# Thread: Ekman's Compilation of MX2 Questions

1. ## Ekman's Compilation of MX2 Questions

Hey everyone, I decided to take the liberty of collecting all the hard MX2 questions that I solved during my HSC year and develop a more organised compilation for students that study MX2.

https://www.dropbox.com/sh/6t6f4tcz5...tions.pdf?dl=0

Feel free to point out any errors, and I will hopefully fix them up as soon as possible

Also a big thanks to Integrand, Sy123 and a few others for helping me validate the answers as well

-Ekman

2. ## Re: Ekman's Compilation of MX2 Questions

Originally Posted by Ekman
Hey everyone, I decided to take the liberty of collecting all the hard MX2 questions that I solved during my HSC year and develop a more organised compilation for students that study MX2.

https://www.dropbox.com/sh/6t6f4tcz5...tions.pdf?dl=0

Feel free to point out any errors, and I will hopefully fix them up as soon as possible

Also a big thanks to Integrand, Sy123 and a few others for helping me validate the answers as well

-Ekman
No way. This file was to good to release props to Ekman.

3. ## Re: Ekman's Compilation of MX2 Questions

I suck. And I'm in holiday mode. So I'm to lazy to do these.

But dayum

4. ## Re: Ekman's Compilation of MX2 Questions

Thanks Ekman; that's awesome.

5. ## Re: Ekman's Compilation of MX2 Questions

I am officially your best friend ever I am going to do them all these holidays yessss

Wow!

7. ## Re: Ekman's Compilation of MX2 Questions

Originally Posted by Ekman
Hey everyone, I decided to take the liberty of collecting all the hard MX2 questions that I solved during my HSC year and develop a more organised compilation for students that study MX2.

https://www.dropbox.com/sh/6t6f4tcz5...tions.pdf?dl=0

Feel free to point out any errors, and I will hopefully fix them up as soon as possible

Also a big thanks to Integrand, Sy123 and a few others for helping me validate the answers as well

-Ekman
Do you happen to have worked solutions to these ?
Regardless thankyou so much for taking the time to make these

8. ## Re: Ekman's Compilation of MX2 Questions

Originally Posted by SammyT123
Do you happen to have worked solutions to these ?
Regardless thankyou so much for taking the time to make these
I made these for integration, complex numbers, volumes and partially mechanics but I threw them in the bin ahaha.

EDIT: After final's I could make it again? ...

9. ## Re: Ekman's Compilation of MX2 Questions

Originally Posted by Drsoccerball
I made these for integration, complex numbers, volumes and partially mechanics but I threw them in the bin ahaha.

EDIT: After final's I could make it again? ...
Why did you throw them away?

10. ## Re: Ekman's Compilation of MX2 Questions

Originally Posted by InteGrand
Why did you throw them away?
I was cleaning and it was in the way and I had no where to put it LOL.

11. ## Re: Ekman's Compilation of MX2 Questions

this is nice..gonna be useful next year

12. ## Re: Ekman's Compilation of MX2 Questions

Hi all, as Drsoccerball requested i'll just post the questions on here from now on, these are all pretty hard.

Could I also get some help with Q10 from the polynomial set? Is it similar logic to Q3?

Resticky?

14. ## Re: Ekman's Compilation of MX2 Questions

Isn't the solution to Q15 of the polynomials section, 8, not 5?

15. ## Re: Ekman's Compilation of MX2 Questions

Originally Posted by wu345
Isn't the solution to Q15 of the polynomials section, 8, not 5?
5 is correct.

$(\alpha + \beta + \gamma - \gamma)(\alpha + \beta + \gamma - \alpha)(\alpha + \beta + \gamma - \beta)$

$= (2 - \alpha)(2 - \beta)(2 - \gamma)$

$Which is the same thing as saying P(2). \therefore P(2) = 5.$

16. ## Re: Ekman's Compilation of MX2 Questions

Originally Posted by Drsoccerball
5 is correct.

$(\alpha + \beta + \gamma - \gamma)(\alpha + \beta + \gamma - \alpha)(\alpha + \beta + \gamma - \beta)$

$= (2 - \alpha)(2 - \beta)(2 - \gamma)$

$Which is the same thing as saying P(2). \therefore P(2) = 5.$
$\noindent If this was the intention of the solution method, maybe the Q. was typed up incorrectly? The Q. asks to find \left(\alpha+\beta - \gamma \right)\left(\beta + \gamma -\alpha \right)\left(\gamma +\alpha - \beta \right), where \alpha,\beta,\gamma are the roots of x^3 -2x^2 + 3x-1=0. So we can't just do what you did above; we could only generally do that if we were adding and subtracting something in each term in the product, which we're not doing for the Q. as asked. If we wanted to do what you did, the Q. should've asked for the value of something like \left(\alpha+\beta \right)\left(\beta + \gamma \right)\left(\gamma +\alpha \right).$

17. ## Re: Ekman's Compilation of MX2 Questions

Originally Posted by InteGrand
$\noindent If this was the intention of the solution method, maybe the Q. was typed up incorrectly? The Q. asks to find \left(\alpha+\beta - \gamma \right)\left(\beta + \gamma -\alpha \right)\left(\gamma +\alpha - \beta \right), where \alpha,\beta,\gamma are the roots of x^3 -2x^2 + 3x-1=0. So we can't just do what you did above; we could only generally do that if we were adding and subtracting something in each term in the product, which we're not doing for the Q. as asked. If we wanted to do what you did, the Q. should've asked for the value of something like \left(\alpha+\beta \right)\left(\beta + \gamma \right)\left(\gamma +\alpha \right).$
Sorry I just activated auto mode :P
You can still do it that way though.
$(2-2\gamma)(2-2\beta)(2-2\alpha)$

$8(1 - \gamma)(1 - \beta)(1 - \alpha)$

$8P(1)$

18. ## Re: Ekman's Compilation of MX2 Questions

Originally Posted by Drsoccerball
Sorry I just activated auto mode :P
You can still do it that way though.
$(2-2\gamma)(2-2\beta)(2-2\alpha)$

$8(1 - \gamma)(1 - \beta)(1 - \alpha)$

$8P(1)$
Yep, and P(1) = 1 – 2 + 3 – 1 = 1, so the answer is indeed 8 as wu345 said.

19. ## Re: Ekman's Compilation of MX2 Questions

Can I please have a hint for Q18 of integration? I simplified the integrand a bit by using difference of cubes and cancelling some common factors but after that im pretty stuck. Chucking into wolfram Alpha and integral calculator resulted in both timing out

20. ## Re: Ekman's Compilation of MX2 Questions

Are these from HSC papers ?

21. ## Re: Ekman's Compilation of MX2 Questions

Does anyone have worked solutions???

22. ## Re: Ekman's Compilation of MX2 Questions

Originally Posted by likeneverbefore
Does anyone have worked solutions???
I made them for most chapters but then i threw them in the bin idk why...

23. ## Re: Ekman's Compilation of MX2 Questions

Originally Posted by Drsoccerball
I made them for most chapters but then i threw them in the bin idk why...
Did Ekman make any solutions?

24. ## Re: Ekman's Compilation of MX2 Questions

haha i hope he did...some questions i really dont know how to start

does ekman come on to this site anymore?

25. ## Re: Ekman's Compilation of MX2 Questions

Originally Posted by InteGrand
Did Ekman make any solutions?
Not too sure tbh... He does have answers but when I asked a while ago he said he didnt have solutions.

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