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    A-levelish.
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    http://www.madasmaths.com/archive/iy...apers/sp_z.pdf
    enjoy
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    Idk what is challenging for you

    Here's one that's probably too easy, prove that n^3 - n is divisible by 6 for n a natural number
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    omg nerd alert
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    Try some UKMT senior past paper questions (Qs 20-25)
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    (Original post by driftawaay)
    omg nerd alert
    omg moron alert
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    (Original post by Awesome Genius)
    omg moron alert
    omg you are ignore listed alert
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    (Original post by driftawaay)
    omg nerd alert
    I see you on virtually every post on TSR. What are you doing with your life? Your profile picture suggests a lot, but I don't want to judge..
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    (Original post by multiratiunculae)
    I see you on virtually every post on TSR. What are you doing with your life? Your profile picture suggests a lot, but I don't want to judge..
    What does it suggest?
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    (Original post by 13 1 20 8 42)
    Idk what is challenging for you

    Here's one that's probably too easy, prove that n^3 - n is divisible by 6 for n a natural number
    Does the proof involve logs?
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    (Original post by driftawaay)
    What does it suggest?
    Your age, firstly (14 perhaps).
    The immature colours also speak a thousand words.
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    (Original post by multiratiunculae)
    Your age, firstly (14 perhaps).
    The immature colours also speak a thousand words.
    Why does my picture make me seem like I am 14?

    Also, how can a color be immature? Do colors have maturity levels?
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    (Original post by OneDayIwill)
    Does the proof involve logs?
    The method of using proof by induction doesn't
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    (Original post by driftawaay)
    Why does my picture make me seem like I am 14?

    Also, how can a color be immature? Do colors have maturity levels?
    No, but a mature person wouldn't stick rainbow colours on their profile picture, would they? You'd look older without them..

    ANYWAY; DOES ANYBODY HAVE OTHER DECENT MATHS PROBLEMS?
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    Question 10. Hints?
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    (Original post by OneDayIwill)
    Does the proof involve logs?
    I don't think logs are helpful for it. Induction works but is not the quickest. Just factorization and some common sense considerations about the integers.
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    (Original post by multiratiunculae)
    No, but a mature person wouldn't stick rainbow colours on their profile picture, would they? You'd look older without them..

    ANYWAY; DOES ANYBODY HAVE OTHER DECENT MATHS PROBLEMS?
    Why you ignoring the posted ones? Too tough?
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    1+1
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    (Original post by multiratiunculae)
    A-levelish.
    I did this problem in my STEP exam this summer. It's really good fun and I'm sure you'll enjoy it.

    Given that;

     sec^2 \bigg( \dfrac{1}{4} \pi - \dfrac{1}{2}x \bigg) = \dfrac{2}{1 + sin(x)}

    and

     \displaystyle \int_{0}^{\pi} xf(sinx) dx = \dfrac{\pi}{2} \displaystyle \int_{0}^{\pi} f(sinx) dx


    Evaluate  \displaystyle \int_{0}^{\pi} \dfrac{x}{1+ sinx} dx


    and  \displaystyle \int_{0}^{\pi} \dfrac{2x^3 - 3 \pi x^2}{(1+ sinx)^2} dx
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    (Original post by multiratiunculae)
    No, but a mature person wouldn't stick rainbow colours on their profile picture, would they? You'd look older without them..

    ANYWAY; DOES ANYBODY HAVE OTHER DECENT MATHS PROBLEMS?
    Poor ivybridge and all those people on FB with their rainbow profile pictures...so many 14 year olds

    And poor you for thinking the animated non existent person in my profile picture is me. Embarrassing.
 
 
 
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