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-1<=x<=1 observe that: 1=1 2x=x+x 3x^2=x^2 + x^2 + x^2 4x^3=x^3 + x^3 + x^3 + x^3 by studying the above arrangements or otherwise find in simplest algebraic form an expression for the limiting sum of the series: 1 + 2x + 3x^2 + 4x^3 + ... + nx^[n -1]

samantha has 3 similar keys in her pocket. to open her front door she tried the keys at random. she stopped trying when she opened the door and she did not use the same key twice find the probability that (1) the door opened when she tried the first key 2 she tried all three keys before the...

Show that (i) cos 46 (degrees) ~ [(root 2)/360)(180 - pi)] (ii) sin 29 (degrees) ~ (1/360)(180(root 3) - 1)) obv it has something to do with 45 + 1 = 46, and 30 - 1 = 29... i then tried using like...limx--> 0 cosx - 1/x = 1 and lim x-->0 sinx/x = 1....because u no - 1 degree is very close to...

(i) show that cos(theta) = [b(a+c)]/2ac (ii) if a=b and c=2b find the area of Triangle AOC No idea how to do part (i)...cosine rule?

integrate [(x)/(1-x)]^0.5 using x= (sin theta)^2 My answer: inverse sine (sqrt(x)) - ((x)(1-x))^0.5 Wolfram is giving some retarded answer, please someone check for me

Just curious as to others' opinions - say like with really hard exams like 2006/2008, or just average exams like 2010, is there any point redoing the papers? I got like 60/84 for those 3 papers which i thought was pretty damn shit... :( So should I redo them to get familiar with them (i.e. i...

There are 4 identical red marbles, 3 identical yellow marbles and 2 identical green marbles arranged in a row. (i) How many different arrangements of just 5 marbles are possible if all 3 colours must be included? Can someone please explain how to do this with copious amounts of detail lol...

Hi guys, new to binomials here, just wondering what you would do in these types of questions: 1. Find the greatest term in (1+3x)^7 if x = 2/5 2. Find the greatest coefficient in the expansion of (1+ (2/3)x)^10 So what do you do with these? Can someone please provide a solution of the...

^ Does anyone know where I can find this paper online + solutions? Thanks!

Quick question is the answer (5!)(4!)/2! = 1440 or (6!)(4!)/2! = 8640? I did (6!)(4!)/2! --> but the solutions say (5!)/(4!)/2!? If the solutions are correct, can someone please explain why? I thought you were meant to treat the 4 vowels as 1 letter, so you would have 6 'letters' instead of 9...

Would anyone know where I could find these solutions? I think there might have been a similar thread but I can't seem to find it. I need the solutions for the 2005 Ext1 Maths Paper most -- I have this one: http://exampapers.web.fc2.com/tests/hs/y12/maths/HSC3USolutions/2005.pdf but the solutions...

Just did the 2010 Maths Ext1 Paper, got a score of 60/84 (left out all the binomial questions because I haven't started binomials yet). Is this enough to get an E4? Or just a high E3? thanks

I'm hoping that would be enough to get an E4, but I haven't done any other papers, so I don't know if 2009 paper was a lot easier than the other ones -- what HSC mark do you reckon I'd get?

http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2002exams/pdf_doc/mathemat_ext1_02.pdf PROJECTILES QUESTION: For Q6 (a) part (iii) I got a maximum height of 27m, however the answers my teacher provided state that it is 15\frac{1}{8}\textup{metres} Can someone please check the answer for me...

Hi guys, having trouble with (ii) of this question Q. A small body is projected vertically downwards, with velocity u, in a medium which offers a resistance kv per unit mass when the speed is v. (i) Prove that the speed approaches a limit that is independent of u. (ii) T seconds later...

Sketch: x = \frac{-4}{3}e^{3-3t} - 2t + \frac{10}{3} Sorry I've no idea what to do with this question, what are some starting steps I can employ to determine the shape of the graph and then sketch it? Thank you, appreciate the help :)

Hi guys, this seems like a relatively simple question, there's just one tiny thing I'm having trouble with: Q. A particle moves in a straight line against a resistance of magnitude kv per unit mass. At a fixed point O on the line, the initial speed is 50m/s, and the speed is reduced to 5m/s...

Sorry but I have no idea what to do with this question: Q. A stone is let fall from a tall building and 1 second later another stone is projected vertically downwards with a velocity of 20m/s. When will the second stone overtake the first? Can someone please explain to me what I am meant to...

http://boardofstudies.nsw.edu.au/hsc_exams/hsc2004exams/pdf_doc/maths_ext1_04.pdf I got 4:28 am -- can anyone check my answer? My solution: equation for simple harmonic motion @ harbour entrance (not the wharf) is y = 3cos(4pi(t)/25) + b --> where b is the centre of motion. As the...

Hi guys, quick question: How is \tan^{-1}(2)-\tan^{-1}(1) = \tan^{-1}(\frac{1}{3}) ??? I don't understand how it works, is there a particular rule??? How would I show/prove the result it in an exam? Basically, I had the expression: \textrm{t}=\frac{4\tan^{-1}(2)-\pi }{4\textrm{kc}}...