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Why not just display mathematics for its beauty? Example, use this: http://www.geogebra.org/cms/en/ (for example) To show what happens if you squash a circle by some factor. Explain how the Conic Sections are derived by showing an actual Cone being cut in different ways. etc etc. There are...

re: HSC Physics Marathon Archive $A particle initally travels with constant acceleration with a velocity$ \ \ u \ \ $after time$ \ \ t \ \ $it has a velocity of$ \ \ v $The distance travelled after time$ \ \ t \ \ $is given by$ \ \ x $i) Prove that$ \ \ v=u+at $ii) Prove that$ \ \ x=ut+...

Is A-level Physics in England similar to HSC Physics (bar social stuff)?

Re: MX2 Integration Marathon \int \frac{\cos^{-1}x \tan^{-1}x }{\sqrt{1-x^2}} - \frac{\sin^{-1}x \tan^{-1}x}{\sqrt{1-x^2}} + \frac{\sin^{-1}x \cos^{-1}x }{1+x^2} \ dx

Re: HSC 2013 4U Marathon $Runners who run with a constant speed, Fred, Alistair, Maggie, and Bob run around a 500 metre track. In the time it takes Bob to finish the race, Alistair has only run 300 metres. When Maggie has finished the race, Fred has run 450 metres. When Alistair finishes the...

Reading this thread: http://math.stackexchange.com/questions/397972/what-is-a-proof Sparks many questions, that I think would be good for people to discuss here. === I think the most interesting question that arises from there, is what or who determines the set of axioms that we...

Re: MX2 Integration Marathon \int \frac{1}{\sqrt[3]{x} + \sqrt{x}} \ dx u^6=x \ \ 6u^5 \ du = dx \Rightarrow \int \frac{6u^5 \ du }{u^2 + u^3} =6\int \frac{u^3}{u+1} \ du = 6 \int u^2 - \frac{u^2}{u+1} \ du = 6\int u^2 - u + \frac{u}{u+1} \ du = 6\int u^2 - u + 1 - \frac{1}{u+1} \ du...

Re: MX2 Integration Marathon The solution I got had ln in it. This is what I was aiming at.

Re: MX2 Integration Marathon Upon your substitution, v=\sqrt{u} , you didn't find du.

Re: MX2 Integration Marathon I don't think so, what was your method briefly?

Re: MX2 Integration Marathon \int \frac{1}{\sqrt{x} + \sqrt[3]{x}} \ dx

Re: MX2 Integration Marathon I_n = \int \sin^{2n}x \sec x \ dx I_{n-1}-I_n = \int \sin^{2n-2}x \sec x (1-\sin^2 x) \ dx I_{n-1}-I_n = \int \sin^{2n-2}x \cos x \ dx = \frac{1}{2n-2} \sin^{2n-1} x \sum_{k=1}^{n} I_{k-1}-I_k = \sum_{k=1}^{n} \frac{1}{2k-1} \sin^{2k-1}x I_n = I_0 -...

Re: MX2 Integration Marathon Using the substitution: u^2=1+x^2 Resolves the integral to: \int \sqrt{2-u^2} \ du Upon the subtitution: u=\sqrt{2} \sin \theta The integral resolves to: 2\int \cos^2 \theta \ d\theta Upon computation: = \sin \theta \cos \theta + \theta + c_1...

There is no reason why it can't happen, just try hard for the trials since they can really change a lot in terms of ranking

Re: MX2 Integration Marathon Its supposed to evaluate to 2013 :( (suprise suprise) Looks like I failed lol

Re: MX2 Integration Marathon That's right lol, 1/3 sec u works. The infinity changes to pi/2.

1. Usually 1mL, but to be sure look at 2 of the written readings on the burette, say 1mL and 2mL, count the amount of lines between them (not including them), if there are 5 lines, then each line is 2mL, if there are 10 then each is 1mL etc. 2. I have not heard of this practise, when starting...

Re: MX2 Integration Marathon Yeah I didn't use partial fractions, I recommend a substitution.

Re: MX2 Integration Marathon \int_{1/3}^{\infty} \frac{5\sqrt{x^2 - \frac{1}{9}} + 69x^6(x^2 - \frac{1}{9})}{x^6(x^2- \frac{1}{9})} \ dx I assure you the numbers are not arbitrary.

Re: HSC 2013 3U Marathon Thread My mistake