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Definitive list of proofs for HL Maths PII
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06-06-2009 11:51pm#1OK, here's what I have, please let me know what proofs are missing:
1. Equation of a tangent to a circle
The equation of the tangent to the circle x^2 + y^2 = r^2 at the point (x1, y1) on the circle is: x1.x + y1.y = r^2
2. Angle between two lines
If θ is the angle between two lines with slopes m1 and m2, then:
tanθ = (m1-m2)/(1+ m1.m2)
3. Cos (A+B)
Cos(A +
= CosA.CosB - SinA.SinB
4. Perpendicular distance from a point to a line
The perpendicular distance, d, from the point (x1, y1) to the line ax + by + c = 0 is given by:
|ax1 + by1 + c| / sq.rt(a^2 + b^2)
5. Difference equations theorem
If α and β are the roots of the quadratic equation px^2 + qx + 2 = 0 and Un = lα^n + mβ^n for all n, then:
pun+2 + qun+1 + run = 0 for all n
6. Cosine Rule
In triangle abc, a^2 = b^2 + c^2 - 2bc.CosA
Then there are a load of possible Trig proofs. I THINK most of these can be answered just using and manipulating information from the log tables.
Please add any I've forgotten0
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anyone have a list of all the smaller proofs for example the tan(a+b)
I tried making it look ''mathsy'', you know with fractions ect..., but the usual mathods I use on a different forum didn't work
. Since I can't make powers, ^2 means to the powers of 2. And to make it clear, all angles are in brackets.
1. cos^2(A) + sin^(2) = 1
2. Cosine formula a^2 = b^2 + c^2 - 2bc cos(A)
3. cos(A+B) = cos(A)cos(B) - sin(A)sin(B)
4. cos(2A) = cos^2(A) - sin^2(A)
5. sin(A+B) = sin(A)cos(B) + cos(A)sin(B)
6. sin(2A) = 2sin(A)cos(A)
This is where this might get hard to understand. By / I mean a fraction
7. tan(A+B) = [tan(A) + tan (B)]/[1 - tan^2(A)]
8. tan2A = [2tanA]/[1 - tan^2(A)]
9. cos2A = [1 - tan^2(A)]/[1 + tan^2(A)]
10. sin2A = [2tanA]/[1 + tan^2(A)]
11. cos^2(A) = 1/2[1 + cos(2A)]
12. sin^2(A) = 1/2[1 - cos(2A)]
If I typed anything wrong let me know. Good luck deciphering
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+1 on this. And to be honest, you have enough time tonight to go over the whole paper before tomorow.On a more serious note, I'd recommend you brush up on the option you're doing more than any other question, it's the one question you can't avoid or do somethign else instead of.
Pick a hard exam year and do out the paper. Dont bother trying to mark it, just make a note of any questions you had trouble with and do them out of your notes. Best way to study maths, regardless of how much time you have!
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Most importantly, asleep before 11:30.
In terms of what to study in particular...
Trigonometry and line proofs
Trig identities
Maclaurin series
Integration by parts
Max/Min questions
Vectors
Solving 3d triangles.
After that, just practice some probability. If you can do all that, it'll at least pull your ass above the pass line.0 -
Dont panic,,,, being positive really does help.
Know your probability well and your option, go over as many examples of them as you can and go over the proofs.
I think it helps to go over the things you're worst at in the morning before you go in, like get up about a hour early,, but it depends on what works for you.
Good luck anyway:)
AND look in the inspiration thread,:):). 0 -
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