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Thread: Cambridge Prelim MX1 Textbook Marathon/Q&A

  1. #101
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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by DatAtarLyfe View Post
    Can't you just let x->infinity, making the y values ->x^2, instead of doing all the algebra above
    You can

    I was taught this way though ~

    (I can do all the algebra in my head but I posted it for OP's sake)
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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by Crisium View Post
    You can

    I was taught this way though ~

    (I can do all the algebra in my head but I posted it for OP's sake)
    cool, just confirming
    I am rather fond of a sizeable Gluteus Maximus and I am incapable of uttering a falsehood

    Quote Originally Posted by Carrotsticks View Post
    I too enjoy sliding up and down smooth vertical poles and creating lots of tension.

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Why is it the highest power of x in the denominator , i thought it was just the highest power in either the numerator or denominator?

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by appleibeats View Post
    Why is it the highest power of x in the denominator , i thought it was just the highest power in either the numerator or denominator?
    It's because your are trying to get rid of the pronumeral in the denominator before you let x-> infinity
    I am rather fond of a sizeable Gluteus Maximus and I am incapable of uttering a falsehood

    Quote Originally Posted by Carrotsticks View Post
    I too enjoy sliding up and down smooth vertical poles and creating lots of tension.

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    For 5)i

    y = (x+1)^3/ x

    i know there is a vertical asymptote of x = 0

    But is there an horizontal asymptote.

    I expanded the numerator and did lim x ---> infinity

    and get x^2 + 3x + 3.....

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Yes, as x tends to , y values will tend to . Note that what we are trying to find is a curve which 'bounds' the graph of f. This is only just for graphical purposes. It is not correct to say since the expression on the LHS still means that y tends on infinity as you increase x. Graphically, however, it will be 'bounded' off by which becomes our oblique (parabolic) asymptote.
    Last edited by VBN2470; 8 Jul 2015 at 6:54 PM.
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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by appleibeats View Post
    For 5)i

    y = (x+1)^3/ x

    i know there is a vertical asymptote of x = 0

    But is there an horizontal asymptote.

    I expanded the numerator and did lim x ---> infinity

    and get x^2 + 3x + 3.....
    In other words, a 'parabolic asymptote'.
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  8. #108
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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by appleibeats View Post
    For 5)i

    y = (x+1)^3/ x

    i know there is a vertical asymptote of x = 0

    But is there an horizontal asymptote.

    I expanded the numerator and did lim x ---> infinity

    and get x^2 + 3x + 3.....
    Just keep in mind these general rules when your trying to identify what kind of asymptotes exist:
    1/ If the highest power of x in the denominator = the highest power of x in the numerator, then you have a horizontal asymptote
    2/ If the highest power of x in the denominator < the highest power of x in the numerator (BY ONE), then you have an oblique asymptote
    3/ If the highest power of x in the denominator < the highest power of x in the numerator (BY TWO OR MORE), then you have another graph as an asymptote

    So in your case, the highest power in numerator was 3 and highest power in denominator was 1, thus you have a parabolic asymptote
    Last edited by DatAtarLyfe; 8 Jul 2015 at 7:27 PM.
    I am rather fond of a sizeable Gluteus Maximus and I am incapable of uttering a falsehood

    Quote Originally Posted by Carrotsticks View Post
    I too enjoy sliding up and down smooth vertical poles and creating lots of tension.

  9. #109
    Ancient Orator leehuan's Avatar
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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    The graph of y=(x+1)^3/x in red

    And it's parabolic asymptote in black.

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  10. #110
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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    I never learnt how to do Pascals triangle, will I ever need it in 2U and or 3U in Year 12?

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by Speed6 View Post
    I never learnt how to do Pascals triangle, will I ever need it in 2U and or 3U in Year 12?
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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by Drongoski View Post
    3U
    Ok thanks Drongoski, one last question, is this something which I can learn independently or will I need a teacher to guide me through it? Also, is it something which can be learnt in one day?

