# gce o level additional paperWatch

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Thread starter 14 years ago
#1
seeing additional maths as a post made me find my old 1988 add maths paper. here are a few questions from it. enjoy, and if you have time see my other post on mind maps and answer question about investigations for me!

1) write down the common ratio of e+e^(1/2)+1+.... calculate the sum of the first six terms. write down in its simplest form the common difference of the arithmetic series A,
log3(2)+log3(6)+log3(18) where log3 denotes log to base 3.show the sum of the first 10 terms of A is 10log3(2)+45.

2)given that f(x)=2x^2+px+18 write down in terms of p the solutions to
f(x)=0.find the range of values of p for which f(x)=0 has unreal roots.
given one root of f(x)=0 is four times the other find the 2 possible valuse of p.find the 2 pairs of solutions of the equation corresponding to these values of p

3)find the set of values for which x^2-2x>0
given f(x)=(x^2-2x)/x-3
find the set of values for which f(x)>0
calculate to 1 dec.place the x-ordinate of each of the 2 turning points of the graph y=f(x)

4)consider a spherical tank of radius 1m containing oil to height h metres,measured from the centre of the sphere.the volume V of fuel in the tank is given by V=pi(2+3h-h^3)/3.
find dV/dh.
the level of fuel in the tank is decreasing at a constant rate 0.002 m/min.
calculate the rate of decrease of the volume of oil in the tank in m^3/min at the instant h=0.3. calculate the 2 values of V when the rate of decrease of the volume of the oil in the tank is 0.00128pi m^3/min.
the area of the surface of the oil in contact with the air is Am^2
write down an expresion for A in terms of h. find the rate of change of the surface area,in m^2/min at the instant when h=0.5.
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