c4 binomial expansion

You're trying to go above or at least at the edge of C4 to answer a simple C4 Q that has a simple method. I said 'we need to', I didn't say no other way. Big extrapolation. This is a semantic discussion.

This is not any harder than C4 and it's only "above" C4 in your opinion because it's dfferent to what the C4 textbook tells you. Another textbook may not even mention the factorising method.

I think the majority of students finish A Level maths thinking that the only way to expand $(x+y)^n$ in C4 is to change it into $x^n(1+\frac{y}{x})^n$. This is a misconception caused by teachers/textbooks.

This is not any harder than C4 and it's only "above" C4 in your opinion because it's dfferent to what the C4 textbook tells you. Another textbook may not even mention the factorising method.

I think the majority of students finish A Level maths thinking that the only way to expand $(x+y)^n$ in C4 is to change it into $x^n(1+\frac{y}{x})^n$. This is a misconception caused by teachers/textbooks.

I want to understand how it actually works, not just learn an rule to do incredibly easy exam questions which I've done dozens of (only slightly hard ones are where you have to use your result for estimations or figure out what value of x you would need for a particular estimation).But yeah I had forgotten all my c2 work on binomial and combinations when I was taught this topic in c4 so I just learnt how to do the questions with very little understanding about why. So far there hasn't been any maths past core a-level, just some algebraic manipulations.

I will add though, that I don't get why nC2=n(n-1)/2 using formula nCk=(n-k)(n-k+1)/k! @Zacken

I think this sort of thing is a recurring problem in A level maths where a concept is stated with little to no introduction or explanation and students are expected just accept it.

But at the same time, there are going to be students who won't understand the finer details required for the explanation, so it's probably better to avoid them

The problem I have with it though, is that you have teachers who aren't willing to explain the finer details to those who would understand them and are inquisitive.

I want to understand how it actually works, not just learn an rule to do incredibly easy exam questions which I've done dozens of (only slightly hard ones are where you have to use your result for estimations or figure out what value of x you would need for a particular estimation).But yeah I had forgotten all my c2 work on binomial and combinations when I was taught this topic in c4 so I just learnt how to do the questions with very little understanding about why. So far there hasn't been any maths past core a-level, just some algebraic manipulations.

I will add though, that I don't get why nC2=n(n-1)/2 using formula nCk=(n-k)(n-k+1)/k! @Zacken

You're wanting to be different and go above the Q level. I can understand why (to show off), but I disagree with it. I was also misinterpreted.

Wondering why it must always be in the form (1+ax)^n when doing the expansion in ascending powers of x? (probably should have found this out before my exam but whatever)

I have never "shown off" in this forum - you are so wrong in thinking this. If this was a C4 student who was revising for their exams then there would be no way that I would allow this discussion to continue because it might confuse the student.

Please read the OP's question again and remember that they have finished C4:



The answer is that it doesn't have to be in that form but it's done to make use of the famous binomial series formula. Plus it makes the expansion easier and it is easier to spot convergence properties.

This is not any harder than C4 and it's only "above" C4 in your opinion because it's dfferent to what the C4 textbook tells you. Another textbook may not even mention the factorising method.

I think the majority of students finish A Level maths thinking that the only way to expand $(x+y)^n$ in C4 is to change it into $x^n(1+\frac{y}{x})^n$. This is a misconception caused by teachers/textbooks.

Yeah, I thought that too. I wish I'd known the other expansion for the exam (for $(x+y)^n$ directly without factoring out), it would've probably saved me time on this year's relatively tricky OCR C4 paper.

Thanks @Zacken and @Notnek for posting

Yeah, I thought that too. I wish I'd known the other expansion for the exam (for $(x+y)^n$ directly without factoring out), it would've probably saved me time on this year's relatively tricky OCR C4 paper.

Thanks @Zacken and @Notnek for posting

Properly reading and copying questions would have saved me a lot more time XD. Fingers crossed 90 ums is mid 80s... At least core 3 was nice apart from the last question.

This may sound like a silly question after all this but this thread has got me rethinking what the main reasons are that C4 textbooks tell students to factorise first.

If students got used to expanding using (x+y)^n = x^n + nx^(n-1)y + ... and not changing the form first, would the expansion be much harder?

And why doesn't the C2 textbook tell students to factorise first when there are integer powers?

@Zacken @RDKGames thoughts?

Memorising a long formula can be harder and more vulnerable under pressure than pulling out a factor and multiplying through on the (1 + x)^n formula given.

It's a small, quick job.

Haha yeah, I messed up C1 this year by misreading not one but 2 questions and I didn't notice my misreads until I had about 10 mins left. I rushed the arithmetic and got the wrong answers in the end when I retried the questions, but hopefully I'll get some method marks. I think the rest of the exams went relatively okay, C4 was very time pressured for me and I had no time to check, which stressed me out a lot, but it seems I did alright. Now the wait till August...

Good luck with your results!

You too and sounds like luckily, I did AS last year although I did find core 1 a nightmare last year too (scrapped an A but made up for it in c2 and stats) from being unprepared and lacking confidence in non calc calculations.

But yeah considering we're both probably gonna apply for physics natsci at cambridge, not getting an A* in a-level maths would definitely scupper chances so fingers well and truly crossed! Did you answer all the questions in c4? I couldn't do about 7 marks and I wish I had spent time checking previous questions rather than banging head against harder questions I couldn't do. I don't know for a fact but I'm fairly sure I forgot +c and also in implicit differentiation question, I think I might have said x^2=4 (which was right), therefore x=ROOT2 (which is obviously wrong). Annoying that silly errors have probably dipped me into 80s.

That said I'm sure you've got an A* for sure rodgenium boi :P (when is your smarty pants seminar thingy on that btw?).

The (x+y)^n formula is just as long as the (1+x)^n formula. They could put (x+y)^n in the formula book instead of (1+x)^n.