how big a change is yr 11 maths to yr 10 maths (1 Viewer)

[cutemouse]

Here's a question kiddies;
int(exp(-a*r^2+a*r*x*cos(theta))*r))

What are your limits, and what are you integrating with respect to?

 

[Shadowdude]

What are your limits, and what are you integrating with respect to?

Maybe its an indefinite integral.

 

[SpiralFlex]

Maybe its an indefinite integral.

From Year 10 -> Year 11 -> Year 12 -> Uni this thread has gone.

 

[Shadowdude]

Let's bring it to the frontiers of maths now:

Are there infinitely many palindromic primes in base 10?

 

[SpiralFlex]

Let's bring it to the frontiers of maths now:

Are there infinitely many palindromic primes in base 10?

Actually, that's no fun. Let's do some Olympaid questions.

 

[Shadowdude]

Actually, that's no fun. Let's do some Olympaid questions.

Oh but that's the frontiers of mathematics. We're taking steps down! =P

 

[hscishard]

What are your limits, and what are you integrating with respect to?

+1 and is theta constant

 

[hscishard]

As Timothy.Siu already answered my question, try:

1. (this is MX2 stuff, perhaps even harder than MX2 stuff - but if you want to give it a shot, go ahead)

2.

How does 8/15 look?

 

[benji_10]

To address bleak's initial concern; just do the work. Do. It. If you do that, then you'll have no problems with the 2U course.

I sucked balls and every dick in the maths department in yr 10 (5 hours learning for addition of algebraic fractions in year 9) but I did the work, and I'm now coming top 10 in the 4U course (In a top 20 school, so yes the cohort is no pushover). The 2U/3U course is designed to be within reach of all students. If you do the work, then you will understand the basics very well and everything you do from then on will thus be built from this understanding. And the 2U course is pretty easy, so don't worry too much. And again, know your calculus. A lot of the content is calculus based (differentiation, integration, mechanics, bit of conics and parametrics, volumes, graphing, applications to the real world blah blah blah), and you'll regret it very much if you don't know what you're doing, and especially why you're doing it.

In short, do the course and don't worry.

PS:
If you want a pain free departure from this world, look at a harder 3U perms and combs or inequality from either q7 or q8 from a pre-1990 4U paper (the papers from then on gradually get dumbed down, imo. Wonder if that says anything about us?)
It will destroy you. Your brain will melt from the mere sight of it. I'm willing to bet that it would make men like Bear Grylls or Chuck Norris shed a tear. Pushing past the sweet irony here, Harder 3U is the hardest topic in 4U. Harder than conics.

And a parting gift (and subsequently bringing the standard down juuuuuust a bit) for suffering through massive wall(s) of text:



All people doing 2U should get this one.

EDIT:
The graph is actually pretty simple. Nowhere near as hard as shadow makes it out to be. Just draw the graph of y=x(1-x^2), ignore all bits below x-axis, then squash it, then reflect the positive bits around the x-axis.
As for the integral, it's between 0 and 1. The loop is made by reflecting the loop between the single root at x=0 and the double at x=1.



There's a 2 in front due to there being 2 areas (above and below). Expand, then integrate. Final answer should be 8/15, like hscishard said.

 

[hscishard]

^ haha nice question

3unit people will have more luck

 

[SpiralFlex]

To address bleak's initial concern; just do the work. Do. It. If you do that, then you'll have no problems with the 2U course.

I sucked balls and every dick in the maths department in yr 10 (5 hours learning for addition of algebraic fractions in year 9) but I did the work, and I'm now coming top 10 in the 4U course (In a top 20 school, so yes the cohort is no pushover). The 2U/3U course is designed to be within reach of all students. If you do the work, then you will understand the basics very well and everything you do from then on will thus be built from this understanding. And the 2U course is pretty easy, so don't worry too much. And again, know your calculus. A lot of the content is calculus based (differentiation, integration, mechanics, bit of conics and parametrics, volumes, graphing, applications to the real world blah blah blah), and you'll regret it very much if you don't know what you're doing, and especially why you're doing it.

In short, do the course and don't worry.

PS:
If you want a pain free departure from this world, look at a harder 3U perms and combs or inequality from either q7 or q8 from a pre-1990 4U paper (the papers from then on gradually get dumbed down, imo. Wonder if that says anything about us?)
It will destroy you. Your brain will melt from the mere sight of it. I'm willing to bet that it would make men like Bear Grylls or Chuck Norris shed a tear. Pushing past the sweet irony here, Harder 3U is the hardest topic in 4U. Harder than conics.

And a parting gift (and subsequently bringing the standard down juuuuuust a bit) for suffering through massive wall(s) of text:



All people doing 2U should get this one.

 

[LightXT]

To address bleak's initial concern; just do the work. Do. It. If you do that, then you'll have no problems with the 2U course.

