Maths Questions

[junglemonkey]

This isn't homework, they're some questions from a Higher paper I just sat last Friday. I just would like to see what you all get. Take a stab at as many as you want. I can't post some of the harder ones cause they have diagrams.



From the non-calculator paper.



1. Solve the equation log(x+1) - 2log(3) = 3 (both logs to the base 2)

2. Given that y = sin(x) + cos(2x), find dy/dx





From the calculator paper.



1. P, Q and R have co-ordinates (1, 3, -1), (2, 0, 1) and (-3, 1, 2) respectively.

a ) Express the vectors QP and QR in component form (That bit's fine)

B ) hence or otherwise find the size of the angle PQR (bit dodgy on my answer here.)



2. A sequence if defined by the recurrence relation Un+1 = kUn + 3

a ) Write down the condition on k for this sequence to have a limit ( -1<k<1 ?)

b )The sequence tends to a limit of 5 as n-infinity. Determine the value of k.



3. An open cubiod measures internally x units by 2x units by h units and has an inner surface area of 12 units.

a ) Show that the volume V units^3, of the cuboid is given by V(x) = 2/3x(6-2x^2) (could not get this part at all)

B ) Find the exact value of x for which this volume is a maximum



I couldn't type up the harder ones cause of the diagrams.

[diane2ns]

1. log(x+1) - 2log(3) = 3 (base 2)

k, so use the prduct rule on the second term so 2log(3)=log(3^2) or log(9)

then u have log(x+1)-log(9)

[diane2ns]