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$ $\sin^{-1}\frac{x-b}{a}+C$ $ . Just recognise that it is in the form as a standard inverse sine integral, but recognising this still (implicitly) requires the substitution u = x - b . EDIT: Just realised I got beaten above :p

Time will be an issue if you make it an issue. You'll need to pace yourself throughout the paper, if you're stuck, just move on to the next question. I don't think too many people finish the whole paper tbh, but there's always that one kid that finishes half an hour early and gets nearly 100%...

According to UNSW, 29 Jun still falls under the Semester 1 Exam period (12 Jun - 29 Jun 2015) so it's fine.

My guess would be around 15% HD (not completely sure though tbh, it could even be something much lower like 10%). Haha, don't worry I'm sure like 95% of the cohort will be feeling this way. Just pace yourself throughout the exam and you should be fine (2 hrs is not very long). Good luck to...

$ $1 = 1$ $ . Done :)

Let $ $\alpha = \sin^{-1}x$ $ and draw a right-angled triangled to show that $ $\sin{\alpha}=\sqrt{1-x^2}$ $ . For 14 (i), again let $ $\alpha = \sin^{-1}x$ $ and use properties of a right angled trangled to find the value of the given expression. (it's the same answer, but instead with a...

The first formula you stated is just the transformation of a polynomial into a product of two lower degree polynomials (the divisor D and quotient Q polynomials) plus a remainder polynomial. Note that deg(R) < deg(D). To answer your question, if you want to sketch your function you can decompose...

Radians.

You would have to manipulate the expression so that it becomes a suitable integrand. For example $ $\sin^{3}x = \sin{x}\(1-\cos^{2}{x})$ $ which is simple to integrate using the substitution $ $u=\cos{x}$ $ But for something like $ $\sin^{4}x$ $ , you would need to express it as $...

You don't need to necessarily memorise those identities, but you should be able to derive them if they were to be asked in an exam. L'Hopital's rule is not in the syllabus and you won't need to use it since all limit questions will require you to utilise the methods you learn in 2U/3U.

Use auxiliary angle method i.e. transformation method to get $ $\sqrt{2}\sin\theta -\cos\theta$ = \sqrt{3}\sin(\theta-\arctan{\frac{1}{\sqrt\2}})=1$ $ and solve from there. EDIT: Method I just posted won't help, you probably need to divide out by some trig. function to simplify the equation...

A matrix is diagonalisable if the direct sum of the eigenspaces is equal to n , where $ A $ is an n\times{n} matrix. This means that $ $A$ $ will consist of $ $n$ $ linearly independent eigenvectors (which follows from $ A $ having $ $n$ $ distinct eigenvalues) which will form the...

The 1.01 factor refers to how much he deposits every month into the bank account, whereas the 1.003 refers to the total accumulated value of the balance at the end of the month. So, AFTER he deposits the monthly amount, THEN whatever the value of the account, it will be multiplied by 1.003...

- At the start of the 3rd month, he will have deposited 1% more than the previous deposit, which is now 500(1.01)*(1.01) - Therefore, at the end of the 3rd month the total balance in his account, which is now $ $500(1.003)^2+500(1.01)(1.003)+500(1.01)^2$ $ will have accumulated to $...

To start you off with (b) (i), $ $(500(1.003)+500(1.01))(1.003)=500(1.003)^2+500(1.01)(1.003)$ $ Let me break it down for you: - In the beginning of the first month, he deposit $500 - At the end of the month he will have an accumulated value of 500(1.003) - At the start of the 2nd month...

Yeah, I think the OP knows that but he mistakenly wrote it down, since he was probably trying to recall which quadrants are positive for which functions and just rushed his post. Obviously, in the real HSC (and even in school exams) what the OP stated (i.e "sin is positive in A and S") won't be...

Got 2 MATH & 1 ACTL all in one week GG, what's worse is that my Calculus and ACTL exam are back to back, FML.

ATSC (All Stations To Central): In Quadrant I: A for All - all trigonometric functions are positive in this quadrant. In Quadrant II: S for Sine - sine and cosecant functions are positive in this quadrant. In Quadrant III: T for Tangent - tangent and cotangent functions are positive in this...

Step (I): Base Case $ $S_1=0+1+8=9$ $ which is divisible by 3. Step (II): Hypothesis (or assumption) $ $S_n=3m$ $ for some $ $m\in\mathbb{Z}$. $ Step (III): Inductive Step: Prove that S_{n+1} is divisible by 3. $...

$ Average speed = $\frac{\text{Distance travelled}}{\text{Time}}$ = $\frac{x(1)-x(0)}{1-0}$ = $\frac{8-4}{1-0} = 4 \text{cm}s^{-1}$ $