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    The Pascal Triangle itself is dead easy; nothing to it. But if you are talking about the many interesting properties associated with it, that requires a bit more algebra.
    Last edited by Drongoski; 8 Jul 2015 at 11:33 PM.
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  14. #114
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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Pascal's triangle is more of a reference point to begin the binomial theorem topic. It's not a major part in the syllabus.

    1 (this is called the '0th' row)
    1 1
    1 2 1
    1 3 3 1
    1 4 6 4 1
    1 5 10 10 5 1
    1 6 15 20 15 6 1
    etc.

    For the binomial theorem, what's interesting is that the expansion of (1+x)^n, the coefficients match up the nth row of Pascal's triangle. Also, Pascal's triangle can be written in combinations. It might also be worth mentioning that the sum of the coefficients on each row is 2^n. Besides that you don't really need much more for MX1.

  15. #115
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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    How do you do question 3 a in exercise 7D?
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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    so the question is y = x^2 1/2

    so make it an improper fraction

    y = x^5/2

    then it simply:

    y' = 5/2 x^ 3/2 which = 5/2 x^ 1 1/2

    you bring down the 5/2 and minus 1 from the power.

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    for question 6a from 10F

    y = x^(1/2) + 1/x^(1/2)

    i don't understand why the curve flattens out as x ---> + infinity?

    why is it not a parabola shape?

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by appleibeats View Post
    for question 6a from 10F

    y = x^(1/2) + 1/x^(1/2)

    i don't understand why the curve flattens out as x ---> + infinity?

    why is it not a parabola shape?
    VBN2470 and DatAtarLyfe like this.

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    How do you find the focus length of the parabola x^2 = 28/5y

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by appleibeats View Post
    How do you find the focus length of the parabola x^2 = 28/5y
    I take it to mean: x^2 = (28/5)y

    In that case simply express in the form: x2 = 4ay

    For this question: x^2 = 4* (7/5)*y

    so, the focal length(not focus length) "a" is 7/5.
    Last edited by Drongoski; 9 Jul 2015 at 2:56 PM.
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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by Drongoski View Post
    I take it to mean: x^2 = (28/5)y

    In that case simply express in the form: x2 = 4ay

    For this question: x^2 = 4* (7/5)*y

    so, the focal length "a" is 7/5.
    Lol, i was right but deleted my post cause i was like "wait wtf, it's 28/5y"
    I am rather fond of a sizeable Gluteus Maximus and I am incapable of uttering a falsehood

    Quote Originally Posted by Carrotsticks View Post
    I too enjoy sliding up and down smooth vertical poles and creating lots of tension.

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    i though the focus length was the distance from the vertex and the focus.

    I got the focus was (0,7/5)

    and the vertex ( 14/5, 7/5)

    so I got the focus length = 14/5

    Where did i go wrong?

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by DatAtarLyfe View Post
    Lol, i was right but deleted my post cause i was like "wait wtf, it's 28/5y"
    sorry about not making it clear

  24. #124
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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    For , vertex is , focus is , hence focal length is .

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by appleibeats View Post
    i though the focus length was the distance from the vertex and the focus.

    I got the focus was (0,7/5)

    and the vertex ( 14/5, 7/5)

    so I got the focus length = 14/5

    Where did i go wrong?
    Your vertex is incorrect. If you look at your original equation, x^2=28/5y, your vertex is actually (0,0)
    To determine the vertex from your equation, you use the standard equation (x-h)^2=4a(y-k), where (h,k) is your vertex. So in your equation, h=0, k=0 and 4a=28/5
    Hence your vertex is (0,0), your focal length is 7/5 and thus your focus is (0,7/5)
    I am rather fond of a sizeable Gluteus Maximus and I am incapable of uttering a falsehood

    Quote Originally Posted by Carrotsticks View Post
    I too enjoy sliding up and down smooth vertical poles and creating lots of tension.

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