Page 1 of 3 123 LastLast
Results 1 to 25 of 67
Like Tree15Likes

Thread: HSC 2017-2018 Maths Marathon

  1. #1
    Taking a break! dan964's Avatar
    Join Date
    Jun 2014
    HSC
    2014
    Uni Grad
    2018
    Gender
    Male
    Location
    South of here
    Posts
    2,946
    Rep Power
    5

    HSC 2017-2018 Maths Marathon

    Welcome to the 2017 HSC 2U Marathon,

    1. Only post questions within the level and scope of 2U HSC Mathematics.

    2. Provide neat working out when possible

    3. Don't flood the thread with multiple unanswered questions/spam.

    4. Challenging questions that a 2U student can pick up easily are okay, but try to stay within the 2U syllabus content.


    Here is a question I've pulled for you (modified from Ascham 2011 2U trial HSC)

    For the curve
    1. Find the stationary points and determine their nature
    2. Find any points of inflexion
    3. Sketch the graphs showing info from (1) & (2)
    4. When is the curve decreasing with downward concavity?

  2. #2
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,812
    Rep Power
    7

    Re: HSC 2017 Maths (Advanced) Marathon


  3. #3
    Hi Φ Green Yoda's Avatar
    Join Date
    Mar 2015
    HSC
    2017
    Gender
    Male
    Posts
    2,882
    Rep Power
    4

    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by leehuan View Post
    If f(x)=0
    then f(x)=f(-x)
    and f(-x)=-f(x)
    thus being both odd and even
    leehuan likes this.
    HSC 2017: 95.05 | School DUX

    Offering Biology Tutoring (93 HSC MARK) PM ME for details

    WSU Class of 2021
    B Physiotherapy

  4. #4
    Junior Member
    Join Date
    Apr 2016
    HSC
    2017
    Gender
    Undisclosed
    Posts
    212
    Rep Power
    2

    Re: HSC 2017 Maths (Advanced) Marathon

    How would you find all the functions that are both odd and even?

  5. #5
    Rambling Spirit
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    6,073
    Rep Power
    7

    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by frog1944 View Post
    How would you find all the functions that are both odd and even?
    Any (real-valued) function (of a real variable) defined on a symmetric interval (about 0) that is both odd and even must satisfy f(x) = f(-x) = -f(-x) for all x in the domain, which implies f(-x) = 0 for all x in the domain, whence f(x) = 0 for all x in the domain (as the domain is a symmetric interval).

    So the only functions with domain and codomain being subsets of R that are both odd and even are those that are identically 0 on a symmetric domain about 0. (If the domain is not symmetric about 0, we can't really talk about f(x) being equal to f(-x) for all x, which is something we need to do for the function to be even. I guess though you still could by saying that it only matters for x such that x and -x are in the domain. But for HSC purposes, the domain is usually symmetric.)
    Last edited by InteGrand; 15 Oct 2016 at 5:55 PM.

  6. #6
    Ancient Orator
    Join Date
    Nov 2015
    HSC
    N/A
    Gender
    Undisclosed
    Location
    Space
    Posts
    4,156
    Rep Power
    5

    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by frog1944 View Post
    How would you find all the functions that are both odd and even?
    What bout even?

  7. #7
    Taking a break! dan964's Avatar
    Join Date
    Jun 2014
    HSC
    2014
    Uni Grad
    2018
    Gender
    Male
    Location
    South of here
    Posts
    2,946
    Rep Power
    5

    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by dan964 View Post
    For the curve
    1. Find the stationary points and determine their nature
    2. Find any points of inflexion
    3. Sketch the graphs showing info from (1) & (2)
    4. When is the curve decreasing with downward concavity?
    The current question...

  8. #8
    New Member
    Join Date
    Aug 2016
    HSC
    2017
    Gender
    Male
    Posts
    14
    Rep Power
    2

    Re: HSC 2017 Maths (Advanced) Marathon

    y = 3x³-6x²+4x+7
    y’ = 9x²-12x+4

    For S.P.
    y’=0
    9x²-12x+4=0
    x= 2/3 y=71/9
    Therefore S.P. at (2/3 , 71/9)


    For I.P
    y′′=0
    y′′=18x-12
    18x-12=0
    x=2/3 y= 71/9
    Therefore I.P. at (2/3 , 71/9)

    Soz don't have time

  9. #9
    Rambling Spirit
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    6,073
    Rep Power
    7

    Re: HSC 2017 Maths (Advanced) Marathon




  10. #10
    Cadet
    Join Date
    Nov 2015
    HSC
    2017
    Gender
    Male
    Posts
    57
    Rep Power
    3

    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by InteGrand View Post


    Which topic?

  11. #11
    -insert title here- Paradoxica's Avatar
    Join Date
    Jun 2014
    HSC
    2016
    Gender
    Male
    Location
    Outside reality
    Posts
    2,456
    Rep Power
    5

    Re: HSC 2017 Maths (Advanced) Marathon

    A cube is inscribed in a right circular cone of height h and radius r so that one side is coplanar with the base and all four opposite vertices are in contact with the curved surface of the cone.

    Find the side length of the cube in terms of h and r.
    Last edited by Paradoxica; 8 Nov 2016 at 1:04 PM.
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

  12. #12
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,812
    Rep Power
    7

    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by Commando007 View Post
    Which topic?
    When you see terms and sums and what not you should be thinking series.

