# Thread: HSC 2018-2019 MX2 Marathon

1. ## HSC 2018-2019 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:

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: Originally Posted by Sy123   Reply With Quote

2. ## Re: HSC 2018 MX2 Marathon  Reply With Quote

3. ## 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  Reply With Quote

4. ## Re: HSC 2018 MX2 Marathon Originally Posted by TheZhangarang 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  Reply With Quote

5. ## Re: HSC 2018 MX2 Marathon

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

6. ## Re: HSC 2018 MX2 Marathon Originally Posted by si2136 Are there answers to Sydney Boys 2002 4u trial? Thanks
https://thsconline.github.io/s/?view...002%20w.%20sol  Reply With Quote

7. ## Re: HSC 2018 MX2 Marathon

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

8. ## Re: HSC 2018 MX2 Marathon Originally Posted by sssona09 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  Reply With Quote

9. ## Re: HSC 2018 MX2 Marathon Originally Posted by dan964 expand
(xa-by) +(ay+bx)i=b+ia
equate real and complex and solve simulataneously for x,y
ohh thank you   Reply With Quote

10. ## 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  Reply With Quote

11. ## Re: HSC 2018 MX2 Marathon Originally Posted by sssona09 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  Reply With Quote

12. ## Re: HSC 2018 MX2 Marathon Originally Posted by si2136 You could if you want to. Rationalise denominator and then solve for it by equating real and imaginary parts
oh okay thanks   Reply With Quote

13. ## 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 :/  Reply With Quote

14. ## Re: HSC 2018 MX2 Marathon Originally Posted by sssona09 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 :/  Reply With Quote

15. ## Re: HSC 2018 MX2 Marathon Originally Posted by 1729 Ahh thank you!!!!!!!!!!  Reply With Quote

16. ## Re: HSC 2018 MX2 Marathon

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

17. ## Re: HSC 2018 MX2 Marathon Originally Posted by sssona09 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.  Reply With Quote

18. ## Re: HSC 2018 MX2 Marathon

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

19. ## Re: HSC 2018 MX2 Marathon Originally Posted by sssona09 if cube root (x+iy) =X+iY show that 4 (X^2-Y^2) = x/X + y/Y  Reply With Quote

20. ## Re: HSC 2018 MX2 Marathon

thank you so much!!  Reply With Quote

21. ## 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  Reply With Quote

22. ## Re: HSC 2018 MX2 Marathon Originally Posted by sssona09 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?  Reply With Quote

23. ## Re: HSC 2018 MX2 Marathon Originally Posted by dan964 Prove by Induction that
is this the question?
yes   Reply With Quote

24. ## Re: HSC 2018 MX2 Marathon

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

thank you  Reply With Quote

25. ## Re: HSC 2018 MX2 Marathon Originally Posted by sssona09 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  Reply With Quote