SunnyBoys
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I've come across this equation from the formula booklet:

Now I haven't actually been this taught this in school and with the exam on wednesday that's not looking too good.
Is there any resources anywhere where it actually teaches this? I'm unsure where to go. I know how to do the normal binomial expansion where the n has an integer. Thanks
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RDKGames
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(Original post by SunnyBoys)
I've come across this equation from the formula booklet:

Now I haven't actually been this taught this in school and with the exam on wednesday that's not looking too good.
Is there any resources anywhere where it actually teaches this? I'm unsure where to go. I know how to do the normal binomial expansion where the n has an integer. Thanks
That's for C4.

You don't need to use it.
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imundercover
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this isn't needed for c2, don't worry. the same formula booklet is used for all modules thats why it's in there.
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SunnyBoys
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(Original post by RDKGames)
That's for C4.

You don't need to use it.
(Original post by imundercover)
this isn't needed for c2, don't worry. the same formula booklet is used for all modules thats why it's in there.
Ah that's a relief, thanks
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Tommy59375
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(Original post by RDKGames)
That's for C4.

You don't need to use it.

The Edexcel formula book lists this under C2, so is this formula required for C2 Edexcel maths?
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RDKGames
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(Original post by Tommy59375)
The Edexcel formula book lists this under C2, so is this formula required for C2 Edexcel maths?
The binomial formula is the one above, but there is a much more simplified version for when the exponent is a natural number, and that's the one you use for C2.
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NotKidding
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(Original post by RDKGames)
That's for C4.

You don't need to use it.
I'm afraid he does need it. I thought they didn't use this in C2 but the Mock paper they created this year has a question where this way of working it out is needed. Did it earlier, was kind of surprised.

However OP I've done most if not all the past papers and i've only ever seen 1 question (the mock paper) need this. It's unlikely that it comes up.
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RDKGames
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(Original post by NotKidding)
I'm afraid he does need it. I thought they didn't use this in C2 but the Mock paper they created this year has a question where this way of working it out is needed. Did it earlier, was kind of surprised.

However OP I've done most if not all the past papers and i've only ever seen 1 question (the mock paper) need this. It's unlikely that it comes up.
Can I see the question?
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NotKidding
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(Original post by RDKGames)
Can I see the question?
http://pmt.physicsandmathstutor.com/...%20Edexcel.pdf

It's Q7
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Tommy59375
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(Original post by RDKGames)
The binomial formula is the one above, but there is a much more simplified version for when the exponent is a natural number, and that's the one you use for C2.

Yes but the problem is in the Edexcel formula book,
- a^n + nC1 a^(n-1) b + nC2 a^(n-2) b^2 + ... + nCr a^(n-r) b^r + ... + b^n (n E N)
AND
- (1+X)^n = 1 + nX + (n(n-1)X^2)/(1x2) + ... + (n(n-1)...(n-r+1)X^r)/(1x2x...xr) (abs(X) < 1, n E R)
both of these are listed under C2.

Are you saying one of the formula given for C2 is not required for C2? Surely in this case it should be listed on the C4 page?

[sorry for lack of formatting, the toolbar did not come up for some reason]
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RDKGames
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At quick glance, clearly you can use the C2 formula because you're told n is a positive integer - ie a natural number.
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RDKGames
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(Original post by Tommy59375)
Yes but the problem is in the Edexcel formula book,
- a^n + nC1 a^(n-1) b + nC2 a^(n-2) b^2 + ... + nCr a^(n-r) b^r + ... + b^n (n E N)
AND
- (1+X)^n = 1 + nX + (n(n-1)X^2)/(1x2) + ... + (n(n-1)...(n-r+1)X^r)/(1x2x...xr) (abs(X) < 1, n E R)
both of these are listed under C2.

Are you saying one of the formula given for C2 is not required for C2? Surely in this case it should be listed on the C4 page?

[sorry for lack of formatting, the toolbar did not come up for some reason]
I didn't do Edexcel but I'm quite certain you don't need it and they put it there because they don't want two different binomial formulae in the booklet perhaps.

To answer whether you need it or not for C2, I'm tagging someone who can confirm notnek, so any questions regarding that you can ask him. You can certainly use it for C2, but in C2 the exponent is always a natural number so you can use the simplified version.
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Tommy59375
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(Original post by RDKGames)
At quick glance, clearly you can use the C2 formula because you're told n is a positive integer - ie a natural number.

How exactly are you able to use the first formula? You don't know what n is so you can't use the nCr button, and it's a disaster to use nCr = n!/(r!(n-r)!) from the formula book.

We were taught to use the second formula (supposedly C4) to do this sort of question.
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RDKGames
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(Original post by Tommy59375)
How exactly are you able to use the first formula? You don't know what n is so you can't use the nCr button, and it's a disaster to use nCr = n!/(r!(n-r)!) from the formula book.

