Maths paper 1

Closet Monkey

Is this all we have to cover for Paper 1 Maths?

• Algebra
• Differentiation
• Integration
• Complex Numbers
• Sequences and Series
• Financial Maths
• Proof by Induction

SmidgeBall

yeah and real number (But they can't really ask you much on that, make sure you know how to draw a line the square root of 2 and the square root of 3) and area and volume may appear in paper one too, but again you can't really study for that at this stage At least for higher level, you didn't specify.

mad turnip

SmidgeBall wrote: »

yeah and real number (But they can't really ask you much on that, make sure you know how to draw a line the square root of 2 and the square root of 3) and area and volume may appear in paper one too, but again you can't really study for that at this stage At least for higher level, you didn't specify.

integration is higher only if i'm not mistaken.

SmidgeBall

I don't know the ordinary course at all...

Monsieur Folie

As far as learning work goes (stuff you can just regurgitate on the page if it comes up), I've got a bit of a list. Not sure if it's complete so if anyone else thinks of something else throw it up and together we'll have everything covered!

- Proof a number is irrational by contradiction
- Constructing root 2, root 3
- Derive formula for an arithmetic and geometric progression
- Prove De Moivre's theorem by induction
- Differentiation by 1st principles of: x^2, x^3, 1/x, x^1/2, Sin x, Cos x.
- 4 Calculus Theorems

Missing anything? Or is there anything there I don't actually need? =P

Informaniac

I think ur missing the nine theorems.....

Monsieur Folie

Informaniac wrote: »

I think ur missing the nine theorems.....

What, the geometry ones? That's paper two..

Informaniac

oh crud yh ur right thats paper two....sorry dont really know the project maths course as we only started doing it september last year and now i have to go sit it on friday

moss1234

ok whats the
- Derive formula for an arithmetic and geometric progression
and
- 4 Calculus Theorems ? :S

ScummyMan

Monsieur Folie wrote: »

As far as learning work goes (stuff you can just regurgitate on the page if it comes up), I've got a bit of a list. Not sure if it's complete so if anyone else thinks of something else throw it up and together we'll have everything covered!

- Proof a number is irrational by contradiction
- Constructing root 2, root 3
- Derive formula for an arithmetic and geometric progression
- Prove De Moivre's theorem by induction
- Differentiation by 1st principles of: x^2, x^3, 1/x, x^1/2, Sin x, Cos x.
- 4 Calculus Theorems

Missing anything? Or is there anything there I don't actually need? =P

What?

Monsieur Folie

I don't know if we need them or not, but our teacher did them with us and they're in the book I have..

A short derivation of the two formulae: arithmetic: n/2[2a-(n-1)d] and geometric: [a(1-r^n)]/(1-r)

I can stick them up if no one has them but the fact that no one has them means I probably don't need to know them in the first place.. They're very simple though, nothing to be worrying about.

Undeadfred

I've never come across the derivation of the series formulae. What is it?

Monsieur Folie

Hang on, I will write them out and stick them up here in the next while. Could somebody with a greater knowledge of the syllabus than I please clarify though? I don't want to be giving people stuff to learn if they don't actually need to learn it, we've enough on our plates. :P

Informaniac

pls put them up our teacher didnt bother with that

yournerd

Gonna do every paper 1 I can get my hands on tomorrow

Monsieur Folie

Okay here they are. Sorry if they're not great, have to do them in a hurry because I'm off to bed! Awkwardness of emailing them to myself from the iPod so I could then try and get them to Boards on the laptop!

Anyway for the Arithmetic Series:
Write it out
Write it out in reverse
Add both lines
Divide by 2

Geometric:
Write it out
multiply by constant - r
Get the difference (Sn - rSn)
You'll be left with a-r^n
Factorise both sides as shown
Isolate Sn

Simples!

Now to the important question, do we even need these?




If these images don't work or are illegible I am sorry, I am exhausted and going to bed. I will write them out neater and take a better photo in the morning before Eng P2 if it transpires that we do actually need them and people are still stuck!

weirdspider

Monsieur Folie wrote: »

Okay here they are. Sorry if they're not great, have to do them in a hurry because I'm off to bed! Awkwardness of emailing them to myself from the iPod so I could then try and get them to Boards on the laptop!

Anyway for the Arithmetic Series:
Write it out
Write it out in reverse
Add both lines
Divide by 2

Geometric:
Write it out
multiply by constant - r
Get the difference (Sn - rSn)
You'll be left with a-r^n
Factorise both sides as shown
Isolate Sn

Simples!

Now to the important question, do we even need these?




If these images don't work or are illegible I am sorry, I am exhausted and going to bed. I will write them out neater and take a better photo in the morning before Eng P2 if it transpires that we do actually need them and people are still stuck!

