4U Maths Question Thread

[jakesilove]

Hey Ms She:

To deal with these questions, the most immediate things I would have done are to find the surface area in terms of x and h and the volume in terms of x and h. Because the question asks us to find S in terms of V and x, we know that we need to substitute h with an expression in terms of V and x in order to eliminate the h from the surface area equation. anyways, you can check out what l mean through observing my working out below. If you have any further questions dont hesitate to ask me!

(Image removed from quote.)

Best Regards
Happy Physics Land

Gorgeous responses HPL, looks like you're really on top of the content! Keep it up!

Jake

[she0071]

Hey Ms She:

To deal with these questions, the most immediate things I would have done are to find the surface area in terms of x and h and the volume in terms of x and h. Because the question asks us to find S in terms of V and x, we know that we need to substitute h with an expression in terms of V and x in order to eliminate the h from the surface area equation. anyways, you can check out what l mean through observing my working out below. If you have any further questions dont hesitate to ask me!

Best Regards
Happy Physics Land

Thankyou!!

[Happy Physics Land]

Hey guys would you mind giving me a hand with this cambridge question?? Thank you very much in advance!



Questions 7 Please thank you!!! )

[RuiAce]

[RuiAce]

[Happy Physics Land]

Ahhh ok so I should have subtracted the area of the sector and the area of the triangle and area of semicircle from the entire area of the circle... hmmm thank you rui that was very elaborate!!!

[amandali]

Which integer n do you take?    would u use n=0,1,2,3  or n=0,+-1, +-2
so when the angle is 4 theta   then there will be 4 solutions ,  3theta=3 solutions
I have the answer attached below

[Happy Physics Land]

Which integer n do you take?    would u use n=0,1,2,3  or n=0,+-1, +-2
so when the angle is 4 theta   then there will be 4 solutions ,  3theta=3 solutions
I have the answer attached below

Hey Amanda:

Interesting question indeed. Personally I would always use n=0,1,2,3 because that clearly tells me the four solutions to this problem. So for me, I use n=0,1,2,3 and got cos(pi/8), cos(3pi/8), cos(5pi/8) and cos(7pi/8) as my roots. If you want to manipulate these values, you can always convert cos(5pi/8) into -cos(3pi/8) and cos(7pi/8) into -cos(pi/8). This is just my approach to these questions and I pretty much have never used n = 0, +-1 or +-2 before.

Hope my answer helps

Best Regards
Happy Physics Land

[RuiAce]

When I talk about cosine, I usually only take a few integer values and that's enough. This is because the general formula for cosine has a ± in it.

When I talk about sine, however, I like to stick with negatives. This way, I keep my angles within the boundaries of -π<x≤π, which is what a principal argument of a complex number will be.

[amandali]

how do you simplify this?

[RuiAce]

how do you simplify this?

There is no neat simplification to this: this is simplified completely by brute force.

[amandali]

how to do part 2 (ii)
why does z1 , z2 and z1+z2  have to be collinear

[RuiAce]

how to do part 2 (ii)
why does z1 , z2 and z1+z2  have to be collinear

[Kezzdee]

Hey Jake,

I'm currently in Year 12 and I'm doing 4U mathematics. I've always done quite well in maths up until around the beginning of year 12, where I've just been struggling with my 4u and 3u maths marks. I'm working quite hard at the moment, although I definitely could be working harder. I usually have a strong grasp on the basic knowledge (component A) parts of maths papers, however I'm never really quite prepared for Component B style questions. In my latest exam, I received 22/25 for the Component A section and a 6/25 for Component B. I'm also having trouble finding a balance between 3u and 4u, as I generally just do 4U maths most days of the week. I was wondering if you had any tips in regards to this kind of issue.

Thanks for your help,
Kezz

[jakesilove]

Hey Jake,

I'm currently in Year 12 and I'm doing 4U mathematics. I've always done quite well in maths up until around the beginning of year 12, where I've just been struggling with my 4u and 3u maths marks. I'm working quite hard at the moment, although I definitely could be working harder. I usually have a strong grasp on the basic knowledge (component A) parts of maths papers, however I'm never really quite prepared for Component B style questions. In my latest exam, I received 22/25 for the Component A section and a 6/25 for Component B. I'm also having trouble finding a balance between 3u and 4u, as I generally just do 4U maths most days of the week. I was wondering if you had any tips in regards to this kind of issue.

Thanks for your help,
Kezz

Hey Kezz!

I think that your concerns are shared with the majority of the 4U cohort (certainly, I felt the same way during my Extension 2 year!).

I'll try to address each of your issues individually, but I just want to preface by saying that close to 60% in a 4U exam is not a bad mark. Even just passing the 4U course should be a massive achievement, because honestly it is a tough bugger. So don't feel disheartened by where you're at: You have the nuts and bolts of the course down, and now it's all about figuring out the second half to maximise your final mark!

Let's talk about balance between 4U and 3U. Firstly, studying for 4U will absolutely help you with 3U, so don't feel like its "wasted" time.
Secondly, it is absolutely hard to balance your subjects when 4U feels like such a drain on your time. The way that I managed to structure it was by forcing myself to stop studying for 4U after a set amount of time/past papers, and making myself do other subjects. The fact is that, even if you studied every day, you wouldn't perfectly understand the course. Once you've acknowledged that fact, it becomes easier to stop yourself studying. Figure out how much time you want to spend on your other subjects, work 4U in (even if you do spend a bit more time on it than others) and stick to that schedule. Don't get carried away trying to derive De Moivre's theorum. To repeat, CHOOSE A 4U MATHS SCHEDULE AND STICK WITH IT!

My only tip for improving your mark for more difficult questions is to just keep doing HSC past papers, over and over. You'll start to see patterns in how to answer certain types of questions, and be able to quickly take the correct route that leads to the answer (rather than following the hundreds of other tempting routes that the Board of Studies have left for you).

I also wrote out a set of notes describing the best methods for approaching really difficult questions. For instance, for Polynomial questions I wrote a detailedish list of "if it looks like this, try this" etc. etc. I do think it helped in my HSC exam, so if you're so inclined give it a go!

Really though, I don't think you're doing badly at all. The 4U course is immense, difficult and just bloody brutal. Keep slugging on, do billions of practice papers, but don't let 4U take over your life. Best of luck!

Jake