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.
Maths Questions
- junglemonkey
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Maths Questions
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- diane2ns
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Re: Maths Questions
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)
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)
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- diane2ns
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Re: Maths Questions
Alive
I used to watch the world pass me by.
I'd sit and wait for it to slow down, but why?
The world gave up on me, that I know.
For the pain goes on, life will no longer glow.
Then one day it hit me like a wall.
There was no reason for me to fall.
For all that I had bottled up inside,
Was a remarkable person waiting to be alive.
I used to watch the world pass me by.
I'd sit and wait for it to slow down, but why?
The world gave up on me, that I know.
For the pain goes on, life will no longer glow.
Then one day it hit me like a wall.
There was no reason for me to fall.
For all that I had bottled up inside,
Was a remarkable person waiting to be alive.