I really don't think they are for learning, they just show the derivation of the formulas. I have the Sn learned just incase but I haven't even seen the first one!

weirdspider

I'm strangely excited for this exam...
(calculus save me )

Monsieur Folie

weirdspider wrote: »

I really don't think they are for learning, they just show the derivation of the formulas. I have the Sn learned just incase but I haven't even seen the first one!

Ah well. They're so simple that once you've seen them once you'll know them if it does happen to come up. I'm so used to having to be able to reproduce derivations from physics that I probably got a bit carried away here.

Side note: This course is brand new and therefore impossible to predict, but anybody reckon I have any weight in saying that there'll be a long-ish question on Financial Maths because it's so new and they'll want to try it out?

Also I was originally thinking we'd get some of the calculus proofs seeing as I heard they're not on the project maths course and therefore we're the last year to have them. Then again, if they're getting all geared up for project maths in the first place, they might just neglect them.

These are just guesses on what we might see, to be clear. I'm not trying to guide my study or predict the paper or anything since it's not possible with such a new course. It's just fun to hypothesise!

Undeadfred

Its on Wikipedia

Slow Show

I can't see those images as my internet is ridiculous but is that just making a geometric/arithmetic series using variables instead of numbers. Nothing's stopping them asking it tbh, it was on one of the mock papers as far as I know! Once you know what you're doing it should be grand.

Something it might be worth having a look over as you can learn it would be the volume proofs for integration, you can be asked to prove the formulae for the volume of a sphere and cylinder.

Monsieur Folie

Slow Show wrote: »

I can't see those images as my internet is ridiculous but is that just making a geometric/arithmetic series using variables instead of numbers. Nothing's stopping them asking it tbh, it was on one of the mock papers as far as I know! Once you know what you're doing it should be grand.

Something it might be worth having a look over as you can learn it would be the volume proofs for integration, you can be asked to prove the formulae for the volume of a sphere and cylinder.

Yeah my friend was actually saying that. I mean if you're good with integration and use the formula from the tables you can usually just figure it out, but I'd much rather be familiar with them so that it's one less thing to stress about on the day.

suitcasepink

Slow Show wrote: »

Something it might be worth having a look over as you can learn it would be the volume proofs for integration, you can be asked to prove the formulae for the volume of a sphere and cylinder.

I dont know what that is

Informaniac

I dont know if this is true or not but a lot of people in my school said half the sixth years who sat project maths in the mock exam failed.....can anybody clarify this? please...

weirdspider

Slow Show wrote: »

I can't see those images as my internet is ridiculous but is that just making a geometric/arithmetic series using variables instead of numbers. Nothing's stopping them asking it tbh, it was on one of the mock papers as far as I know! Once you know what you're doing it should be grand.

Something it might be worth having a look over as you can learn it would be the volume proofs for integration, you can be asked to prove the formulae for the volume of a sphere and cylinder.

Ah jeez, really?! They should really make the syllabus more clear...only finding this out a day before Paper 1. *Ugh yet another thing to learn*

weirdspider

Informaniac wrote: »

I dont know if this is true or not but a lot of people in my school said half the sixth years who sat project maths in the mock exam failed.....can anybody clarify this? please...

Yes apparently the DEB was quite difficult and I'd agree...I'd like to think it won't reflect the actual exam but that may be wishful thinking!

Monsieur Folie

Wasn't there a 97% pass rate in honours maths last year, though? Don't worry guys, if people start failing it'll make their precious new course look bad. Short of you leaving everything blank and/or getting absolutely everything completely wrong in both papers, there is a very low chance of failure, I'd imagine. :P

EvM

Monsieur Folie wrote: »

As far as learning work goes (stuff you can just regurgitate on the page if it comes up), I've got a bit of a list. Not sure if it's complete so if anyone else thinks of something else throw it up and together we'll have everything covered!

- Proof a number is irrational by contradiction
- Constructing root 2, root 3
- Derive formula for an arithmetic and geometric progression
- Prove De Moivre's theorem by induction
- Differentiation by 1st principles of: x^2, x^3, 1/x, x^1/2, Sin x, Cos x.
- 4 Calculus Theorems

Missing anything? Or is there anything there I don't actually need? =P

How might one prove De Moivre's with induction?

Monsieur Folie

EvM wrote: »

How might one prove De Moivre's with induction?

What book do you have? I have "Active Maths 4" and it's in it. Hang out, I'll write it out anyway, to make sure I know it off myself. :P

bitburger

Informaniac wrote: »

I dont know if this is true or not but a lot of people in my school said half the sixth years who sat project maths in the mock exam failed.....can anybody clarify this? please...

im in a class of around 15 adults, one of us passed the mock, i got 39.5% still cannot decide if i should drop to foundation or not, im completley unprepared but i might just risk the OL paper tomorrow, i would be totally fine with just getting a D

Monsieur Folie

Apologise again for the quality of the photo but hopefully it's legible. This is how I prove De Moivre's theorem by induction. It's actually not too bad and if you remember the rule for multiplying polar numbers together then it doesn't take long either!

