Higher Maths, Paper Two

subway_ie

I’ve got a very basic question about Higher Maths, Paper Two: How exactly do you draw circles? I’ve never really been able to; don’t have a clue what to do. Nothing specifically about it in the book – it’s probably too fundamental. Anyway, any advice/guide on/to drawing circles for Paper Two, Question One?

PrecariousNuts

find centre, radius. set compass to radius, draw... profit

they never ask to draw them when you can do all of the operations via maths

accensi0n

compass! pfft.
its not a feckin art exam man, you can just lash down a circle freehand.

subway_ie

Is there not some kind of method for getting, say three points on the circle or something? I know they probably won't ask to draw the circle, it's more for interpreting the question properly than anything else. Up until know, I've never bothered drawing the question - but my maths teacher keeps warning me to draw them. Just don't want to get caught out on something I had been warned about again and again. Don't want another repeat of the retardedness of paper one.

Mutant_Fruit

The only drawing you ahve to do is freehand. They are not expecting works of art here. You dont even have to use graph paper if you dont want to.

Basically, just freehand a circle, and choose random points and write in known values such as the radius etc.

DS

Yeah the last thing you want to do is start worrying about a sketch that's just to help you get an idea of the mechanics of the question. There's no marks for it, because you don't have to do one. Someone correct me if I'm wrong but I think the only time you ever have to sketch something is paper 1 Q6/7.

Mutant_Fruit

Sometimes you have to sketch that curvy thingy that has no max/min. Whatever its called. The one that has the asyptotes etc.

subway_ie

I'm not worrying about it, just wondering what the right way to do it was. Anytime I did it before (maybe once or twice) I just did it freehand, looked a bit **** really.

penguincakes

Touch pen/pencil/marker/crayons (not yellow) to paper. Execute quarter-circle turn to the left as if you were rubbing the rim of a mug (look I don't have many tools to work with here). Repeat x 4.

Mutant_Fruit

so you're going to draw a circle with 5 quarters? The origional quarter circle, and then 4 more quarter circles? Thats one crazy ass circle...

subway_ie

Originally posted by Mutant_Fruit
so you're going to draw a circle with 5 quarters? The origional quarter circle, and then 4 more quarter circles? Thats one crazy ass circle...

See where my confusion comes from? All these razy 5/4 circles. Madness.

penguincakes

Originally posted by Mutant_Fruit
so you're going to draw a circle with 5 quarters? The origional quarter circle, and then 4 more quarter circles? Thats one crazy ass circle...

Sorry musta missed one, repeat X 5 then

DS

As long as you do 4 quarters it doesn't matter how many more you do, they'll just be making the line darker

PrecariousNuts

Just finished trig, the circle and most of vectors. My eyes are watering

I'M LOVIN' IT!

PrecariousNuts

Anyone else staying away from probability? I don't mind it at all but for an exam situation I'd like to know if I have the right answer or not. I have an uncany ability to always pick the wrong option out of combination or permutation when the question doesn't make it clear.

Also, is anyone doing groups, elipses or further probability? If so I'd like to get an autograph, you must be the only one in the country.

DS

Anyone else staying away from probability?

No siree bob. Difference equations and statistics are laughably easy. Admittedly probability is hit and miss, but you have LOADS of time for it, and if you just focus and keep a clear head it's a breeze. I'm definitely doing 6 & 7 before trig anyway. Funny how the "option" question is the one question you have to do :rolleyes: Q8 is pretty straightforward though. I don't think I've ever seen a hard max/min Q.

PrecariousNuts

What ones are you skipping?

Lantis

Skipping vectors and some other question I don't like.

Doing probability for my option. \m/

subway_ie

I'm doin' the standard 1,2,3,4,5,8. Never revised statistics/probability, so I don't have any choices if ****ty questions come up. The one I'm most worried about is vectors.... those damn visual ones always feck me up. 2003 vectors were easy enough, so let's hope they keep it up. In fact, I'm just after doing (most of) the 2003 paper, and it's a nice paper overall. The question 8 practical thing was a bit off-putting, but it's doubtful something like that would come up again.

DS

I'm going to do as much as I can in the following order: 1,2,3,6,7,8,4,5

Haven't done many full paper 2s timing myself so I'm not too sure how much I'm aiming to get done, I'll find out over the weekend.
It's the proofs that'll kill you. That's the advantage of skipping trig, you cut out a lot of proofs, but I'd be stupid not to go over them anyway. Circle is long but always doable, same for line. Everyone who I've talked too has the idea that vectors are piss easy, but you get some really nasty part c's. It can often be a very simple question on the other hand. Tip for anyone not decided on their questions: start with the part c's on the trig Q's, if you can do them go on with the rest of the question. Good way of avoiding wasting time on a question you're not going to finish off. You can come back to them in the end once you've got 6 Q's in the bag.

