1) Since you want the letters of KOALA in order, fix those first:
__ K __ O __ A __ L __ A __
The lines indicate the spots the letters of GUMTREE can be placed
2) Choose the spot for the letter G: 6 spots means 6 ways to do so. Then our arrangement becomes something like (depending on...
Number of ways with both students with at least 1 book = Total number of ways - Number of ways that one student has no books
Using that, we have:
Total number of ways= 2x2x2x2x2x2 = 2^6 (each book can go to 2 positions)
Number of ways where one student has no books =2
Hence Number of ways...
I did SAV and IRRM, both of which are pretty easy. None of them really that interesting to be honest. It doesn't really matter which finance course you choose as they are generally good WAM boosters. Henry Yip's tests aren't hard and he scales pretty generously too.
normal generally have slightly less content (around 1 topic less than higher). For higher, the topics they share with the normal level would include an extension. This is compensated by the fact is much easier to get a higher mark (HD+) in higher than normal if you are decent at maths.
Although to do it properly is difficult, using some tricks make it easy. These tricks shouldn't really be used for normal questions. This is really a more educated trial and error keeping in mind the design of the question.
The idea is to note that since we are adding 2 real numbers on left...
See that \frac{z_1}{z_2}=r(\cos\theta+i\sin\theta) where r is the modulus and \theta is the argument. Your aim is then to find the theta and r.
r is obvious to find.
Consider \theta. We know that the sides z1, z2, z1-z2 forms a triangle with side lengths 3,4 and \sqrt{37} respectively (draw a...
Re: 2012 HSC MX2 Marathon
question kinda hints to use GP
Noting that |\sin x|< 1 for 0 < x < \frac{\pi}{2}, see that:
\int \frac{\sin x+1}{\cos x} dx &= \int \frac{1-\sin^2 x}{\cos x (1-\sin x)} dx = \int \frac{\cos x}{1-\sin x} dx=\int \cos x \sum_{n=0}^\infty \sin^n x dx
Assuming...