HSC 2014 Maths Marathon (archive) (4 Viewers)

hi im trash · Aug 21, 2014

Re: HSC 2014 2U Marathon

dunjaaa said:
Nothing is wrong with the question, I promise haha

Ah sorry!
is it 88pi/15?

dunjaaa · Aug 21, 2014

Re: HSC 2014 2U Marathon

The answer you should try to obtain is: 5488pi/15

hi im trash · Aug 22, 2014

Re: HSC 2014 2U Marathon

dunjaaa said:
The answer you should try to obtain is: 5488pi/15

Hmm, how do you find the volume in the y=10 thing? i had 40pi i don't really know how to get 400pi

edit: nvm i think i confused my r and h :X

trungduong12 · Aug 24, 2014

Re: HSC 2014 2U Marathon

No one post any more questions in two days ~~~

Sent from my iPhone using Tapatalk

dunjaaa · Aug 25, 2014

Re: HSC 2014 2U Marathon

Question:

Screen shot 2014-08-25 at 10.50.04 PM.png

photastic · Aug 25, 2014

Re: HSC 2014 2U Marathon

dunjaaa said:
Question: View attachment 30822

photastic · Aug 25, 2014

Re: HSC 2014 2U Marathon

dunjaaa · Aug 26, 2014

Re: HSC 2014 2U Marathon

Q:

Screen shot 2014-08-26 at 1.37.23 AM.png

dunjaaa · Aug 26, 2014

Re: HSC 2014 2U Marathon

Q:

Screen shot 2014-08-26 at 4.15.58 PM.png

integral95 · Aug 26, 2014

Re: HSC 2014 2U Marathon

dunjaaa said:
Q: View attachment 30827

Heh, it can be solved by inspection

dunjaaa · Sep 22, 2014

Re: HSC 2014 2U Marathon

Screen shot 2014-09-22 at 10.16.51 PM.png

Simile · Sep 23, 2014

Re: HSC 2014 2U Marathon

Hello,

Could you help me with the 2u hsc paper,2012 question 16b and 16c.

Sorry I did not post it, I do not know how to.

Thanks.

Pikachuisgod · Oct 8, 2014

Re: HSC 2014 2U Marathon

Integral cot x - (cosec^2)x d (actual 2 unit question)

photastic · Oct 8, 2014

Re: HSC 2014 2U Marathon

Pikachuisgod said:
Integral cot x - (cosec^2)x d (actual 2 unit question)

ln(sinx) + 2cos(x)/sin^3(x) + C

Pikachuisgod · Oct 9, 2014

Re: HSC 2014 2U Marathon

aarondapho said:
ln(sinx) + 2cos(x)/sin^3(x) + C

It's ln sin x + cot x + c

photastic · Oct 9, 2014

Re: HSC 2014 2U Marathon

Pikachuisgod said:
It's ln sin x + cot x + c

Whoops, I integrated the first term but derived the second term :S

faisalabdul16 · Oct 9, 2014

Re: HSC 2014 2U Marathon

$\int cotx - cosec^{2}x dx \\ \\ = ln(sinx)+ cotx + c$

Pikachuisgod said:
Integral cot x - (cosec^2)x d (actual 2 unit question)

Sy123 · Nov 22, 2014

Re: HSC 2014 2U Marathon

TOPIC: Arithmetic and Geometric Series

$\\ $i) Show that$ \ (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$

$\\ $ii) Hence show that$ \ (k+1)^3 - k^3 = 3k^2 + 3k + 1$

$\\ $iii) Show that$ \ 1 + 2 + 3 + \dots + 100 = 5050 \ \ $(HINT: Arithmetic series)$$

$\\ $iv) Show that$ \ (2^3 - 1^3) + (3^3 - 2^3) + \dots + (101^3 - 100^3) = 3(1^2 + 2^2 + \dots + 100^2) + 3(1+ 2 + \dots + 100) + 100$

$\\ $v) Hence show that$ \ 1^2 + 2^2 + \dots + 100^2 = 338350$

integral95 · Nov 22, 2014

Re: HSC 2014 2U Marathon

Sy123 said:
TOPIC: Arithmetic and Geometric Series

$\\ $i) Show that$ \ (a+b)^3 = a^3 + 3a^2b + 3ab^2 = b^3$

$\\ $ii) Hence show that$ \ (k+1)^3 - k^3 = 3k^2 + 3k + 1$

$\\ $iii) Show that$ \ 1 + 2 + 3 + \dots + 100 = 1010 \ \ $(HINT: Arithmetic series)$$

$\\ $iv) Show that$ \ (2^3 - 1^3) + (3^3 - 2^3) + \dots + (101^3 - 100^3) = 3(1^2 + 2^2 + \dots + 100^2) + 3(1+ 2 + \dots + 100) + 100$

$\\ $v) Hence show that$ \ 1^2 + 2^2 + \dots + 100^2 = 1027170$

I think it's meant to be 342390 (you didn't divide by 3)

FrankXie · Nov 22, 2014

Re: HSC 2014 2U Marathon

Sy123 said:
TOPIC: Arithmetic and Geometric Series

$\\ $i) Show that$ \ (a+b)^3 = a^3 + 3a^2b + 3ab^2 = b^3$

$\\ $ii) Hence show that$ \ (k+1)^3 - k^3 = 3k^2 + 3k + 1$

$\\ $iii) Show that$ \ 1 + 2 + 3 + \dots + 100 = 1010 \ \ $(HINT: Arithmetic series)$$

$\\ $iv) Show that$ \ (2^3 - 1^3) + (3^3 - 2^3) + \dots + (101^3 - 100^3) = 3(1^2 + 2^2 + \dots + 100^2) + 3(1+ 2 + \dots + 100) + 100$

$\\ $v) Hence show that$ \ 1^2 + 2^2 + \dots + 100^2 = 342390$

a few typros:

part (i) $=b^3 $ at the end should be $ +b^3$

part (iii) 1010 should be 5050

part (v) the result should be 338350

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