Maths H P2 Disaster Prevention.

For that question:

A is equal to 12(x/60)=x/5 km.
B is equal to 6(x/60)=x/10 km.


Therefore, B has travelled a total of x/10 km, but the total distance is 4km. So the distance remaining is (4 minus x/10)

Using Pythagoras' theorem (if you draw a diagram, you'll see why), you have D^2=(x/5)^2 + (4-x/10)^2

Therfore 2D(dD/dX)=2(x/5)(1/5) + 2(4 minus x/10)(-1/10)

and then go from there. Sorry if it's not clear. It's very hard to do it without a diagram.

2e

Thanks... I can see how to do that one now. But in general how do you go about doing them??? Sorry if it seems like I'm asking the same question again, but I am not able to get my head round them and as the cone came up last year I'm worried it'll be a distance one again. THANKS!! (again)

If there are two variables in it, you have to find a link. Ex: If it tells you to find the maximum area that a four-sided fence of perimeter 30m has, you can see straight away that 2x + 2y=30. So Y=(15-x).

So the area A=xy.

And that's equal to x(15-x)

=15x-x^2.

Then differentiate to find the max/min area, and let it = 0

dA/dX=15-2x=0

Therefore x=7.5

and Y=15-7.5=7.5 (Ok I picked out a bad example, as it doesn't make sense. )




So A=xy=7.5(7.5)=whatever

To check whether it's a maximun or minimum, we find te second deriative:

d^2A/dX^2=-2

Sice the answer is less than zero, it is a maximum.

So the answer is the "whatever" above.


So, the steps are:

If there are two variables, find the link.

Differentiate and let it be equal to zero.

See if your answer is a max or a min by finding the second deriative.

State your answer.

JackKelly

first of all READ THE QUESTION!

They always ask you to put something in terms of something else. That bit is the key so go no further without doin that. In 2004 for example, they ask for volume of cylinder in terms of r and pi. So get what the normal formula is for vol of a cylinder

Vol = (pi)(R^2)(h)

You have to get rid of H, but we know

Circumfrence + H = 3

H = 3 - Circumfrence

H = 3 - (2)(pi)(R)

So Vol in terms of pi and r = (pi)(r^2)(3 - (2)pi(r))

Than go onto the next piece. The Easy part.

Max or Min is when f '(x) = 0 Max is when f ''(x) < 0 etc etc.

Apologies if i did something wrong,have no paper and im still thinking in vectors!

EDIT: Got there before me ^ . The first part is always the hard bit, so get that and you have it.

Its been a max min prob for the last two years, a Maclaurin Series before that, so it could always be a McLaurin this time.

snappieT

Probability is a piece of piss. I'll also be doing vectors, trig and statistics, with the line as a backup. I will be avoiding the circle at all costs.

JackKelly

Yea, i hate the circle too for some reason. I'll do it if i have to.

I hate the circle for the same reason I hate probability: there's usually something awkward in the question.

That being said, I still prefer it a LOT more than probability.

JackKelly

only good thing about prob is that you can do the questions fairly quickly, so if you do ok in the rest of the paper, you can still do the two prob's on top of that in <20 mins.

2e

TimAy wrote:

only good thing about prob is that you can do the questions fairly quickly, so if you do ok in the rest of the paper, you can still do the two prob's on top of that in <20 mins.

Thats my masterplan too!!!!!!!!! Then I have extra time to do the circle/ line depending on which is easier.

Scarinae

How do people find questions 6 and 7 difficult? I think probability etc is the easiest thing on the course, I'm surprised they haven't made it more difficult. Maybe there are two types of people who do higher Maths - those that hate probability and love trig, or those that hate trig and love probability?
I was surprised there weren't more proofs on paper 1. I mean, x squared from first principles? that's so easy it's unbelievable

BraveheartGal

me loves the circle!
vectors...kinda freakin out about em. i always had it in my head that theyre p easy and they are but jus looked at 2/3 of em there and theyre trickier than i thought

ill prob do
circle
vectors
probability and trig (3 out of the 4, depends on how tough they are)
and the stupid horrible god forsaken calculus question

2e

I know but it sucked it only being a part a. :-( I find trig and probabilty fairly handy but I always make stupid mistakes that I can never find afterwards, even if i go at snails pace. Thats why I'm doing it quick and fitting in an extra question. Plus unlike other questions you never know if your right or not. (e.g stuff like give answer in surd form).

Scarinae

Yeah I'm gonna be doing The Line, the two Trig questions, the two Probability/Statistics ones and Further Calculus

BraveheartGal

the line

*shudders in horror....sideshow bob style*

2e

My deffo qs:2 prob, 2 trig, option, vectors. Extra: eaisest of the 2 left, probably and hopefully circle!!

