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Use the ≥ symbol in the last two lines - you do not need to write equals and it makes your proof difficult to follow.

You will learn and practice 2u throughout the year. However, your teacher at a certain point may say that you will no longer be taking 2u assessments (for example in my school we only did the first 2 assessments if u were in 4u). If you continue beyond that point, you have to take 4u into the...

Particularly regarding USYD, which major best complements an economics degree? Can anyone who is familiar with one or both \provide some info on what they entail, what it's like to study them and how useful they each might be?

You will need to know the basic concept of combinations for a year 12 topic - 'binomial probability'. And as mentioned, it is likely to be in your trials and hsc.

It is a fiction piece

P(x)/(x^2+x) by polynomial division, and then u will get the remainder.

It's new to ext1. However, it was a part of the old Ext. 2 syllabus, so you can find some relevant qs there, although they will probably be much harder than the standard you will need for ext1 tests.

Technically it could be done by a dilation of a circle, although I'd expect that to be within the 2u course. Perhaps upload the question for us to look at?

I looked up the question in cambridge and it appears that it asks you for a relationship between u(n) and u(n-2) Think carefully about the cases before you write anything. Case 1: Using the factors sin^n(x) and cos^2(x) The integral of cos^2x is quite complicated in that involves sin(2x)/4...

Be careful. The subsitution is x = asinu. This should give you a primitive in terms of u of -1/a * ln|cscu + cotu| Final answer: -\frac{1}{a}ln\left|\frac{a}{x}+\frac{\sqrt{a^2 - x^2}}{a} \right|+C

sin(10x) and cosx are not multiples of derivatives of each other, and it doesn't seem like you can manipulate powers here. Looks like you need to use products to sums. Reverse chain rule

Alternatively, let x = tan(theta)^2 You'll end up with the integral of 2tan(theta)^2 with new boundaries pi/4 and 0. I've checked and this confirms Drongoski's answer.

When t=0, x=0, v=V x = asin(nt) v= ancos(nt) When t=0, v=V V= an a= V/n Rewriting the v and x functions, we get x = V/n * sin(t) v = Vcos(nt) For v to equal 0; 0=Vcos(nt) nt = pi/2 t = pi/2n The displacement at that time = V/n * sin(n * pi/2n) Hence distance = V/n

EDIT: Should be theta = pi/4 and theta = 0 in the 2nd and 3rd lines.

Personally I remember the order DETAIL which is a similar concept Differentiate to the following priority; Exponentials Trig functions Algebra (polynomials) Inverse Trig functions Logarithms

LIATE is the order for the functions that are best to integrate. cosx is a Trig function therefore is better to integrate, while e^2x is Exponential so better to differentiate.

'swift' and 'a thrift'

Because it technically is a full reference sheet to use for both year 11 and year 12 exams

Go to THSC and do many, many practice tests to prepare for your yearly. Make sure you are doing them under exam conditions and marking them as well.

This is because squaring complex nos with arg (-2pi/3) gives them an arg of -4pi/3, which is an equilvalent arg to 2pi/3 and therefore satisfies the condition.