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its not that bad, just act as if its a normal plus or minus sign. When you multiply a plusminus sign by a plusminus sign (i.e. you square it) you get a plus, and I think thats all you really need to know. Or just split it into two cases, 1. when its a plus, 2. when its a minus etc

they're basically my favourite parts of the course :P do you have another topic youd prefer? a more conventional one lol (Im thinking demoivres/polynomials/complexy things you can get cool questions with those)?

"Sydney Grammar School, Mathematics Department, Extension 2 Exercises, 2011, Book One/Two". It's not even a real textbook, its a cheaply printed volume of notes and exercises with a light blue/light green (for book1/book2) cardboard cover. And I think grammar thought the other textbooks were...

yeah that um it was in my 4u textbook. sydney grammar has its own textbook/handout that it hands out for 4u, apparently all the commercially available ones are crappy. They used to do that for 3u as well, until it got turned into the cambridge 3u book (pender, sadler, shea, ward are all...

I assume they just subbed back in (x +/- root(x^2 - 4))/2 into the original equation and manipulated it using index laws/general algebra. You gotta be careful of the plusminus sign though but it should be alright? no tricks involved the other way to do it would be to start from: a+b+c = -3...

pretty poor bet lol. try horses instead. thanks for the encouragement though yeah thats right, its a bit of a joke problem in a way coz its a bit unmotivatable after you do the trig sub (the usual neat solutions teachers have for it are just like, try this, magic it works). once youve done the...

highly doubt ill come first, the grammar paper was really nice on me in particular and the markers were nice with some random oddities. got 83/84 for 3u

120

I cant read the handwriting and I dont know the question, but I assume you would if you get the right answer and its not one of those "prove volume = something" questions you'd get full marks. Does anyone know if you need the preamble to do with \delta x etc? Like the limiting sum thing...

yeah I initially forgot to end with [ /tex]

I go to sydney grammar Suppose it had a repeated root w. Then taking the derivative, the following two are true: w^n - w^{n-1} = 1 nw^{n-1} - (n-1)w^{n-2} = 0 Note eqn (1) implies w is nonzero. From that we can divide by w^{n-2} in (2) to obtain: nw - (n-1) = 0 w = \frac{n-1}{n} < 1 Now...

w*w^2*w^3*...*w^{5k-1} = w^{1+2+...+5k-1} = w^{\frac{5k(5k-1)}{2}} = (w^5)^{\frac{k(5k-1)}{2}} = 1 and w+w^2+w^3+...+w^{5k-1} = \frac{w(w^{5k-1}-1)}{w-1} = \frac{w(\frac{w^{5k}}{w}-1)}{w-1} = \frac{w(\frac{1}{w}-1)}{w-1} = -1 So combining the answer is 2. Now try this question, it's from my...

This thing has a massive problem with rigour towards the end of the sum. (The reasoning, take n->infinity and then just let the 1+k/n term be zero doesnt work when the k youre dealing with is really big). It's probably enough for HSC though. Also theres a minus sign wrong , should be 1 - (k-1)/n...

You can look at this geometrically as well. If O is the origin, A represents z, and B represents z+1, and C represents 1, then because z has unit modulus (implied by z = cistheta), and because then AB has length 1 (try tail-to-tip addition or whatever) then OAB is isosceles. Another way of...

You're missing a solution that you'd obtain from the 3(y+5) = -4(x-2) case (i.e. 4x + 3y + 7 = 0). Also you got the arithmetic wrong, -8-15= -23 :P

You dont need all that stuff listed earlier, you can do this question almost straight out using the AM-GM for two variables. \noindent (1-a)(1-b)(1-c) = (b+c)(a+c)(a+b) \ge (2\sqrt{bc})(2\sqrt{ac})(2\sqrt{ab}) = 8abc The first step is just using the a+b+c=1 condition, whereas the second step...

Yep that's right.

rawr try this Find the integral (dx) from 0 to 1 of [ln(1+x)]/(1+x^2) (sorry I dunno how to use latex)

Is this question from a past SGS trial? It looks very familiar.

It's not a paradox, it's probability zero. The problem is that "probability zero" and "never occurs" are not always equivalent statements when dealing with infinite sets. Similarly "probability 1" actually means "almost always occurs" rather than "always occurs", see...