how was half yearlies??? (2 Viewers)
- Thread starter suiyi_z
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kpq_sniper017
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for the accelerants......
are u doing 4U maths in yr 11???
coz at my school, i did prelim. 2&3U last year (yr 10) on top of the school certificate exam (i had yr10 and yr11 exams at around the same time)......
this year, yr 11, im doing hsc 2&3U
and next year, if i choose to, i can do 4U in yr 12 (but not this year)
u gotta pretty good to do 4U in yr 11.....how many schools let u do that?
are u doing 4U maths in yr 11???
coz at my school, i did prelim. 2&3U last year (yr 10) on top of the school certificate exam (i had yr10 and yr11 exams at around the same time)......
this year, yr 11, im doing hsc 2&3U
and next year, if i choose to, i can do 4U in yr 12 (but not this year)
u gotta pretty good to do 4U in yr 11.....how many schools let u do that?
Zarathustra
Dasein
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- Sep 28, 2003
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- Male
- HSC
- 2004
This was in my half yearly - can someone post up a worked solution.
Prove that x^n has a minimum turning point for which n is a positve even integer.
Prove that x^n has a minimum turning point for which n is a positve even integer.
let y = x ^ n
y' = nx^(n - 1)
= 0 if x = 0
:. turning pt at x = 0
at x = 1
y' = n ie. y'>0
:. to have minimum pt, at x = -1, y'<0
at x = -1, y' = n(-1)^(n-1)
:. for y'<0, n-1= odd
:. n= odd +1 which is even.
if n<0 then y'>0
:. x^n has min. turning pt if n is positive even integer.
Just one minor comment. The conclusion following y' = 0 at x = 0 should be that there is a stationary point at x = 0, not a turning point. It is the test which follows that shows that the stationary point is actually a turning point.
After all, y = x<sup>n</sup> has a minimum turning point at (0, 0) for n = 2, 4, 6, ... and a horizontal point of inflexion
for n = 3, 5, 7, ...
After all, y = x<sup>n</sup> has a minimum turning point at (0, 0) for n = 2, 4, 6, ... and a horizontal point of inflexion
for n = 3, 5, 7, ...
function: x^n
first derivative: n*x^(n-1)
n is a positive integer (2, 4, 6, and so on).
(n-1) is then greater than zero and is an odd number.
When x = 0, the first derivative is zero
When x > 0, the first derivative is positive
When x < 0, the first derivative is negative
So, there's a minimum point at x = 0.
first derivative: n*x^(n-1)
n is a positive integer (2, 4, 6, and so on).
(n-1) is then greater than zero and is an odd number.
When x = 0, the first derivative is zero
When x > 0, the first derivative is positive
When x < 0, the first derivative is negative
So, there's a minimum point at x = 0.
Sarzzabelle
CEO
I did so bad.. but we only had like an hr to do it in so if i'd only had like 30mins more i woulda done way better.
suiyi_z
Member
we're from smiths hill high school, selective school in wollongong. every accelerant from our school is expected to do 4u in yr 11. we usually don't have many ppl getting 100% raw on 3u paper..last time i got 97 but that was pretty easy paper.
and can i ask...are all the 3u papers in every school pretty much the same level of difficulty or does it vary alot? becuase when its soemthing like the 3u or 4u course the range of difficulty should be the same right? but i know ppl that have got average scaled mark of 90 for schoool marks that got 95 in hsc. they told me it was becuase our school set harder tests..ppl did better in hsc etc. but i'm thinking that there shouldn't be that bigger difference right?
and can i ask...are all the 3u papers in every school pretty much the same level of difficulty or does it vary alot? becuase when its soemthing like the 3u or 4u course the range of difficulty should be the same right? but i know ppl that have got average scaled mark of 90 for schoool marks that got 95 in hsc. they told me it was becuase our school set harder tests..ppl did better in hsc etc. but i'm thinking that there shouldn't be that bigger difference right?
It varies alot. A big lot. And, to some extent, it needs to. In an academically selective school, especially one like SGS or JRAHS or NSGHS, you need a harder paper than the HSC to effectively distinguish between the top students in the year...
suiyi_z
Member
yea i see your point, i just thought that for extension courses especially for maths that the difficulty is supposed to be more streamlined. but i really don't think i've seen any easy papers from our school..our prelim yearlies were shocking, very hard. my freinds from earlier years tell me that our marks will be scaled alot becuase we're selective and most other schools won't do as well as us...well i'm hoping they'll be scaled anyway, i want around 96 for 3u