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I consider it an incredible step up from extension 1. It shows you the beauty and elegance of mathematics and the multiple ways of approaching a question.

I did the general formula for the trapezoidal rule. You will learn this soon enough. Dividing by 4 in this case is the number of trapezia I used. Wait, isn't that formula (b-a)/2*{f(a)+4f[(a+b)/2]+f(b)} or is that Simpson's?

(2x+1)(5-x2-x)6 = (-1/7)*[-7(2x+1)(5-x2-x)6] = (-1/7)(-14x-7)(5-x2-x) = (-1/7)(derivative of initial equation) Note that (-1/7)*-7 = 1 You can put the -1/7 out the front of the integration. That making sense?

Using 5 function values [sub integer values of x into y = x(x-4) from 0-4]: x 0 1 2 3 4 y 0 -3 -4 -3 0 Area: 0~4x(x-4)dx approximately = h/2[y0+y4+2(y1+y2+y3)] where h = b-a/n = (4-0)/4 = 1 {n = number of trapezia} and y values are from the table Area approximately =...

(a) f(x) = (x1/2+1)3 f'(x) = 3(x1/2+1)2*(1/2)x-1/2 = (3(x1/2+1)2)/2x1/2 (b) ~[3(x1/2+1)2/2x1/2]dx = (x1/2+1)3 +C ~[(x1/2+1)2/x1/2] dx = (2/3)~[(3(x1/2+1)2)/2x1/2]dx = 2/3(x1/2+1)3 +C

(a) f(x) = (2x2+3)1/2 f'(x) = (1/2)(2x2+3)-1/2*4x = 2x/(2x2+3)1/2 (b) ~2x/(2x2+3)1/2dx = (2x2+3)1/2 +C ~x/(2x2+3)1/2 = 1/2*~2x/(2x2+3)1/2dx = 1/2(2x2+3)1/2 +C

(a) f(x) = (5-x2-x)7 f'(x) = 7(5-x2-x)6(-2x-1) = (-14x-7)(5-x2-x)6 (b) ~f'(x)dx = f(x) +C where C is a constant ~(-14-7)(5-x2-x)6dx = (5-x2-x)7 +C ~(2x+1)(5-x2-x)6dx = -1/7*~(-14x-7)(5-x2-x)6dx = -1/7(5-x2-x)7 +C

A concept is a theme, a universal idea about humanity. We all belong or do not belong to groups throughout our lives. This is why belonging is a common theme for all humans. Belonging relates to other sub-themes such as acceptance, assimilation, social-isolation, segregation, culture...

^^^ You're doing fabulously.

Have a read of the threads labelled IMPORTANT.

I think my aim will be to get a UAI higher than the lowest one at James Ruse. :D On topic: there's no short cut - hard work and consistency is the key to HSC success. Be sure you are doing school work most days and in moderation.

Start constant revision/doing all the set work. Re-reading/viewing texts and keeping your written work simple (but adding sophisticated language).

You can hate it but it's important in being able to speak, write, read, view and represent the different ideas of this world in a clear and logical way and become an articulate member of society.

I kind of wished I dropped to standard. I feel an obligation to try harder in advanced (hopefully this helps in the long run).

Nicely done. Keep it up. :)

Re: First round assessments Percentages: English - 100 Maths - 77 Maths Ext 1 - 89 Maths Ext 2 - 55 Chemistry - 71 Music 1 - 85 Religion 1 - 93 Many ups and downs. Hope they all eventually go to the up range!

I wouldn't say that if I were you. It's going fast enough, trust me. We're almost half way through the content of the subjects! And those external exams are closer than you think. Not to mention, when it is October 2009 - the weeks before your exams you'll be hoping the HSC year goes slower...

School is intense, as expected; but it's fine. Hang in there and we'll be able to come out the other end better people. How's life for you Elisa?

Those marks are fine. Don't be negative. :)

Seconded.