We were taught to use the second formula (supposedly C4) to do this sort of question.
Not really a disaster.

Coefficient of x^2 is \frac{n!}{2!(n-2)!}k^2

Coefficient of x^3 is \frac{n!}{3!(n-3)!}k^3

Equate the two:

\frac{n!}{2!(n-2)!}k^2= \frac{n!}{3!(n-3)!}k^3

Divide by k^2n! leaves you with \frac{1}{2!(n-2)!}=\frac{k}{3!(n-3)!}

Now (n-2)!=(n-2)(n-3)! and 3!=3\cdot 2!

Rewrite it: \displaystyle \frac{1}{2!(n-2)(n-3)!}=\frac{k}{3\cdot 2!(n-3)!}

Multiply through by 2!(n-3)!

 \frac{1}{(n-2)}=\frac{k}{3} \Rightarrow 3=k(n-2)

Took me less than 4 mins, and I'm not even sure if the examiner would've given you the marks for using the C4 formula as this tests your understand of the factorial notation, but notnek can tell confirm/deny that.
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Tommy59375
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(Original post by RDKGames)
Not really a disaster.

Coefficient of x^2 is \frac{n!}{2!(n-2)!}k^2

Coefficient of x^3 is \frac{n!}{3!(n-3)!}k^3

Equate the two:

\frac{n!}{2!(n-2)!}k^2= \frac{n!}{3!(n-3)!}k^3

Divide by k^2n! leaves you with \frac{1}{2!(n-2)!}=\frac{k}{3!(n-3)!}

Now (n-2)!=(n-2)(n-3)! and 3!=3\cdot 2!

Rewrite it: \displaystyle \frac{1}{2!(n-2)(n-3)!}=\frac{k}{3\cdot 2!(n-3)!}

Multiply through by 2!(n-3)!

 \frac{1}{(n-2)}=\frac{k}{3} \Rightarrow 3=k(n-1)

Took me less than 4 mins, and I'm not even sure if the examiner would've given you the marks for using the C4 formula as this tests your understand of the factorial notation, but notnek can tell confirm/deny that.

Thanks for that, I'd not have thought of doing it like that... when I say "disaster" I meant, it was when I tried! I don't think they could rightfully withold marks because you didn't use the "right" method though -- there are usually more than one way to get to the right answer and if you've used a valid formula there's nothing wrong. They would have to say "Using the so and so formula..." in the question wouldn't they? For example, it's allowed to use y-y1=m(x-x1) at GCSE, although not expected, and in C1 AP questions, and C2 GP questions you're allowed to list out all the terms and add them, instead of just using the Sn formula.
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username3128778
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pretty sure you can use either

the ncr formula - you can use for positive integers

the binomial formula for ALL values

http://www.examsolutions.net/tutoria...=C2&topic=1308
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Discrepancy
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It's part of the specification Edexcel maths GCSE expanding two or more binomials.
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Sir Cumference
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Tommy59375 NotKidding Both formulae are part of C2 and you'll see them both used in Edexcel textbooks. So you can use either in an Edexcel C2 exam as long as you use them correctly.

The (1+x)^n formula is useful when you have a question where n is left as a variable. You'll see questions like this in the Edexcel textbook but I haven't seen one like this in Edexcel exams for the last 10 years. I have seen questions like this in older papers though (that mock paper question above is pre-2007 I think). RDKGames has shown that you can still use the (a+b)^n formula for a question like this although the working will probably be harder.

I teach both formulae with an emphasis on the (a+b)^n formula since this will be used the most in C2 but I recommend students practice some textbook questions using the (1+x)^n formula. I'd prefer it if there were more exam questions where the (1+x)^n formula was useful so it was clear to students/teachers that both formulae should be taught. At the moment I feel that a large percentage of students completely ignore the second formula, which is a probably why you won't see it being useful in the 2017 exam. Or alternatively the (1+x)^n formula should only be part of C4. This won't be an issue in the new linear exams where C2 and C4 topics are part of the same exam papers.
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Sir Cumference
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(Original post by RDKGames)
Took me less than 4 mins, and I'm not even sure if the examiner would've given you the marks for using the C4 formula as this tests your understand of the factorial notation, but notnek can tell confirm/deny that.
For Edexcel exams it would be fine to use the "C4 formula" to tackle this question in C2 and that would be the expected method. If this question was in the 2017 paper then I feel it would cause a lot of problems.
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RDKGames
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(Original post by notnek)
For Edexcel exams it would be fine to use the "C4 formula" to tackle this question in C2 and that would be the expected method. If this question was in the 2017 paper then I feel it would cause a lot of problems.
Mhm... Nevertheless, it's a nice test on factorials when the exponent is unknown, though this is easily dodged by using the actual version of the binomial formula. Shame.
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