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There's a long way and a shortcut: Long way: 1. Note that BC is parallel to AD. Find the gradient of BC and this must therefore be the gradient of AD. Find the equation of the line AD. 2. Note also that DC is parallel to AB. Find the gradient of AB and this must therefore be the gradient of...

These are the three possible positions of D that make it a parallelogram (3 is stuffed up because it doesn't really fit on your diagram but the point should be clear):

Yeah this can't be right. I think 98 HSC mark could have been top in state but the raw would have been over 100 I would imagine.

@Carrot- how the eff do you latex/type that fast? That was amazing. Oh and I think for 4) there is another point (-2,2) considering where AC is parallel to BD

If you give me fifteen mins- I'll write up all the answers by hand and scan them- hopefully others can latex some whilst I'm doing them. Also, 4 has more than one answer

No worries bro Trust me- you'll be fine. You seriously underrate your ability imo

Yeah but you've already sat the exam... Like you can't change your answers based on what we tell you etc.

Yeah that's what I'd recommend. Actually what I would do is do heaps of maths when it wasn't near test time and then ignore it in the weeks leading into tests. I did this because I found I wouldn't forget maths so I could prepare for the tests from heaps far away but subjects like chem, I need...

Why wouldn't you be able to ask?

The other thing with this is that a lot of people who never seriously tried before suddenly start going hard. Like I've put in heaps more effort this year than I did last year and my ranks have stayed almost exactly the same (down a tiny bit in some subs and up a tiny bit in others) because...

Just try and learn from your mistakes and come back hard in year 12 when it all counts- good luck :) And if you need help with questions, you can always post them here and we'll try and help. Yeah this would be frustrating- in our last two 3U tests, four of the top five got full marks in both...

Me? No way- there are quite a few people on BOS alone that are way more talented than me at maths. Hopefully I'll end up with a HSC mark of 96 or maybe 97 for 4U- that's the goal.

Lol at pretty happy being 99%. Seriously congrats- that's a heaps good mark. And easy tests piss me off but dropping only one mark is heaps good. Any other tests back yet?

You recognise that this will decompose into a quadratic and conventiently 9^x=(3^2)^x=(3^x)^2 -> therefore you can write the function as a quadratic in terms of 3^x

Depends on you personally. There is no definitive answer. Like for me personally, I'd go down the neither route and not write notes but use other peoples. This is what works for me. I'd probs recommend typing just because it saves time but you should try both and see which one helps you absorb...

Now I'm going to look like an arrogant dick but personally I'd repeat with anything below 98 tbh

1. Calculate the MPC by looking at the change in consumption over the change in income 2. Calculate the multiplier using the formula: k=1/(1-MPC) 3. Multiply $40bn by k to get the increase in equilibrium level of income 4. Add that to $300 bn

What I would recommend doing is do it quickly like I did it to get x=0,1 and then sub in both values to the original equation to check your answer. This way, you can be sure you are correct.

Please tell me you aren't serious... Yes your working is perfectly correct and the answer is right but when you have something like 3^x=3, you can just write straight out, x=1- its pretty obvious but it'll save you heaps of time in a test.

Yeah whoops- fixed that