Page 1 of 2 12 LastLast
Results 1 to 25 of 40
Like Tree9Likes

Thread: HSC 2018 MX2 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
    2,774
    Rep Power
    4

    HSC 2018 MX2 Marathon

    Welcome to the 2018 Maths Ext 2 Marathon

    Post any questions within the scope and level of Mathematics Extension 2. Once a question is posted, it needs to be answered before the next question is raised.
    This thread is mainly targeting Q1-15 difficulty in the HSC.

    Q16/Q16+ material to be posted here:
    HSC 2017-2018 MX2 Marathon ADVANCED

    I encourage all current HSC students in particular to participate in this marathon.

    Have fun ^_^

    Note: For quick access to previous year's marathons:
    http://community.boredofstudies.org/...urce-list.html

    Unanswered question from 2017 marathon:
    Quote Originally Posted by Sy123 View Post







  2. #2
    This too shall pass Sy123's Avatar
    Join Date
    Nov 2011
    HSC
    2013
    Gender
    Male
    Posts
    3,732
    Rep Power
    7

    Re: HSC 2018 MX2 Marathon

    Last edited by Sy123; 18 Oct 2017 at 4:59 PM.

  3. #3
    New Member
    Join Date
    Aug 2016
    HSC
    2018
    Gender
    Male
    Posts
    7
    Rep Power
    1

    Re: HSC 2018 MX2 Marathon

    i) x^2+y^2=1

    ii) x^2+(y-im(z))^2=1

    I've probably misinterpreted the question given it does seem overly simple

  4. #4
    This too shall pass Sy123's Avatar
    Join Date
    Nov 2011
    HSC
    2013
    Gender
    Male
    Posts
    3,732
    Rep Power
    7

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by TheZhangarang View Post
    i) x^2+y^2=1

    ii) x^2+(y-im(z))^2=1

    I've probably misinterpreted the question given it does seem overly simple
    I made a typo in writing the first question, it should be fixed now. Your second answer however has a 'z' there but this is not a proper cartesian equation for the locus, you want only 'x's and 'y's

  5. #5
    Executive Member
    Join Date
    Jul 2014
    HSC
    2017
    Gender
    Female
    Location
    SYD
    Posts
    1,683
    Rep Power
    4

    Re: HSC 2018 MX2 Marathon

    Are there answers to Sydney Boys 2002 4u trial? Thanks

  6. #6
    Taking a break! dan964's Avatar
    Join Date
    Jun 2014
    HSC
    2014
    Uni Grad
    2018
    Gender
    Male
    Location
    South of here
    Posts
    2,774
    Rep Power
    4

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by si2136 View Post
    Are there answers to Sydney Boys 2002 4u trial? Thanks
    https://thsconline.github.io/s/?view...002%20w.%20sol
    si2136 likes this.
    2014 HSC
    2015 Gap Year
    2016-2018 UOW Bachelor of Maths/Maths Advanced.

    Links:
    View English Notes (no download). Purchase a downloadable/printable copy on SELLFY here + Year 10 notes
    Maths Notes - Free Sample
    Chemistry Notes Sample + Buy (soon)

    thsconline: https://thsconline.github.io/s/ (2017 papers uploaded)

  7. #7
    Cadet
    Join Date
    Oct 2015
    HSC
    2018
    Gender
    Female
    Posts
    55
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    if (x+iy)(a+ib) = b+ia, express x,y in terms of a,b
    thank you!!

  8. #8
    Taking a break! dan964's Avatar
    Join Date
    Jun 2014
    HSC
    2014
    Uni Grad
    2018
    Gender
    Male
    Location
    South of here
    Posts
    2,774
    Rep Power
    4

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by sssona09 View Post
    if (x+iy)(a+ib) = b+ia, express x,y in terms of a,b
    thank you!!
    expand
    (xa-by) +(ay+bx)i=b+ia
    equate real and complex and solve simulataneously for x,y
    sssona09 likes this.
    2014 HSC
    2015 Gap Year
    2016-2018 UOW Bachelor of Maths/Maths Advanced.

    Links:
    View English Notes (no download). Purchase a downloadable/printable copy on SELLFY here + Year 10 notes
    Maths Notes - Free Sample
    Chemistry Notes Sample + Buy (soon)

    thsconline: https://thsconline.github.io/s/ (2017 papers uploaded)

  9. #9
    Cadet
    Join Date
    Oct 2015
    HSC
    2018
    Gender
    Female
    Posts
    55
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by dan964 View Post
    expand
    (xa-by) +(ay+bx)i=b+ia
    equate real and complex and solve simulataneously for x,y
    ohh thank you

  10. #10
    Cadet
    Join Date
    Oct 2015
    HSC
    2018
    Gender
    Female
    Posts
    55
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    find x,y if
    2z/(1+i) - 2z/i = 5/(2+i)

    can't seem to get it,, do I sub x+iy later

  11. #11
    Executive Member
    Join Date
    Jul 2014
    HSC
    2017
    Gender
    Female
    Location
    SYD
    Posts
    1,683
    Rep Power
    4

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by sssona09 View Post
    find x,y if
    2z/(1+i) - 2z/i = 5/(2+i)

    can't seem to get it,, do I sub x+iy later
    You could if you want to. Rationalise denominator and then solve for it by equating real and imaginary parts
    sssona09 likes this.

