Maths paper 1

Mutant_Fruit

What formulae thingies do we have to be able to prove? I can do all the differentiation stuff, but what else do we have to know? (i'm not doing induction).

Swifty

You doin honours? Well as far as I know, the only other thing you need on paper 1 is the factor theorem, which came up last year so you can pretty much rule that one out. I may be wrong but the only formulae I've learned to PROVE are the differentiation ones, the factor theorem and the induction one you're not doing. I suppose you might call the differentiation from first principles proofs, you should know how to do all the different types of first principles, I have a feeling one of those will come up this year.

Sometimes you are asked to use integration methods to find volume proofs but again one of those came up last year and I think they're going to lash on one of those hard area questions this year.

subway_ie

Factor theorem
De Moivres Theorem
Induction
Derivation from first principles of:
X^2
X^3
SinX
CosX
Root X
1/X
Sum Rule
Product Rule
Quotient Rule
Differential thingy by induction (can't remember the name, basically dy/dx = nx^(n-1)

Two of those standard proofs use induction (de moivres and the last one), so you should have a rough idea of it.

Swifty

Ah yeah, forgot De Moivre's, but if you know induction you know that

Mutant_Fruit

Grand, i spent 15 mins learning how to do the DY/DX proof thingy this evening, and thats everything then. I know all that stuff, so i should be grand.

BRING IT ON!

subway_ie

Stop your "bring it on" madness. Please, think of the children.

Mutant_Fruit

Good luck! Hope everything comes up that we've all done before.

Celt

3 ****ing questions on differentiation on ordinary paper, 3 out of 8

bollocks

Mutant_Fruit

WOO WOO WOO WOOOOOO!

I did ALL 8 honours questions, and i'm pretty sure i got em right aswell. If only everything is like that.

3 down, 13 to go...

Celt

Originally posted by Mutant_Fruit
WOO WOO WOO WOOOOOO!

I did ALL 8 honours questions, and i'm pretty sure i got em right aswell. If only everything is like that.

3 down, 13 to go...

cunt

NeoSlicerZ

sweet paper. I think i only dropped about 15 marks in total

Celt

Neo can I get access to UDC so I can slag Macca for being a coward

DEmeant0r

I think I got an A1 in that ordinary level paper.

seamus

Originally posted by Celt
3 ****ing questions on differentiation on ordinary paper, 3 out of 8

bollocks

Sounds about right, no? I thought there was always at least two differentiation questions, so it was never worth your while ignoring differentiation.

Differentiation is easy money tbh.

PrecariousNuts

I managed to do 7, my only problem was with Q6 (c) but I probably did it right anyway. I can't believe it was that easy.

Higher level

c0rk3r

Ordinary level Paper one answers,my answers. dispute away.

Q1 (a)6 (b)i 7000 ii 16660 iii44740 (c)i2703 ii2252.5 iii2297.5

Q2 (a)i -39 (b)i(3 & 0.5) iiproven (c) 2^1 ii 2^1/2 iii x=3.5

Q3 (a)x=3 (b) proven (c) p=2

Q5 (a)40,35,30,25,20 (b)i a=6 d=5 ii n=31 iii 402 (c) -4,16,-64 ii -819 iii proven to be true

Q6 (a)k=-4 (b)i (-1,-3) (3,1) ii 3xsquared -6x iii max(0,1) min(-2,-19) iv /\/ (shape) v f(x)<0 = -1, 1, 2 {x>0 = 0, 3} vi f`(1)<0

Q7 (a)i 10x4 ii -8x (b)theres lots of cubes etc,not typing it out! iiproven true (c) i 3m/s ii t=20 iii 860m iv4m/s cubed


I wrote my answers on the exam paper and brought the paper out.... if you wanted to know.

NeoSlicerZ

i answered Q.1,2,3,5,6,7,8 ;-)

got everything out basically cept 8.b.ii that got me -_-

subway_ie

Did the usual question 1,2,3,6,7,8. 1 part (c) was a bit of a fukc up, 2 was sound, messed up the last part of the matrices in (c) part (ii), 6 (c) part (ii) another feck up. Q7 (c), again, ****ed it up. Q8 (b) part (ii) and (c). This whole leaving cert thing isn't going too well for me...

Swifty

Originally posted by Mutant_Fruit
WOO WOO WOO WOOOOOO!

