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Thread: Math B Regents Multiple Choice Questions

  1. #1
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    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.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by badandy328 View Post
    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)

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

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

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

    do you think you could take it from here?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by badandy328 View Post
    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 $\displaystyle \frac {(x - h)^2}{a^2} + \frac {(y - k)^2}{b^2} = 1$

    the choice is obvious here, there is only one choice that resembles that form
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by badandy328 View Post
    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 $\displaystyle i^2 = -1$

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

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

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

    .........$\displaystyle = \frac {7 + i}{10}$
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  5. #5
    Senior Member ecMathGeek's Avatar
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    This should make it a bit more easy for us to help you.

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

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

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

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

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

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

    [btw, I'm bored.]
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by badandy328 View Post
    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)
    $\displaystyle \left( a^x \right)^{ \frac {2}{3}} = \frac {1}{a^2}$

    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

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

    equating the powers we obtain.

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

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

    $\displaystyle M=tan\theta$, which is answer (1).
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by badandy328 View Post
    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).

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

    remember, $\displaystyle QO = 1$

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

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

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

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

    $\displaystyle \Rightarrow \sin ( \theta) = QS$
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  9. #9
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    Quote Originally Posted by Jhevon View Post
    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).

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

    remember, $\displaystyle QO = 1$

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

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

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

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

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