Higher Maths Paper 1

joshrogan

I'm slightly nervous for it, I fail by 1% in the mocks but I made alot of really silly errors.

For tommorow I'm confident I'll being able to get a C/B+ on paper 1 since I know all the theorems and I'm pretty good at the questions we've focused on(1,2,3,6,7 and good with 8 except for some of the area ones).


Also I'm worried they'll make it harder since it is the last year of this maths program and they will want to justify the new system by making more fail this year than next years exam.

biggaman

i'm kinda annoyed about the time
I have geo in the morning and I'm gonna study that instead of maths. Hope to Feck i'll be able to answer teh questions, havent done one in a few days
Just haven't the time for both

michaelm82803

yeah im very nervous about tomorrow.. i've kinda put a lot of pressure on myself but i need an A1/A2! but even though i know im capable of it im still so worried ill open the first page and see a question i cant do and freak out!
But at the moment im just going over all the exam questions for P1.. works like a charm

Prinkle

Hoping to do Maths in college in September so I need at least a b3 I think. Aiming for the A though so I'm pretty nervous. Especially for proofs, always mixing up the differentiation ones. I can take tomorrow morning to study though, I'm wrecked after English.

peckingduck

The statistics have to remains around the same level every year. No matter how smart/stupid we all are compared to last year, overall the percentages will remain almost identical in each subject for every grade. Hence no more/less than last year will fail. It would make the system show precedence to one year over another, or make one paper look easier than another year's.

PJelly

Our teacher gave us a crapload of theorems to learn for the course in one big lump, and I know them fairly well but I'm just wondering which specific ones come up on paper one?
I don't want to be revising paper 2 theorems by mistake beforehand.

kpac

The theorems which are asked on P1 are:
- Factor theorem [If f(k)=0 prove (x-k) is a factor of f(x)]
- DeMoivres theorem [by induction]
- Differentiation addition [d/dx(u+v) = du/dx + dv/dx]
- Differentiation product rule [d/dx(uv) = v(du/dx) + u(dv/dx)
- Differentiation quotient rule [d/dx(u/v) = [v(du/dx)-u(dv/dx)]/v^2]
- Differential rule [d/dx(x^n) = nx^(n-1)]

And of course the standard first principles rules, x^2, 1/x, sqrt(x), sin x, cos x.

hunii07

kpac wrote: »

The theorems which are asked on P1 are:
- Factor theorem [If f(k)=0 prove (x-k) is a factor of f(x)]
- DeMoivres theorem [by induction]
- Differentiation addition [d/dx(u+v) = du/dx + dv/dx]
- Differentiation product rule [d/dx(uv) = v(du/dx) + u(dv/dx)
- Differentiation quotient rule [d/dx(u/v) = [v(du/dx)-u(dv/dx)]/v^2]
- Differential rule [d/dx(x^n) = nx^(n-1)]

And of course the standard first principles rules, x^2, 1/x, sqrt(x), sin x, cos x.

Is that all the theorems... I'm so worried about it tomorrow and I can't think is there any more?

partyatmygaff

There's the integration proofs too...

kpac

Oh yes, volume of a cone and sphere about the x-axis. Handy once you know them.

nommm

I'm dreading tomorow. Just sat down and attempted a few questions and I can't do any of them. Making lot's a stupid mistakes. I hope it's just because I'm tired.

hunii07

nommm wrote: »

I'm dreading tomorow. Just sat down and attempted a few questions and I can't do any of them. Making lot's a stupid mistakes. I hope it's just because I'm tired.

You're probably just tired....My teacher said you can't study or concentrate properly after 8 o clock...:)

aranciata

Anybody think circular integrals will come up? I believe it's only been asked once (and they gave you the hint to let it = sinx)

aranciata

aranciata wrote: »

Anybody think circular integrals will come up? I believe it's only been asked once (and they gave you the hint to let it = sinx)

Came up in 1999 and not since to my knowledge... they did give the hint to let x=2sinx, but it was still an entire part C!

PJelly

aranciata wrote: »

Came up in 1999 and not since to my knowledge... they did give the hint to let x=2sinx, but it was still an entire part C!

I hope it comes up! Very doable and an easy 20 marks!

JamJamJamJam

hunii07 wrote: »

Is that all the theorems... I'm so worried about it tomorrow and I can't think is there any more?

In complex numbers you could have to prove the conjugate of (sum of two complex numbers) equals sum of conjugate of one and the conjugate of the other...
Or the same but with products instead of sums...
^those two are straightforward - you might be able to do it even without studying them!

There's also the conjugate root theorem and there's nothing too tricky in that either, but I personally wouldn't guess the proof without having a look at it first!

Prinkle

JamJamJamJam wrote: »

There's also the conjugate root theorem and there's nothing too tricky in that either, but I personally wouldn't guess the proof without having a look at it first!

Sorry, which one is that? Have really got to start looking at my proofs!

hunii07

Prinkle wrote: »

Have really got to start looking at my proofs!

me too:(

JamJamJamJam

Prinkle wrote: »

Sorry, which one is that? Have really got to start looking at my proofs!

