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Re: HSC 2015 2U Marathon ^ To solve for x, you would do the following: $ $5^{x-1}=3^{x}$ \\ \Rightarrow\, $(x-1)\ln5=x\ln3$ \\ \Rightarrow\, $x\ln5-\ln5=x\ln3$ \\ \Rightarrow\, $x(\ln5-\ln3)=\ln5$ \\ \Rightarrow\, $x=\frac{\ln5}{\ln5-\ln3}$ $

Induction is only asked in the 3U/4U papers, not 2U.

Yep I managed to figure it out before, but thanks anyways :) To use LaTeX, you need to insert [tex.] [/tex.] command (without the dots) and insert your text/mathematics between them. Use $$ signs too. Use this guide as a starting point...

Sum of first 10 terms is 100 and sum of next 10 terms is 300, which means sum of the first 20 terms is 400. So you would have: $ $S_{10} = \frac{10}{2}[2a+9d]=100$ & $S_{20} = \frac{20}{2}[2a+19d]=400$ $ Solve simultaneously to get a=1 and d=2. Hence, the series is 1+3+5+7+...

I have uploaded the 2014 Algebra Test 2 + Solutions to the Dropbox folder :) I will also upload some of the 2013 Algebra Test 2 + Solutions soon as well, just for additional practice, but they are pretty much the same as 2014. This time, the solutions just include the answer, no working out...

No disadvantage.

Since you want to major in Accounting & Finance you must complete ACCT1511 & FINS1613. You must also complete FINS1612 for the Finance major, so take that for SEM2. MARK1012 Marketing Fundamentals is also a popular choice by many Commerce students, and I hear it is a pretty easy course so do...

You have $ $y=\frac{x^2+15+14}{x+1}=\frac{(x+1)(x+14)}{x+1}=x+14 . But $ $x\neq-1$ $ so the point of discontinuity occurs at $ $(-1,13)$ $ .

Dropbox folder updated with 2014 Calculus Test 2 + Worked Solutions (Ver. 3a). Good luck for Calculus Quiz 2 in Week 9. :)

Just to add in some other subjects: ACCT1511 - haven't done this course yet, but I hear no scaling (for SEM2 at least) ACTL1101 - has some scaling upwards but not too much (relatively easier final exam + strong cohort) ECON1102 - no scaling, final mark is determined by the sum of your raw marks...

$ $\frac{\text{ d}}{\text{ d}x}[\log\tan{3x}]=\frac{3\sec^{2}{3x}}{\tan{3x}}=\frac{3}{\sin{3x}\\cdot\cos{3x}}$ $

Re: MX2 2015 Integration Marathon You will then need to break each part of the integrand and express it in terms of u. THEN substitute in to express your final integral in terms of u ONLY and go on from there.

Re: MX2 2015 Integration Marathon ^ Your method is correct, but you shouldn't be mixing u's with x's, keep your variable the same throughout as your manipulating the integrand as this is not mathematically sound which could result in a loss of marks in the HSC exam.

+1. Both 1151 and 1251 ain't great in terms of scaling (I'd say 1141/1241 is much better) even though difficulty is bumped up a whole heap for final exams. Quality of students doing 1151/1251 is pretty good overall (well above average) so I can see why this would be the case (although there are...

Re: MX2 2015 Integration Marathon Use the substitution $ $u = x + \frac{1}{x}$ $ .

I don't really know the structure of a Double Major in Finance and Financial Economics since I don't do these majors, but from what my mates are doing, they usually complete the compulsory FINS courses by their second year before moving onto their additional FINS electives. Note that most of...

Refer to this :) http://community.boredofstudies.org/115/university-new-south-wales/332024/unsw-%E2%86%92-guide-transferring-internally-law.html

Re: HSC 2015 3U Marathon Another fascinating problem in Probability is known as the the Birthday Problem (or Birthday Paradox). It may seem rather counter-intuitive at first, but it essentially computes the probability of a pair of persons sharing the same birthday given a set of $ $n$ $...

Re: HSC 2015 4U Marathon ^ Do you have Cambridge 4U? That may help since they have pretty solid examples you can follow, if you're struggling, then go back to 2U and revise (and try to understand) the ideas behind basic volumes of solids of revolution. This can help form a basis on which you...

Re: HSC 2015 4U Marathon $ Alternatively, you can find the volume of the region bounded by $y=x^2$, $x=1$ and the $x$-axis, and find the volume of the the region bounded between the two axes, $y=1$ and $x=1$ (i.e. volume of a cylinder of radius $1$), then take the difference of the two volumes...