Proofs we should know/understand? (1 Viewer)

[townie]

What proofs do you reckon we should know off by heart for the HSC, or at least have a good knowledge of.

The only ones i can think of are

- the tangent/secant proof PQ^2=QR.QS
- d(0.5v^2)/dx=dv/dt
- all the parabola one's (although i suppose they're not proofs, rather derrivations)

any other ideas?

 

[Estel]

You should have a good knowledge of ALL proofs.

 

[Li0n]

except for maybe say, derivation of inverse functions
they arent that hard but i dont think theyll ask you to show that d/dx sin^-1x = whatever

 

[Estel]

It's possible they'd lead you through it.
Having known it before would be an advantage.


Of course, I'd learn the proofs just to convince myself.

 

[Xayma]

Why not? They aren't hard at all and really can be done without much remembering at all.
Let sin^-1 x=y
x=sin y
dx/dy=cos y
=cos (sin ^-1 x)
=√(1-x²)
dy/dx=1/dx/dy
∴ dy/dx=1/√(1-x²)

 

[Estel]

I'd be inclined to say they wouldn't just ask it outright like that because I've seen that sort of thing in 4U trials...

 

[Grey Council]

mmm
I think what Xayma meant was that, even though it might not be asked:
Why not? They aren't hard at all and really can be done without much remembering at all.



so even though you may be right, Estel, (gah, what is it anyway? Is Estel a boy or a girl? :S:S:S) there is no harm in knowing it.

I don't know it. I don't even know what Xayma is talking about, lol.

but, as for proofs, hmm. You should have a knowledge of everything ,really. :-\

 

[Xayma]

I was responding to Li0n. About d/dx sin^-1 x=whatever.

I don't see why they couldn't put it as a two mark question early on.

 

[Li0n]

i wouldn't mind it in a test either, i just presumed that since its on the standard integrals sheet, they wouldnt.

 

[mojako]

You should have a good knowledge of ALL proofs.

disagree =p
it's a good idea to know them but in most exams you can get away without knowing them

and, as you said it yourself, they normally lead you through it
hmm... but its possible that the lead-up isnt easily understood by the majority of students...

I just quickly went through the syllabus and I dont think there are any particular proofs that are significantly more likely to be asked than other proofs, so I prefer not to list them since if I do I need to list them all and they wont be useful.

Oh, if you have the syllabus, go to page 16:
"Finite series and further properties of bonomial coefficients"
(I've said this be4 in the ext2 forum but I'll repeat again)
bonomial... it hasn't been fixed yet.
(the ext2 syllabus had at least 1 real error.. not a simple typo.. and its fixed in the 2nd edition)

 

[Estel]

I say to understand the proofs not on the basis that they will be tested, but on the basis that it's good for you to understand what all your assumptions are based on, and what you can/can't do.
It's also good for your mathematics in general... not necessarily memorising the proof, but understanding it, and being able to adapt it.

 

[withoutaface]

I read somewhere that they can't ask the tangent secant proof anymore, you just need to know the formula.