I did ALL 8 honours questions, and i'm pretty sure i got em right aswell. If only everything is like that.

3 down, 13 to go...

Eh.. all 8? how exactly did you manage that?

I'm happy enough with the maths, I didn't expect to get every single part of every single question out going in and I didn't get off to a great start because Q1 was unusually tricky. Q2 was fine, Q3 also fine, Q6 good too, missed out on two parts in both Q7 and Q8. Definately no A1 but I'd expect a nice high C from that, will have to wait and see how paper 2 goes.

subway_ie

Originally posted by Swifty
Eh.. all 8? how exactly did you manage that?

I was thinking the same thing...

will have to wait and see how paper 2 goes.

That's the thing - look at last years paper 1, lovely questions, nice and short. Paper two was a disaster for most people and their was even an internal review of the SEC ordered by the minister after the reaction people had to the paper.

Swifty

Questions I had trouble with..

Q1 - (b) (ii) Christ I hate indices, did my fair amount of panicking at this one it's not nice not to be able to get one out at this early stage.

Q1 - (c) (ii) A big fat WTF? here.. how are you expected to cube the bracket with the three numbers without spending all day at it?

Q3 - (b) (ii) They didn't end up equal, looked over it about 3 times and could find no mistake there must have been though

Q7 - (b) (ii) Didn't end up perpendicular, whatever I did wrong.

Q7 - (c) (ii) Didn't know what to do here, wasn't actually sure what you were supposed to differentiate.

Q8 - (b) (ii) Can't beleive I didnt spot how to do this one, I was told after the exam

Q8 - (c) (ii) Made a small attempt by subbing in -h, 0 and h in the original equation but didn't know what to do then.

Too many mistakes you think?

Suaimhneach

It was a deadly paper. Only had a problem with 6 c and 8 c. But I did 7 questions so that's cool!

Mutant_Fruit

Eh.. all 8? how exactly did you manage that?

Well, i managed it because i knew how to do em all. the only thing i was a bit uncertain about was proving the yoke in the induction question, but i made a very good attempt at it (if anyone wants to write out the solution for me that;d be great).

I origionally wasn't even going to bother with the induction question, as i can't really induct well, but since i had 7 questions finished with 45 mins to go, i gave it a shot.

Crash

nice enough paper - dropped 25-45 marks - so worst case thats a B1, best case just scraped an a1

Smellyirishman

A1 here in ordinary (could be an unlucky A2)

misread one question (they warned me so much) and didnt do it by first principles, and also messed up the complex numbers root question thingy

I did Q 1(HA),2,3,4,6,7 how come no-one does 4? thats quite a good one.

Mutant_Fruit

Too many mistakes you think?

You can afford to make 20 screw-ups and still get an A1. So, assuming you made one stupid mistake in each of those parts you got wrong, thats 7 screwups. So, you are still more or less on target. Deduct more marks accordingly if you could barely get a question started, but so far not too bad.

claire h

I could actually do the questions! Really wasn't expecting that.

Q2(c)(i) was tricky, I got k=3 but I wasn't sure about it.

Q3(c), got weird numbers in my matrix but I think my methods were okay.

Q5(a), couldn't do it, I had the general formula but it wasn't working out for me. Did this as an extra question though so I'm not too bothered.

Q6(c)(ii), didn't have a clue. The 'hence' threw me; couldn't see how you'd connect the two.

Q8(c)(ii), not so great.


>>Q1 - (c) (ii) A big fat WTF? here.. how are you expected to cube the bracket with the three numbers without spending all day at it? <<

Did you read the 'hence'? Put the bits in the brackets equal to the bits in the question before it (a-x=p, b-x=q) and it's the same, so you can use the yoke above for it.

>>Q7 - (c) (ii) Didn't know what to do here, wasn't actually sure what you were supposed to differentiate.<<

I tried differentiating both of them and then did dx/dy of the first one, turned it over to get dy/dx, and subbed in the (1+x/1-x) wherever I had a e^2y. Worked out, don't know if I got the right ps and qs though.

Swifty

I'm hoping they're nice and generous with the attempt marks 'cause I gave everything a shot, just didnt get out the ones I mentioned above.

Mutant_Fruit

Q7 - (c) (ii)

you reorganised the yoke til it was e^(2y) = .....

then you took the log of both sides, and ended up with 2y Ln(e)= Ln.....
(using rules of logs to bring the 2y down).

