Hey Mr Bicen, Could you please explain why at 9:16 we say (x+2)^2+1>1 and not 0. Following from the previous step, I thought that that it would be (x+2)^2+1>0
Hi sir, the edexcel textbook mentions a proof is a ‘logical’ argument, and involves working through ‘logical’ steps. I don’t really understand what this ‘logical’ means in the context of a proof, could you please explain it. Thank you.
Logical, put simply, means that one step follows on from the previous step. If something is logical, then it flows and makes sense, and is clear. You explain what you do, and it is well reasoned - so with a proof, each like follows on from the previous line, and any ‘new ideas’ of the proof are explained by you.
Hi Bice, topics on proof are just this playlist, then Proofs on Contradiction Year 2 chapter 1 - first topic - and then chapter 8 core pure 1. Is that everything on proof? Thanks (Doing AS FM)
So if you want two DIFFERENT odd numbers, 2n +1 and 2m + 1 is best (or use p and q). If you want two CONSECUTIVE odd numbers, then use the same letter for both, and have one with 1 and the other with 3, e.g. 2m+1 and 2m+3. (Note: consecutive odds would be like 17, 19, or 29, 31 for example)
@@MuhammadHameed-hl2fc These are different odd numbers that are 4 apart - so too specific. What if it works for odd numbers that are 4 apart, but not all odd numbers? So we need to be as general as the wording of the question suggests, and use n and m for each one separately.
I also wanna know at 7:15 why you put n2+1 before n2 like ik otherway around the answer will be negative but there is nothing i believe in question that tells that. Help!
It’s only because when we find the difference between two numbers, we do the larger subtract the smaller. Think about if someone asked you to find the difference between 60 and 100. You would do 100-60 rather than 60-100. If you do it the wrong way round, and get a negative answer, you can just negate it to find the absolute difference!
Could you please explain Question 9 in Ex 7D: 3n^2 - 4n + 10 - prove it is positively for all values of n. The exam book worked solutions don’t make sense please could you help me
So all they've done is completed the square on the 3n^2 - 4n + 10 expression. Once you complete the square, it becomes clear that the expression is always greater than 26/3, so is therefore always positive!
so just to clarify, if 3 vertices are given and we have to prove that the triangle is right angle triangle, we cannot use pythagoras theorem? So obviously dont start with P.theorem. if I start calculating dis between all 3 sides, then next logical step would be to state P. theorem, then insert values to show that c^2 =a^2+b^2, that'd be correct proof right?
Incredible Video sir Thank you.
great vid
Hey Mr Bicen,
Could you please explain why at 9:16 we say (x+2)^2+1>1 and not 0. Following from the previous step, I thought that that it would be (x+2)^2+1>0
We could say that too! I put 1 because of the fact we had also added 1 to it, so I know it is also greater than 1. Just a bit of extra detail!
Hi sir, the edexcel textbook mentions a proof is a ‘logical’ argument, and involves working through ‘logical’ steps. I don’t really understand what this ‘logical’ means in the context of a proof, could you please explain it. Thank you.
Logical, put simply, means that one step follows on from the previous step. If something is logical, then it flows and makes sense, and is clear. You explain what you do, and it is well reasoned - so with a proof, each like follows on from the previous line, and any ‘new ideas’ of the proof are explained by you.
@@BicenMaths Thank you, that makes sense
Hi Bice, topics on proof are just this playlist, then Proofs on Contradiction Year 2 chapter 1 - first topic - and then chapter 8 core pure 1. Is that everything on proof? Thanks (Doing AS FM)
That's everything! You don't need Proof by Contradiction for AS FM though!
Hi Mr Bicen, for 9:43, I used 2n+3 and 2n+1, and got 8n(n+1)+10 which is 2 more than 8 so is it correct? Thank you :)
Yep! Still correct! 👍🏼
sir, u know for the notations could you use eg, 2n+3 for a different odd number or do you have to use 2m+1
corresponding to an odd number being 2n+1
So if you want two DIFFERENT odd numbers, 2n +1 and 2m + 1 is best (or use p and q). If you want two CONSECUTIVE odd numbers, then use the same letter for both, and have one with 1 and the other with 3, e.g. 2m+1 and 2m+3. (Note: consecutive odds would be like 17, 19, or 29, 31 for example)
@ I get ur point but eg 2n+3 and 2n+7 are still both DIFFERENT odd numbers or is it best just to use n for one and m for the other
@@MuhammadHameed-hl2fc These are different odd numbers that are 4 apart - so too specific. What if it works for odd numbers that are 4 apart, but not all odd numbers? So we need to be as general as the wording of the question suggests, and use n and m for each one separately.
@@BicenMaths ok thx
I also wanna know at 7:15 why you put n2+1 before n2 like ik otherway around the answer will be negative but there is nothing i believe in question that tells that. Help!
It’s only because when we find the difference between two numbers, we do the larger subtract the smaller. Think about if someone asked you to find the difference between 60 and 100. You would do 100-60 rather than 60-100. If you do it the wrong way round, and get a negative answer, you can just negate it to find the absolute difference!
@@BicenMaths ohh got it thanks😅
I just wanna asked for deduction questions you take two different variables can we take two same variables like (2n+1)(2n+1)?
You could do, but I’m not sure why you’d want to do this? Maybe if you were looking at multiplying two odd numbers with your example?
@@BicenMaths no like for no reason
Wouldn’t that just be the same number if it asks for two different numbers you wouldn’t be able to do that.
Instead of the concluding statement you used at 10:58, can i just write QED instead? Is that allowed in ms?
I am not sure on this one actually! I haven’t marked proof type questions officially before, so cannot comment either way. Apologies!
Could you please explain Question 9 in Ex 7D: 3n^2 - 4n + 10 - prove it is positively for all values of n. The exam book worked solutions don’t make sense please could you help me
So all they've done is completed the square on the 3n^2 - 4n + 10 expression. Once you complete the square, it becomes clear that the expression is always greater than 26/3, so is therefore always positive!
so just to clarify, if 3 vertices are given and we have to prove that the triangle is right angle triangle, we cannot use pythagoras theorem? So obviously dont start with P.theorem. if I start calculating dis between all 3 sides, then next logical step would be to state P. theorem, then insert values to show that c^2 =a^2+b^2, that'd be correct proof right?
Yes, that would also be correct!
Just so you know question 1 in exercise 1D uses proof by exhaustion not proof by deduction