* Higher level Maths = The Aftermath *

LilMissCiara

Well.. From one extreme to another...

Easiest Paper 2 ever! Lovely, lovely questions!

How's everyone after it?

higgz

< 0........(negative).......................C

Brilliant paper Two. Couldn't get the tan(A+B) question but otherwise a BEAUTIFUL paper. A million times better than Paper One.

The SEC have redeemed themselves

LilMissCiara

∈ of N...(positive).........................B

higgz wrote: »

Brilliant paper Two. Couldn't get the tan(A+B) question but otherwise a BEAUTIFUL paper. A million times better than Paper One.

The SEC have redeemed themselves

To prove it I did the thing with the proof slopes of a line but switched it so it was opposite.. :L

Couldn't get 7Cii out.. I used 3 pages and all..! :P

john1741

Quite good paper, few parts I couldnt get and wish I had time for Q6 but I think I passed after P1, maybe managed a C if lucky

BrendaN_f

∈of C....(complex)........................D

hopefully i did enough to clear myself of a fail, and maybe even get a C-something. nice fair paper, i guess if you are good at maths it was a dream come true

Maybe_Memories

It's not online yet.
Anyone want to post it so I can start on solutions?

LilMissCiara

∈ of N...(positive).........................B

Maybe_Memories wrote: »

It's not online yet.
Anyone want to post it so I can start on solutions?

I haven't time to scan it but I'll post the questions that have no diagrams!

Maybe_Memories

Sound!

LilMissCiara

∈ of N...(positive).........................B

Q1
A
The following parametric equations define a circle.
X=2+3SinQ Y=3CosQ (Q is theta! :P)

What is the cartesian equation of the circle?

B
Fine the equation of the circle that passes through the points (0, 3) (2, 1) and (6, 5)

C
The circle C1: x^2 + y^2 -8x +2y -23 = 0 has centre B and radius R1
The circle C2: x^2 + y^2 +6x +4y +3 = 0 has centre B and radius R2

i)Show that C1 and C2 intersect at 2 points
ii) Show that the tangents to the C1 at these points pass through the centre of C2.



Q3
A
P and Q are the points (-1, 4) and (3, 7) respectively,
Find the co-ordinates of the point that divided [PQ] internally in the ration 3:1

B
f is the transformation (x, y) --> (x', y') where x' = x-y and y' = 2x+3y

L1 is the line 2x-y-1=o

i) Find the equation of the line f(L1) the image of L1 under f.
ii) Prove that f maps every pair of parallel lines to a pair of parallel lines.. You may assume that f maps every line on to a line.
iii) The line L2 is parallel to the line L1.
f(L2) intersects the x-axis at A' and the y axis at B'.
The area of triangle A'OB' is 9 square units where O is the origin.
Find the 2 possible equations of L2.
iv) Given that A' = f(A) and B' = f(B) show that the triangle AOB is not equal to the triangle A'OB'

C
No C part

michaelm82803

∈ of N...(positive).........................B

Maths paper 2 - a dream! finished with 35 minutes to spare! it kinda makes up for paper 1 except i still don't think oll get my A1 overall now ah well, still delighted! that intercircle question was odd.. got something out but really it was the only question i didn't get out..
what did everyone else think?

LilMissCiara

∈ of N...(positive).........................B

Q6
A
2 adults and four children stand in a row for a photograph. How many different arrangements are possible if the 4 children are between the 2 adults.

B
i) Solve the difference equation U(n+2)-6U(n+1)+8U(n)=0 given that U(0) = 0 and U(1) = 5

ii) For what value of n is U(n) = 30(2^n)

C
5 cards are drawn together at random from a standad pack of 52 playing cards. Find, in decimal form, correct to 2 significant figures the probability that:
i) All Cards are Diamonds
ii) All Cards are of the same suit.
iii) The 3 cards are the ace, 2, 3, 4, and 4 of diamonds
iv) The five cards include the 4 aces.


Mammy just tole me Irish is at 1.30.. Thought it was 2..! :P So that's all I have time for!

NSNO

Loved that paper.

Got 2, 3, 6 and 8 fully out. Didn't get 1 (c)(ii) for lack of time or 4(c) (ii) for lack of time either. Had all the expressions the way I wanted them though so I'll get the attempts on both.

