Applied Maths

PrecariousNuts

1990 Q10 b and 1991 Q10a, any ideas on how to do these two lads?

I've pulled my hair out with the 1990 one trying to find out what they are asking, and the integral of

1/(y^2 + y)

doesn't seem to feature in any of my maths books.

Am I missing something or just losing it?
The answer to above worked out to be Ln(y) - Ln(y+1) or just Ln(y/(y+1)) however I can't seem to remember any rules to do this one, any help would be appreciated.

silverside

There is no rule for it; the simples thing is to express it as a partial fraction (I think this is on the LC syllabus), then the integration is simple as you have seen (something like integral of (1/y - 1/y+1) = ln(y) -ln(y+1).

PrecariousNuts

Oh yeah partial fractions, feck the feckers. Not exactly on the syllabus for integration but I should have seen it.

Thanks a million

DS

For 1991 10a:

1/y + y = (1 + y^2)/y

that gives:

dx/x = ydy/(y^2 + 1) -> simple substitution, u = bottom line

For 1990 10b:

F = ma
F = 8a
8a = 16
a = 2

a = 0 at t = 0
a = 2 at t = 10
therefore, because the force increases uniformly, da/dt = (2 - 0)/10 = 1/5

da = dt/5
a = t/5

The rest is straightforward enough.

dv/dt = t/5
Get t in terms of v:
v = (t^2)/10
t = root(10v)

ds/dt = (t^2)/10
Get t in terms of s:
s = (t^3)/30
t = cuberoot(30s)

Put your 2 values for t equal and you're home and dry.

Love question 10, can't believe it's a full question. Another reason why this is by far the best LC subject in terms of work vs reward.

subway_ie

One of those partial fractions type differentials came up on our applied AND maths mocks this year, threw me for a good few minutes. I think they're covered in the sequences and series chapter in most maths books (which is a bit weird, since it's algebra...), so barely anybody had it revised. I'm sure it was probably the same way when it came up on the official paper.

DS

You don't have to use partial fractions for that particular one by the way. The first thing that came into my head when I did it was completing the square i.e.

y^2 + y = (y + 0.5)^2 - 0.5^2

You have to use a weird integration rule then though that isn't on the maths course, 1/(a^2 - x^2)
Works out though.

PrecariousNuts

Sorry I got it wrong, I meant to say 1989 Q10b.

I'm just not sure how to use the information given in this question/understand what it is asking.
I can solve differential equations no problem, (you should have seen how pissed off I was when I saw the word partial in your reply, it immediately clicked) but sometimes I find it hard to use the information given. In this case I tried

a = -v^2 as initial equation

I tried vdv/ds = -v^2 and dv/dt = -v^2 but couldn't figure out how to get the average speed.

DS

Proportional i.e. not equal

a = dv/dt = -kv^2 where k is a constant

You can then use simultaneous equations to find k using your 2 sets of data, t=0 v=6, s=35 v=3.
Average speed is simply s/t

PrecariousNuts

ah right, thanks

pigeonbutler

Sorry to change topic slightly but to generalise a bit more how are people generally fixed for applied maths?

I agree with whoever said it's the best LC subject for work Vs reward. Pity I did nothing at all in it until about Xmas of this year. I'm still hoping for a B in it anyway cuz i'm very comfortable with:

Connected particles
statics
Projections
Q 10 a) B can be dodgy

I'll make a good fist of collisions too and Q1. too.
Relative velocity is really easy but i still struggle with it.
SHM might be lucky for me. I can prob pick up 20-30 marks on it if i really have to.

The marking scheme does tend to be very generous in Applied Maths. If you get half a question right you'll get about 75-80% of the marks because of the way they're allocated.

subway_ie

Applied shouldnt be *that* bad. I'll be studying for the 4 free days leading up to it - need to work on question 8 proffs - still haven't learned them properly yet :dunno: . Linear motion, projectiles, connected particles, impacts and collisions, differentials are all usually ok. Relative velocity can be a bitch, but it's going to probably be one of my 6 - that or rigid body rotation (definetly a question I'm going to do if it's a "lollipop" type part (b)). Just hoping that Question 5 isn't one of those "Show that..." and for the love of God, pleaseeeeeeeeeeeeeee don't ask a wedge with an attached pulley in question 4. That would be a total nightmare for me. Apart from that, not too bad.