PrecariousNuts

I love the trig proofs. Nearly all of the time I see the path I have to take, the rest I go with my gut. Excellent suggestion about starting with the part cs however it might be very off putting if you can't get one out.

By love I mean are usually easy but annoying, and by proofs are you including the cos(A+B) ones etc?

purplepolkadot

oooooooh i'm doing groups!!! i feel all special. i shoulda recommended it to yiz ages ago cos it's REALLY REALLY easy and basically the same thing every year.


if you bring one of those little blue vaselines in with you you can use it to draw a perfect circle, and it's just an 'aid' so they're allowed, before any pedantry ensues.


anyone have ANY THEOREM PREDICTIONS OR WHAT PROOFS THEY THINK ARE GONNA COME UP?!?!?!??!?!?

DS

and by proofs are you including the cos(A+B) ones etc?

Yeah all the page 9 heroes you have to prove. How tedious...
I ****in hate the identities you're talking about, where you prove something=something using all the rules. I mean, I just don't see the point of it, it seems so random and useless.

it's REALLY REALLY easy and basically the same thing every year

Ditto for Q8

claire h

Originally posted by Discharger Snake
I mean, I just don't see the point of it, it seems so random and useless.

As opposed to the rest of the maths course, which has so much use in everyday life. I know my life has changed utterly now that I can differentiate cos x by first principles....

DS

Calculus is incredibly useful really, you can apply it to everything. Anyway what I meant to say was that proving trig identities is more about trial and error than actually using logic and intelligence to arrive at a solution.

subway_ie

Originally posted by Discharger Snake
Calculus is incredibly useful really, you can apply it to everything. Anyway what I meant to say was that proving trig identities is more about trial and error than actually using logic and intelligence to arrive at a solution.

Well, for some people it's totally trial and error. But others can see "patterns" in the question/result and know exactly what to do and when from the very begining. I think those kind of questions test your maths abilities more than most questions on the paper. Instead of just testing what you've learned off and done over and over and over again like the trig identity proof, they actually require a bit of creative thinking.

DS

But others can see "patterns" in the question/result and know exactly what to do and when from the very begining

You can't know "exactly" what to do, you'd be einstein otherwise. You see a pattern and you think it'll work, you try it, and it might work. But sometimes it doesn't and you end up with a big mess. The only things you can learn off are proofs and part a's. If you try to learn off anything else you're gonna get a C at most. Almost everything on the paper requires creative thinking. That sort of thing is just boring compared to a good practical question in differentiation or something. I dunno, maybe I just don't like them and never will.

subway_ie

Ok, well maybe not "exactly" - but have a very good idea of how to do it. It might not be the most creative question on Paper 2 - but it definetly needs alot more thought than the triple simultaneous questions on paper one or the absolutely pathetic rates of change in Q6/7.

DS

Here's my bare bones revision checklist for today. Mostly proofs, obviously, plus a couple things that could catch you out.

Q3
-proof of angle between two lines
-proof of perpendicular distance
-image of a line segment, proving that the image is a line segment
Q4/5
-12 proofs of pg 9 identities
Q6/7
-proof of difference equations formula
Q8
-estimating pi with sum of two inverse tans

Mutant_Fruit

-proof of difference equations formula

is that the same as Q7 (B) (i) in 1994? is that they way you'll be asked to prove it?

subway_ie

Originally posted by Discharger Snake
Q4/5
-12 proofs of pg 9 identities

Which ones are those?

For the maclaurin series, I hear (1 + x)^m is a likely one, with a ratio test added in at the end. Obviously its not guaranteed to come up, but it wouldn't hurt revising it.

DS

Originally posted by Mutant_Fruit
-proof of difference equations formula

is that the same as Q7 (B) (i) in 1994? is that they way you'll be asked to prove it?

Yeah that's the one. We could be up for a 10 year anniversary

Which ones are those?

The first 12. The sine and cosine rules, and then the first 5 from the left and right columns i.e. cos(A+B) to (cosA)^2 and then cos2A to (sinA)^2

subway_ie

Originally posted by Discharger Snake
The first 12. The sine and cosine rules, and then the first 5 from the left and right columns i.e. cos(A+B) to (cosA)^2 and then cos2A to (sinA)^2

Just went looking for a log book to see which ones you were talking about... somehow I've managed to take two log books from the exam centre. Dunno how the feck that happened. :dunno:

Do we have to be able to prove the Sine rule as well as the cosine rules? I don't remember ever doing that?

Time Magazine

I don't think the sine rule is on the course. Cosine is definitely. I'm almost sure sine rule isn't though. Is there an example in the papers of the maclaurin series you said?

subway_ie

Originally posted by Angry Banana
Is there an example in the papers of the maclaurin series you said?

I'm not too sure about the actual papers, but if you have the "Less Stress More Success" revision book then it's in there somewhere near the end of the Maclaurin section. Just remember, it's only a guess that something like that will come up. Don't bother trying to learn it off or anything, just revise over it.

