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Solve for x: \frac{|2x-1|}{x} \ge x+1

Yes I am.

Cambridge is crap for theory. It's alright for exercises though since they give you the level of difficulty of CSSA exams. But then again, I don't think the 4U textbooks out there are all that great. They tend to fail in the area of conciseness. Hence why you need to make your own notes.

It should be used with caution because you can have a situation where y''=0 upon substitution. I mean for most cubics (and quartics for that matter), in my opinion, you'd be crazy to test the nature using the first deriv test. This is especially since most curve sketching questions ask you to...

I think it is... that's how I was always taught (and is taught in many reputable textbooks such as Coroneos). But if upon substitution of the abssica of the stat. pt, y''=0; this means no new information and you need to use the 1st deriv sign test to clarify its nature.

If and only if every HSC Physics paper was like that of this year... it'd be awesome!

Apparently not... I think you have to use the fact the trip is 500 km somehow and maybe something else :S

Math in Focus Challenge Ex 2. Trying to write solutions for them lol.

The cost of running a car at an average speed of v km/h is given by c=150+\frac{v^2}{80} cents per hour. Find the average speed, to the nearest km/h at which the cost of a 500km trip is a minimum. Answer: 110km/h. This may well be a 2U question. Hard to tell though since it's in a 2U/3U book.

It was a low Band 5 this year ;)

or you could square both sides, since both sides of the inequality are positive.

Re: 2 Unit Revising Marathon HSC '10 ...

lol, I would've gotten about 88 if the ATAR was simply an average of all my HSC results. Which is wrong by quite a bit.

Life is unfair, cancer is unfair, the HSC is unfair. Deal with it.

You want a hard one? haha (i) Show that 1 is a root of h^3-9h^2+8=0 and find the other roots. (ii) A hemi-spherical bowl has a radius of 3m. Oil is poured into the container at a constant rate of \frac{\pi}{3}m^3/min. When the depth is h metres, the volume of the oil is...

Wrong.

The lines y=0, 3x-4y+3=0 and 3x+4y-15=0 are the sides of a triangle. (i) Find the coordinates of the centre of the circle inscribed in the triangle. (ii) Hence or otherwise write down the equation of the circle.

Given the product rule of differentiation, \frac{dy}{dx}=uv'+vu' where u and v are functions of x, explain why \frac{d^2y}{dx^2}=uvw'+uv'w+u'vw where u, v and w are all functions of x.

Sounds like nothing much has changed since my (now old) Physics teacher did Senior marking in 1990 (except for the course, lol)... before they moved to Homebush.

Re: 2 Unit Revising Marathon HSC '10 hehe... It's supposed to be a 'novice seperator'. Hence why I asked it.