Maths-Ext 1/2 Marks Lost and Hardest Topics (1 Viewer)

CM_Tutor

Moderator
Moderator
Joined
Mar 11, 2004
Messages
2,644
Gender
Male
HSC
N/A
Here is how sub works out:
--- remove equation that is not displaying ---

Now I'm sure you can see how this works out from here - far from elegant but it still works!

As for another trig sub, maybe :
--- remove equation that is not displaying ---
Neither of those equations is displaying for me. However, is the trig substitution that I know does works, and so I have modified your post and elaborated a bit so that it does display, as follows, for those who want to see the working:












I don't have time to look at the other solution at this moment, but will check it later today. :)
 

Qeru

Well-Known Member
Joined
Dec 30, 2020
Messages
368
Gender
Male
HSC
2021
anyone bothered to finish off the sectan integrating in the cos2theta substitution lol.? btw, u would factor out sec tan , and yeet that out with a sec theta = u substitution.

any smarter way than doing that algebra in cos2theta solution?
Yes but really difficult to spot is to use the 'reverse quotient rule,' whenever we are integrating a rational function it;s always a good idea to keep this trick in mind.

First note that
So rewriting the integral:



This is in the form where

So
 

idkkdi

Well-Known Member
Joined
Aug 2, 2019
Messages
2,454
Gender
Male
HSC
2021
my Cambridge ext 1 is like 750 lmao :\\


But isn't getting a band 6 based of the difficulty, I read something on SMH that was about extension subjects and having higher % of kids who get band 6, mainly cuz its something they are good at and willing to invest time into it, that's why music extension got like 50% or something band 6s?idk could be wrong, feel free to correct me tho.



and wdym algebra grind? copious amounts of working out or wot?
cambridge ext 1 for yr 12's even longer iirc and 4u questions are probably another level up from what you do in 3u.

idrc about this band 6 stuff.

some tricky working out. specific things you need to do to get to an answer.
And yes, copious amounts of working out in certain cases.
 

Jojofelyx

Well-Known Member
Joined
Jan 3, 2021
Messages
410
Gender
Female
HSC
1998
cambridge ext 1 for yr 12's even longer iirc and 4u questions are probably another level up from what you do in 3u.

idrc about this band 6 stuff.

some tricky working out. specific things you need to do to get to an answer.
And yes, copious amounts of working out in certain cases.
Ah shit, I see. anyway too good for band 6's, they better make a b7 just for you xo
 

CM_Tutor

Moderator
Moderator
Joined
Mar 11, 2004
Messages
2,644
Gender
Male
HSC
N/A
I said I would post looking at the approach. @vernburn was correct, it does work... but it's certainly not as easy a solution as the approach, and to show that it matches the standard result that



requires some difficult binomial work (especially to complete without any structure provided). So, here it is:



























Now, consider that:















So, returning to the integral and putting (**) into (*), we have:



And we have where and so:



And so, from (***):











So, the result is the same but with a different constant of integration.
 
Last edited:

Qeru

Well-Known Member
Joined
Dec 30, 2020
Messages
368
Gender
Male
HSC
2021
It didn't load for me as well but looking at what @idkkdi said it seems like we convert it to sec and tan, but then wouldn't be better heres my working:















 

idkkdi

Well-Known Member
Joined
Aug 2, 2019
Messages
2,454
Gender
Male
HSC
2021
It didn't load for me as well but looking at what @idkkdi said it seems like we convert it to sec and tan, but then wouldn't be better heres my working:















I said I would post looking at the approach. @vernburn was correct, it does work... but it's certainly not as easy a solution as the approach, and to show that it matches the standard result that



requires some difficult binomial work (especially to complete without any structure provided). So, here it is:



























Now, consider that:















So, returning to the integral and putting (**) into (*), we have:



And we have where and so:



And so, from (***):











So, the result is the same but with a different constant of integration.
open image in new tab with right click for vernburn. it doesnt load for me either lol.
btw i meant at the u = costheta step sub in CM's solutions you could factor out a sectan and use a use a sec substitution.
 
Last edited:

quickoats

Well-Known Member
Joined
Oct 26, 2017
Messages
969
Gender
Undisclosed
HSC
2019
lmao its weird to think aa 75 raw gets around 90, and a 92 raw would get like a 95-96, 17 more marks raw = 5-6 more HSC marks, rip in peace.
Yep there’s definitely diminishing returns. 50 raw goes to like 80 whereas 99 raw goes to 99 and 100 raw goes to 100.
 

CM_Tutor

Moderator
Moderator
Joined
Mar 11, 2004
Messages
2,644
Gender
Male
HSC
N/A
It didn't load for me as well but looking at what @idkkdi said it seems like we convert it to sec and tan, but then wouldn't be better heres my working:















Yep, there are multiple substitutions possible. I think the and then method would actually be simpler as a direct substitution.

The most efficient, though, is your reverse quotient rule approach. I have never seen that before in more than 20 years of tutoring etc, so I am very impressed! :)
 

vernburn

Active Member
Joined
Aug 30, 2019
Messages
161
Location
Vern Gang
Gender
Male
HSC
2020
The most efficient, though, is your reverse quotient rule approach. I have never seen that before in more than 20 years of tutoring etc, so I am very impressed! :)
Look at the 2014 4U last question. Many people used the reverse quotient rule to get it out in a few lines lol
 

Qeru

Well-Known Member
Joined
Dec 30, 2020
Messages
368
Gender
Male
HSC
2021
Look at the 2014 4U last question. Many people used the reverse quotient rule to get it out in a few lines lol
Yup thats where I got that technique from. For anyone interested, the integral is:
 
Last edited:

Qeru

Well-Known Member
Joined
Dec 30, 2020
Messages
368
Gender
Male
HSC
2021
Also try this integral from the MIT integration bee:
 
Last edited:

Nacseo

Newest Member
Joined
Aug 12, 2020
Messages
156
Gender
Male
HSC
2023
Yes but really difficult to spot is to use the 'reverse quotient rule,' whenever we are integrating a rational function it;s always a good idea to keep this trick in mind.

First note that
So rewriting the integral:



This is in the form where

So
Jeez my head hurt just by looking at these equations, I'm also gonna apply for Ext 1 Maths, but now when I see this I'm like, sh*t, SH*T.
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top