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they virtually gave you the answer for the induction question in the first bit..it was simple

id be inclinded to say 75 out of this paper would be low band 5, the difficulty wasnt there

agree it was damn easy...i mean what was hard about it??..hopefully i can get about 110 im sure ppl will get perfect scores tho

heres a decent alternate solution / 5t^2+3 (1996HSC, Q1,c) | t(t^2+1) / = I_n (5t⁴+3t²) / (t⁵ + t³) (times num/ denom by t^2/t^2) = log_e(t⁵ + t³)

S Sin^6x dx = S Sin^6xcosx / cosx dx ( * by cosx/cosx) let u = sinx, du = cosx dx = S u^6 / cosx du but u = sinx, therefoce sqr(1-u^2) = cosx = S u^6 / sqr(1-u^2) du - which is simple to integrate

hehe usually i dont post anymore but im in a good mood from my umat scores :) (btw it would be good if someone got latex or some math program for this board like other maths forums do) anyway area under y = lnx (from 1 to n) > area under sum of trapeziums from 1 to n nlnn - n + 1 >...