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For this curve, y=0 is an asymptote beyond the points of inflexion. ie. if the pts of inflexion at x=a and x=-a (which they would be, as the function is even), then y=0 is an asymptote for x<-a and x>a.

cosx=x\\cosx-x=0\\Let\ P(x)=cosx-x\\ P'(x)=-sinx-1\\By\ Newton's\ Method\ z_2=z_1-\frac{P(z_1)}{P'(z_1)}\ Let\ z_1=0.5\\z_2=0.5-\frac{P(0.5)}{P'(0.5)}\\=0.5-\frac{0.3775...}{-1.479...}\\=0.755222417...\\=0.76\ (to\ 2\ dp)

Find: \int{e^{-x^2}}dx

A bit too late isn't it? There'd be quite alot of catching up... I mean angle between 2 lines, a point that divides a line into a given ratio, circle geometry, general solutions, trig results, polynomials... You'd need to work extra hard this term.

Just do lots of questions... seriously. I actually got the circle geometry question in my trials. And I thought I sucked at it before. A bit tricky though... It incorperated geometry too (ie. angle sum of a quadrilateral is 360 deg).

Re: Leaving school depression? *troll alert*

I think in Ext 1 you only consider roots of multiplicity of 2. ie. If a is a double root of P(x) then P(a)=P'(a)=0. But in Ext 2 you can be asked roots of other multiplicity. This was in our Year 11 preliminary exam for Ext 1. The question was something like, if a is a double root of P(x), then...

It is. :)

lol which other teacher in the state claims that you can't find the gradient of a curved graph? :P

Hahah how's Ball treating you guys? XD

Hmm, then it should be something more sophisticated. Good old SKB XD

Okay... sorry if I annoyed you too much. gl for your trials :)

Umm, a "black box" (usually a non ohmic resistor) electric circuit practical, where you have to determine the relationship between voltage and current?

How many marks was it? Knowing who wrote the trial, I'd say it's been pilfered from somewhere. heh

Well then, take your guess?

Eh? How does that work out? :S Where does it say that they are double roots? EDIT: Also P(x) is monic, so what's the 'k' all about?

A monic polynomial P(x) of degree 4 has exactly two zeros at x=3 and x=-3 and it is even. (i) Show that there are many such polynomials and find their general form. (ii) If this polynomial has a value of -45 when x=2 find the unique polynomial P(x) Thanks =D

"School/Age/Preferred Uni Course" -- If I told you the school I went to, that'd be too easy :P. I'm about your age, I think XD... Preferred uni course? I dunno Gender? Can't you tell?

\text{The polynomial P(x) is given by}\ P(x)=x^3-x^2-8x+12\\(i)\ \text{Factorise P(x) completely given that P(x)=0 has a repeated root}\\(ii)\text{The polynomial Q(x) has the from Q(x)=P(x)(x+a) with P(x) as given above}\\ \text{and where the constant a is chosen so that}\ Q(x)\ge 0\for\ all\...

Have a guess :)