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Arnold is good if you bother to learn the concepts. Coroneos if you want some hard questions. If you just want to 'cram' then do papers.

oh.. forgot .. yes you have to prove the cauchy schwarz. what about AM-GM?

week 4-5.

ask someone smart inthe class or work it out yourself, it's most rewarding the last way

q 25) answer is D, 4: let the width of the 18 rectangle be A and that of the 12 triangle be B you can see that the area of the whole rectangle is: (A+B)*(18/A + 12/B) = 30 + 18(B/A) + 12(A/B) >= 30 + 2*sqrt(18*12) by the AM-GM inequality = 30 + sqrt(846) 30^2 = 900 29^2=841...

enak, the middle is to be considered also so :P no

apologize for the long post, please make corrections as it is likely that I've made mistakes half of this is hindsight wisdom for me q 26) the number is 6037 and that will make the answer 16. start with 10 keep adding 21 until the second condition is satisfied, then add 21*23 until the...

the car one should be 6 I think: there are 6 routes from P to Q(satisfying the conditions), count it. you want order reversed so, that means so now two cars can go by the same route. I put down (d)4 yesterday .. hopeless me

the answer for the squares one was 4 275 936 184 all sums are 9,10,11 or 12. and we know there are atleast 4 different sums when you consider the middle square and it's 4 sums. Don't ask me how I got that one.

Probability - Get yourself clear about when to add number and when to multiply. You can get probaility involving intervals, not just discrete variables. Inequalities: The cauchy-schwarz inequality is another useful one. (SUM {a_ib_i } )² <= SUM...

here's the proof for it n^12 - n^8 -n^4 -1 = n^8(n^4 - 1) - (N^4 -1) = (n^8 -1)(n^4 -1) = (n^4 + 1)(n^2 + 1)(n+1)(n-1)(n^2+1)(n+1)(n-1) you will have to realise that n^2 + 1, n^4 + 1 are not multiples of 4. (odd^2 is congruent to 1 modulo 4.) or: odd number^2 =(2n+1)^2 = 4n^2...

the uncertainty principle only says certain pairs of measurements can never be precise mathematically for any measurements: p*q>h/4PI E*T>h/4PI where p, q, E,T are the uncertainties in momentum, position, energy, time.

what are the others dubious ones?

personally stuffed up big time :P

yah unfortunately

If you can understand what you read on your own(ie. 'outside study' does not mean tutoring), you should well be ahead and what you learn should be much more solid than others. You should inform the principal about your concerns. It doesn't affect you that much since you are first in school...

positive and negative are assigned to directions, so if acceleration is considered negative in one direction so is velocity, displacement, forces, etc etc. following that, sometimes you have resistance which is proportional to v^2, and that will complicate things a little when you assign the...

It's not that different in maths and physics, just remember to derive your formulae always, leaning physics gives you an edge in this. basics, results that can be used: 1.)change in momentum with respect to time is force: dp/dt = F where p = mv and when m is constant(almost always in...

the best preparation for exams is to explain things to others. If you can do it, it means you truely understand the concepts and usually from a variety of aspects

force due to gravity is mg downwards the component parallel to the plane equals mg*sin(t) where t is the angle of inclination of the plane, show this fact with a diagram. we're told that sin(t) = 1/30 so.. that makes mg/30 yes this is examinable, it's not that hard considering no calculus...