Hi! I'm Kyle, a 2nd year Oxford undergraduate studying Maths at Corpus Christi College.
I aim to be an understanding and friendly face, whilst being thorough with the material I cover. I've acheived A* grades in Maths, Further Maths and Additional Further Maths, plus I have a decent amount of volunteering experience, a lot of which working with kids of many ages.
I'll make sure the lesson is tailored to exactly what you want to cover. Whether that be going through a concept for the first time, or going through past exam questions. I want to make sure it's the best experience possible for you!
I hope to make the sessions enjoyable for both you and I! Work should be about enjoying what you study and I hope to be able to instill a little of my passion in you!
|Further Mathematics||A Level||£20 /hr|
|Maths||A Level||£20 /hr|
|.MAT.||Uni Admissions Test||£25 /hr|
|.STEP.||Uni Admissions Test||£25 /hr|
|Additional Further Mathematics||A-Level||A*|
|Before 12pm||12pm - 5pm||After 5pm|
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Jacob (Student) October 30 2016
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Using integration by parts, we can re-write the integral of ln(x) as (x*ln(x) - int(x*(1/x))) = x*ln(x) - x
Therefore, evaluating between 2 and 4 gives us (4*ln(4) - 4) - (2*ln(2) - 2) = 2ln(16/2) - 4 + 2 = ln(64) - 2. So a = 64 and b = 2
First we state the formula for sin(x+y)
sin(x+y) = sin(x)cos(y) + cos(x)sin(y)
Letting y = 2x
sin(x+2x) = sin(x)cos(2x) + cos(x)sin(2x)
Now sin(2x) = 2sin(x)cos(x) and cos(2x) = 1 - 2sin^2(x), substitute these into the formula gives us
sin(3x) = sin(x)(1-2sin^2(x)) + cos(x)(2sin(x)cos(x))
sin(3x) = sin(x) - 2sin^3(x) + 2sin(x)cos^2(x)
Now cos^2(x) = 1 - sin^2(x)
sin(3x) = sin(x) - 2sin^3(x) + 2sin(x)(1-sin^2(x))
sin(3x) = sin(x) - 2sin^3(x) + 2sin(x) - 2sin^3(x)
sin(3x) = 3sin(x) - 4sin^3(x)
Now letting x = 10, we get
sin(30) = 3sin(10) - 4sin^3(10)
Rearranging and evaluation sin(30) = 1/2
8sin^3(10) - 6sin(10) + 1 = 0
Hence sin(10) is a root of the cubic equationsee more