PrecariousNuts

If you know thats where you have problems, shouldn't you just learn it off? Thanks for reminding though, I had completely forgotten about those ones.

I'll be very happy with a B in it. I took the subject outside school and the only help I've gotten with it was a week of Institute grinds at Easter. I'm alright at the subject but those twats just end up turning it into pure maths. Thank god for the bang on marking scheme though, usually only 5 marks out of 25/30 for getting the answer. Most of the time I can't be arsed juggling their stupid trig equations etc.

I'm going for projectiles, connected particles, differential equations, maybe collisions and rigid body rotation especially if there is a proof. Relative velocities are ok, I'll pick it if a wind question comes up. I'm still a bit dodgy on Q1 but I should be ok when the time comes.

Mutant_Fruit

If a paper like 1998 comes up, we're all screwed beyond belief. Otherwise, B2+ i'd say. I'm grand enough in it.

I can always get a question started. In statics i get all the equations 90% of the time, but i cant always solve em. So i plan to do about 6 statics questions today... bwuh hu ah ahaaa!

I'm still a bit dodgy on Q1 but I should be ok when the time comes.

Aren't we all? That question is impossible to predict. It varies the most from year to year. Whereas with statics or relative velocity, you'll find there is very little variation that can be asked.

Thats why Q1 shouldn't be in your top 6 questions, it should be a definate number 7.

subway_ie

Originally posted by Mutant_Fruit
Thats why Q1 shouldn't be in your top 6 questions, it should be a definate number 7.

Did you know that Question 7 is the third worst answered question on the paper? The average mark is 32.0 out of 50. Just fyi, here's the performance in different questions, in their order of preference of candidates:
Q3 - 45.7
Q4 - 40.3
Q1 - 31.9
Q10- 40.1
Q5 - 33.0
Q2 - 33.4
Q8 - 44.5
Q7 - 32.0
Q6 - 33.2
Q9 - 23.8

Basically, the top 6/7 are my choices, feck the last 3.

The papers seem to have been getting a bit easier since the 1998 one (not that hard), so let's hope that they've gotten even more generous...

Sev

Originally posted by subway_ie
Q1 - 31.9.

Surprising how low that mark is considering how generally easy that question is supposed to be.

Those statistics you have, are they based on like the last number of years of leaving cert applied maths? or just last year's results. Because last year's question 1 was indeed tricky, and last year's 3 and 4 were also very simple.

I'd agree with your choices on the top 6 in your list.. 1,2,3,4,5 and 10. They are in my opinion the easiest questions on the paper (although I never studied for question 8). They are the ones anyway, that I felt you could intuitively do without a whole lot of knowledge of applied maths. They were my top 6 going into the exam, and they were the 6 I did in the exam, and Im sure I aced every one of them. (That said, if I had seen just SHM for Q6, I probably would have done that over Q5.. Q5 was a bit of an epic). Last year was also a pretty damn easy paper as applied maths papers go, so dont get too confident.

subway_ie

Originally posted by Sev
Last year was also a pretty damn easy paper as applied maths papers go, so dont get too confident.

Yeah, uually they don't give two easy papers in a row. Last year was the year to do the leaving cert - gorgeous business, applied, physics and (most of the) maths papers. If only this year was as easy/easier.

The stats are only from 2003 - so they're not totally comprehensive, but I'd imagine that they're roughly the same each year. Question 1 was a bit of a surprise in 9th place, so it just shows how careful you have to be about picking questions before you go into the exam. I've only got room for swapping one question MAX (Q8, probablly for Q2, even though I still don't know the methods...)

DS

Q1 is one of the questions where you never really know what you're going to have to do. It could be straightforward, you could miss something in the question and be completely clueless. Last year's "just" was a really evil bastard trick in all fairness. They should have bolded it at least. I'm doing Q1 6th or 7th (if time allows), when I'll be more relaxed having the rest in the bag and won't be rushing.

Q3 and 10 are really straightforward, it's the same thing every year. Q4 is nice too, it's really a case of just making sure you don't forget a force, and get your equations right. If you've seen the type of question before (wedge, pulley etc.), which is highly likely, then you're grand.

As for 2, 5 and 6, it depends on how mean they want to be. I'm hoping for an A1 anyway. They don't do it in my school (I did a weekly grind), so I'll be on my own in the hall with the examiner. Should be interesting.

subway_ie

Originally posted by Discharger Snake
They don't do it in my school (I did a weekly grind), so I'll be on my own in the hall with the examiner. Should be interesting.