Then ln(e) should be recognised as being 1... basic stuff here.

so you get 2y= Ln....

therfore y= 1/2Ln.... and you use rules of logs to bring the half up, and the thing in the Ln becomes squar-rooted if you know what i mean.

Then its just a differentiation question as per usual.

The answer is 1/1-x^2

Swifty

Originally posted by claire h


Q3(c), got weird numbers in my matrix but I think my methods were okay.

Don't worry about that everyone I spoke to said they got strange numbers aswell. You get numbers in the thousands yea?

Did you read the 'hence'? Put the bits in the brackets equal to the bits in the question before it (a-x=p, b-x=q) and it's the same, so you can use the yoke above for it.

I'm looking at it now I really can't see a way to sub in anything in those brackets!

Swifty

Ah ****, now I see what you mean in Q1 (c), claire.

PrecariousNuts

The induction question: 2^n >= n^2

test for 4

16=16... grand

assume true for k

2^k >= k^2

we want to get

2^(k+1) >= (k+1)^2

multiply the original by 2

2.2^k >= 2k^2

that becomes

2^(k+1) >= 2k^2

thus

2^(k+1) >= (k+1)^2

provided

2k^2>= (k+1)^2

this works out to have k = 1+- root two >= 0
and since you're told n>=4 this holds as true

Mutant_Fruit

yeah, i showed it was true for n=4, assumed it was true for k, then let n=k+1 and got a bit stuck there, and i did a bit of waffle, and then said this is true. Then a little more of the usual waffle of "Since its true for k+1, then it must be true for 5, therefore its true for 6... therefore true for all n E reals. And wrote Q.E.D. and left it. I'll get at least the attempt marks for that

PrecariousNuts

Originally posted by claire h
I could actually do the questions! Really wasn't expecting that.

Q2(c)(i) was tricky, I got k=3 but I wasn't sure about it.

Q3(c), got weird numbers in my matrix but I think my methods were okay.

Q5(a), couldn't do it, I had the general formula but it wasn't working out for me. Did this as an extra question though so I'm not too bothered.

Q6(c)(ii), didn't have a clue. The 'hence' threw me; couldn't see how you'd connect the two.

Q8(c)(ii), not so great.

Q2(c) is correct
Q3(c) same
Q5(a) very easy, I don't see how you could have gone wrong
Q6(c) is must admit that this was quite hard however I proved that 2 of the roots were imaginary and I hope it was sufficient.

3[(x+2)^2 + 1] = 0
(x+2)^2 = -1
+-(x+2) = i
x = -2 + i
x = -2 - i

hopefully thats in someway right

PrecariousNuts

and lets all pray that paper 2 is as easy

Mutant_Fruit

Q6(c)(ii),

That got me too, but not for long. For one real root, it can only cross the axis at one point, ok? Remember the way it asked you to get the derivitive of f(x). The derivitive = 0 at a max or min.

So all you had to do was set the derivitive equal to 0, and show that it couldn't equal 0 for any real value for X. That meant there was no maximum or minimum, and since there was no max or min, it was just like a striaght line to infinity, meaning it could only cross the axis once. Q.E.D.

PrecariousNuts

haha! brilliant I wrote those exact words down at the last minute for the sake of it!

DS

Loved that paper, 6 Q's done in an hour, did an extra one and then just went over them a few times, didn't bother with 3 for some reason. I wrote all my answers in my paper and so did my friend, and we got all the same answers, so I think we're both heading pretty close to 200 marks on paper 1, which is a bloody fantastic way to be relaxed going in for paper 2, which after the controversy last year can't be too bad.

Someone asked about the induction proof, the last bit was a bit tricky. Here's what I did starting from P(k+1):

2.2^k > (k+1)^2
2^k > 1/2(k+1)^2
Which is true if:
k^2 > 1/2(k+1)^2 -> from P(k)
2k^2 > (k+1)^2
2k^2 > k^2 + 2k + 1
k^2 - 2k - 1 > 0 -> cue me staring blankly at the page for a couple of minutes before thinking of completing the square
(k-1)^2 - 2 > 0
(k-1)^2 > 2
k-1 > root(2)
k > 1 + root(2)
which is true, as k > 4

Obviously I used > there instead of >= for convenience.

