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The third question. Yep, you can in fact I consider it overkill because the amount of maths teachers is scarce, they are always looking for more. In fact, if you do so you are going down Jonathan Le's direction (aka @Carrotsticks who is an legend that left Bored of Studies to become a maths...

A good school in terms of what? What are you looking for? You know people think of a school as a good school for many different reasons and a good school for one person might not be such a good school for someone else so be specific about what you are looking for? This should be done as a group...

Agreed. For what I see I wrote that post as an optional challenge for the forum starter. The reason is that in Extension II for mathematics you are not always given the substitution for integrals and as such students will not be overly dependent on a substitution. If that was not the message you...

Also note since you are in extension II try doing this without the substitution now. You should not have an adult holding your hand for these questions unless it is an unobvious one.

Oh you are going to have to do a lot of integration by parts for that

For part c the answer that comes to me is just \frac{3}{\sqrt{2}}+\frac{i}{\sqrt{2}}, -\left(\frac{3}{\sqrt{2}}+\frac{i}{\sqrt{2}}\right), \frac{1}{\sqrt{2}}+\frac{3i}{\sqrt{2}}, -\left(\frac{1}{\sqrt{2}}+\frac{3i}{\sqrt{2}}\right) Your four roots in the form a+ib @MAK03

We all have the same idea for @=)(= but yeah things go crazy at times. But hey @=)(= keep posting questions. It shows you have the desire to learn from those who came before you.

Well, that is fine. I am not getting mad, just a word of caution.

So for part b start with the fact that the length of 7+24i is 25. and then the r which is length is the fourth root of 25 equalling \sqrt{5}. The argument is very simple as well. First we see that for \cos{\theta}+i\sin{\theta} is...

Be careful of making such prophesies for one needs to let the person learn at their own rate and not be pressured unfairly. What you say might not occur and he might burn out if he does not know what he is doing.

I just finished my HSC maths adv and ext 1 this year, and the best advice I can give (or atleast the thing that made me improve the most) is to do as many past papers as possible, also I felt that during the tests the best thing when tackling hard questions is just to make a start and even if it...

Lets do this the easy way shall we. First, start with I_{0}=\frac{1}{1}, I_{1}=-\frac{2}{3}=-\frac{4}{6}=\frac{\left(-1\right)^{1}2^{2}\left(1!\right)^{2}}{3!}...

No, because if you do that you will have both sides being equal which is no longer an inequality.

The only time this is a t-formula question is when you are working with t=\tan\left(\frac{x}{2}\right). I imagine instead of calling it the t-formula it should be called the trig formula because it involves three aspects of trig the tangent and it’s counterpart sec and also cosine and sine.

Okay Since Drongoski has done Q8 for you I will take over for Q4. With Q4 You see here that 2\cos{\left(2x-\frac{\pi}{3}\right)}=\sqrt{3} \cos{\left(2x-\frac{\pi}{3}\right)}=\frac{\sqrt{3}}{2} For 0 \leq{x}\leq{\pi} We can turn this into -\frac{\pi}{3}\leq{2x-\frac{\pi}{3}\leq{\frac{5\pi}{3}...

Personally, I would lean towards Modern History because yes you might have to do it in Year 12 but the ideas that you learn from it can be seen in real life very frequently especially with NSW/Australia society because through learning Modern history you can analyse what is happening and how you...

How is this a good thing. What happened to the high standards that USYD used to have?

3. The approach will go like this Since both Ns are the same then what we are working with is that suppose we put one N at the start and leave it alone and then there are 8 positions to put the next N so there we will have 8 times the something that we will explore later on. By doing so we have...

Where is the diagram?

Oh right, so you found the textbook's mistake congrats on saving tk8 the confusion of debating which answer is right. Thank you for clarifying the issue here.