The conjugate root theorem is the one that says if you have a quadratic with real coefficients, then the conjugate of one root is also a root!

As in if you have ax^2 + bx + c = 0
And if one root is p + iq, the conjugate root theorem says the other root is p - iq

aranciata

JamJamJamJam wrote: »

The conjugate root theorem is the one that says if you have a quadratic with real coefficients, then the conjugate of one root is also a root!

As in if you have ax^2 + bx + c = 0
And if one root is p + iq, the conjugate root theorem says the other root is p - iq

How is it proven to you know? Is it online or in Aidan Roantree's textbooks? or Less Stress More Success??

FREAKING OUT cause i've never seen/heard that before! any help would really be appreciated!

kpac

And as long as there's no imaginary part to any equation, the second root will always be the conjugate of the first one.

hunii07

aranciata wrote: »

How is it proven to you know? Is it online or in Aidan Roantree's textbooks? or Less Stress More Success??

FREAKING OUT cause i've never seen/heard that before! any help would really be appreciated!

I'm the same I know how to get the conjugates but i didnt know there was a proof:(

aranciata

hunii07 wrote: »

I'm the same I know how to get the conjugates but i didnt know there was a proof:(

I read it came up in the 1999 paper and looking at the question (i assume it's 3b part 2), it's not exactly a "proof" and the answer could maybe be gotten by doing a minus-b?

If it were a proper proof surely it would be in the proof section of Less Stress More Success? I could be ENTIRELY wrong though haha!

kpac

Yeah, simply doing -b will show the other root.

partyatmygaff

It's not a proper proof. The quadratic formula is enough to prove it.

Maybe_Memories

Could someone please post up the paper whenever they're out of the exam?

Absolutely dying to see it

aranciata

kpac wrote: »

Yeah, simply doing -b will show the other root.

phew! it's good to know it though, might be handy if i'm stuck for time or have to verify an answer!

that 1999 paper might be a good one to do before the exam, lots of stuff there that haven't come up in a while! might do it now

hunii07

aranciata wrote: »

I read it came up in the 1999 paper and looking at the question (i assume it's 3b part 2), it's not exactly a "proof" and the answer could maybe be gotten by doing a minus-b?

If it were a proper proof surely it would be in the proof section of Less Stress More Success? I could be ENTIRELY wrong though haha!

kpac wrote: »

Yeah, simply doing -b will show the other root.

Thanks yeah I know how you'd get it but I was freakin out there when someone mentioned it as a proof... thanks

RHunce

Please god leave there be no volume of a cone or sphere in question 8! I was out for them, I would be totally screwed!

hunii07

RHunce wrote: »

Please god leave there be no volume of a cone or sphere in question 8! I was out for them, I would be totally screwed!

agreed I hate them

kpac

hunii07 wrote: »

agreed I hate them

They're simple! As long as you can do basic intergration you can do these proofs.

River Song

The integration ones are my most favourite of all of them

I hope that the S/S question is easy, I always do it as I'm trying to avoid the 4 Diff. proofs.

I've been told I'm more than able for an A, but it's ALWAYS paper 2 that screws me over...fun weekend ahead.

hunii07

Generally integration is one of my better questions .. I don't know I still don't like those proofs though

Maybe_Memories

Michael_E wrote: »

I've been told I'm more than able for an A, but it's ALWAYS paper 2 that screws me over...fun weekend ahead.

Me too. I did my LC last year, got 97% on Paper 1, did crap on paper 2, and in the end I got an A2, but I was 0.12% from an A1, a single mark... :rolleyes:

Marking scheme crucified me. I made two tiny mistakes on paper 2. Should have lost 3 marks for each, so 6 in total. But, the way the marking scheme was changed around I lost a total of 30 marks for two tiny addition mistakes... :rolleyes:

River Song

Maybe_Memories wrote: »

Me too. I did my LC last year, got 97% on Paper 1, did crap on paper 2, and in the end I got an A2, but I was 0.12% from an A1, a single mark... :rolleyes:

Marking scheme crucified me. I made two tiny mistakes on paper 2. Should have lost 3 marks for each, so 6 in total. But, the way the marking scheme was changed around I lost a total of 30 marks for two tiny addition mistakes... :rolleyes:

Oh God, that sucks ><

I just did a mock for my teacher the other week. Got an A1 in paper 1, got a B3 in Paper 2 :rolleyes: I am just going balls-out this weekend for paper 2 ><

kpac

Obviously most people here prefer paper 1? I prefer paper 2 to be honest...

RHunce

kpac wrote: »

They're simple! As long as you can do basic intergration you can do these proofs.

Care to explain how they work for somebody who never did them?

River Song

RHunce wrote: »

Care to explain how they work for somebody who never did them?

Sphere

• Draw a circle of equation x^2+y^2=r^2. Radius = r and centre = (0,0)
• Then say that the points it cuts the x-axis are (0,r) and (0,-r) .... they're where we rotate through the x-axis to make our sphere. (i.e. limits)
• Re-arrange equation to get y^2=r^2-x^2
• Intergrate (pi)(y^2) dx between r and -r.

