**HL Maths P2 Before/After

finality

You know if you were asked to explain "if and only if"?

Could you give an example like x=2 iff x is an integer greater than 1 and less than 3? Or is that too obvious? :L

ehshup

finality wrote: »

You know if you were asked to explain "if and only if"?

Could you give an example like x=2 iff x is an integer greater than 1 and less than 3? Or is that too obvious? :L

it doesn't matter how obvious it is, it's a clear example encapsulating the idea of iff.

Hayezer

'if and only if' lolwut? I'm frightened about the amount of stuff I've never seen before

K_1

ChemHickey wrote: »

Are people using their calculators to find the line-of-best-fit?

If so, how do you do it on a Sharp

You buy a casio :P


Anyone know where I could find a proof of the cosine rule in the obtuse case? We only did it in acute case and I can't find an easy one anywhere for obtuse.

ChemHickey

ehshup wrote: »

refer to http://inside.lambton.on.ca/Nav/index_html?RECORDID=1408&TYPE=28

Thanks

ChemHickey

K_1 wrote: »

You buy a casio :P


Anyone know where I could find a proof of the cosine rule in the obtuse case? We only did it in acute case and I can't find an easy one anywhere for obtuse.

Just draw the diagram on a circle of radius b where the obtuse side lies from (0,0) to the edge of a part in the second quadrant, label this (bCosA,bSinA). Extend this point out past the circle (first quadrant) to a point lying outside the circle called (c,0) and find distance lal by distance formula.

Hope it kinda makes sense.

waiting4

so whats the timing break down of this paper?

K_1

ChemHickey wrote: »

Just draw the diagram on a circle of radius b where the obtuse side lies from (0,0) to the edge of a part in the second quadrant, label this (bCosA,bSinA). Extend this point out past the circle (first quadrant) to a point lying outside the circle called (c,0) and find distance lal by distance formula.

Hope it kinda makes sense.

Any chance you could scan it and put it up?! Sorry!:o

Mista

ChemHickey wrote: »

Jeeeez. :P

Theres no such thing as a crooked line :P

Also, what this "if and only if" thing? O.o

Nazata

ChemHickey wrote: »

Yes, and yes. But I'd say they'd only give that to us in Q6A with a specific theorem.

Thanks. Question 6 seems an awful lot of work for 25 marks, though there's a good chance they'll just ask theorem 11, 12 or 13 I suppose...

leaveiton

Another stupid question coming through!

In the theorems, especially theorem 11 where you have to construct a few things (Draw a few lines etc) is it okay to do it all on the one diagram?

ChemHickey

Mista wrote: »

Theres no such thing as a crooked line :P

Also, what this "if and only if" thing? O.o

I added in the straight part as you can have a "curved line". You never know where they'll deduct a mark or two!

It's just a maths term. I think we need 1 example, and seeing as I hadn't one prepared, I'll probably just use finality's one.

BL1993

For iff, just say

'a triangle is equilateral iff its 3 angles are 60 degrees'

ChemHickey

K_1 wrote: »

Any chance you could scan it and put it up?! Sorry!:o

My scanner doesn't work!

I don't do it this way, and I didn't watch the whole thing but hope this helps.

Mista

leaveiton wrote: »

Another stupid question coming through!

In the theorems, especially theorem 11 where you have to construct a few things (Draw a few lines etc) is it okay to do it all on the one diagram?

Yep I usually do it in a different colour pen.. but just make sure its done right in pencil first :P

Also, you have to explain your construction before you do the proof..

ChemHickey wrote: »

I added in the straight part as you can have a "curved line". You never know where they'll deduct a mark or two!

It's just a maths term. I think we need 1 example, and seeing as I hadn't one prepared, I'll probably just use finality's one.

A curved line is a curve :P I'm going into this too much..

Guess I will too... whats the definition for it?

leaveiton

Mista wrote: »

Yep I usually do it in a different colour pen.. but just make sure its done right in pencil first :P

Also, you have to explain your construction before you do the proof.

Thanks! Yeah I know how to lay out the wording of it, just wasn't sure if I could do it all on the one diagram

sarahmocks

anyone have a list of the things they could ask us to explain e.g. random sampling?

MattHelders

Stupid question but my mind has gone blank so can someone tell me how to do this?

A random variable x follows a normal distribution with mean 150 and standard deviation 20. Find P( 170<x<190)

That is supposed to be less than or equal to

finality

MattHelders wrote: »

Stupid question but my mind has gone blank so can someone tell me how to do this?

A random variable x follows a normal distribution with mean 150 and standard deviation 20. Find P( 170<x<190)

That is supposed to be less than or equal to

That's easy because it's between 1 and 2 standard deviations above the mean. So it's (.95-.68)/2 because it's only for one side. So P is 0.135 or 13.5% of the values would be between 170 and 190. You could also do this by z scores.

leaveiton

MattHelders wrote: »

Stupid question but my mind has gone blank so can someone tell me how to do this?

A random variable x follows a normal distribution with mean 150 and standard deviation 20. Find P( 170<x<190)

That is supposed to be less than or equal to

Convert to z-values by doing (170 - 150)/20, and (190 - 150)/20

Take your readings from the highest z-value first (the 190 - 150 one). Then take the readings from the lower one, and take it away from one. Then take the result that you got there away from your first reading.

Hope that made sense, sorry if not.

EDIT: Or do what finality said :P

finality

Z scores gives a slightly different answer (13.59%). Hmm. I wonder would you be penalized for doing it by empirical rule?

ChemHickey

finality wrote: »

Z scores gives a slightly different answer (13.59%). Hmm. I wonder would you be penalized for doing it by empirical rule?

No, there'd be a window of an answer. It's just so much easier doing empirical rule.

MattHelders

What do you do if you get a minus z score?

leaveiton

MattHelders wrote: »

What do you do if you get a minus z score?

You take it as positive, get the reading, and then take that away from 1.

ChemHickey

MattHelders wrote: »

What do you do if you get a minus z score?

1 minus the positive value for it as it is a perfectly symmetrical graph.

MattHelders

Can someone tell me where proof by contradiction is in Active Maths?

Or give me a breakdown of it?

ChemHickey

MattHelders wrote: »

Can someone tell me where proof by contradiction is in Active Maths?

Or give me a breakdown of it?

It's not.

just allow root 2 to be a/b where a and b have no common factors

then a = b root 2. Therefore a^2 is 2b^2 and so a must be even. Therefore a can be written like a=2k where k is any number(like induction)

Sub 2k into original and find b^2 which turns out to be 2a^2. so b is 2z where z is any number

This means root2 is 2k/2z which contradicts us saying a and be having no common factors.


Excuse any mistakes. I'm half asleep.

Pepperr

For another example of the proof by contradiction, can you say..

a^2 + b^2 < 2ab

a^2 -2ab + b^2 < 0

(a - b)^2 < 0
But brackets ^2 are always positive so

a^2 + b^2 > 2ab

Thanks in advance!

Luno

Can't bring myself to leave the house, getting nervous about all the boxes. What if I don't colour them all in time?

MattHelders

Everybody in my class is distraught at the paper. I was happy with mine but they're making me nervous. Hoping for around 65% on that paper to add to around 50% in paper 1