# Math Help - Math B Regents Multiple Choice Questions

1. ## Math B Regents Multiple Choice Questions

I'm doing review for the MAth B Regents as some of you know and there were a couple in the multiple choice section i just didn't get. Here is the link to the the answers:http://www.nysedregents.org/testing/mathre/b-key605.pdf
And here is the link to the questions:http://www.nysedregents.org/testing/mathre/b605.pdf

I just need to know the work necessary to figure out these problems. The numbers i need help in are 4,12,13,15,16, and 20. Thanks guys.

2. Originally Posted by badandy328
I'm doing review for the MAth B Regents as some of you know and there were a couple in the multiple choice section i just didn't get. Here is the link to the the answers:http://www.nysedregents.org/testing/mathre/b-key605.pdf
And here is the link to the questions:http://www.nysedregents.org/testing/mathre/b605.pdf

I just need to know the work necessary to figure out these problems. The numbers i need help in are 4,12,13,15,16, and 20. Thanks guys.
Didn't you post this paper already? why didn't you ask to do these questions in the last post?

4)

$\frac {x^2 - 9x}{45x - 5x^2}$ ....what are the largest common factors in the top and bottom? pull them out

$= \frac {x(x - 9)}{5x(9 - x)}$

$= \frac {x - 9}{5(9 - x)}$

do you think you could take it from here?

3. Originally Posted by badandy328
I'm doing review for the MAth B Regents as some of you know and there were a couple in the multiple choice section i just didn't get. Here is the link to the the answers:http://www.nysedregents.org/testing/mathre/b-key605.pdf
And here is the link to the questions:http://www.nysedregents.org/testing/mathre/b605.pdf

I just need to know the work necessary to figure out these problems. The numbers i need help in are 4,12,13,15,16, and 20. Thanks guys.
The formula for the equation of an ellipse is $\frac {(x - h)^2}{a^2} + \frac {(y - k)^2}{b^2} = 1$

the choice is obvious here, there is only one choice that resembles that form

4. Originally Posted by badandy328
I'm doing review for the MAth B Regents as some of you know and there were a couple in the multiple choice section i just didn't get. Here is the link to the the answers:http://www.nysedregents.org/testing/mathre/b-key605.pdf
And here is the link to the questions:http://www.nysedregents.org/testing/mathre/b605.pdf

I just need to know the work necessary to figure out these problems. The numbers i need help in are 4,12,13,15,16, and 20. Thanks guys.
13)

for this you need to remember that $i^2 = -1$

$\frac {2 + i}{3 + i} = \frac {2 + i}{3 + i} \cdot \frac {3 - i}{3 - i}$ ...rationalize the denomenator

......... $= \frac {6 + i - i^2}{9 - i^2}$

......... $= \frac {6 + i - (-1)}{9 - (-1)}$

......... $= \frac {7 + i}{10}$

5. This should make it a bit more easy for us to help you.

4. Written in simplest form, the expression $\frac{x^2-9x}{45x-5x^2}$ is equivalent to:

12. Which equation, when graphed on a Cartesian coordinate plane, would best represent an elliptical racetrack?
(1) $3x^2 + 10y^2 = 288,000$
(2) $3x^2-10y^2=288,000$
(3) $3x+10y=288,000$
(4) $30xy=288,000$

13. The expression $\frac{2+i}{3+i}$ is equivalent to:

15. A crate weighing $w$ pounds sits on a ramp positioned at an angle $\theta$ with the horizontal. The forces acting on this crate are modeled by the equation $Mw\cos\theta = w\sin \theta$, where $M$ is the coefficient of friction. What is an expression for M in terms of $\theta$?
(1) $M=\tan \theta$
(2) $M=\cot \theta$
(3) $M=\sec \theta$
(4) $M=\csc \theta$

16. If $(a^x)^\frac{2}{3}=\frac{1}{a^2}$, what is the value of x?

20. In the accompanying diagram, $\overline {PR}$ is tangent to circle $O$ at $R$, $\overline {QS} \perp \overline{OR}$, and $\overline{PR}\perp\overline{OR}$. What measure represents $sin\theta$?

