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We can express the above as a quadratic in x, after expanding and simplifying we should have the LHS equal to (n+3)x^2-(5n+7)x+6n+3 , and we want to find the values of n such that (n+3)x^2-(5n+7)x+6n+3 > 0 for all real x. This means if we sketch our quadratic, it should lie above the x-axis...

n(x^2-5x+6)-7x+3x^2+3 > 0 ?

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread So you found that \dfrac{\text{ d}y}{\text{ d}x}=0 when t = 0 , which means the derivative is 0 at the point (x,y) = (6(0), 3(0)^{2}) = (0,0) . To sketch the graph of the curve defined by those parametric equations, we...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Yes.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread For y=(1-x)^{\frac{1}{4}}-2 , y(1) = -2 so you certainly include the point (1,-2) when sketching y = f(x). Derivative is undefined at x = 1 (hence not differentiable at that point), so the graph of y = f(x) at x = 1 will contain...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread For x^2=\dfrac{28}{5}y , vertex is (0,0) , focus is (0, \dfrac{7}{5}) , hence focal length is \dfrac{7}{5} .

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Yes, as x tends to \pm{\infty} , y values will tend to x^2+3x+3 . Note that what we are trying to find is a curve which 'bounds' the graph of f. This is only just for graphical purposes. It is not correct to say \lim_{x...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Firstly, notice that the function f, defined as $ $f(x)=x^2+\frac{1}{x^2}$ $ is positive for all $ $x\neq{0}$ $. Also, note that f(-x) = f(x) which means that f is an even function, so the graph of f will be reflected across the...

There are actually ways to solve DEs (Differential Equations), 3U/4U goes only as far as substituting a given expression to show that it is satisfies the equation etc. To know the solution to a DE depends on the type of DE and you won't really need to know this at the high school level. Your...

MATH2111 77 DN MATH2601 82 DN MATH2901 85 HD Overall, got lower than what I was expecting :( (esp. for Algebra and Stats) but in the end can't do much.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread a) Standard differentiation of functions $ $y'(x)=\frac{1}{2}x^{-\frac{1}{2}}-\frac{3}{2}x^{\frac{1}{2}}$ $ b) Set y'(x)=0 and solve for x, will give you critical points for y c) Since you know the critical points of y...

Re: MX2 2015 Integration Marathon $ $\frac{\pi}{2n}\ln{\frac{n-1}{n+1}}$ $ ?

Re: HSC 2015 4U Marathon $Suppose that $f$ is a continuous increasing (and hence invertible) function on $[a,b]$. Let $c=f(a)$ and $d=f(b)$. Show that if $a,b,c,d\geq{0}$ then \\\\ $\int_{c}^{d} f^{-1}(t)\text{ d}t=bd-ac-\int_{a}^{b}f(x)\text{ d}x$.$

Then I can say it is definitely a LOT more Maths rigorous than any of the compulsory cores offered at UNSW (FINS2624 (Portfolio Management) having the highest level of maths, covering only basic algebraic manipulation and random statistics here and there). Not sure about the electives though, I...

Is that part of the Finance major under Commerce, or the Financial Mathematics major under Advanced Maths?

ACTL2111 (Financial Mathematics for Actuaries) Ease 6/10. Definitely one of the hardest courses I have done this semester, lots of notation to cover and it really requires you to wrap your head around concepts that seem pretty confusing initially. The mid-semester exam and final aren't easy...

I think Crocker is a bit too much imo, other tutors don't really seem to have a problem if students quietly talk between themselves, but Crocker takes it to the next level and just kicks them out of the tute lol.

+1. University maths is nothing like high school, it takes time to actually understand what is going on, whereas high school just repeats itself with an overload of questions that students can just blindly solve if they know the method well enough. Uni maths requires understanding, which is why...

For (iii), T(v_1) = v_1 and T(v_2) = v_2, since the projection of vectors lying on a plane onto the plane is that vector itself. Taking co-ordinate vectors of T(v_1) and T(v_2) w.r.t. the ordered basis will give (1, 0, 0)^T and (0, 1, 0)^T as the first two columns. Then, since v_3 is orthogonal...

Paper looks similiar to past years, can't really comment on scaling since it depends on the cohort's performance, will write up some solutions for the paper soon :) How did you find it mreditor?