Are you sure about that? We do it as a proper subject in our school, and have an examination centre for it - but everybody in the area has to come to our school to do the exam so there won't be anybody sitting on their own in the hall... Are you sure they're not going to ship you off to another school?

DS

Well that's what I assumed would happen originally, they do it in the Bish (other Galway school), so it would be logical enough. But I asked my vice principal about it (ages ago), and (apparently) she checked it out and said I'd be doing it in the hall on my own, it being an official exam centre and they have to provide for me blah blah. That said, she's notoriously full of ****, like telling our physics class (she teaches physics too) our practical copy is evaluated and is worth 10% of our LC grade, just to scare us. So no I'm not positive. Is there any regulation about minimum students per centre or anything like that? I'll have to check this out a bit more :rolleyes:

subway_ie

Originally posted by Discharger Snake
Well that's what I assumed would happen originally, they do it in the Bish (other Galway school), so it would be logical enough. But I asked my vice principal about it (ages ago), and (apparently) she checked it out and said I'd be doing it in the hall on my own, it being an official exam centre and they have to provide for me blah blah. That said, she's notoriously full of ****, like telling our physics class (she teaches physics too) our practical copy is evaluated and is worth 10% of our LC grade, just to scare us. So no I'm not positive. Is there any regulation about minimum students per centre or anything like that? I'll have to check this out a bit more :rolleyes:

Ring up the department (Or the SEC maybe?) and get it checked out. Usually they wont let you do it on your own in a hall with a supervisor for a single student - you'll be packed off to some other school, especially if you're near some other school where they have an applied class (the bish, etc). In my school (about 30 mins from Galway City/the Bish), they cater for all the students who do it themselves at home/through grinds in the local area (usually 5-10), bringing the numbers up to about 20-30 per exam centre.

Pythia

Nope, you're wrong as I sat a paper for my JC with only me(female) and examiner(male) in the hall in my own school.

Explosive_Cornflake

But, he's right, the girls school near we're i used to go, used to have to come to our place to do music exams.

subway_ie

Originally posted by RachG
Nope, you're wrong as I sat a paper for my JC with only me(female) and examiner(male) in the hall in my own school.

I never said you *had* to be with other people, just that they usually try and have as few exam centres as possible. Usually, if there are a few people doing a subject like applied maths at home, then they travel to the closest school that offers it as a subject. Doesn't necessarily have to happen, but usually does. I don't see how you being male or female would make any difference though...

Healio

Originally posted by subway_ie
Yeah, uually they don't give two easy papers in a row. Last year was the year to do the leaving cert - gorgeous business, applied, physics and (most of the) maths papers. If only this year was as easy/easier.

I heard the physics is going to be easiers because the numbers doing it are dwindling away, theres only around 6,000 doing it this year.

Samurai

The papers seem to have been getting a bit easier since the 1998 one (not that hard), so let's hope that they've gotten even more generous...

have a look at 1999

subway_ie

Originally posted by Samurai
have a look at 1999

Hmmm. The only hard question in that was Q.5 (a), the one with the side and top view and the weird distance equations. You'd have gotten most of the marks by using PCLM and Newtons law of restitution. Find V1, V2, get 60-80% of marks. Make an attempt at the next part, get another maybe 5-10% of the marks.

I remeber getting stuck on Q4 too - but that's only because I'm crap at wedges - but like I said, make a decent attempt and you'll get most of the marks.

D-Generate

I had my 5th year summer test today but it was a full Leaving Cert paper which had to be done in 2 hours, eek! Wasn't too bad though because we have been finished the course for about 2 months and been revising ever since.
The questions i will probably do are
Relative Velocity, Q2,
Projectiles, Q3,
Connected Particles, Q4,
Collisions, Q5
Hydrostatics, Q9,
Calculas, Q10.
I would also do a circular motion question if it came up that year but going by the past couple of years where they haev given it i doubt it is likely for this year and next year.
Hydrostatics is much the same every year so basically all you need to learn is, partially immersed rod, u-tube/mixtures, and also just a fully immersed body.
Relative Velocity is very easy, especially the current and wind ones.
Collisions is usually pish easy except for that year where one sphere is dropped on to another sphere. I think it is 1992, basically anyone who got an A1 in that paper did not do that question.
Calculas.... what more can I say
Easiest A1 subject in my opinion. Course is very short so no excuse for not doing well in it.

