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Just a question Why are there inflexion points there and there? y=e^{f(x)}\\y'=f'(x)e^{f(x)}\\y''=f'(x)f'(x)e^{f(x)}+e^{f(x)}f''(x)=e^{f(x)}\left[(f'(x))^2+f''(x)\right]=0 $ for points of inflexion.$ But neither the function nor the exponential have inflexion points?? Also what's the...

Hey guys, I probably won't get an interview but...if you get an interview for the merit/entry scholarship can you...perhaps change the date if you're overseas or what not? Probably 99% no but I'm just checking. Thanks.

Question/Ponder Why exactly do we need to 'order' things when doing a binomial probability? E.g. 1997 HSC MX1 c) In a game of Sic Bo, three regular, six-sided dice are thrown once. i) In a single game, what is the probability that all three dice show 2? ii) What is the probability that...

Is it as grueling as I've heard it to be? It takes a little more than 1 hour to get to usyd from my house so I'd have to leave before 7...which is the earliest ever O_O. Might consider chickening out with math1001 during the summer haha. Thanks

I've been just shit at probability/perms/combs all my life (Q5 of 2011 2U paper baby). Any tips/tricks/worksheets I can get my hands on? We're not doing it in class because my teacher is a **** but it features in every HSC paper... Thanks

Does anyone have a scan of a page of this? I'm looking for the writing booklets with big spacing (the ones used in HSC) Thank you!

Just wanting opinions. I have applied for the E12 scholarship at USYD. I have to write a few hundred words by tonight if I am to apply for it (personal statementy stuff). Also I have to harrass my principal tomorrow to write a recommendation for me... TBH I'm not actually that...

Do all first year science units have labs? If not, which units do not? (And are they easy to pass? lol) Thank you.

Need a hint for ii) Thankyou!

ABC is a triangle with sides a, b, c. If a^2+b^2+c^2=ab+bc+ca, show that ABC is equilateral. I have tried most things like cosine rule or sine rule...Then I remembered... a^2+b^2+c^2\geq ab+bc+ca (Which I proved) And equality occurs iff a=b=c. Hence as a^2+b^2+c^2= ab+bc+ca, then a=b=c. That...

Just wanted to check my logic. 4c) Containers are coded by different arrangements of coloured dots in a row. The colours used are red, white, and blue. In an arrangement, at most three of the dots are red, at most two of the dots are white, and at most one is blue. i) Find the number of...

It's nearly the end of the course. I have about half of Quanta and 1/4 of Ideas left to do of notes. Should I bother? I want to get onto past papers asap. I have other sources I can study from. Thoughts?

I saw the solution in the blue mansw book a while back but wasn't quite sure. With v) the answer was b<0. Here is my working (it is a bit long winded but meh) $For real roots, one stationary point must be below or on the axis. Stationary points occur when $ P'(z)=0 \Rightarrow 4z^3+2bz=0 \\...

Question 13 of my trials. a) $A sequence $ u_1, u_2,u_3\cdots $ is defined by $ u_1=2, u_2=12 $ and $ u_n=6u_{n+1}-8u_{n-2} $ for $ n\geq3. $ Use mathematical induction to show that $ u_n=4^n-2^n $ for $ n\geq1 (3 marks) Yes, the u_{n+1} should indeed be u_{n-1}. I realised this in the exam...

This was in our first asst...which I lost marks on. Anyway I was looking through the proof again and tried it again...Does it work? Prove by induction 3-\frac{1}{n}\geq \left(1+\frac{1}{1^3}\right) \left(1+\frac{1}{2^3}\right) \left(1+\frac{1}{3^3}\right) \cdots \left(1+\frac{1}{n^3}\right) $...

I'm applying for USYD merit/entry scholarship...any tips on the personal statement? I know there are some on the website and I have looked at them. Has anyone here applied and got it before? Thanks

Hi guys, Recently I found out you could study 1st year courses at summer school and possibly accelerate your degree. I may want to do this with first year maths units. Does anyone have any experience with summer school? Would you recommend doing it? I would personally like to get ahead...the 3...

The integral of 0 is simply a constant? Can the idea of the 'area under the curve' be applied here? - Seems not?

I think someone posted a similar question but I wanted to clarify: 'If \theta +\epsilon = \frac{\pi}{2}...$ Show that the equation of the chord PQ has equation $ ay=b(\cos\theta+\sin\theta)x-ab $ Where $P(a\sec\theta,b\tan\theta), Q(a\sec\epsilon, b\tan\epsilon) I have subbed in P, and shown...

Was doing some inequalities induction and got me thinking... Oftentimes we need to prove LHS\geq RHS and we'll say for example LHS=1 and RHS=1\leq LHS. If we know that LHS=RHS, without the equality, does the statement LHS\geq RHS still hold? Because we know that it isn't greater, it is simply...