Sorry i thought i'd lost the paper but i just found it again.
These are what i consider to be the harder questions:
5b) Homer simpson borrows $15000 at 11.95% per annum reducible interest, calculated monthly. the loan is to be repaid in 60 monthly installments of $333.30 at the end of each month.
The amount A(n), of the load remaining after n months is given by:
A(n) = M(R^n) - 333.30((R^n)-1)/(R-1) where m is the principal amount borrowed.
(i) find the exact value of R
(ii) After 2 years, homer inherits $1500 and wishes to pay this towards his loan. By how many months is the term of his load reduced, by paying this extra amount?
6a)
i) find the equation of the tangent to the parabola x=2at, y=at^2 at the point P where t=p
ii) If the point Q is the point where t=q, and O is the origin, show that if OQ is parallel to the tangent, then q=2p
iii) If M is the midpoint of PQ, find the equation of the locus of M as P and Q vary along the parabola such that OQ remains parallel to the tangent at P
6b) use induction to prove that ln[(n+2)l] > n+2, for n=> 4
7a) All the letters of the word ENCUMBRANCE are arranged in a line. Find the total number of arrangements, which contains all the vowels alphabetically in order but separated by at least one consonant.
I'd say that 7a is one of the hardest such questions i've seen for a long time. some of our top students and the teacher spent a long time trying to figure out how to get to the answer of it.