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Re: HSC 2013 3U Marathon Thread $a) How many ways can you arrange the word CARROT, if the letters R and A must be together$ $b) By considering the scenario of separating$ \ n \ $people into 2 groups, in 2 different ways show that$ \binom{n}{0} + \binom{n}{1} + \dots + \binom{n}{n} =2^n...

Idk I reckon that's a little generous

No one has gotten 100 raw since 1993

Re: HSC 2013 4U Marathon I'd rather just add on 2014 stuff here tbh =(

See 2012 Q16 a Besides the Q16 difficulty of 2012 and 2013 are relatively the same, the difference between the papers being is that the middle questions in 2013 were harder than 2012

Your exam was easier That's for sure

I'm a little disappointed in the lack of Harder 3U :/

ahhh bad luck man :/ I made sure to redo a lot of the 'find' questions in the exam and I was able to understand everything, I don't think I made too many silly mistakes though I felt like there should of been more proofs but yea

yes yes yes yes yes yes yesssss holy crap man yes =))))))))))))))))

The only hard part was making your own angle really Everything else is just algebra

Re: HSC 2013 4U Marathon Challenge complete?

Good luck everyone!

Re: HSC 2013 4U Marathon $Prove for real$ \ \ a,b,c,d |ab+cd| \leq \sqrt{a^2+c^2} \sqrt{b^2+d^2}

Re: HSC 2013 2U Marathon Would you need to? The proof only uses that g'(a) = 0, which is a sufficient to prove the result

Re: HSC 2013 4U Marathon Hopefully this is a valid proof $Take a monic quadratic$ x^2 + ax + b=0 \ \ $with roots$ \ \ x_1 \ \ x_2 $This quadratic has distinct real roots if and only if$ \ \ a^2 - 4b > 0 \therefore \ \ (x_1 + x_2)^2 - 4x_1 x_2 = (x_1 - x_2)^2 > 0 \ \ \ \fbox{1} $Take a...

Re: HSC 2013 4U Marathon Is there an elementary solution to Carrot's problem then? If not can someone post another question

Re: HSC 2013 2U Marathon $Prove the following$ $i)$ \ \ \sin^2 x + \cos^2 x = 1 $ii)$ \ \ \log_a b = \frac{\log_c b}{\log_c a} $iii) A triangle constructed in a circle with one side$ $ as a diameter is a right angled triangle$

Re: HSC 2013 2U Marathon $Prove that the volume of a sphere with radius$ \ \ r \ \ $is$ \ \ \frac{4\pi r^3}{3}

Re: HSC 2013 2U Marathon g'(x) = f'(x) (\ln f(x) + 1) \therefore \ \ g'(a) = f'(a) (\ln f(a) + 1) \ \ \fbox{1} $From the original equation$ g(a) = f(a) \ln f(a) g(a) + f(a) = f(a) (\ln f(a) +1) $therefore, due to$ \ \ \fbox{1} \ \ \frac{g'(a)}{f'(a)} = \ln f(a) + 1 \ \ $if$ \ \ f'(a)...

Re: HSC 2013 4U Marathon Yep http://i.imgur.com/wRLNGGU.jpg Hopefully its right