Maths Extension 2 Predictions/Thoughts (36 Viewers)

[lawfirm]

this is quite a contentious issue.

the syllabus, cambridge and steve howard texts say it should be derived, not quoted.

yet in nesa's 2021 hsc solution they just quoted it without derivation

it's a bit silly to have to derive every time

it's a bit like using pythagoras theorem. it's a well known formula, very silly to have to prove it every time you use it.

fair enough if it is a more esoteric formula hardly anyone knows about, better to derive it.

but for more well-known results it's a waste of time deriving it.

and conveniently in the marking feedback for the cohort they left that question so who knows if they specified that "better students just wrote the formula"

 

[coolcat6778]

It's really retarded NESA thinks just cause the formula isn't from pure maths, that you have to derive it. This is one of the ways NESA thinks physics isn't mathematics.

This is WA's reference sheet btw.

 

[tywebb]

yeah well before the 2021 hsc everyone kind of thought it's not quotable, then the 2021 exam happened and it's not the question itself that threw a spanner in the works, but nesa's solution which quoted it without derivation contrary to what had previously been assumed.

in the new syllabus that starts next year they made it clearer that it will be quotable

 

[lawfirm]

yeah well before the 2021 hsc everyone kind of thought it's not quotable, then the 2021 exam happened and it's not the question itself that threw a spanner in the works, but nesa's solution which quoted it without derivation contrary to what had previously been assumed.

in the new syllabus that starts next year they made it clearer that it will be quotable

I just read the marking criteria and on the website to it, it says "They are not intended to be exemplary or even complete answers or responses"...
I read that as "we (NESA) are allowed to just write the formula... but you aren't".

 

[killer queen]

wait how do you derive that formula

 

[tywebb]

wait how do you derive that formula

it in cambridge

 

[lawfirm]

wait how do you derive that formula

Or use a general formula for x (like x=acos(nt+alpha) + c), differentiate to v, square both sides for v^2, use sin(x)^2 + cos(x)^2 = 1, sub x back in

 

[tywebb]

Or use a general formula for x (like x=acos(nt+alpha) + c), differentiate to v, square both sides for v^2, use sin(x)^2 + cos(x)^2 = 1, sub x back in

yeah. steve howard book has alternative solution like this but he use sin

 

[lawfirm]

can someone pls clarify if this is right, converse is just flip the if then, negation is writing the case that is the 'opposite'. Like 'for all n then x' negated is 'there exists an n that is not x'. Contrapositive is flip and negate both.
and question for negation; if the properties of a variable are defined outside the if then statement, do they stay the same? also, why do 'if x then y' statements negated become 'x, not y' or smth (no if then).
sorry that's a lot, thanks though

 

[killer queen]

yeah converse is right, and I think you're right for negation too. it becomes "x not y" because a negation basically disproves the statement, so like you accept the premise is true but the implication is false, almost serving as a counterexample of sorts? e.g. the negation to "for all integer x, if x is odd, then x^2 is odd." the negation would be "there exists odd x where x^2 is not odd." which would have disproven the initial statement if it was true. the properties outside the "if-then" I think stay the same like in this example, x remains an integer, but I could be wrong/you might be talking about something else".

anyways I might be totally wrong but I think this is true

 

[lawfirm]

yeah converse is right, and I think you're right for negation too. it becomes "x not y" because a negation basically disproves the statement, so like you accept the premise is true but the implication is false, almost serving as a counterexample of sorts? e.g. the negation to "for all integer x, if x is odd, then x^2 is odd." the negation would be "there exists odd x where x^2 is not odd." which would have disproven the initial statement if it was true. the properties outside the "if-then" I think stay the same like in this example, x remains an integer, but I could be wrong/you might be talking about something else".

anyways I might be totally wrong but I think this is true

yeah cool, thanks. for the outside statements I mean something like 'x, y subset z, for all x if x >0, there exists a y where xy is less than 0'. Do I change the "for all x" because its outside the if.
Sorry if its a dumb question

 

[killer queen]

yeah cool, thanks. for the outside statements I mean something like 'x, y subset z, for all x if x >0, there exists a y where xy is less than 0'. Do I change the "for all x" because its outside the if.
Sorry if its a dumb question

it's okay! language of proof is weird bro

I think since those are like the bounds of what x and y can be you don't change them, as the negation disproves the original statement within these original bounds? like in the earlier example it could've been written as "if x is odd, then x^2 is odd, x subset z" and the negation would be "x is odd and x^2 is even" or sm like that, still with x subset z? I might've been wrong about using there exists in my prev example my apologies...

 

[lawfirm]

it's okay! language of proof is weird bro

I think since those are like the bounds of what x and y can be you don't change them, as the negation disproves the original statement within these original bounds? like in the earlier example it could've been written as "if x is odd, then x^2 is odd, x subset z" and the negation would be "x is odd and x^2 is even" or sm like that, still with x subset z? I might've been wrong about using there exists in my prev example my apologies...

nah that's ok I think I get it now thanks. proof is by far the worst topic and tbh not far behind vectors cause its glorified proof in ex2

 

[princesspiggy]

does anyone have like a tier of hsc papers from easiest to hardest??

 

[lawfirm]

does anyone have like a tier of hsc papers from easiest to hardest??

For me, 2020, 2021, 2024, 2022, 2023, but I know many people thought 22 was worse

 

[Realstudytips]

im scared af if they try to replicate 2022 difficulty

 

[lawfirm]

im scared af if they try to replicate 2022 difficulty

same except nesa will probs align 40 ish % of the cohort to e4 again anyway so it'll come out in the wash

 

[Allan Mekisic]

I don’t really think you need to prove any formula that’s within the Syllabus unless they ask you to. For example in 2020, they got students to prove the vector ratio division formula in Q 15 (b) parts (i) and (ii) and then encouraged you to apply it to parts (iii) and (iv). I think it will be obvious if they want you to prove a formula. If that were not the case then you could not quote anything. Eg you would have to prove Z = cos theta + isin theta

 

[C2H6O]

why do 'if x then y' statements negated become 'x, not y' or smth (no if then).

its worth noting that . to explain this lets say A is the statment I am in sydney, and B is the statement i am in australia. if we make a truth table we get

	A: I am in sydney	A': I am not in sydney
B: I am in australia	True	Possibly true
B': I am not in australia	False	Possibly true

The implication states that if A is true, then B must be true (confirmed by column 1). however if it doesnt mean that if A isn't true B isnt true, it could be either (column 2).
so we need to find a statement that covers all true/possibly true statements, because that's where the preposition could be satisfied. We need to cover the first row and second column of the truth table, and it will be an or () (exactly 1 or 2 of the statements is true). first row is B, and second column is A', so we have the statement
if you negate it you then get
dont need to know the reasoning but remember how to negate implications just in case

 

[v.tex]

For me From easiest to hardest

2021, 2020, 2023, 2024, 2022