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Do you mean your teacher can't solve cubics either? x<SUP>3</SUP>+x-2=0 so test divisors of 2, in particular, 1 works, so x<SUP>3</SUP>+x-2=(x-1)(x<SUP>2</SUP>+x+2)=0 and the discriminant for the second factor is -7 so x=1 and the points are (1,1), (1,-1). If no divisor worked you could use...

Sometimes Maclaurin series expansion makes a problem easier. All I did was get the expansion Σ(-1)<SUP>n</SUP>x<SUP>n</SUP> for 1/(x+1) and then multiply by x<SUP>9</SUP> and went from there. It wasn't hard and you don't have to be a genius to use it. Here's more info...

Someone asked in another thread about inflections for f(x)=x<SUP>9</SUP>/(1+x). It's easy. Use Maclaurin series and 9th derivative test. This would be far more elegant than the syllabus method. f(x)=Σ(-1)<SUP>n</SUP>x<SUP>n+9</SUP>. So if f''(x)=0 then x=0. f<SUP>(n)</SUP>(0)=0 for...

Yeah. The syllabus is only supposed to show the minimum that is required. It's not supposed to be abused in such a way as to act like a tool with which to exclude all other knowledge. Such abuse leads to mediocrity. The Stage 6 syllabuses will be changed soon and so I've made a submission for...

To prove a theorem every time one uses it, whether it's in an exam or not, would be quite stupid. It's a little off-putting isn't it? - By design, I would suggest. I think it might just be his way of trying to force you (or convince you) to just stick to the syllabus and not do anything...

Theorems should be proved, whether they are in the syllabus or not. I have proved the third derivative test two ways in my first post in this thread. But there's no need to continue reproving it every time one uses it. Actually, once is enough. I only did it two ways to show the...

Yeah. Evidently, selective schools are selective of their students, but not of their teachers. goburnacat is obviously a better mathematician than her teacher. Marking a student incorrect when she is correct will be seen by the intenational mathematical community as idiotic. And on the...

Yeah. It's not just stupid. It's an abomination. Most of what is education is encouragement. How encouraging is it for someone enlightened by the 3rd derivative method only to be penalised for it just because the teacher doesn't know it? Not very. And therein lies the failure of the...

A mark from a good teacher is worth more than a mark from a bad one.

You should definitely learn testing either side of the point as well because sometimes this is more efficient than 2nd or 3rd derivative methods, eg., if it's a quotient it'll be hard to differentiate 2 or 3 times, so if testing either side happens to be a more efficient method for a particular...

This says more about your teachers' lack of mathematical knowledge than about your own mathematical ability. If your solution is correct, you should demand to get the mark. Assessments should be about your mathematical ability and not about either your teachers lack of mathematical knowledge...

There are concerns about lowering of NSW standards through any move to a national certificate (Patty, 2006). Future arrangements must add value to what exists and certainly must not lead to any reduction in quality or standards (Masters, et al., 2006)). OK. I'm not going to change my website...

http://www.boredofstudies.org/view.php?course=2 http://www.kewpid.net/james-ruse-past-exams http://nsweduserv.freefronthost.com/maths/ME1papers http://intrepix.tripod.com/en/notes/maths.html http://members.optusnet.com.au/limkw

OK. Buy speed2's 1995-2004 HSC's for $10 and get my 2005 one FREE. Note however that my 2005 solutions are a bit different to the MANSW one.

The MANSW ones can be ordered from http://www.mansw.nsw.edu.au/publications/2006-hsc-books.pdf

I put up some of my solutions. 2003: http://www.angelfire.com/ab7/fourunit/sol.pdf 2004 (8b only) http://www4.tpgi.com.au/nanahcub/2004hsc8bsol.pdf 2005: http://www.angelfire.com/ab7/fourunit/2005hscsol.pdf<!-- google_ad_section_end -->

Is that the MANSW book? I have been on the MANSW HSC solutions committee in recent years and have been invited to go on it this year. But I haven't decided yet if I'll go on it this year. I want to see the 2006 HSC papers before I decide.

OK. Well here's one, but I prefer my determinants method above. It's faster and more elegant.

The website is www.fourunitmaths.cjb.net It seems one of the servers I previously linked to has recently created a new redirect which says one has to "log in" to access resources. So with no further ado I have changed the links so that they no longer have silly login requests or redirecting...

Well if the original circle is |z-a|=r, I got (again using determinants) that the new one has centre conj(a)/(|a|²-r²) and radius r/||a|²-r²| - but it is not necessary to find these things in order to answer your original question. It can be...