  13. #13
    Cadet
    Join Date
    Oct 2015
    HSC
    2017
    Gender
    Male
    Posts
    55
    Rep Power
    3

    Re: HSC 2017 Maths (Advanced) Marathon

    Hey guys, how do I go about doing this: find the values of l that will make the quadratic y=(l+6)x^2-2lx+3 a perfect square. And can someone explain what 1/alpha + 1/beta is when doing the roots of a quadratic.

  14. #14
    Hi Φ Green Yoda's Avatar
    Join Date
    Mar 2015
    HSC
    2017
    Gender
    Male
    Posts
    2,882
    Rep Power
    4

    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by dragon658 View Post
    Hey guys, how do I go about doing this: find the values of l that will make the quadratic y=(l+6)x^2-2lx+3 a perfect square. And can someone explain what 1/alpha + 1/beta is when doing the roots of a quadratic.
    The expression is a perfect when the discriminant is rational.

    1/alpha +1/beta = alpha+beta/alpha*beta which is sum of roots/product of roots
    HSC 2017: 95.05 | School DUX

    Offering Biology Tutoring (93 HSC MARK) PM ME for details

    WSU Class of 2021
    B Physiotherapy

  15. #15
    Cadet
    Join Date
    Oct 2015
    HSC
    2017
    Gender
    Male
    Posts
    55
    Rep Power
    3

    Re: HSC 2017 Maths (Advanced) Marathon

    Thanks bro

  16. #16
    Hi Φ Green Yoda's Avatar
    Join Date
    Mar 2015
    HSC
    2017
    Gender
    Male
    Posts
    2,882
    Rep Power
    4

    Re: HSC 2017 Maths (Advanced) Marathon

    Insert three geometric means between 8 and 1/32.
    HSC 2017: 95.05 | School DUX

    Offering Biology Tutoring (93 HSC MARK) PM ME for details

    WSU Class of 2021
    B Physiotherapy

  17. #17
    New Member
    Join Date
    Sep 2016
    HSC
    2016
    Gender
    Undisclosed
    Posts
    19
    Rep Power
    2

    Re: HSC 2017 Maths (Advanced) Marathon

    If I'm interpreting your question correctly:







  18. #18
    Senior Member
    Join Date
    Aug 2016
    HSC
    2018
    Gender
    Undisclosed
    Posts
    571
    Rep Power
    2

    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by dan964 View Post
    Welcome to the 2017 HSC 2U Marathon,

    1. Only post questions within the level and scope of 2U HSC Mathematics.

    2. Provide neat working out when possible

    3. Don't flood the thread with multiple unanswered questions/spam.

    4. Challenging questions that a 2U student can pick up easily are okay, but try to stay within the 2U syllabus content.


    Here is a question I've pulled for you (modified from Ascham 2011 2U trial HSC)

    For the curve
    1. Find the stationary points and determine their nature
    2. Find any points of inflexion
    3. Sketch the graphs showing info from (1) & (2)
    4. When is the curve decreasing with downward concavity?
    I took a photo but apparently it exceeds the size allowed

  19. #19
    -insert title here- Paradoxica's Avatar
    Join Date
    Jun 2014
    HSC
    2016
    Gender
    Male
    Location
    Outside reality
    Posts
    2,456
    Rep Power
    5

    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by boredofstudiesuser1 View Post
    I took a photo but apparently it exceeds the size allowed
    multiple photos *muahaha*
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

  20. #20
    Cadet
    Join Date
    Apr 2015
    HSC
    2016
    Gender
    Male
    Posts
    74
    Rep Power
    3

    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by boredofstudiesuser1 View Post
    I took a photo but apparently it exceeds the size allowed
    Just upload it to imgur or another image hosting site and use the IMG tags

  21. #21
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,812
    Rep Power
    7

    Re: HSC 2017 Maths (Advanced) Marathon

    Last edited by leehuan; 7 Dec 2016 at 3:14 PM.

  22. #22
    New Member
    Join Date
    Sep 2016
    HSC
    2016
    Gender
    Undisclosed
    Posts
    19
    Rep Power
    2

    Re: HSC 2017 Maths (Advanced) Marathon



    If one function, but not both functions, is monotonic decreasing, then the product of their first derivatives will be negative, and so will be monotonic decreasing.
    frog1944 likes this.

  23. #23
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,812
    Rep Power
    7

    Re: HSC 2017 Maths (Advanced) Marathon

    Correct, but small technicality error: Monotone means the inequality isn't necessarily strict (≥)
    Last edited by leehuan; 7 Dec 2016 at 8:29 PM.
    Lugia101101 likes this.

  24. #24
    New Member
    Join Date
    Sep 2016
    HSC
    2016
    Gender
    Undisclosed
    Posts
    19
    Rep Power
    2

    Re: HSC 2017 Maths (Advanced) Marathon

    Thanks for clearing that up; none of my teachers were able to tell me definitively.

  25. #25
    New Member
    Join Date
    Sep 2016
    HSC
    2016
    Gender
    Undisclosed
    Posts
    19
    Rep Power
    2

    Re: HSC 2017 Maths (Advanced) Marathon




Page 1 of 3 123 LastLast

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •