nightweaver066
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- HSC
- 2012
Re: 2012 HSC MX2 Marathon
I like this question.
I like this question.
If you want some Pure Maths questions unrelated to the HSC, then feel free to make your own thread in the 'Extracurricular Maths' section: http://community.boredofstudies.org/forumdisplay.php?f=238Why don't we add some pure maths questions in here,
here's a fave one of mine, combinatorics
A permutation of the set where is a positive integer, is said to have property if for at least one . Show that, for each , there are more permutations with property than without.
Hint: Indicator functions will help, and think about counting sets
we learn factorial notation for combs and perms and how to apply them, that is about all lol.Thanks, but it is related to the HSC albeit a fair extension.
You guys do combinatorics in the HSC right? The above question can be solved purely combinatorially.
Generally, rotation around a line parallel to the Y axis is more easily done using Shells.Hey guys just two questions
1/ what are some ways to determine whether a question should be done with shells or slices
2/ if I'm given a shape like x^2(6-x^2) find area enclosed in 1st quadrant rotated about the y axis how do I go about it?
First part split the integral as two terms then the integral with the i in it cancels out due to the sine function and we are left with 2x integral of f(x)cos(x). Second part use the property f(x) = f(a-x), add the two integrals, the icos(x) term cancels and the result follows.This one might look like it is beyond the course but it can be solved using methods within the scope of Ext2 level.
Suppose that f(x) is an even function. Show that
Hence evaluate
yeah I agree with with you, the question seems like it isnt in the scope of the ext 2 courseFirst part split the integral as two terms then the integral with the i in it cancels out due to the sine function and we are left with 2x integral of f(x)cos(x). Second part use the property f(x) = f(a-x), add the two integrals, the icos(x) term cancels and the result follows.
I am a bit skeptical regarding this question being within Ext2 level without proper justification because we are taking the Riemann integral of a complex-valued function. It may require justification that it works in this case because is a vector space. Other students might get confused about having an i in the integral.
why not?can you treat 'i' as a constant?