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Original post by DJMayes
Why? Are we taking x+4 \sqrt{x+4} as only the positive square root of x+4 x + 4? If so then that would explain what I've done wrong.

By definition, x+4>0\sqrt{x+4} >0 i.e. it always denotes the positive root.

As has been said many times before, this is probably one of the worst taught tidbit in school maths.
EDIT: As above.
Original post by und
x\sqrt{x} is always positive (obviously x0x\geq 0). We write ±x\pm \sqrt{x} if it can be negative.


Original post by Farhan.Hanif93
By definition, x+4>0\sqrt{x+4} >0 i.e. it always denotes the positive root.

As has been said many times before, this is probably one of the worst taught tidbit in school maths.
EDIT: As above.


Thank you both; I'll be sure to remember it for future reference :smile:
the way I think about remember it is that, otherwise, there would be no point in the plus or minus in the quadratic formula. Dunno if that helps.
Original post by ben-smith
the way I think about remember it is that, otherwise, there would be no point in the plus or minus in the quadratic formula. Dunno if that helps.


It does make sense, and I probably should've picked up on it long before now.
Original post by shamika
The Hong Kong A-Levels are incredible; they're almost exactly what I would cover in Pure, and the Applied isn't too shabby either. Pity they've stopped them now. They have a very wide syllabus (much wider than the UK A-Levels; in particular, they treat functions, limits and continuity/differentiability more rigorously), so you might want to skip those questions. Some of the questions are very STEP like indeed; some of them can quite easily appear as parts of questions in a first year undergrad exam.

The grading system was absolutely insane though; only 1% of students got an A. They are definitely not equivalent to the UK A-Levels, so an AAA entry requirements is :O

Papers are available online (search HKALE Pure Mathematics) from 1981 onwards. Great additional practice if you want it (and also something to help bridge the gap between A-Levels/university for Analysis). Overall I reckon STEP is harder though.


STEP what is harder, I, II or III?

Given only a small proportion (is it 1%?) get an A grade in the Hong Kong A-Levels, would be it harder to get an S in STEP (12% in III) or A in HK A-Levels?
Original post by dugdugdug
STEP what is harder, I, II or III?

Given only a small proportion (is it 1%?) get an A grade in the Hong Kong A-Levels, would be it harder to get an S in STEP (12% in III) or A in HK A-Levels?


You've got to remember though that those sitting STEP (especially 2 and 3) are already roughly the top 1-3% of a-level candidates: I think around 70k take maths yearly and its less than 1k who sit STEP III- though of course not all the best mathematicians will sit it (they will go into other fields/leave education) so its hard to really say. I remember reading somewhere (possibly on Siklos' website?) that STEP is aimed roughly at the top 2%.
Original post by dugdugdug
STEP what is harder, I, II or III?

Given only a small proportion (is it 1%?) get an A grade in the Hong Kong A-Levels, would be it harder to get an S in STEP (12% in III) or A in HK A-Levels?


What In One Ear said (you could've figured that out yourself, don't let us Imperial mathmos down :biggrin:)

EDIT: This document states around top 7% for applied mathematics and 5% for pure mathematics get an A. The 1% is for the top grade in the new HKDSE exam. Maybe I should think about moving to HK to teach maths there :biggrin:
(edited 11 years ago)
Original post by shamika
What In One Ear said (you could've figured that out yourself, don't let us Imperial mathmos down :biggrin:)

EDIT: This document states around top 7% for applied mathematics and 5% for pure mathematics get an A. The 1% is for the top grade in the new HKDSE exam. Maybe I should think about moving to HK to teach maths there :biggrin:


I hope you're not serious about teaching maths in HK!

They're incredible snobbish in that in their eyes, Oxbridge is way ahead, anything else apart from HYSMP, just doesn't compare. (I know you're from Imperial).

I recall an incident with a BBC friend of mine strolling along HK's waterfront with a caucasian friend, when they were approached by some school students who wanted to practise their English.

They totally ignored my friend and insisted on speaking to his friend (even though he was German and spoke English with an accent)!

PS I didn't read What In One Ear wrote and even if I did, my maths days are well behind me now!
(edited 11 years ago)
Original post by dugdugdug
They're incredible snobbish in that in their eyes, Oxbridge is way ahead, anything else apart from HYSMP, just doesn't compare.

Pfft, Yale. :colonhash:

:tongue:
Original post by ukdragon37
Pfft, Yale. :colonhash:

:tongue:


Princeton is where the party's at. :cool:
wow some people are keen on STEP already! I hadnt even considered it untill January!
Original post by Lord of the Flies
Princeton is where the party's at. :cool:


:hand: Gotta be MIT.

[video="youtube;lJtHNEDnrnY"]http://www.youtube.com/watch?v=lJtHNEDnrnY[/video]
Original post by ukdragon37
...


:eek:

Touché.

3:21 LOL
(edited 11 years ago)
Original post by Lord of the Flies
Princeton is where the party's at. :cool:


Princeton :love:

Also, thanks for earlier :tongue:
Original post by cpdavis
Also, thanks for earlier :tongue:


No problem :h: Enjoying second year?
Original post by Lord of the Flies
No problem :h: Enjoying second year?


Yeah second year is going well. At the moment, the modules that I am enjoying are both Intermediate Dynamics (considering doing a project in it next year :yep: ) and PDE's and complex variables. I sort of get analysis, but I was never a pure man myself :nah: :wink: :tongue:

How are you finding A2? :h:
Original post by cpdavis
Yeah second year is going well. At the moment, the modules that I am enjoying are both Intermediate Dynamics (considering doing a project in it next year :yep: ) and PDE's and complex variables. I sort of get analysis, but I was never a pure man myself :nah: :wink: :tongue:

How are you finding A2? :h:


Hmm! Sounds interesting! :wink: I'm on a gap year (and consequently spending far too much time on TSR) :rolleyes:
Original post by Lord of the Flies
Hmm! Sounds interesting! :wink: I'm on a gap year (and consequently spending far too much time on TSR) :rolleyes:


I'm at uni and spend too much time (although modding and PS's takes up a large proportion :ahee:) What made you decide to do a gap year? Are you looking at at first year material? :smile:
Original post by cpdavis
I'm at uni and spend too much time (although modding and PS's takes up a large proportion :ahee:) What made you decide to do a gap year? Are you looking at at first year material? :smile:


Wasn't a choice, my somewhat complicated situation was such that I was obliged to take one. I've looked at some yes, but I don't want to get too distracted either. I prefer to have a strong ground basis rather than knowing more but having less confidence (for now of course - I'm obviously eager to learn loads more when I get to university!) :h:

Enjoy your intermediate dynamics & partial differential equations! :biggrin:
Let zz be any complex number. Find the smallest constant α\alpha such that (z)+(z)αz.|\Re(z)|+|\Im(z)| \le \alpha|z|.

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