Higher Maths, Paper II

Cathy

How did everyone get on? I thought it wasn't a bad paper, although I got stuck on a couple of part cs.

Anyway, here are my answers:

Q1 - a - (x + 1)^2 + (y - 5)^2 = 13
b - i - p = -6
ii - (1,0) (4, 3)
c - i - messed it up a bit, but should get some of the marks
ii - same

Q2 - a - 12/37 i - 35/37 j
b - i - d = 1/4 a + 3/4 c
ii - db = 5/4 a + 9/4 b
iii - I proved that |od| + |db| = |ob|, so they're all collinear
c - messed it up, should get attempt marks

Q3 - a - (3,2)
b - i - 3
ii - k = -32
c - i - f(L): y = [(2m - 1)/(m + 1)]x + c/(m + 1)
f(K): y = [(m + 2)/(1 - m)]x
ii - m = (root 13 - 3)/2
m = (- root 13 - 3)/2

Q4 - a - i - 15/17
ii - 240/289
b - i - proof & deduction
ii - theta is an element of the solution set {41, 139, 221, 319}
c - i - 4 - 2 root 2
ii - pi(4 root 2 - 26/3) + 4 root 2

Q5 - a - proof
b - i - 2
ii - -1sin 2x
c - i - 5
ii - 13
iii - 45 degrees

Q8 - a - - x cos x + sin x
b - didn't have time to write down the answer
c - i - 3 pi r^2 - 2 pi^2 r^3
ii - 1/pi



I'd really appreciate it if someone would tell me that every single answer ^ is right...

subway_ie

I don't have the answers, but at least you can laugh at my pitiful attempts and rest safe in the knowledge that you'll have done better than I have:
My fúck ups:
Q1:
(b) - must have fecked up finding p, got (-2,1) and (-2,0) for the points of intersection.
(c) - (ii) - only got one equation, with mad figures. Stuck the two points into the general circle equation, used the fact that f^2 = c to get the simultaneous. Don’t know what happened after that...

Q2:
(b) - Messed it up. Totally. Might get an attempt mark. Maybe. Hopefully. (Wishful thinking).
(c) - I said p = ai + bj and q = ci + dj. Tried to sub them in, but didn't work out.

Q3:
(a) Don't know if I used the right formula... point looked ok though.
(b) (ii) - Wrote down K=2. Feckin Retard. Think I had K=27 or 37 or something like that.
(c) (ii) I used the fact that K is perpendicular to L in the first part, with an equation y = (-1/x), since the y-intercept is at the origin. Then for part 2, I said that slope of f(L).f(L) = -1. Don't think it came out right.

Q4:
b) (ii) Got it out at the last minute, but got a value of 270 degrees, when everybody else got 60 degrees.
c) (ii) Got a weird answer of 8 - 2pi - 3pi/2 + pi/root2. Assumed that ¦bc¦ = root =32 and that the two angles of the big triangle are 45, and then used bcSin45 to get the length ¦ac¦, added it to radius. Then, for part (ii), got the area of each sector individually and took it away from the area of the triangle (8 I think?).

Q5:
a) - Feck. Used pg 9 identities to prove it, when I should have used the unit circle. I didn't prove, I "showed" which is just feckin retarded since I knew how to do it. :mad:
c) - (iii) - tried to use the angle between two lines formula for some unknown reason (probably because I was dreaming about it all night) so I messed about with that forawhile and then ran out of time, so I just stuck down theta = pi/4 = 45 degrees. Total guess.

Q8:
a) Forgot the feckin " + c ". Arghhhhhhh. 1/3 of the marks for one feckin letter.
b) (iii) Don't know if it's right, but I guessed Un = X^(2n-2) / (n + 1)!.... most people in my centre got different answers though.
c) (ii) - r = volume = 1/pi. Seemed a bit dodgy in the exam, but apparently nearly everybody got it.

Overall, a paper riddled with stupid mistakes. Bye bye "A".

PrecariousNuts

All of them seem to check out but I got 3+-2root2 for the slopes in question 3...

I got a slightly different answer for Q4c... 8 - pi(4 - 2root2)

You forgot +c in Q8 a

and the final answer in Q8 c is 1/pi

Cathy

Originally posted by PrecariousNuts
All of them seem to check out but I got 3+-2root2 for the slopes in question 3...

I got a slightly different answer for Q4c... 8 - pi(4 - 2root2)

You forgot +c in Q8 a

and the final answer in Q8 c is 1/pi

I can't believe I forgot the bloody c... :rolleyes: Oh well. And I did get 1/pi for Q8, c, I just forgot to write it in. I don't think I did too badly anyway - hopefully, with paper I, I'll get my B.

PrecariousNuts

I thought it was a pretty cool paper, far easier than any of the sample/past papers. I think I might have got an A overall.

Mutant_Fruit

A1 all the way! Did 6 questions, and got em mostly (if not all) right, according to the answers in this thread and my paper2 thread, and i got most if not all of the answers in paper1 right.

Did 2 extra q's in paper 1, and 1 extra in paper2. I'm well proud of myself.

subway_ie

Originally posted by PrecariousNuts
I thought it was a pretty cool paper, far easier than any of the sample/past papers. I think I might have got an A overall.

I think it was a bit harder than most past papers... maybe a bit easier than mock papers, but definetly on a par (probably a little more difficult since it was under exam conditions) with past paper 2s.

Cathy

It wasn't half as difficult as last year though.

oeNeo

Ug, that paper was terrible. I hope I got enough right to pass it though.

oeNeo

Btw for the trig proofs (I didn't know these off by heart), were they really easy or did I just do something wrong? I got them all done in 3 or 4 lines by using page 9.

Cathy

Yeah, they weren't too bad at all.