DS

Q.5 (a), the one with the side and top view and the weird distance equations

Anyone else think that's a really bad question? For it to make sense (and thus work out), you have to assume that the spheres have negligible radius, otherwise the positions they refer to are completely open to interpretation i.e. is it at the centre of the 1st sphere, where the 2 spheres meet, or at the centre of the 2nd sphere etc. That really annoyed me

Collisions is usually pish easy except for that year where one sphere is dropped on to another sphere. I think it is 1992, basically anyone who got an A1 in that paper did not do that question.

That was a mad aul question alright. The teacher in the Bish can't do it and neither could my grinds teacher. He was loving me when I got it out

subway_ie

Originally posted by D-Generate

Hydrostatics is much the same every year so basically all you need to learn is, partially immersed rod, u-tube/mixtures, and also just a fully immersed body.

Be careful with hydrostatics, it's generally the hardest question on the paper. In 2003, the average mark was 23.8. Thats 47.6% - definetly not a grade you should be getting if you're doing applied.

subway_ie

Originally posted by Discharger Snake
Anyone else think that's a really bad question?

I think the worst part of the question was the diagram - unless you read it carefully (the note about "side view" and "top view", it looks like its either some kind of pool table, or the spheres are moving vertically. The second collision, where you had (y - d)/(V1) = (y / V2) + (d / eV2) was definetly the hardest line, and after you got that it was piss easy. At least they gave you the result in part (i), so that you could still do part (ii) without proving part (i) properly. When I look at it again though, it was a damn long question whn you count part (b) aswell.

subway_ie

Originally posted by D-Generate
Collisions is usually pish easy except for that year where one sphere is dropped on to another sphere. I think it is 1992, basically anyone who got an A1 in that paper did not do that question.

I don't think the spheres are actually "dropped" onto each other... when I did it I just messed around with breaking up their velocities...

DS

D-Generate's actually talking about Q5 1990, where one sphere is dropped onto another, the line of centres making an angle of 45 degrees with the vertical.

subway_ie

Haven't even looked at that question before - keeping it for the 3 days leading up to the applied exam. Looks interesting though...

DS

VERY interesting. The thing I like about hard questions is you always understand the concept better after them, and you have less respect for the less challenging ones as a result.

DS

Actually, we should do up the ultimate bastard of a paper using past questions, just for fun. It'd be good for anyone who hasn't come accross some of the harder ones before. Q5 has to be 1990. Couple more I did recently: Q6 02, Q10 96 (easy once you realise the trick, but it's mean if you don't), Q4 93 (those tensions will get you, worst wedge Q ever). Any other nominations?

subway_ie

Q.1 - 1995/1990
Q.2 - 1990/1999
Q.3 - 2001 (B)/1997 (b)
Q.4 - 1993
Q.5 - 1990
Q.8 - 1995/1996
Q.10 - 1996

That's just after a quick look through the papers - not necessarily the ones that everybody has trouble with, just the ones I struggled on. Apart from Q.10 and Q.5, I've never tried either of those.

subway_ie

Does anybody know what the story is with drawing diagrams in applied? Like in Question 4, connected particles, if they ask you to draw a set of diagrams showing all the forces on each particle, should you do them on graph paper or just in your answer book? You probably have to do the graphs for question 1 on graph paper, but not too sure about diagrams.

PrecariousNuts

I would doubt that you have to do any diagrams on graph paper. They are just representations of whats going on, there is no need for them to be to scale or accurate. Doing question one on graph paper is like doing a trig question using a ruler and protractor. Or I could be horribly wrong

subway_ie

Originally posted by PrecariousNuts
Doing question one on graph paper is like doing a trig question using a ruler and protractor. Or I could be horribly wrong

Well I think question 1 all depends on whether they say "sketch". Sketch meaning rough, not to scale - but sometimes they ask you to draw an "accurate graph" so I'd say you'd definetly need graph paper for that.

I wonder if they'd care if I do my Q4 diagrams on graph paper - not to scale or anything, just looks neater. Our teacher mentioned before about doing diagrams/graphs on graph paper... can't remember if it was for maths or applied though.

Mutant_Fruit

if you have graph paper, use it. But personally i never bother. My graphs are always freehand sketches (i suppose tech helps with that )