1. HSC 2018 MX2 Marathon

Welcome to the 2018 Maths Ext 2 Marathon

Post any questions within the scope and level of Mathematics Extension 2. Once a question is posted, it needs to be answered before the next question is raised.
This thread is mainly targeting Q1-15 difficulty in the HSC.

Q16/Q16+ material to be posted here:

I encourage all current HSC students in particular to participate in this marathon.

Have fun ^_^

Maths Ext 2 Resource List

Originally Posted by Sy123
$\\ Suppose you are analysing the decay of particles from a radioactive source, suppose you discover that the probability that the source emits \ k \ particles from your source in an hour is \\\\ p_k = \frac{e^{-\lambda} \lambda^k}{k!}, \ k \geq 0 \\\\ Where \ \lambda \ is a constant and a positive integer, the rate of emission for your source.$

$\\ (a) By considering the ratio \frac{p_{k+1}}{p_k} or otherwise, find the most likely number of particles to be emitted in an hour$

$\\ (b) Suppose you have a friend and she is analysing the decay from her own radioactive source, and that in fact the probability that \ n \ particles are emitted from her source in an hour is \\\\ q_n = \frac{e^{-\mu} \mu^n}{n!}, \ n \geq 0 \\\\ Where \ \mu \ is a constant and a positive integer, the rate of emission in her source.$

$\\ Show that the probability that the sum of your and her observations is \ m \ is given by, \\\\ r_m = \frac{e^{-(\lambda + \mu)} (\lambda + \mu)^m}{m!}, \ m \geq 0$

2. Re: HSC 2018 MX2 Marathon

$\\ Consider the function in the complex plane, \ f(z) = z + i\text{Im}(z). \\\\ i) Find a locus in the complex plane, where for every \ z \ that lies on that locus, then \ |f(z)| = 1 \\\\ ii) Find the locus in the complex plane of \ f(z) \ for all \ |z| = 1 \ , sketch this locus or describe its shape$

3. Re: HSC 2018 MX2 Marathon

i) x^2+y^2=1

ii) x^2+(y-im(z))^2=1

I've probably misinterpreted the question given it does seem overly simple

4. Re: HSC 2018 MX2 Marathon

Originally Posted by TheZhangarang
i) x^2+y^2=1

ii) x^2+(y-im(z))^2=1

I've probably misinterpreted the question given it does seem overly simple
I made a typo in writing the first question, it should be fixed now. Your second answer however has a 'z' there but this is not a proper cartesian equation for the locus, you want only 'x's and 'y's

5. Re: HSC 2018 MX2 Marathon

Are there answers to Sydney Boys 2002 4u trial? Thanks

6. Re: HSC 2018 MX2 Marathon

Originally Posted by si2136
Are there answers to Sydney Boys 2002 4u trial? Thanks
https://thsconline.github.io/s/?view...002%20w.%20sol

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