[btw, I'm bored.]

6. Originally Posted by badandy328
I'm doing review for the MAth B Regents as some of you know and there were a couple in the multiple choice section i just didn't get. Here is the link to the the answers:http://www.nysedregents.org/testing/mathre/b-key605.pdf
And here is the link to the questions:http://www.nysedregents.org/testing/mathre/b605.pdf

I just need to know the work necessary to figure out these problems. The numbers i need help in are 4,12,13,15,16, and 20. Thanks guys.
i'm a bit rusty on number 15) i think i'll come back to it, if someone doesn't answer it

16)
$\left( a^x \right)^{ \frac {2}{3}} = \frac {1}{a^2}$

when we raise a base with a power to another power, we multiply the powers.

1 over something is the inverse of the something, we undo it by taking the negative of the power of the base

$\Rightarrow a^{ \frac {2x}{3}} = a^{-2}$

equating the powers we obtain.

$\frac {2x}{3} = -2$

$\Rightarrow x = -3$

7. Originally Posted by ecMathGeek
15. A crate weighing $w$ pounds sits on a ramp positioned at an angle $\theta$ with the horizontal. The forces acting on this crate are modeled by the equation $Mw\cos\theta = w\sin \theta$, where $M$ is the coefficient of friction. What is an expression for M in terms of $\theta$?
(1) $M=\tan \theta$
(2) $M=\cot \theta$
(3) $M=\sec \theta$
(4) $M=\csc \theta$
Since $Mwcos\theta=wsin\theta$, dividing by $wcos\theta$, we get:

$M=tan\theta$, which is answer (1).

8. Originally Posted by badandy328
I'm doing review for the MAth B Regents as some of you know and there were a couple in the multiple choice section i just didn't get. Here is the link to the the answers:http://www.nysedregents.org/testing/mathre/b-key605.pdf
And here is the link to the questions:http://www.nysedregents.org/testing/mathre/b605.pdf

I just need to know the work necessary to figure out these problems. The numbers i need help in are 4,12,13,15,16, and 20. Thanks guys.
20)

Okay, again i think i'm thinking too hard about this, but here is the way i see to do it. (save me ecMathGeek if it's too much work).

$\sin(180 - \theta) = \frac {QS}{QO}$ ............ $180 - \theta$ is the angle under line $QO$

remember, $QO = 1$

So, $\sin (180 - \theta) = QS$

Now $\sin (180 - \theta) = \sin ( \theta)$ ....but let's prove this

$\sin (180 - \theta) = \sin (180) \cos ( \theta) - \sin ( \theta) \cos (180) = QS$

$\Rightarrow 0 + \sin ( \theta) = QS$

$\Rightarrow \sin ( \theta) = QS$

9. Originally Posted by Jhevon
20)

Okay, again i think i'm thinking too hard about this, but here is the way i see to do it. (save me ecMathGeek if it's too much work).

$\sin(180 - \theta) = \frac {QS}{QO}$ ............ $180 - \theta$ is the angle under line $QO$

remember, $QO = 1$

So, $\sin (180 - \theta) = QS$

Now $\sin (180 - \theta) = \sin ( \theta)$ ....but let's prove this

$\sin (180 - \theta) = \sin (180) \cos ( \theta) - \sin ( \theta) \cos (180) = QS$

$\Rightarrow 0 + \sin ( \theta) = QS$

$\Rightarrow \sin ( \theta) = QS$
You did it as easily as it can be done, with the exception that you demonstrated why your answer is true.

10. I said it once and I'll say it again, YOU GUYS ARE THE BEST!!!! The reason why i didn't ask this in the last topic about the Math B Regents is becuase I was afraid Perfect Hacker would give me an infraction to add to my collection for begging or something like that. I tend to get a lot of those. Anyway thanks again.