Cone

• Draw a line y=mx (it passes straight through the origin and is diagonal).
• Label a point on this line (r,h)
• So the vertical distance = r (radius) and the horizontal height = h (height)
• If you turn it 90dgs clockwise, it looks more like a cone that way, if you're having trouble visualising it.
• So you can say the slope [m] of this line is the rise over the run so it's r/h
• Replace r/h for m in -> y=mx
• So you now intergrate (pi)(y^2)dx between h and 0.

Maybe_Memories

RHunce wrote: »

Care to explain how they work for somebody who never did them?

You've got a formula in the tables, V = pi (integral of y dx between b and a)
you need to get y in terms of x, so if its a cone or cylinder, just put in the equation of the line, the distance between the x axis and the highest point on y is your base radius, distance between the origin and this x point is your h.

Same with a sphere, except you're dealing with y squared

River Song

RHunce wrote: »

Care to explain how they work for somebody who never did them?

I can write both out quickly and post them here if you like?

kpac

RHunce wrote: »

Care to explain how they work for somebody who never did them?

Basically, the integral of pi times y-squared with respect to x between r and -r will give you 4/3(pi)(r^3)

The cone is similar enough. The integral of pi times y-squared with respect to x between h and 0. It's hard to explain in words.


EDIT: we're not quick enough...

partyatmygaff

Michael_E wrote: »

Sphere

• Draw a circle of equation x^2+y^2=r^2. Radius = r and centre = (0,0)
• Then say that the points it cuts the x-axis are (0,r) and (0,-r) .... they're where we rotate through the x-axis to make our sphere. (i.e. limits)
• Re-arrange equation to get y^2=r^2-x^2
• Intergrate (pi)(y^2) dx between r and -r.

Cone

• Draw a line y=mx (it passes straight through the origin and is diagonal).
• Label a point on this line (r,h)
• So the vertical distance = r (radius) and the horizontal height = h (height)
• If you turn it 90dgs clockwise, it looks more like a cone that way, if you're having trouble visualising it.
• So you can say the slope [m] of this line is the rise over the run so it's r/h
• Replace r/h for m in -> y=mx
• So you now intergrate (pi)(y^2)dx between h and 0.

Proofs are far easier to remember in this format. I do this for all my proofs.

Maybe_Memories

Okay, guy above did a way better job at explaining

in case anyone wants to know why you multiply by pi, pi is the area of a unit circle, so when you have a the area of a triangle, multiplying it by the area of a circle spreads the triangle out making a cone.

Okay that was a terrible explanation, but hey, it makes sense to me

Digits

Area of a circle by integration methods. Likely to come up guys? I cant find the proof if anyone would care to tell me?

aranciata

anybody know how to find the roots of a cubic? (1999 paper is hard, grr)

aranciata

aranciata wrote: »

anybody know how to find the roots of a cubic? (1999 paper is hard, grr)

without guessing, cause I have a kx^2

partyatmygaff

aranciata wrote: »

anybody know how to find the roots of a cubic? (1999 paper is hard, grr)

If you have a Casio FX-83...

Push mode and switch to table mode. Type in the cubic equation and set start and end values and the step value to 1. Look for where f(x)=0 and they are your roots.

Then work backwards to show your steps on the exam paper

Maybe_Memories

Digits wrote: »

Area of a circle by integration methods. Likely to come up guys? I cant find the proof if anyone would care to tell me?

Equation of a circle is y^2 + x^2 = r^2, rearrange and take square roots to get

y = root(x^2 - r^2)

Plug this into formula i mentioned a few posts above

There;s a substitution for this, which I don't remember off the top of my head, someone mentioned it as the thing on the 1999 paper.

Integrate between r and -r, unsubstitute if thats even a word...

Should be okay

River Song

I'm working on deriving the area of a circle proof, I doubt it'll come up. It's not in my book (T&T)

aranciata wrote: »

without guessing, cause I have a kx^2

• Sub in 0, 1, -1, 2, -2 ......... for x. When you find a value for x that makes the equation = 0, you can say f(number) = 0, therefore (x - number) is a factor.
• Divide that (x - number) into the original equation, you'll find a quadratic equation.
• The two roots of that quadratic, and the original (x - number) are your 3 roots of the cubic.

partyatmygaff

Ah... are you on Q3bii of 1999?

You use long division to get a quadratic and you solve that for the remaining two roots.

Divide [LATEX]z^3 - (k)z^2++(22)z - 20 [/LATEX] by [LATEX]z-3-i[/LATEX]

Maybe_Memories

partyatmygaff wrote: »

If you have a Casio FX-83...

Push mode and switch to table mode. Type in the cubic equation and set start and end values and the step value to 1. Look for where f(x)=0 and they are your roots.

Then work backwards to show your steps on the exam paper

This.

Also, to find one of the roots straight away, if you have ax^3 + bx^2 + cx + d, one of the factors has to be d/a, so firstly try that and the negative value of it.

Get a factor from the root, divide into the cubic to get a quadratic.