Mathematics Question Thread

[jaskirat]

Need help with this question

[RuiAce]

Need help with this question

[ekhan_01]

Hi,

there's no solutions and I have noooooo idea on what to do

Thank you

[12070]

Hi,

there's no solutions and I have noooooo idea on what to do

Thank you

I wouldn't be worried about questions like at the moment. The first two are some what manageable but the last one is designed to sort out extension students. For i you have to use right angle trig to find UO and then minus TO thus giving you UT. You'll then use UTxST for ii but honestly, unless you have absolutely everything else nailed in the course I wouldn't spend any time worrying about it.

[jamonwindeyer]

For the first one, use some right angled trig. You'll find:



Next, we just multiply the width of the rectangle from Part (i), with the height, which we established was \(r\sin{\theta}\). You'll get:



The last bit requires you to differentiate this function of area and find the maximum, but the method is a little different than normal. The hardest bit is the derivative itself, which requires the product rule and the chain rule as well. You should get:



Now to prove that \(\theta=\frac{\pi}{12}\) corresponds to a maximum, we actually need to just substitute into this expression to prove it puts the derivative equal to zero. You'll also need to substitute values slightly smaller and larger to prove it is a max and not a min this is the atypical bit, but we do it because finding the exact value of \(\frac{\pi}{12}\) is, if memory serves, otherwise impossible with 2U methods - So we just use their indicator to guide us a brief rundown but hopefully it helps!

[Mymy409]

A man contributes $1200 each year into a superannuation for the first 30 years of his working life. For the next 15 years, until retirement, He decides to increase this and invests a total of $5000 each year. If the investment earns 8% p.a. paid yearly over the whole year period, how much will his investment be worth upon retirement?

Need help with this. Thanks.

[Ali_Abbas]

Now to prove that \(\theta=\frac{\pi}{12}\) corresponds to a maximum, we actually need to just substitute into this expression to prove it puts the derivative equal to zero. You'll also need to substitute values slightly smaller and larger to prove it is a max and not a min this is the atypical bit, but we do it because finding the exact value of \(\frac{\pi}{12}\) is, if memory serves, otherwise impossible with 2U methods - So we just use their indicator to guide us a brief rundown but hopefully it helps!

Or you can do this:

[winstondarmawan]

Hello! Would appreciate help with the following:
https://scontent-syd2-1.xx.fbcdn.net/v/t34.0-12/20623991_1288382307953956_1340814897_n.png?oh=19ee69f9b0f7024aa8306b170b649109&oe=59841D89 (Part iii)
I got alpha = 0.64 radians and beta = 0.93 radians, for part ii if that helps. TIA

[Shadowxo]

Hello! Would appreciate help with the following:
https://scontent-syd2-1.xx.fbcdn.net/v/t34.0-12/20623991_1288382307953956_1340814897_n.png?oh=19ee69f9b0f7024aa8306b170b649109&oe=59841D89 (Part iii)
I got alpha = 0.64 radians and beta = 0.93 radians, for part ii if that helps. TIA

What I would do is get the area of each sector and add them, then subtract the area of the rectangle. This should give half of the area enclosed.
It would be something along the lines of


P.S. Way I solved the earlier question by ekhan was to find the maximum area was using sin(2x) and cos(2x) double angle formulae, is this taught in 2U?

[jamonwindeyer]

Very true! But 2U students don't learn the method to get the exact answer there, only a decimal approximation with their calculator - Which seems really strange in honesty because it means you HAVE to prove it by substitution, but that's what it was

A man contributes $1200 each year into a superannuation for the first 30 years of his working life. For the next 15 years, until retirement, He decides to increase this and invests a total of $5000 each year. If the investment earns 8% p.a. paid yearly over the whole year period, how much will his investment be worth upon retirement?

Need help with this. Thanks.

Hey Mymy! Have you made a start at all? Any progress you can share for us? Only because this is a question students normally can start but not finish and I'd love to take it from where you left off

Remember to build up the pattern!

P.S. Way I solved the earlier question to find the maximum area was using sin(2x) and cos(2x) double angle formulae, is this taught in 2U?

Nah, unfortunately not!

[RuiAce]

I wouldn't be worried about questions like at the moment. The first two are some what manageable but the last one is designed to sort out extension students. For i you have to use right angle trig to find UO and then minus TO thus giving you UT. You'll then use UTxST for ii but honestly, unless you have absolutely everything else nailed in the course I wouldn't spend any time worrying about it.

No this was certainly in my 2013 2U CSSA paper. I think it's fair to worry about it.

[Disney]

Hey guys! I'm very confused how to answer questions on superannuation with series! Particularly something like:

Jenny puts aside $20 at the end of each month for 3 years. How much will she have at the end of the 3 years if the investment earns 8.2% p.a. paid monthly?

Also how is best to prepare the night before for a 2u exam? Kinda stressing that I don't know my stuff

[12070]

No this was certainly in my 2013 2U CSSA paper. I think it's fair to worry about it.

I'm just saying that there probably won't be a max/min question involving right trig tomorrow. I did do that question a while ago but I could have spent the whole day studying questions like that only to walk into the exam and not know how to do one involving some other piece of theory. Then my whole day would have basically been wasted.

[RuiAce]

I'm just saying that there probably won't be a max/min question involving right trig tomorrow. I did do that question a while ago but I could have spent the whole day studying questions like that only to walk into the exam and not know how to do one involving some other piece of theory. Then my whole day would have basically been wasted.

The way I see it, it's a max/min question. Maybe it won't involve trig, but it will be in there. The previous parts were trig, and that may or may not appear, but it doesn't change that the last part is a max/min question and I think it's fair enough to worry about max/min problems if they cause trouble. (I highly doubt they would've neglected all other kinds of problems.) The fact that trig was combined it with is a less important point.

I also don't think 2U maths is a good subject to be predicting questions.

[RuiAce]

Hey guys! I'm very confused how to answer questions on superannuation with series! Particularly something like:

Jenny puts aside $20 at the end of each month for 3 years. How much will she have at the end of the 3 years if the investment earns 8.2% p.a. paid monthly?

Also how is best to prepare the night before for a 2u exam? Kinda stressing that I don't know my stuff

This question was started off at the start of this page. Please give more insight as to where the problems are.

How much studying have you been doing despite the stress? Because even people who have studied lots stress, but sometimes they just don't realise what they know.