JackKelly

Fishie wrote:

How do people find questions 6 and 7 difficult? I think probability etc is the easiest thing on the course, I'm surprised they haven't made it more difficult. Maybe there are two types of people who do higher Maths - those that hate probability and love trig, or those that hate trig and love probability?
I was surprised there weren't more proofs on paper 1. I mean, x squared from first principles? that's so easy it's unbelievable

Yea seems to be two types of people. I love trig and i don't mind Prob too much. Still, i'll try and avoid it.

That X2 by 1st principles was v easy. it should have been in part b though.

Scarinae

TimAy wrote:

That X2 by 1st principles was v easy. it should have been in part b though.

Are they usually part b's? I'm a very forgetful person

There isn't really much they can ask you for the Line, is there? It's a very Junior Cert style question I think, not much to it

BraveheartGal

it is the easiest first principle on the course, was hopin for quotient cos that wld have been worth a lotta marks! and i knew it off in a song!

OTliddy

BraveheartGal wrote:

vectors are p*** easy
theyre the matrices of paper 2

What!?!? Linear transformations are the matrices of paper 2. If there is any question I won't be doing it'll be vectors.

Scarinae

BraveheartGal wrote:

it is the easiest first principle on the course, was hopin for quotient cos that wld have been worth a lotta marks! and i knew it off in a song!

Yeah, I'd heard the quotient rule was due as well (probably on this board, now that I think about it!) It's a pity yeah, cos it would have been a nice easy 20 marks! You made up a song about it?!?

BraveheartGal

it was a good song too
had a bit of rap in it too
cos im all street
*cough*

BraveheartGal

OTliddy wrote:

What!?!? Linear transformations are the matrices of paper 2. If there is any question I won't be doing it'll be vectors.

the only thing i remember bout when we were doin the line
was the fact that my teacher had a new tie that week



vectors are luverly! what are you on?!?

OTliddy

BraveheartGal wrote:

the only thing i remember bout when we were doin the line
was the fact that my teacher had a new tie that week



vectors are luverly! what are you on?!?

Nothing! All our class hates vectors. They're so quirky.

mrs. hamlet

Omg, im screwed 2moro!!

I LOVE probability and vectors! We never did statistics though so i can't do q7!

I'm not too worried about the option either!

But the circle and line! :eek:
And i hate trig with a passion! It's just so bleh...

the smiley one

mrs. hamlet wrote:

Omg, im screwed 2moro!!

I LOVE probability and vectors! We never did statistics though so i can't do q7!

I'm not too worried about the option either!

But the circle and line! :eek:
And i hate trig with a passion! It's just so bleh...

The line is lovely (it's just algebra in disguise), circle does not really deviate from past papers.... trig look - look over formulas and proofs.....

DIE probability DIE (but keep the stats and difference equations...)

mrs. hamlet

Me and trig just don't get on! I'm going to be pickin' the trig question that looks the easiest cuz i'm only doin' 1! All those proofs....
and the perpendicular dist proof is tipped to come up!

I hope they have not put in some complication for the difference equation!

In further calculus, i'm hopin we might get a max/min prob for b and a mclaurin series for c!

I think the max/min was the a part in our mocks which was strange....

Scarinae

mrs. hamlet wrote:

Me and trig just don't get on!

Ditto

JackKelly

any ideas for the maclaurin series? TanX has come up so i hope it wont reappear.

BraveheartGal

can anybody help me out with the option question?

2000 paper 2, b (i)
its integration by parts but its the trickier integration by parts

youve to integrate e ^2xCosxdx
i integrated it, then integrated it again but im completely stuck

if someone cld post up the solution id love ya forever cos i reckon that type of int. by parts will come up because it hasnt come up since 2000

thanks!

Crumbs

BraveheartGal wrote:

can anybody help me out with the option question?

2000 paper 2, b (i)
its integration by parts but its the trickier integration by parts

int(e^2x.cosx)dx

Let u = cosx and dv = e^2x.dx

Should get it out as (cosx.e^2x)/2 + 1/2[int(e^2x.sinx)dx]


Integrate that last bit by parts again to get (sinx.e^2x)/2 - 1/2[int(e^2x.cosx)dx]


Jam that back into the first part, multiply out the brackets and you should get:

int(e^2x.cosx)dx = (cosx.e^2x)/2 + (sinx.e^2x)/4 - 1/4[int(e^2x.cosx)dx]


Rearrange to get:

5/4[int(e^2x.cosx)dx] = (2cosx.e^2x + sinx.e^2x)/4


Some more manipulation:

int(e^2x.cosx)dx = (e^2x/5)(sinx + 2cosx) + c


Hmm, that's messy and I tried to summarise it as short as I possibly could.
Just ask if you need more clarification on any part of it.

E&OE