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Math Help - 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)

    \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?
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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 \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 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}
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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 \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.]
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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)
    \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
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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 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).
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  8. #8
    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).

    \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
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  9. #9
    Senior Member ecMathGeek's Avatar
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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).

    \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.
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  10. #10
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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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