I sucked balls and every dick in the maths department in yr 10 (5 hours learning for addition of algebraic fractions in year 9) but I did the work, and I'm now coming top 10 in the 4U course (In a top 20 school, so yes the cohort is no pushover). The 2U/3U course is designed to be within reach of all students. If you do the work, then you will understand the basics very well and everything you do from then on will thus be built from this understanding. And the 2U course is pretty easy, so don't worry too much. And again, know your calculus. A lot of the content is calculus based (differentiation, integration, mechanics, bit of conics and parametrics, volumes, graphing, applications to the real world blah blah blah), and you'll regret it very much if you don't know what you're doing, and especially why you're doing it.

In short, do the course and don't worry.

PS:
If you want a pain free departure from this world, look at a harder 3U perms and combs or inequality from either q7 or q8 from a pre-1990 4U paper (the papers from then on gradually get dumbed down, imo. Wonder if that says anything about us?)
It will destroy you. Your brain will melt from the mere sight of it. I'm willing to bet that it would make men like Bear Grylls or Chuck Norris shed a tear. Pushing past the sweet irony here, Harder 3U is the hardest topic in 4U. Harder than conics.

And a parting gift (and subsequently bringing the standard down juuuuuust a bit) for suffering through massive wall(s) of text:



All people doing 2U should get this one.

What is this I dont even...

 

[SpiralFlex]

To address bleak's initial concern; just do the work. Do. It. If you do that, then you'll have no problems with the 2U course.

I sucked balls and every dick in the maths department in yr 10 (5 hours learning for addition of algebraic fractions in year 9) but I did the work, and I'm now coming top 10 in the 4U course (In a top 20 school, so yes the cohort is no pushover). The 2U/3U course is designed to be within reach of all students. If you do the work, then you will understand the basics very well and everything you do from then on will thus be built from this understanding. And the 2U course is pretty easy, so don't worry too much. And again, know your calculus. A lot of the content is calculus based (differentiation, integration, mechanics, bit of conics and parametrics, volumes, graphing, applications to the real world blah blah blah), and you'll regret it very much if you don't know what you're doing, and especially why you're doing it.

In short, do the course and don't worry.

PS:
If you want a pain free departure from this world, look at a harder 3U perms and combs or inequality from either q7 or q8 from a pre-1990 4U paper (the papers from then on gradually get dumbed down, imo. Wonder if that says anything about us?)
It will destroy you. Your brain will melt from the mere sight of it. I'm willing to bet that it would make men like Bear Grylls or Chuck Norris shed a tear. Pushing past the sweet irony here, Harder 3U is the hardest topic in 4U. Harder than conics.

And a parting gift (and subsequently bringing the standard down juuuuuust a bit) for suffering through massive wall(s) of text:



All people doing 2U should get this one.

EDIT:
The graph is actually pretty simple. Nowhere near as hard as shadow makes it out to be. Just draw the graph of y=x(1-x^2), ignore all bits below x-axis, then squash it, then reflect the positive bits around the x-axis.
As for the integral, it's between 0 and 1. The loop is made by reflecting the loop between the single root at x=0 and the double at x=1.



There's a 2 in front due to there being 2 areas (above and below). Expand, then integrate. Final answer should be 8/15, like hscishard said.

I thought you had to do some fancy 4U method to find the area.

 

[benji_10]

Because it was a function of y^2 or was it because shadow was trying to scare us with his "harder than MX2" graph?

Questions like these often hark back to basics. If you root it, then it becomes a 2U integral. Knowing what the graph looks like helps a lot, because then you'd know the limits and the fact that you need a 2 out front.

 

[SpiralFlex]

Because it was a function of y^2 or was it because shadow was trying to scare us with his "harder than MX2" graph?

Questions like these often hark back to basics. If you root it, then it becomes a 2U integral. Knowing what the graph looks like helps a lot, because then you'd know the limits and the fact that you need a 2 out front.

Ribbon graph...

 

[benji_10]

Fair enough

 

[Shadowdude]

I meant that you probably wouldn't have to graph it in MX2. The integral is easy enough, and quite neat.

I think the question I posted shows a very important part of HSC mathematics: There is often a very easy way to do a question.

Spot it, and the answer pops out at the end. So always look for a 'trick' to the question so you can do the question in like five or six lines.


If anyone else wants to post a question, go ahead.

 

[AAEldar]

 

[bleakarcher]

=integral[(x^4+x^2+1)/(x^2+x+1)] dx
=integral[x^2-x+1] dx
=(1/3)x^2-(1/2)x^2+x+C

 

[AAEldar]

=integral[(x^4+x^2+1)/(x^2+x+1)] dx
=integral[x^2-x+1] dx
=(1/3)x^2-(1/2)x^2+x+C

I'm not exactly sure which way you did it, but the answer is right (you have a typo though, should be , which is obviously what you meant from the line before).