  12. #12
    Cadet
    Join Date
    Oct 2015
    HSC
    2018
    Gender
    Female
    Posts
    55
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by si2136 View Post
    You could if you want to. Rationalise denominator and then solve for it by equating real and imaginary parts
    oh okay thanks

  13. #13
    Cadet
    Join Date
    Oct 2015
    HSC
    2018
    Gender
    Female
    Posts
    55
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    E+ni is a root for ax2+bx+c=0
    where a and b and c are real
    show that an^2 =aE^2 + bE +c

    so I figured that the other root is E-ni but I've tried using product of roots, but can't seem to prove this :/

  14. #14
    Junior Member 1729's Avatar
    Join Date
    Jan 2017
    HSC
    2018
    Gender
    Male
    Location
    Sydney
    Posts
    154
    Rep Power
    1

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by sssona09 View Post
    E+ni is a root for ax2+bx+c=0
    where a and b and c are real
    show that an^2 =aE^2 + bE +c

    so I figured that the other root is E-ni but I've tried using product of roots, but can't seem to prove this :/
    sssona09 likes this.

  15. #15
    Cadet
    Join Date
    Oct 2015
    HSC
    2018
    Gender
    Female
    Posts
    55
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by 1729 View Post
    Ahh thank you!!!!!!!!!!

  16. #16
    Cadet
    Join Date
    Oct 2015
    HSC
    2018
    Gender
    Female
    Posts
    55
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    how do i divide x^3-2-2i by x+1-i

  17. #17
    Junior Member Sp3ctre's Avatar
    Join Date
    Nov 2016
    HSC
    2017
    Gender
    Male
    Location
    NSW
    Posts
    174
    Rep Power
    1

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by sssona09 View Post
    how do i divide x^3-2-2i by x+1-i
    It's the same as any long division, but just treat -2-2i and 1-i each as one term.
    sssona09 likes this.
    HSC 2017: English Adv - Maths Ext 1 - Maths Ext 2 - Chemistry - Physics
    ATAR Aim: 97.30

  18. #18
    Cadet
    Join Date
    Oct 2015
    HSC
    2018
    Gender
    Female
    Posts
    55
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    if cube root (x+iy) =X+iY show that 4 (X^2-Y^2) = x/X + y/Y

  19. #19
    Junior Member 1729's Avatar
    Join Date
    Jan 2017
    HSC
    2018
    Gender
    Male
    Location
    Sydney
    Posts
    154
    Rep Power
    1

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by sssona09 View Post
    if cube root (x+iy) =X+iY show that 4 (X^2-Y^2) = x/X + y/Y
    sssona09 likes this.

  20. #20
    Cadet
    Join Date
    Oct 2015
    HSC
    2018
    Gender
    Female
    Posts
    55
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    thank you so much!!

  21. #21
    Cadet
    Join Date
    Oct 2015
    HSC
    2018
    Gender
    Female
    Posts
    55
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    rove by Induction that z1+z2+zn = z1 +z2 +zn

    where the LHS has a big conjugate line on the top and RHS has small conjugate lines

    edit: solved
    Last edited by sssona09; 8 Nov 2017 at 6:47 PM.

  22. #22
    Taking a break! dan964's Avatar
    Join Date
    Jun 2014
    HSC
    2014
    Uni Grad
    2018
    Gender
    Male
    Location
    South of here
    Posts
    2,774
    Rep Power
    4

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by sssona09 View Post
    rove by Induction that z1+z2+zn = z1 +z2 +zn

    where the LHS has a big conjugate line on the top and RHS has small conjugate lines
    Prove by Induction that
    is this the question?
    2014 HSC
    2015 Gap Year
    2016-2018 UOW Bachelor of Maths/Maths Advanced.

    Links:
    View English Notes (no download). Purchase a downloadable/printable copy on SELLFY here + Year 10 notes
    Maths Notes - Free Sample
    Chemistry Notes Sample + Buy (soon)

    thsconline: https://thsconline.github.io/s/ (2017 papers uploaded)

  23. #23
    Cadet
    Join Date
    Oct 2015
    HSC
    2018
    Gender
    Female
    Posts
    55
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by dan964 View Post
    Prove by Induction that
    is this the question?
    yes

  24. #24
    Cadet
    Join Date
    Oct 2015
    HSC
    2018
    Gender
    Female
    Posts
    55
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    find z suvh that (Im)z=2 and z^2 is real

    thank you

  25. #25
    I love trials pikachu975's Avatar
    Join Date
    May 2015
    HSC
    2017
    Gender
    Male
    Location
    NSW
    Posts
    2,057
    Rep Power
    3

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by sssona09 View Post
    find z suvh that (Im)z=2 and z^2 is real

    thank you
    So let z = x + 2i

    (x+2i)^2 = x^2 + 4xi - 4
    Since it is real then Im(z^2) = 0
    so 4x = 0
    x = 0

    Hence z = 2i
    sssona09 likes this.
    Offering tutoring for Biology, Maths, Maths Ext 1, and Maths Ext 2.

    Solar Education - CHEAP Quality Tutoring

    Buy my books/notes cheaply here!

    --------------------------------------------------------------------------------

    2016 HSC (Accelerated): // 2U Maths (97) // SOR 1 (48) //
    2017 HSC: // English Adv (91) // Bio (96) // Phys (95) // 3U Maths (99) // 4U Maths (97) //
    ATAR: 99.75

Page 1 of 2 12 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
  •