 10cm and 15cm, and the included angle between these two sides is increasing at a rate of 10degrees per hour, at what rate is the area of the triangle changing when the included angle is 60degrees? (nearest tenth) Answer: 6.5cm^2/hr

55. I. C. Cleerly has 6 boys in his class and 8 girls in his class. Two of the boys and 3 of the girls wear glasses. He randomly selects two students to pass out papers. What is the probability that both are boys or both wear glasses? Answer: 26%
I got a close enough answer by doing something like:
Is this the proper way?

[mathperson]

For 55, you would also have to subtract 1/(14 * 13) from the answer you have to get 26%. You would have to do so because you have included 2 boys wearing glasses twice.

[88bobcat]

31. If a triangle has two sides of lengths 10cm and 15cm, and the included angle between these two sides is increasing at a rate of 10degrees per hour, at what rate is the area of the triangle changing when the included angle is 60degrees? (nearest tenth) Answer: 6.5cm^2/hr

The area of a triangle given two sides and their included angle is



Differentiation with respect to time ,



So, now it's a plug-n-chug:

[sxk1693]

The second one is a related rates problem. A of triangle = .5absinc. Differentiate this equation and plug in pi/3.

ILOVECALCULUS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[redhawk2015]

53. In the expansion of , the absolute value difference of the coefficients of the 3rd and the 5th term is? Answer: 2700

I know how to do it using the binomial theorem (and Pascal's triangle), but is there a faster way to do this type of problem?

Edited for plus sign.

[007math]

TI-89.

EDIT: It might not be a bad idea to make a program for coefficients of binomials.

EDIT2: You mean a +, not a * right?

[nsguy1350]

53. In the expansion of , the absolute value difference of the coefficients of the 3rd and the 5th term is? Answer: 2700

I know how to do it using the binomial theorem (and Pascal's triangle), but is there a faster way to do this type of problem?

Yes, 007math is correct when he said you should be using a plus sign instead of multiplication.

I use my 89 (the expand function on the F2 menu) to do this, but you could easily find both coefficients and then divide.

The third term is and the fifth term is .
.
.
Become familiar with the combination coefficients for the binomial expansion. After that, just plug in the x coefficient into the x power, and the y coefficient into the y power.

[007math]

Does anyone think that as if Mr. White is writing these tests to be calculator driven? There are so many questions that can be solved directly on the TI-89 and so many that are repeated for which one can make a program.

I find it funny that on the Calculator test you cannot use programs but on the mathematics test you can...it seems as if it should be the other way around.

[nsguy1350]

Does anyone think that as if Mr. White is writing these tests to be calculator driven? There are so many questions that can be solved directly on the TI-89 and so many that are repeated for which one can make a program.

I find it funny that on the Calculator test you cannot use programs but on the mathematics test you can...it seems as if it should be the other way around.

You're right. I plug lots of stuff in directly into the 89. Easy.
I don't write any programs though. I'm for getting rid of them! Then I get an extra advantage over those that use them :P

I don't really think programs should be allowed on either. Then, you don't really solve the problem, you just plug stuff in.
Still, though, that sounds like what I can do with my 89 :P so I don't know. I guess programs on the 83/84 are legitimate in order to keep up with the 89 capability.

[redhawk2015]

Can someone tell me why the answer to #21 on 2012-B is C and not D? They both appear to be the same to me...

[88bobcat]

Can someone tell me why the answer to #21 on 2012-B is C and not D? They both appear to be the same to me...

They are the same. I believe this is a test-writing error.

[nsguy1350]

Can someone tell me why the answer to #21 on 2012-B is C and not D? They both appear to be the same to me...

I don't remember if this was the one, but I remember there were two correct answer choices for a problem, which I believe to be the one you're talking about.
It has x variables in it, right?

[007math]

#21. Answers C and D are equivalent, hence both are correct. I will be making the change on
answer choice D to be 4x – 5x^2, leaving answer C as the correct answer.

[redhawk2015]

OK, thanks.

Can someone tell me why the answer to #21 on 2012-B is C and not D? They both appear to be the same to me...

I don't remember if this was the one, but I remember there were two correct answer choices for a problem, which I believe to be the one you're talking about.
It has x variables in it, right?

It was an integral problem, one answer choice was factored while the other was equivalent but not factored.