Advanced Higher Maths 2011-2012 : Discussion and Help

Original post by JordanR

Maths revision is really rustling my jimmies.

Since it's you, I'm guessing this is a good thing. I don't really know. :p:

Reply 1141

JordanR

12

Original post by Quintro

Maths revision is the only type of revision I don't mind :tongue:

Yeah I don't really mind it much either. The thought of it is far worse than it actually is, I think.

Original post by TheUnbeliever

Since it's you, I'm guessing this is a good thing. I don't really know. :p:

Reply 1142

Original post by JordanR

Yeah I don't really mind it much either. The thought of it is far worse than it actually is, I think.

Definitely. I've been putting it off all week, but when I started a few days ago it was fine.

Reply 1143

sweetestwave

7

Original post by Quintro

To find the volume of revolution about the y-axis use this formula:

Unparseable latex formula:

\pi\displaystyle\int x^{2} dy \\[br]

Notice that this is the exact same as the formula for the rotation around the x-axis, except the y and x are swapped.

You'd start by finding the volume formed when the bottom curve is rotated around the y-axis.

Then, if you do the same with the top curve and the y-axis, you have another 3D shape (that sort of looks like a spinning top).

Try and think about this visually, if you have the first shape that was formed, and you take away the second (spinning top-like) shape, you are left with the shape that would be formed by rotating the shaded area around the y-axis.

If you need any more help just ask. :smile:

Thank you so much, it makes a lot more sense now. One question though, how do you find the limits? I feel like it's obvious and I'm being silly, but I don't see where 4 and 0 come from at all.

Reply 1144

Original post by sweetestwave

One question though, how do you find the limits? I feel like it's obvious and I'm being silly, but I don't see where 4 and 0 come from at all.

They're the bounds of the shape on the y-axis. See graph.

Reply 1145

Hype en Ecosse

20

Revision starts tomorrow...lol...

I'm sick at Unit 1 and 2. Matrices I've got down, I just have a tendency to make a silly arithmetic mistake when finding the inverse of a 3x3. Proofs are good. I sat a second prelim the other day and it asked me to turn a base 10 number into a base 7 number. I didn't even know what was in the course! I didn't want to risk trying to make up an algorithm from scratch, so just spent half an hour counting it out on my fingers. Got the right answer anyway, just have to find some notes on it so I can do this easy question quickly in an exam...can anyone point me towards any?

Revise vectors, too. Then I'm good.

(edited 11 years ago)

Reply 1146

Original post by sweetestwave

Thank you so much, it makes a lot more sense now. One question though, how do you find the limits? I feel like it's obvious and I'm being silly, but I don't see where 4 and 0 come from at all.

The limits define the range of y-coords that you want to rotate. So if you set the limits to be between 0 and 4, only the part of the curve that is located between y = 0 and y = 4 gets rotated around the y-axis.

The reason that they were set between 0 and 4 in this question, is because those are the y-coordinates of the points at which both curves intersect.

Reply 1147

sweetestwave

7

Original post by Quintro

The limits define the range of y-coords that you want to rotate. So if you set the limits to be between 0 and 4, only the part of the curve that is located between y = 0 and y = 4 gets rotated around the y-axis.

The reason that they were set between 0 and 4 in this question, is because those are the y-coordinates of the points at which both curves intersect.

That seems so obvious, not sure how it confused me so much. Thank you though :3

Reply 1148

Original post by Hype en Ecosse

finding the inverse of a 3x3.

We got shown it once in class but I haven't really bothered revising it. I can't see how they could ask it in the exam because it would be nearly impossible to mark. Might look over it so I don't end up hitting my head against the table in the exam.

