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coz ap^3 = q(3pq-bq^2) every factor of q is a factor of RHS hence a factor of LHS. now, since gcd(p , q) = 1 so any factor of q cannot be factor of p or p^3, therefore must be a factor of a. therefore every factor of q is a factor of a so q|a

1) compasses are essential 2) you should get one of those templates, save time

3 u is damn hard.. you get 17 mins or so per question.. by the way, turtle, how long did the 3U exam take you?

yeah that was me W-E-A-K was my signature until few days ago

from 1 to 8, skipping graphs

I usually use the 5 mins to allocate time for each question

depends on what you want out of the HSC: if you are considering University, PD/H/PE, Business and geography is usually at a disadvantage for average performances.

affinity: repeats the above to classmates classmates: what's the point, we're not going to use it after the HSC

(i) x, y are real numbers satisfying log_3[x+7] + 2*cos[y + 2003] = 4 find ( |x-2| + |x - 722| )/6 , justify your answer. log_3 is logarithm base 3. (ii) explain the significance of your answer to (i).

maths extension 2 is the real physics course

well d(e^x + 1) = e^x dx so your line = # (e^x+1) - 1 / sqrt( e^x + 1) d(e^x + 1) = # sqrt(e^x + 1) - 1/sqrt(e^x + 1) d(e^x + 1) = (2/3)(e^x + 1)^(3/2) - 2 sqrt(e^x + 1) + c

You're fine with whatever method as long as you give the correct answer for integration.. unless they are asking you to prove something, then becareful

3Pi/2 is the official answer x = 2, -2, -pi/2 pi/2 3pi/2 basically what ND did. first to find possible solutions squaring both sides, equating indices (2x^2 - 10)|cos(x)| = |x| cos(x) cos(x) = 0 solutions, -pi/2, pi/2 3pi/2 else if cos(x) != 0 (2x^2 -10) = |x|...

that's obvious... we're always the most important :p

1.) it's 1/ (45 C 6) lotto's not P 2.) should be 12/(45 C 6) coz from the 6 + 2 numbers, there are 6*2 combinations which takes five from the '6' and 1 from the '2' so it's 12/total number of combinations

a>0 find the sum of all solutions for x in the close interval [-2,6] for: a^( (x^2 - 5)*|cos(x)| ) = (sqrt(a))^( |x|cos(x) )

inverse... textbooks write tan^-1

you don't. I was trying to say that there's no point in remembering theorems.. they will lead you through the proof. they are in the textbooks though

simpson's theorem was question 4b last year ptolemy's theorem states that for a cyclic qud ABCD AB*CD + BC*AD = AC*BD most of those questions are in arnold's book

I didn't finish with (1) if n is even the it could be established by the power mean inequalities that LHS >= RHS qith equality iff sin(x) =cos(x) gets nastier with odd powers though, coz there are solution in the second and fourth quad