Is it worth learning proofs of specific concepts in A-level maths?

E.g sine rule/m1m2=-1/power rule in differentiation etc

I love seeing how things came about and doing the proof is aesthetically pleasing however I books generally don't contain proofs and teachers don't have a clue. Is it even worth learning them?

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Reply 1

TenOfThem

Original post by UKBrah

Depends on what worth you are looking for

You will not gain exam marks

You will extend your maths skills by studying and understanding (not learning) proofs and other basic concepts

Reply 2

Doglamlico

It's definitely worth looking at them and understanding them, and most of them are in the book (it just says "you will not need to know this"). As for 'learning' them off by heart, there's no need, and not even the finest mathematicians will bother, as there are proofs for everything in maths, so you'd never be able to learn them all. As long as you've seen it and are convinced that 'the proof is nice, it can be proven' then your mind will accept it.

e.g. I remember looking at the power rule for differentiation in the C1 book, accepting it as a nice proof, but I can't remember the proof itself.

Reply 3

UKBrah

Original post by TenOfThem

Depends on what worth you are looking for

You will not gain exam marks

You will extend your maths skills by studying and understanding (not learning) proofs and other basic concepts

Ye, where can I find such proofs? Is there a book dedicated to proofs? I want to be a better mathematician!

Original post by The Polymath

Yeah the power rule proof is sick, but how does one expand a binomial to the power of n?!?

Reply 4

Doglamlico

Original post by UKBrah

Ye, where can I find such proofs? Is there a book dedicated to proofs? I want to be a better mathematician!
Yeah the power rule proof is sick, but how does one expand a binomial to the power of n?!?

Binomial expansion?

Reply 5

UKBrah

Original post by The Polymath

Binomial expansion?

How far out would you have to expand before being able to apply the limit?

Reply 6

TenOfThem

Buy a decent text book

Bostock and chandler probably still have a few proofs

Reply 7

Dark Lord of Mordor

Original post by UKBrah

How far out would you have to expand before being able to apply the limit?

Expand it fully, but you wouldn't need to write out all the terms, just the first few and the final few.

Reply 8

UKBrah

Original post by TenOfThem

Buy a decent text book

Bostock and chandler probably still have a few proofs

Original post by Dark Lord of Mordor

Expand it fully, but you wouldn't need to write out all the terms, just the first few and the final few.

Then you would use the limit as delta x -> 0 and the middle terms would cancel yeah cheers :smile:

Reply 9

gaffer dean

Original post by UKBrah

For C1, they may ask you to prove that the sum of an arithmetic series is "Sn = n/2[1a+(n-1)d]" and the proof is quite easy to learn and it's in the core textbook. Check the specification: http://www.edexcel.com/migrationdocuments/GCE New GCE/UA024850 GCE in Mathematics issue 2 180510.pdf if you're still not sure.

(edited 11 years ago)

Reply 10

UKBrah

Original post by gaffer dean

Im on MEI atm so I dont have to, but I will when im doing C2 after jan.

Reply 11

gaffer dean

Original post by UKBrah

Im on MEI atm so I dont have to, but I will when im doing C2 after jan.

Alright, I heard MEI's a lot harder than edexcel?

Reply 12

UKBrah

Original post by gaffer dean

Alright, I heard MEI's a lot harder than edexcel?

Considerably, there's a proof chapter.

Reply 13

MissBetBet

Original post by gaffer dean

Alright, I heard MEI's a lot harder than edexcel?

I do MEI but as I haven't studied any other boards I can't judge the relative difficulty.

But put it this way: my friend, who graduated from Oxford in Theoretical Physics years back, was surprised at my 97 in C2 saying "Especially in MEI, wow that is good!".

So apparently there is a difference? :')

Reply 14

Mr M

Study Forum Helper

It simply isn't true that one Awarding Body has more difficult A Levels than another. It is Ofqual's job to make sure the standards are exactly the same. If they weren't the same, all schools and colleges would immediately switch to the easier exam in order to maximise their position in League Tables.

Reply 15

MissBetBet

Original post by UKBrah

Considerably, there's a proof chapter.

We didn't even learn the proof chapter, just logic and luck really, it's only ever 2-3 marks on the paper, and sometimes does even crop up..

Reply 16

MissBetBet

Original post by Mr M

Or some schools want to teach the exam board that requires to learn and apply methods, rather than simply regurgitate what they've learned.
But your way makes more sense generally. :wink:

Reply 17

Mr M

Study Forum Helper

Original post by MissBetBet

Or some schools want to teach the exam board that requires to learn and apply methods, rather than simply regurgitate what they've learned.

It would be lovely to think that might happen (and I suppose it might in some independent schools) but state education is now a marketplace and League Table positions are everything.

Reply 18

MissBetBet

Original post by Mr M

It would be lovely to think that might happen (and I suppose it might in some independent schools) but state education is now a marketplace and League Table positions are everything.

That is unfortunately very true..
But that is the reasoning my maths teachers have given us for choosing MEI for my school (a good state school). Can't think of any other reason really, because it is a good department..

Reply 19

UKBrah

Original post by MissBetBet

We didn't even learn the proof chapter, just logic and luck really, it's only ever 2-3 marks on the paper, and sometimes does even crop up..

I tried a go at it but it just doesnt make sence even with livemaths.
I've learnt the logic which is simple as it gets but proving if something is divisible by 9 leaves me clueless.

Regardless what did you get in C1?