The only question mark for me was 6c(ii). I made a pretty good attempt I think, but I'm not sure if I proved it properly. Anyway:

You have an expression for f'(x) from part (i) which you have to use.
What I said was that f(x) having only one root means it only crosses the x-axis once.
So, the first thing you do for that type of question is find the turning points.
You should have gotten 3[(x+2)^2+1] for f'(x) yeah?
Well put that = 0
And you get (x+2)^2 = -1
x+2 = root(-1) -> unreal roots
Therefore there are no turning points (I couldn't get my head around this, I was so fixed in the notion that a cubic equation always has 2 turning points, never seen anything like this before)
It can only cross the x-axis once, because there are no turning points.
That's the best I could do.

As for Q1c(ii)...
It's clear from the "Hence", and from examining it a bit that p=a-x, q=b-x, and p+q=a+b-2x
So you have the same equation here, with one difference:
In your equation -3pq(p+q)=0
So sub in your values:
-3(a-x)(b-x)(a+b-2x)=0
Which is a terrifyingly simple cubic equation simplified for you (some people in my class went multiplying that out without realising the answer was right there)
So from that equation, it's clear that:
a-x=0 x=a
b-x=0 x=b
a+b-2x=0 x=(a+b)/2

Stench Blossoms

Originally posted by c0rk3r
Ordinary level Paper one answers,my answers. dispute away.

Q1 (a)6 (b)i 7000 ii 16660 iii44740 (c)i2703 ii2252.5 iii2297.5



5 (a)40,35,30,25,20

sorry but i think ya have them wrong... in q1 part (c)iii it asked how much MORE wud ya have to pay...

and in question 5 i think that bits wrong aswell

Raskolnikov

A friend showed my the this years paper, wow, it was even easier than the joke of a paper we had in 2002.

c0rk3r

aye 1 (c)iii is wrong! misread the question, probably lose 5 marks.no biggy. can afford to lose 60marks overall and still get an A1.

If 5 (a)i is wrong i'll take my own life! its not wrong

Crucifix

I was happy with the paper. I'm not saying I did well, but the paper could've been far worse.

Stench Blossoms

Originally posted by c0rk3r
aye 1 (c)iii is wrong! misread the question, probably lose 5 marks.no biggy. can afford to lose 60marks overall and still get an A1.

If 5 (a)i is wrong i'll take my own life! its not wrong

i dunno but if d=5 which is a positive how cum ut number decrease? doesnt that only happen wen "d" is negative??

i could be mistaken but i dont think i am...

conZ

Ordinary level paper was decent enough. I'd say I hit a B.

C0rk3r,
For question 1 c part 3, you got Q1 (c) €2297.50. That's wrong. The question went : "If the pump had registered the correct volume delivered, how much more would have been paid?"

You were meant to take the actual payment, €2252.50 from €2297.50, and give the difference.

c0rk3r

Originally posted by orla
i dunno but if d=5 which is a positive how cum ut number decrease? doesnt that only happen wen "d" is negative??

i could be mistaken but i dont think i am...

d=-5

aye conz as i said in a previous post i was mistaken although it was no huge mathematical blunder.May only cost me 5marks.

Mutant_Fruit

blunder=3 mark loss, and slip=1 mark.

popinfresh

I got the whole of Q8 C to work out, I was well chuffed
what u had to do for part b was sub in the f(-h) f(o) anf f(h). When u subbed in f(0) u gt=ot c=y2, then you make a simultanious equation out of the other 2. then 2a will work out as having a h^2 at the bottom which canceled out. Also I couldn't get 5 (c) to work ****in induction

Healio

ordinary level q1 easy marks= 50/600 x 100/1 = 8.33333%

Barbie_666

Originally posted by conZ
Ordinary level paper was decent enough. I'd say I hit a B.

C0rk3r,
For question 1 c part 3, you got Q1 (c) €2297.50. That's wrong. The question went : "If the pump had registered the correct volume delivered, how much more would have been paid?"

You were meant to take the actual payment, €2252.50 from €2297.50, and give the difference.

oh man.........

Seifer

I did 7 questions, got all the a's and b's. I know I got two of the c's completely right and I got one part at least of the others. I'd say I got an A on it but not sure if I made it to A1. Hope to secure that on paper 2 which is a hard thing to do.
I'm only doing maths this weekend as my next proper test isn't till wednesday; biology. Hate to have to study for geography too:p