EvM

Monsieur Folie wrote: »

What book do you have? I have "Active Maths 4" and it's in it. Hang out, I'll write it out anyway, to make sure I know it off myself. :P

.

Ah, I have New Concise Project Maths 4 and Im quite sure its not in it . That'd be much appreciated in any case

Undeadfred

Monsieur Folie wrote: »

Apologise again for the quality of the photo but hopefully it's legible. This is how I prove De Moivre's theorem by induction. It's actually not too bad and if you remember the rule for multiplying polar numbers together then it doesn't take long either!

You jumped loads of steps going from the 2nd last line to the last line

wow exuberant

Can financial maths be a 50 marker?

Monsieur Folie

Undeadfred wrote: »

You jumped loads of steps going from the 2nd last line to the last line

Do I need to write it out though, since if you remember the rule for multiplying polar numbers that's all you really need?

Maybe I'll go through the process tomorrow if it comes up though, just to be safe.

Undeadfred

Monsieur Folie wrote: »

Do I need to write it out though, since if you remember the rule for multiplying polar numbers that's all you really need?

Maybe I'll go through the process tomorrow if it comes up though, just to be safe.

That's fine for the modulus, but for the argument you have theta on one side and k(theta) on the other. You cant use multilication of powers for that, you have to use page 14-15 of the tables, unless there's something I'm missing here

Monsieur Folie

Hmm, I'm fairly sure if two numbers are in polar form you can just add those bits if you're multiplying, or subtract them if you are dividing.. I'll look into it now though, thank you for pointing that out.

Slow Show

Where did you get that proof from M.Folie? I can see how it works but I, and I reckon most other people, have a different proof where R isn't included in the formula and you end up having to use a formula in the tables book. Tbh I'd be a bit wary of your proof as the formula given in the tables book is (costheta +isintheta)^n = cosntheta + sinntheta), and I reckon that's where you should be working from not with z's and the like, as I don't think that strictly proves the theorem though I could definitely be mistaken!

EDIT: Thinking it over your way with the modulus is probably fine.

HPMS

Can the proof of de moivre's theorem for n is an element of Z be asked? It says in the book beside the n E N that that make be asked but it doesn't specify if the other one can be??

Undeadfred

Monsieur Folie wrote: »

Hmm, I'm fairly sure if two numbers are in polar form you can just add those bits if you're multiplying, or subtract them if you are dividing.. I'll look into it now though, thank you for pointing that out.

Oh **** yeah sorry you're right God what am I saying.

Btw, the one in my book doesn't have a modulus either and uses page 14-15 of the tables book when multiplying it out

weirdspider

HPMS wrote: »

Can the proof of de moivre's theorem for n is an element of Z be asked? It says in the book beside the n E N that that make be asked but it doesn't specify if the other one can be??

Yup it can be

Undeadfred

You know for the proof of the differentiation rule it says n E No (N underscore o)

What is No? (N underscore o)
Am i right in guessing that its Natural numbers including 0?

HPMS

weirdspider wrote: »

Yup it can be

Thank you!!

Btw, the one in my book does have a modulus...uses the same formula as on page 20 of the tables:

r(cosX + isinX)^n = r^n(cosnX + isinnX)

Is that what you're all talking about?

CookieMonster.x

weirdspider wrote: »

Yup it can be

It says in the syllabus 'prove de moivre's theorem by induction for n E N so unless it's written somewhere else I presume we don't?

HPMS

CookieMonster.x wrote: »

It says in the syllabus 'prove de moivre's theorem by induction for n E N so unless it's written somewhere else I presume we don't?

Oh really? Well then the syllabus must be right! That's a relief cause I really was not looking forward to learning that proof!

aoifemcg94

Please tell me this mainly on about higher maths?
because if not, WHAT :O :L

CookieMonster.x

HPMS wrote: »

Oh really? Well then the syllabus must be right! That's a relief cause I really was not looking forward to learning that proof!

Well I presume that's right.. Hopefully! It looks complicated enough without all that negative integer stuff! Hopefully I'm right and it's just N!

shawnanana

EvM wrote: »

.

Ah, I have New Concise Project Maths 4 and Im quite sure its not in it . That'd be much appreciated in any case

De moivre's is in New Concise Project Maths 5 on page 60

weirdspider

CookieMonster.x wrote: »

It says in the syllabus 'prove de moivre's theorem by induction for n E N so unless it's written somewhere else I presume we don't?

I'm not sure, my teacher told us we do and she really seems to know her stuff! Sorry to cause any confusion but it may be worth learning if you have extra time to be safe.

yournerd

ahhhhhhhhhhhhhhhhhhhhhhh

lostatsea

weirdspider wrote: »

I'm not sure, my teacher told us we do and she really seems to know her stuff! Sorry to cause any confusion but it may be worth learning if you have extra time to be safe.

She obviously doesn't know her stuff. The syllabus is very clear: Prove De Moivre's for n an element of N. End of story.