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Prove true for n=1 U1 = 2^1 - 1 U1 = 1 therefore true for n=1 assume true for n=k, (i.e. Uk = 2^k - 1) Prove true for n=k+1 (i.e. Prove U(k+1) = 2^(k+1) -1) AND: U(n+1) = 2Un + 1 LHS = U(k+1) =2Uk + 1 =2(2^k - 1) + 1 =2.2^k - 2 + 1 =2^(k+1) - 1 =RHS

Piker! Try them! They are not impossible. Just... challenging...

Nope. I didn't actually get what that part was on about: dropping to general what? ... I dropped Ancient History, picked up extension 2 maths and extension German, then I dropped extension German again. Leaving me with 11 units.

Re: help to me? Look, honey. Did you ever play that game at daycare or preschool or whatever where you learn that just because you know what's going on doesn't mean that everyone else does? Every second you save in typing jargon means another 10 seconds in which we have to translate it into...

could we just accept here that 1 and 0 are different numbers? The proofs just don't work. deal.

what's the point of that?

Enjoy it, guys! Next year all you get is 'Study Breaks.' No kidding.

yup. the samurai ones in SMH are fun.

I did about 1250 words in 5.5 minutes reading at ultra-sonic speed so... probably 900 words for 5 minutes, 1800 for 10. Depends on how nuch you need to fit in. A decent length essay, basically. I wish our time limit had been 10 instead of 5. I had to cut down my speech heaps.

If you're not getting above 85% in 3 unit I would say you'll find the course sontent of 4u pretty damn hard. You also need to have a really good grasp of simple concepts. Then you also need a bit of lateral thinking to get around the weirder questions, to save you going the long way (like...

There are some really fun gym classes you can do: like at newcastle uni there's body jam, which is sort of a cross between aerobics and dance. Karate and other martial arts are fun. You don't have to be good, or strong, or flexible to start, you don't feel bad when you're unco cause no one else...

My maths teacher is awesome: he does irish dancing... and he... uhm... gave us a bit of a demo once... [insert awkward silence here]

If I was you I'd just pick up physics and modern, then the year after, only if you are performing really really exceptionally well in any of you subjects, you could pick up maths 4u english 4u extension Latin if they offer it extension history

anyone seen it?

anyway, you should be cherishing your life while you still have it. Yr 12 is the year for all-nighters. yr 11 you should keep you innocence and be out partying instead.

I think it should be = 2bsin((theta-y)/2)cos((theta-y)/2) cause then you just use the sin2x = 2sinxcosx or, in this case, sinx = 2sin(x/2)cos(x/2)

I do 11 units, and cause I have 4 offline classes per week and 1 unsupervised I get 9 frees.

try to avoid songs if you can. it's harder to find techniques. if you do, make sure the WHOLE SONG is revolving around the theme, not just a bit of it. What aos are you doing? post the lyrics up too.

Your face is the english way

There's a reason for the prelim course. You need to know that stuff. If you can fit in additional study and start your year 12 prep as well, go for it. But it's better to build your foundations well.