Honours Maths Proofs

Feddd

Can anyone give me a list of the mandatory proofs for Paper 2 or a website with them? My notes for them have suddenly all gone missing.

analyse this

1. Perp. Distance from point to line
2. Cosine rule
3.Cos (A-B) and all the other trig proofs that follow on from that
4.Equation of tangent to circle of centre (0,0) and radius r i.e. xx1+yy1=r^2
4. Loads of trig stuff that I am too tired to explain...Cos2A...Sin2A.. etc

nick23

Circle: Tangent Theorem
Line: Angle between lines
Perpendicualr distance formula
Trig: cos^2A + sin^2A = 1
compound angle formula
COsine rule
Discrete maths: Difference equation formula

analyse this

Line: Angle between lines

came up last year... I think I might just ignore it:D

chas_88

analyse this wrote:

came up last year... I think I might just ignore it:D

you'd learn that in 5 minutes if you wanted to, just in case. it's probably the easiest proof on paper 2 anyway.

tolosenc

chas_88 wrote:

it's probably the easiest proof on paper 2 anyway.

Well, it is IN the the tables. Essentially.

melsman

nick23 wrote:

Circle: Tangent Theorem

is that xx1 + yy1??? dont recognise the name

JC 2K3

chas_88 wrote:

you'd learn that in 5 minutes if you wanted to, just in case. it's probably the easiest proof on paper 2 anyway.

What about sin2A and cos 2A?

E92

No shortcuts with Honours Maths. There were no proofs in Paper1,meaning there should be plenty of them in paper 2(hopefully).

analyse this

Do we need to be able to derive Maclarin Series?

chas_88

JC 2K3 wrote:

What about sin2A and cos 2A?

I don't even count those as proofs.

mp3guy

analyse this wrote:

Do we need to be able to derive Maclarin Series?

That's not a proof, and you will have to if you do question 8.

JC 2K3

I looked over the proofs last night, and honestly, they seem almost easier than the JC ones(talking partly relative to ability level at the time).

I don't understand how the line transformation proofs are considered "proofs" tbh....

analyse this

Yeah exactly they are basically common sense! Take two parallel lines, translate them and they are parallel!:D

JC 2K3

The proof given in texts and tests for proving that the line is mapped is like:
Substitute the expressions for x and y in terms of x' and y' into the line equation.
Substitute the expressions for x' and y' back to x and y.
Therefore, a line transformation maps a line.

???

analyse this

Yeah the book can be pretty vague! Its so frustrating when it jumps a line and doesn't state what it did!!AAAGGH:mad:

JC 2K3

Well, it doesn't do that there, I'm just saying that substituting values in and then out again doesn't prove anything that wasn't already obvious.

I don't really have a problem with them jumping unnecessary lines tbh.

MathsManiac

Some transformations map lines to lines and others don't. So, it's a fairly significant thing to prove that all transformations of this particular form do map lines to lines, (and segments to segments, etc.)

I think a good teacher would have shown you other transformations that don't map lines to lines, so that you would appreciate the significance of what's being proved here.

JC 2K3

Surely such a transformation would involve squared variables etc. ?

It's just kind of obvious that a linear transformation maps a line to a line...

And I do have a good teacher, I just haven't payed attention in class for about 6 months.

MathsManiac

A transformation that maps a line to a curve might involve squared variables alright (or some other non-linear functions). I wasn't suggesting that transformations of the type I mentioned were on the syllsbus, just pointing out that what you're proving is significant, and that having a look at such transformations makes one realise this significance.

And why is it obvious that a linear transformation should map a line to a line? Is it just because someone decided to call it linear?

By the way, a linear transformation that is non-invertible might NOT map a line to a line. For example, the transformation x'=12x+16y, y'=9x+12y maps the line 3x+4y=6 onto the point (24, 18).

Nehpets

"compound angle formula"

what is that?

MathsManiac

Nehpets wrote:

"compound angle formula"

what is that?

Probably meant to say "compound angle formulae" (or formulas).

The formulae for cos(A+B), sin(A+B), tan(A+B), cos(A-B), sin(A-B), tan(A-B) are often called "the compound angle formulae", (because the angles they talk about are made up of other angles).

Nehpets

Oh cool, phew!