I don't get A level Pure maths PROOFS

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curiousperson123
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When you get a question, I sometimes don't know which one it is and how to do it properly.
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Matureb
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Please give an example.
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curiousperson123
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(Original post by Matureb)
Please give an example.
https://www.mathsgenie.co.uk/resourc...pure-proof.pdf

1) I didn't know I had to find the minimum point
2) Do I have to say disproof by counterexample at the end because I got it right and I knew it was disproof by counter example but I didnt say it in my answer and solution did.
4) Didn't know how that was disproof by counter example until someone on tsr helped me.
7) was confused about how to approach the question until I looked at the solutions.
10) didn't know I had to find the minimum value

and the fact that there will be more different kinds of proof questions with different ways of solving them scares me!
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DFranklin
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(Original post by curiousperson123)
https://www.mathsgenie.co.uk/resourc...pure-proof.pdf

1) I didn't know I had to find the minimum point
2) Do I have to say disproof by counterexample at the end because I got it right and I knew it was disproof by counter example but I didnt say it in my answer and solution did.
4) Didn't know how that was disproof by counter example until someone on tsr helped me.
7) was confused about how to approach the question until I looked at the solutions.
10) didn't know I had to find the minimum value

and the fact that there will be more different kinds of proof questions with different ways of solving them scares me!
For (1) and (10), you don't have to find the minimum point - you can do it purely algebraically by completing the square.
A question I have to ask is how after doing (1), you still didn't know how to do (10) when they are so similar?

For (2), I think it's fine to say "It's false because when n = 3 you get 3^2-3+3 = 9 which isn't prime" without explicitly using the work counterexample. But if you're worried it is easy to write instead "n=3 is a counterexample because 3^2-3+3 = 9 which isn't prime".

(4) Having seen the question in context I think it's fine to say (x+y)^2 = x^2+y^2+xy =/= x^2+y^2 (i.e. I think the solution you mentioned in the previous thread would have been fine).

(7) What confused you about this?
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davros
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(Original post by DFranklin)
For (1) and (10), you don't have to find the minimum point - you can do it purely algebraically by completing the square.
A question I have to ask is how after doing (1), you still didn't know how to do (10) when they are so similar?

For (2), I think it's fine to say "It's false because when n = 3 you get 3^2-3+3 = 9 which isn't prime" without explicitly using the work counterexample. But if you're worried it is easy to write instead "n=3 is a counterexample because 3^2-3+3 = 9 which isn't prime".

(4) Having seen the question in context I think it's fine to say (x+y)^2 = x^2+y^2+xy =/= x^2+y^2 (i.e. I think the solution you mentioned in the previous thread would have been fine).

(7) What confused you about this?
I don't know if it's just me being picky but there seem to be a few liberties being taken in this exam around assumptions about the domain of interest (i,e, not making the domain explicit in every case), or what 'n' and 'x' conventionally represent.

At least one of the 'proofs' would break down if n were chosen to be sqrt(2), and (7) would be perfectly true if "a number" meant " a positive integer" but would be meaningless if " a number" could include complex numbers
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DFranklin
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(Original post by davros)
I don't know if it's just me being picky but there seem to be a few liberties being taken in this exam around assumptions about the domain of interest (i,e, not making the domain explicit in every case), or what 'n' and 'x' conventionally represent.

At least one of the 'proofs' would break down if n were chosen to be sqrt(2), and (7) would be perfectly true if "a number" meant " a positive integer" but would be meaningless if " a number" could include complex numbers
To be honest I think that's being a bit over-pedantic, although at the same time since part of "proof" at this level is "being pedantic" I can't totally disagree. I'm not sure how "commercial" the site is, but the questions don't look to be authored to the standard of an exam board or publisher, so I'm inclined to be a little lenient.

Regarding Q7: I don't think you have to go complex; what about negative numbers? My own pedantic concern here is that arguably the statement has no free variables so is either always true or always false (c.f. the statement "for all x in R, x^2 >=2" has no free variables and is always false). I don't expect the given answer took that approach, but it might have done.
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davros
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(Original post by DFranklin)
To be honest I think that's being a bit over-pedantic, although at the same time since part of "proof" at this level is "being pedantic" I can't totally disagree. I'm not sure how "commercial" the site is, but the questions don't look to be authored to the standard of an exam board or publisher, so I'm inclined to be a little lenient.

Regarding Q7: I don't think you have to go complex; what about negative numbers? My own pedantic concern here is that arguably the statement has no free variables so is either always true or always false (c.f. the statement "for all x in R, x^2 >=2" has no free variables and is always false). I don't expect the given answer took that approach, but it might have done.
I didn't look at the front sheet too closely, so I sort of assumed it was an 'official' exam paper, but if it's made-up stuff then that's not too bad!

I was just thinking that even at A level it would be good practice / etiquette to write things like "If n is an integer then..." or "prove or disprove the following statement for all real values of x...."., for the benefit of the student if nothing else
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DFranklin
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(Original post by davros)
I didn't look at the front sheet too closely, so I sort of assumed it was an 'official' exam paper, but if it's made-up stuff then that's not too bad!

I was just thinking that even at A level it would be good practice / etiquette to write things like "If n is an integer then..." or "prove or disprove the following statement for all real values of x...."., for the benefit of the student if nothing else
Oh for sure - they are very badly written for proper exam questions! As you say, even as examples it's not ideal for students - how can they get an idea of how to be precise in a proof if the person writing the question isn't being precise? But at the same time, I think you'd have to be actively looking for loopholes to say "what if n is actually irrational".
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curiousperson123
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(Original post by DFranklin)
Oh for sure - they are very badly written for proper exam questions! As you say, even as examples it's not ideal for students - how can they get an idea of how to be precise in a proof if the person writing the question isn't being precise? But at the same time, I think you'd have to be actively looking for loopholes to say "what if n is actually irrational".
(Original post by davros)
I didn't look at the front sheet too closely, so I sort of assumed it was an 'official' exam paper, but if it's made-up stuff then that's not too bad!

I was just thinking that even at A level it would be good practice / etiquette to write things like "If n is an integer then..." or "prove or disprove the following statement for all real values of x...."., for the benefit of the student if nothing else
These are the solutions to the questions. Feel free to take a look.

https://www.mathsgenie.co.uk/resourc...e-proofans.pdf
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DFranklin
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(Original post by curiousperson123)
These are the solutions to the questions. Feel free to take a look.

https://www.mathsgenie.co.uk/resourc...e-proofans.pdf
I'm sure it's fine at A-level (I doubt my answers were much better than this at A-level, for example), but if I submitted proofs like this at university they'd come back with a substantial amount of red ink, leaving me to suspect the creator didn't do a maths degree. (Although it's 95% "bad style" rather than anything too serious; the equivalent of writing "boy rode bike supermarket" instead of "The boy rode his bike to the supermarket" in an essay. You can *understand* the version without connectives, but it doesn't flow well or give the reader much confidence).

[It's definitely more glaring/grating when it's in a topic about proofs as opposed to just algebra churning too, because arguably "the point" of a proof is to explain to the reader why something is true, and if your argument is hard to follow, it may fail on that criterion even if it technically does what's necessary to prove the result].
Last edited by DFranklin; 1 month ago
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