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I need help with the following Math questions!!

feodornfeodorn Registered User Posts: 16 New Member
edited May 2011 in SAT Preparation
Improve Your SAT Scores with the SAT Skills Insight (why is it negative...?)
Improve Your SAT Scores with the SAT Skills Insight

I need a thorough explanation for the second one, please.
Post edited by feodorn on
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Replies to: I need help with the following Math questions!!

  • ProjectAmericaProjectAmerica Registered User Posts: 35 Junior Member
    1.

    it is negative because the slope is (y2-y1)/(x2-x1)
    let r=4=y1 and s=5=x2
    than, (0-4)/(5-0) is -4/5, which equals -r/s
    you can tell if the slope is negative if it falls down to the right side, if it rises to the right side it is alway positive

    btw i don't know the second one :D
  • wittynicknamewittynickname Registered User Posts: 99 Junior Member
    2. E

    There are two strategies for 2.

    The first, more obvious is to factor each equation to find which one doesn't have x-1 as a factor

    The second is much faster, but a little harder to notice.
    If (x-k) is a factor of f(x), then f(k)=0. So, simply substitute 1 for x (make sure you realize it's the opposite of the number given, if it had said x+1, you would substitute -1)
    All of them will equal 0 except e.

    BTW this is a late ALG 1, early ALG 2 concept, if you need a more thorough explanation, I can explain it more in detail.
  • feodornfeodorn Registered User Posts: 16 New Member
    Oh, I see. Subtracting the coordinates gives you negative, duh.

    "btw i don't know the second one"

    Let's hope someone else does. :p
  • feodornfeodorn Registered User Posts: 16 New Member
    @witty

    You've lost me there with the function. More details would be good.
  • feodornfeodorn Registered User Posts: 16 New Member
    And here is a simple one I forgot how to do: Improve Your SAT Scores with the SAT Skills Insight

    Also, which angle rules are needed to solve this?
  • wittynicknamewittynickname Registered User Posts: 99 Junior Member
    Have you had Alg. 2, I can explain the concept, but it would help if I knew how much math experience you have
  • wittynicknamewittynickname Registered User Posts: 99 Junior Member
    For the angle one, remember that a triangle must have 180 total degrees.

    The large triangle is isoceles, so you know that both base angles are equal.
    180-40(the given angle)=140
    since both angles are equal, divide by 2
    140/2=70

    Now you know both base angles are 70. Now work with the angle bisectors. The base angles of the smaller triangle must both = 35 because 70/2=35.

    Now subtract those two angles from 180 to get 110.
    180-35-35=110 answer a
  • feodornfeodorn Registered User Posts: 16 New Member
    @witty Not much, but explain it in as many ways as you could if you have time. :P
  • wittynicknamewittynickname Registered User Posts: 99 Junior Member
    Ok, quadratic equations (in this case parabolas) are are equations where variables (x) are raised to the power of 2.

    In high school algebra, you will probably work mainly with parabolas, which are shaped like u's

    When you have a quadratic function, it means y=ax^2+bx+c
    where a, b, and c are coefficients, which will be given.
    (In answer choice A, a=1, b=-3, and c=2)

    When dealing with parabolas the main characteristics looked at are the vertex (bottom of the u if a is positive, top of the upsidedown u if a is negative)



    Note: I'm just splitting it so I can know how much you need to know
  • wittynicknamewittynickname Registered User Posts: 99 Junior Member
    A google image search will show you what parabolas look like.

    Due to the shape of a parabola, their graphs have the potential to pass through the x-axis 0 times or 2 times.
    When it passes through 0 times you deal with complex numbers (numbers involving i - I don't think they appear on the SAT)
    When it passes through twice, you can calculate its intercepts
  • wittynicknamewittynickname Registered User Posts: 99 Junior Member
    Finding the intercepts requires a process called factoring, which writes the equation as a product of two binomials, instead of the sum of three terms.

    ex. (2x+1)(x+1)=2x^2 + 3x + 1
  • feodornfeodorn Registered User Posts: 16 New Member
    Yes, I see. Thank you. I could also just quickly do the factoring on a ti-89 and compare.

    And I got up to the 70 degree angle step, but wasn't sure how to proceed. Thanks again.
  • wittynicknamewittynickname Registered User Posts: 99 Junior Member
    Mastering factoring can require lots of practice for some, and is a confusing concept at first.

    When factoring a quadratic equation, check if a is positive. If it is negative, multiply both sides of the equation by negative 1.

    ex. -3x^2 +2x +2 ----> 3x^2-2x-2

    next, list the factors a across from the factors of c, ignoring negatives
    ex. x^2 + 2x + 1
    -factors of a= 1,1
    -factors of c=1,1

    Now at this point, it gets tricky, and many different circumstances can happen, I will show you a simplified version.

    set up two sets of parenthesis so that you have (?x+?)(?x+?).
    Factors of a will be the question marks next to x, and factors of c will be question marks after the +. Our example limits the choices, making it much easier
    so in our example x^2 + 2x + 1 = (x+1)(x+1)
  • wittynicknamewittynickname Registered User Posts: 99 Junior Member
    The way factoring ties into the problem is when you calculate intercepts.

    If y=0 then it is an x intercept AND one of the two terms in the equation written as a product(factored) must equal 0 - (0 times anything will equal 0)
    So each part of the factored equation can be set equal to 0 and then solved for x
    (x+1)(X+1)=0
    x+1=0
    x=-1

    The SAT problem is just giving you the reverse. If you know that x-1 is a factor, then you know that y=0 when x=1 (the sign changes when you solve for x). When you substitute 1 into the problem, if it doesn't equal 0, then you know that x-1 isn't a factor, and therefore, the choice you are looking for
  • feodornfeodorn Registered User Posts: 16 New Member
    I see. Thanks a lot!

    Now how do you figure out something like this in a timely manner
    Improve Your SAT Scores with the SAT Skills Insight
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