As a refresher i set myself a task of completing all the misc exercises in the bostock and chandler A-level book (red ). I have ploughed through what must be in region of 500 past A-level questions (from 1970s-1980s) and out of them i am unable to give a solution to the follwing.
If anyone could be so kind to help me finish off this book i would be grateful.
It is not necessarily the case they are hard problems.
They may well have been met when i'd already done 30-40 questions from the chapter and i ran out of mental power or im just not able to do them
1) a curve is
Find equation of normal at point with parameter p and find the point in
1st quadrant of which normal is also normal to curve at another point.
2) If Sn=a^r(1+a+a^2+.....a^r) by considering (1-a)Sn show that
(1-a)Sn=(1-a^(2n+2))/(1-a^2) - a^(n+1)[1+a^(n+1)]/(1-a)
3) In the binomial expansion of (p+q)^n write down the term containing p^r. If p=1/6, q=5/6 and n=30, find the value of r for which this term is greatest in value.
book answer: 5. is there quick way apart from working the values out upto 5 then seeing they go down at 6?
4) given y=[(1+x)/(2+x)]^1/2 find value of dy/dx at x=2. Deduce the increase in value of y when x increases in value from 2 to 2+e with e small
book answer: rt(3)e/30.
5) use vector geometry to prove the internal bisectors of the angles of a triangle are concurrent.