PrecariousNuts

Q4 proofs = tables, easy
Q5 a, no tables
b, easy

Cathy

So do you think I'm roughly on track for a high B with the answers above?

PrecariousNuts

Oh yes most definately, sure you get a ton of marks for just attempting the question and every part c had 2 or more parts, you'll be grand.

Cathy

Oh good good good good good. Thank you. Now I'm going to forget Maths until October and study some Biology and French...

PrecariousNuts

Hopefully bio won't turn out like the new home ec course, I'm just going over the mind numbing ecology before I get stuck into the good stuff. Ps, know your experiments well, supposedly the easiest marks on the paper.

Cathy

Originally posted by PrecariousNuts
Hopefully bio won't turn out like the new home ec course, I'm just going over the mind numbing ecology before I get stuck into the good stuff. Ps, know your experiments well, supposedly the easiest marks on the paper.

Was that a bad exam? I wasn't talking to anyone who sat it... too busy pretending to study. Ecology will be grand, it's just Junior Cert stuff really. The experiments should be okay if I look over them. And my Biology teacher was saying that we should know the answers to the sample papers from the Department - a few of the questions are likely to come up. And it won't do any harm knowing it anyway...

PrecariousNuts

Well everyone was saying that there were far too many questions being asked and not enough time to elaborate on anything. I'll probably learn off those sample paper answers, thanks for the tip.

penguincakes

How in the name of feck is 8 c ii 1/pi ? Am I missing something?

v(r) = 3*pi*r^2 - pi*r^3

v'(r) = 6*pi*r - 3*pi*r^2 = 0

6*pi*r = 3*pi*r^2
2*r = r^2

r = 0
r = 2

v(2) = 3*pi*4 - pi*8 = 12pi - 8pi = 4pi

(I now realise I ****ed it up in the exam again, had r = 1/2 rather than 2 but still I can't see 1/pi anywhere)

Mutant_Fruit

the volume is pi(r^2)H

h = 3 - 2(pi)(r)

work it from there

(EDITED)

Cathy

Originally posted by penguincakes
How in the name of feck is 8 c ii 1/pi ? Am I missing something?

v(r) = 3*pi*r^2 - pi*r^3

v'(r) = 6*pi*r - 3*pi*r^2 = 0

6*pi*r = 3*pi*r^2
2*r = r^2

r = 0
r = 2

v(2) = 3*pi*4 - pi*8 = 12pi - 8pi = 4pi

(I now realise I ****ed it up in the exam again, had r = 1/2 rather than 2 but still I can't see 1/pi anywhere)

From part i, the volume of the cylinder is (3 pi r^2) - (2 pi^2 r^3). Differentiate this to get 6 pi r - 6 pi^2 r^2. Let this equal to 0. So 6 pi r = 6 pi^2 r^2. Cancel off the 6s, the pi and the r to get 1 = pi r. Divide both sides by pi to get r = 1/pi. Then sub this into the maximum volume to get: (3 x pi / pi^2) - (2 x pi^2 / pi^3). This works out to give you 3/pi - 2/pi, which ends up at 1/pi.

penguincakes

Wait wait wait where are we getting pi^2 from?

3 = r + h

h = 3 - r

v = pi*h*r^2 = pi * (3 - r) * r^2 = 3*pi*r^2 - pi*r^3

right?

Errr...

Wait. **** **** ****. I misread the question. Ok.

Seifer

I wouldn't give the sample paper too much credit as if you look at the physics and chemistry ones for 2002, not a lot of the same stuff came up on the actual exam paper for that year.
I was pretty sure I'd gotten an A1 one till I started posting here but an A definately (I might still get the A1).:)

Cathy

Well, knowing it isn't going to hurt anyway. I'm hoping for a relatively easy paper, since it's the first year of the new syllabus... and most of the samples are easy enough.

livingupatree

did any1 else get (x^2n-2)/(2n-2)! ?

Mutant_Fruit

did any1 else get (x^2n-2)/(2n-2)! ?

I got pretty much the same, except where you ahve 2n-2 i have 2n. i started from n=0.

livingupatree

Yeah 2n seems to be generally accepted. Oh well, a C3 will do for me anyway! Thanx

DS

Yeah 2n seems to be generally accepted. Oh well, a C3 will do for me anyway! Thanx

See this topic for why it's actually 2n-2, you were right, but it doesn't make a huge difference.

Thraktor

Originally posted by subway_ie
Q2:
(c) - I said p = ai + bj and q = ci + dj. Tried to sub them in, but didn't work out.

I did the exact same thing, except all I could get it down to was:

[(a²+b²+c²+d²)/2]+ad-bc = a²+b²+ad-bc

right at the end, I decided to take a stab at it, stating "but a²+b²=c²+d², therefore...", knowing it would balance the equation, and hoping there was some good reason that a²+b²=c²+d² which they'd give me marks for without mentioning. Found out after that, in fact, a²+b² did equal c²+d², as the two lines are perpendicular (or parallel or something), and they can't mark me down for not mentioning that, as I wouldn't have put it in without knowing why. Which essentially means that I went from getting an attempt mark to getting full marks through mere fluke. Exact same sort of thing happened to me during the mocks as well, actually.

Mutant_Fruit

your lucky, thats what you are. I was in the exact same position. I had the thing narrowed down to a²+b²=c²+d², and i was stumped. So i just wrote, this is true, therefore they are perpendicular.

It was later on that i noticed that (mod P) = (mod Q) and basically that meant a²+b²=c²+d², so i added that line in afterwards, just to prove i did know what i was talking about.

DS

It actually works out very nicely if you don't use i and j components. Just multiply everything out, some things will cancel, and you'll have a few p.p's and q.q's, which become |p|^2 and |q|^2, which are equal.