Original post by Hype en Ecosse

it asked me to turn a base 10 number into a base 7 number

I knew this was in the course, but we were never taught it either. If you find any notes online or anything for it then I'd appreciate if you post them in here. May as well look over them for a few minutes in the off chance that it appears. :smile:

Reply 1149

Original post by Hype en Ecosse

I sat a second prelim the other day and it asked me to turn a base 10 number into a base 7 number. I didn't even know what was in the course! I didn't want to risk trying to make up an algorithm from scratch, so just spent half an hour counting it out on my fingers. Got the right answer anyway, just have to find some notes on it so I can do this easy question quickly in an exam...can anyone point me towards any?

Easier to demonstrate than explain. 5481 decimal to octal:

5481 = 8*685 + 1
685 = 8*85 + 5
85 = 8*10 + 5
10 = 8*1 + 2
1 = 8*0 + 1

Then read the digits bottom to top: 12551

Reply 1150

Original post by TheUnbeliever

Easier to demonstrate than explain. 5481 decimal to octal:

5481 = 8*685 + 1
685 = 8*85 + 5
85 = 8*10 + 5
10 = 8*1 + 2
1 = 8*0 + 1

Then read the digits bottom to top: 12551

Oh wow, much easier than I expected it to be! Thanks for that :smile:

Reply 1151

Hype en Ecosse

20

Original post by TheUnbeliever

Easier to demonstrate than explain. 5481 decimal to octal:

5481 = 8*685 + 1
685 = 8*85 + 5
85 = 8*10 + 5
10 = 8*1 + 2
1 = 8*0 + 1

Then read the digits bottom to top: 12551

Is that seriously it? Sweet.

So if I wanted to turn an octal number into decimal, I just repeat the process but with 10 instead of 8?

Reply 1152

Original post by Hype en Ecosse

So if I wanted to turn an octal number into decimal, I just repeat the process but with 10 instead of 8?

Yes, although you'd need to be careful to remember you were using octal when performing your arithmetic (e.g.

12551_8 = 12_8\times 1044_8 + 1_8

). To be honest, I would just multiply out using the place values (

1\times 1 + 5 \times 8 + 5\times 64 + \ldots

). i.e. for the simplicity (since your calculator is fairly unlikely to have an octal mode) I would do all translations via decimal.

EDIT: And obviously this does work for other bases, I'm just using octal because I can easily check I'm not making mistakes.

(edited 11 years ago)

Reply 1153

Original post by TheUnbeliever

.

You just made me realise my calculator has an octal mode, AW YEAH.

Anyway, yeah I think would just do it using the second way you mentioned since I'm used to decimal to binary from computing.

Reply 1154

john4994

Hi everyone :smile:

I thought I'd make this thread for last minute thoughts and feelings about the exam, and then for any post-exam discussions :biggrin:

Only 2 days to go, and a lot of content still to get through.

Hopefully the boundaries stay at:

A : approx 68%
B : approx 56%
C : approx 46%

Reply 1155

Kelz_26

I miss maths! :frown:

Good luck for Monday everyone, hopefully your paper will be better than last years! :smile:

Reply 1156

JordanR

12

Right, basically got vectors down now. Just needs a tiny tiny bit of work. Fine for all the calculus. Maybe need a little bit of refreshment on complex numbers. Should be fine for any proof questions. Matrices... if I can remember all the methods and formulae, fine.

Reply 1157

Still need to do:

- Little bit of vectors. DONE
- Recap how to find all of the roots of equations like z^3 = 8. I'm kind of okay with it, but I just need to do a few practise questions so that I'm comfortable with it should it appear.
- Proof by contradiction
- Proving by induction that something is divisible by an integer. DONE - easier than expected! :smile:

- Finding how a curve approaches an asymptote, where you divide all terms by the highest degree x-term or something. (Our teacher explained it differently and I had no idea what he was talking about.)
- Finding the limit of a function. Looks pretty simple judging from the marking schemes, but I've got a feeling it relates to the technique mentioned above.
- Finding the locus in the complex plane - we were actually never shown this at all. DONE - can't believe there were 5 marks for this last year

Other than that I'm pretty much sorted, I'll just need read over all the formulae I need to remember and make sure I'm ok with it.

(edited 11 years ago)

Reply 1158

qno2