# Cset - Single Subject - Math, Subtest 3 Calculus May 21 2005

Discussion in 'Single Subject Tests' started by s_z, Apr 14, 2005.

1. ### s_zRookie

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Apr 14, 2005   hi every1,

I am studying to the calculus test for May 21.

1)Does anybody want to open a study group in Woodland Hills Area?

2) can anybody show me the solution to this problem?

it's stupid, but I can't solve it:

An fly moves vertically (in inches) along the Y-axis, according to the position equation: s(t)= 1/2(t)^3-5(t)^2+3(t)+6, where t represents seconds. At what time(s) is the position of the fly 30 inches below the origin?

I can't seem to get these answers....can somebody solve this for me? 3) do any of you know if we need to memorize all the trig derivatives?
4) does anybody know if we need to memorize trig angles and their trig numbers?
5) I want to recommend to all of you to use the following books: calculus the easy way, the complete idiots guide to calculus and download the test examples form the website.

Tnx

2. 3. ### lilxdebsRookie

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Apr 18, 2005

with the position 30 inches below the origin, the equation would end up being

-30 = 1/2(t)^3-5(t)^2+3(t)+6

then you would add 30 to both sides to get an equation where you can find the zeros

0 = 1/2(t)^3-5(t)^2+3(t)+36

i then multiplied both sides by 2 so that all coefficients were integers

0 = (t)^3-10(t)^2+6(t)+72

then you solve for the zeros. we know that there are 0 or 2 positive roots and one negative root (by looking at the sign changes of the terms. i don't remember the exact theorem behind it). i used the fact that all roots will be of the form + or - p/q where all p are factors of 72 and all q are factors of 1 (ie the coefficient of the t^3). i forget what theorem that is too...

you can find one of the zeros to be 4, then by synthetic division you are left with t^2-6t-18=0.

using the quadratic formula, you find that positive and negative 3+3(3)^1/2 are roots. obviously the time cannot by negative, therefore the only two solutions left are 4 and positive 3+3(3)^1/2, which is approximately 8.196.

sorry that i forget all the theorems i stated. i know the concepts but the name of each eludes me at this time. i'm taking the subtest III in may too but sorry, woodland hills is a bit too far for me. good luck to you, though.

4. ### s_zRookie

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Apr 18, 2005

so, how do I get from 0 = (t)^3-10(t)^2+6(t)+72 To t^2-6t-18=0
I was trying to use Cardano Formula but I am not sure that's what you mean. Can you be more specific?
What book are you using? We can compare notes through here or through my Email...I can't seem to get any resolution from my family or friends. I guess that with math I am on my own.

E-mail: ziv@affordablecaviar.com

5. ### s_zRookie

Joined:
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Apr 18, 2005

hi every1,

I am studying to the calculus test for May 21.

1)Does anybody want to open a study group in Woodland Hills Area?

2) can anybody show me the solution to this problem?

it's stupid, but I can't solve it:

An fly moves vertically (in inches) along the Y-axis, according to the position equation: s(t)= 1/2(t)^3-5(t)^2+3(t)+6, where t represents seconds. At what time(s) is the position of the fly 30 inches below the origin?

I can't seem to get these answers....can somebody solve this for me?

3) do any of you know if we need to memorize all the trig derivatives?
4) does anybody know if we need to memorize trig angles and their trig numbers?
5) I want to recommend to all of you to use the following books: calculus the easy way, the complete idiots guide to calculus and download the test examples form the website.

Tnx

6. ### lilxdebsRookie

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Apr 18, 2005

i've figured out all the theorems and concepts i'm using so let me try this again.

since you understand how to get to 0 = (t)^3-10(t)^2+6(t)+72, i'll start from there.

we know by the RATIONAL ROOT THEOREM, that the zeros of this function (t)^3-10(t)^2+6(t)+72 are quotients of the form p/q (with some further complications that i'm not going to go into). all possible values for p are the factors (positive and negative) of 72, the constant, and all possible values for q are the factors (positive and negative) of 1, the coefficient of our term of highest degree.

using DESCARTES' RULE OF SIGNS, we can see that there are either 0 or 2 positive roots. we can also find that there is exactly one negative root.

by trial and error, using SYNTHETIC DIVISION, you can find that 4 is a zero. therefore, you end up with the factorization of
(t-4)(t^2-6t-18)=0

if you multiplied this out, you would get the original equation of
0 = (t)^3-10(t)^2+6(t)+72

going from there, you can see that t=4 is a root and that t^2-6t-18 is not easily factored. so we use the QUADRATIC FORMULA. we then end up with
t=3+3(3)^1/2
and
t = -(3+3(3)^1/2) = -3 - 3(3)^1/2

we quickly discard the second because the time will not be negative. therefore, we're left with the roots of 4 and 3+3(3)^1/2. or using decimal form, 4 and 8.196.

i have no idea what the cardano formula is so i can't help you with that. i believe that this is the more traditional way of solving this formula, however. for more explanations on the theorems and concepts i stated, you can easily google them. sorry, it's difficult to write it out.

to study, i'm using my friend's old AP calculus Barron's book. this information, though, you can find in schaum's precalculus outline, which i used for subtest I. I also have a stewart's calculus book to study. but mainly i'm going off of the barron's right now. hope this all helps.

7. ### s_zRookie

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Apr 19, 2005

Great ! Thanks. I will check it out because I remember other formulas that do not work.

anyway, I will check Barron's book also.

You should try the the complete idiots guide to calculus , It's not bad if you are working all day and falling asleep on books at night. the book is very cozzy, I fall asleep on it every night.

Do you have any knoledge about what should I focus on while studying?

8. ### lilxdebsRookie

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Apr 19, 2005

i'm just using the study guide outlines that you can find on the cset website. i use those to study, then i take their practice problems like a test, and then i go back and look at all the concepts where i'm a little weak.

9. ### s_zRookie

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Apr 19, 2005

If you have any other things you want to ask maybe I can help.

I am just getting used to the English terms. I graduated in Europe and there they use a different kind of math curriculum.

There are methods I use and they don't even teach it here.

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Apr 19, 2005

11. ### mike 1143Rookie

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May 4, 2005

I just visited the purplemath site. I am studying for Subtest 1 SS Math, and found a few links that were helpful. I also found a link that I have bookmarked for Subtest 2.

BTW, I invested \$49.99 in acethecset for math, and found it a disappointment. It was the most recommended math prep I heard of. It was interesting to find the discussion on the number theory to be word for word identical to Wikipedia. The quizzes were an order of magnitude easier than the sample test on the CSET site, and the format they use (small portion of screen) made the proofs hard to follow. Overall, I think I got what I paid for, but nothing more.

Mike