Mathematics Extension 2 - 2016 Post-HSC Exam Thoughts (2 Viewers)

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,109
Gender
Male
HSC
N/A
And 14aii
14 a(ii): cos(x) is odd about x = pi/2, so raising cos(x) to an odd power (or more generally, applying any odd function to it) will maintain this property.

In other words, (cos(x))^(2n-1) is also odd about pi/2 for any positive integer n, so integrates to 0 over 0 to pi (integrating a function over an interval where it's odd about the midpoint is 0, since the area above the x-axis is cancelled out symmetrically by that below).

 
Last edited:

calamebe

Active Member
Joined
Mar 19, 2015
Messages
462
Gender
Male
HSC
2017
Answer to q 10? 12 d ii), 13 c ii)?
For 12 d ii), I just subbed in y = c^2/x and rearranged to get a quadratic, then used the product of roots. 13 will take too long to type out, but just set T2 greater than T1 and solve for w.
 

calamebe

Active Member
Joined
Mar 19, 2015
Messages
462
Gender
Male
HSC
2017
Yeah I just showed that the discriminant was equal to zero, and hence that was a double root of the derivative, and thus as it is also a root of the function, it must be a triple root.
 

Glyde

Member
Joined
Jan 28, 2015
Messages
120
Gender
Male
HSC
2016
i thought it said 'prove it is a double root', so i showed that the derivative could equal zero. will i get some marks?
 

Users Who Are Viewing This Thread (Users: 0, Guests: 2)

Top