Maths Paper II Q c ii (Vectors) 1999

cocoa

ok, I'm going to spell this right out to you because you're clearly not catching on easily.

Imagine a, b, c and d are all points.
Now move a to o
Now move b, c and d under the same transformation.

The only thing that's changed is the question looks a ****load neater. All of the lines mentioned in the question originate at a.

sniped by tomlowe, *agrees*

Tomlowe

also im pretty sure that the marking schemes are copyrighted, so you cant just stick them up on the internet and make a profit, its somewhere on the examinations website

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dan719

Tomlowe wrote:

redefining is the same as moving, but it doesnt matter in this particular question because there is no reference to the origin: all the vectors are transformations from one to the other and all the vertices of angles are at a, so redefining a as the origin doesn't change any angles.

P(1) says: 1(2) is even, which is true
assume k(k+1) is even
(k+1)(k+2)
=2(k+1) + k(k+1)

2(k+1) is even as it is divisible by 2
we assumed that k(k+1) is even

the sum of two even numbers is an even number, so 2(k+1) + k(k+1) is even.

Since the truth of P(k) implies the truth of P(k+1) and the statement is true for n=1, the statement is true for all n E N (less 0)

As far as I can see if you make a logical progression without using numbers to prove a statement in general then apply it to the specific in question, that should be absolutely fine.

No you misunderstood me. The question itself is piss easy, and it can quite easily be done using induction but why not use so called pure logic.

Statement one. Any even number multiplied by an odd number is always = to even number. e.g 6x3=18

if k is even, k+1 is odd but from above odd by even = even

if k is odd , k+1 is even and again using above. This is just as acceptable as and in my view more elegant then using induction. In this case induction just seems too heavy handed as it were.:D

ZorbaTehZ

cocoa wrote:

ok, I'm going to spell this right out to you because you're clearly not catching on easily.

Imagine a, b, c and d are all points.
Now move a to o
Now move b, c and d under the same transformation.

The only thing that's changed is the question looks a ****load neater. All of the lines mentioned in the question originate at a.

sniped by tomlowe, *agrees*

You realize that you said redefine a as the origin, not use transformations?

Tomlowe

yep, sure, but for leaving cert purposes id always use induction (and would always be told to anyway)

Pure logic should be fine, but seems like you're making a hell of a lot of trouble for yourself

Tomlowe

zorbatehz: same thing

cocoa

ZorbaTehZ wrote:

You realize that you said redefine a as the origin, not use transformations?

you realise that it's quite annoying that while everyone else I talk to understands the word "redefine" to mean imagine everything moves with it/imagine it was always there but for you I have to go to the trouble of explaining it slowly?

ZorbaTehZ

Letting a be the origin.

As opposed to:

Letting a be the origin and moving all the other points through the same transformation.

How is that the same thing?

Tomlowe

redefine a as the origin means move the origin to a, not move a to the origin