DS

Sorry you're right sine rule doesn't have to be proved. You have to prove (sinA)^2 + (cosA)^2 = 1, that's what I left out instead of sine rule.

Mutant_Fruit

1999 Paper2, Question 7 C.

Its easy, i know it is, but i can't get the feckin thing to work out.

I worked out the b in terms of a to be 4a/5

i worked out standard deviation to be sq_rt[( 61a^2)/25]

I;m resonably certain the standard deviation is wrong, bt for the life of me i cna;t find the mistake.

claire h

It's the sq_rt[(74a^2)/100], or (root74)(a)/10.

The four yokes you add together after taking away the mean from the original numbers are -3a/5, 7a/5, -4a/5, and 0, and then dividing by four. Probably just a sign mistake or something.

subway_ie

Originally posted by Mutant_Fruit
1999 Paper2, Question 7 C.

I can scan in a solution if you want, but like Claire H says, it's probably just a sign error.

Mutant_Fruit

-4a/5???

I got -8a/5.

B= 4a/5, the mean is 8a/5.

Therefore isnt the third figure going to end up being -b, which is -8a/5...

a solution would be nice

subway_ie

Quality isn't great, but you should be able to make it out:

claire h

Originally posted by Mutant_Fruit
-4a/5???

I got -8a/5.

B= 4a/5, the mean is 8a/5.

Therefore isnt the third figure going to end up being -b, which is -8a/5...

a solution would be nice

b (original figure) - 2b (mean) = -b
4a/5 - 8a/5 = -4a/5

Look, reread what you've written. You have b = 4a/5, -b must therefore be -4a/5, not -8a/5.

eta: ah, nevermind, you have the solution now anyway.

Mutant_Fruit

i made a rediculous mistake when i was doing it. at least it was only a 3 mark mistake.

DS

I've done everything now apart from the pg 9 proofs. It's gonna be a struggle to force myself through them, firstly because 4 and 5 are my fallback Q's, secondly because my ****ing wisdom tooth decided to go mental on me and now I can barely eat, never mind concentrate at a desk. I'm on the nurofen and antibiotics and tincture of mirrh and whatever else you can think of. Great how the immune system tends to go to sleep at times like this.

subway_ie

Wisdom teeth are weapons of satan. I was in agony during the orals with mine. Totally fecked up my french because of that and a hugeeee migraine. Luckily I've relaxed a bit since then...
The only question I'm worried about right now is the line. Maybe the circle aswell. Not so much because they're hard, but they're so damn long sometimes. The trig proofs aren't hugely imortant - as long as you have a rough idea you'll figure it out in the exam. Just did 5 paper twos today. Lookin forward to tomorrow.

DS

Maybe do 6 and 7 first, then you'll feel like you have all day for the circle and the line, which are by far the longest. Might do that myself actually. Although I'll be a bit jittery on the first Q, so probability probably wouldn't be the best for that, best with something more formulaic. Like the circle. *sigh* :rolleyes:

subway_ie

Originally posted by Discharger Snake
Maybe do 6 and 7 first, then you'll feel like you have all day for the circle and the line

:dunno: Haven't even looked at probability/statistics since we did it in 4th year. Even then I didn't really look at them properly. Plus at least with the circle and line you have a rough idea whether your answer's right. They might be long, but at least they're predictable and (semi) easy.

oeNeo

For anyone doing question 8, any tips on how to do the general test ratios? The second parts on the Maclaurin series.

Our teacher did one class on this and absolutely no-one knew what she was doing.

"Write down the general term and use the Ratio Test to show that the series converges for all x E R"

(The one I'm looking at is 2001 B ii)

Mutant_Fruit

Basically, once you write down the terms up to the one including x^7, you will see a pattern in the way the numbers increase.

You then have to think, and write up something in a general way, that will represent any term in the sequence by only having to substite in a letter. just like the Un of a series.

if i write 1 + x + x^2 + x^3 and ask you to write out the general term, youd write x^(n-1). That way, when you put in 1, you get x^0, which is 1 (the first term), when you put in 2 you get x (the second term) etc

You just do that for the series.

Then, when you have Un, you just substitute in "n+1" for N, to get U(n+1) and then divide U(n+1) by Un and get the lim as n -> infinity. You should get a number like 1/2 or 2 or something like that.

Very easy once you do one or two.

PrecariousNuts

Deffo no 6 or 7 for me, I'm going to rip through the circle, then the line, vectors and hopefully the trig won't be a complete ass of a question. The one thing trig has going for it is that most of the part c's are just one liners like prove sin(A+B) blah. Q8 should be easy too, ratio test as an entire part c lol

oeNeo

Hm, sounds pretty doable actually. My maths teacher was babbling on for ages about all sorts of stuff, but you seemed to have put it nice and simple. Cudos to you.