Utter dream of a paper. Wanted an A2 overall and I think I may have just scraped it. I'm delira:D

higgz

< 0........(negative).......................C

Q2 - lovely vectors Q. Nothing difficult
Q4 - Visually, 2x doesn't look like the radius, but just assume it is
Q5 - tan(A+B) Didn't get that one. Helicopter was 1,000m
Q6 - n=4, The 5 cards question was tedious. I think I got it though. Kept getting like 0.00004 or something.
Q7 - 16 paths to the bottom. Last Q was 1/16. The part c was something like the 4th root of something?
Q8 - Nothing too difficult.

Overall a nice paper.

irish_man

< 0........(negative).......................C

Yeah a beaut of a paper. Hopefully I didn't make too many slips but I know I made a couple. Q5 was lovely. It so easy. As was Q3 & 8.

I thought it was a fair paper after a very unfair paper 1.

stann007

∈ of N...(positive).........................B

a grand paper really ........ nothing was difficult but the tan2A/Tan2B=-1 was really hard

Catacomb

higgz wrote: »

Brilliant paper Two. Couldn't get the tan(A+B) question but otherwise a BEAUTIFUL paper. A million times better than Paper One.

The SEC have redeemed themselves

I turned Tan(A+B) into Tan(A-(-B)) used the "Tan(A-B)" formula for it and then turned all the resulting Tan(-B)'s into -Tan(B)?

:rolleyes: I wonder if that will get marks, it just seemed to easy for my liking?

mystic

HL Maths Paper 1 being discussed on Liveline now.

http://www.rte.ie/radio1/liveline/

joshrogan

Yea I'm hoping for a C/B again now after that paper, originally aimed for a B but with paper one it was lowered .

kpac

Very happy with that paper. Thanks SEC.

Daniel S

∉ of Q....(craaaaazy)....................Fail

Ah shíte, if everyone did good, won't that mean a hard marking scheme?

Catacomb

mtb_kng wrote: »

Ah shíte, if everyone did good, won't that mean a hard marking scheme?

they'll probably just won't mark paper 1 easier??

or do both papers have to fit the bell curve independantly?

spurious

Catacomb wrote: »

or do both papers have to fit the bell curve independantly?

It's the total grade.

Lux23

TRY THIS AT HOME PROJECT MATHS HIGHER LEVEL

Gold jewellery is made from a gold alloy. The purity of the material is measured by its carat rating, given by the formula c - 24mg/mt, where

c = carat

mg = mass of gold

mt = total mass

A jeweller is recycling gold jewellery. He has the following old jewellery in stock: 147 grams of 9 carat gold; 85 grams of 18 carat gold. He can melt down this old jewellery and mix it in

various proportions to make new jewellery of different carat values. The value of the old jewellery is equal to the value of its gold content only.

Gold is valued at €36 per gram. What is the total value of the jeweller’s stock?


Does anyone know the answer to this Project Maths question?

Maybe_Memories

Paper 2 still not up..
so expect solutions around 8.30 ish

LilMissCiara

∈ of N...(positive).........................B

Maybe_Memories wrote: »

Paper 2 still not up..
so expect solutions around 8.30 ish

http://examinations.ie/archive/exampapers/2011/LC003ALP200EV.pdf :P

Gumbi

∈of C....(complex)........................D

hmmm... I didn't think it was easy. It was generally more straightforward, but still a bit tough imo.

PJelly

∈ of N...(positive).........................B

It was a grand paper. I'd be expecting a B1 from that.
I'm still gutted about paper one. All together, I think I'll get a C2 now. Not enough.

augmented reality

Lux23 wrote: »

TRY THIS AT HOME PROJECT MATHS HIGHER LEVEL

Gold jewellery is made from a gold alloy. The purity of the material is measured by its carat rating, given by the formula c - 24mg/mt, where

c = carat

mg = mass of gold

mt = total mass

A jeweller is recycling gold jewellery. He has the following old jewellery in stock: 147 grams of 9 carat gold; 85 grams of 18 carat gold. He can melt down this old jewellery and mix it in

various proportions to make new jewellery of different carat values. The value of the old jewellery is equal to the value of its gold content only.

Gold is valued at €36 per gram. What is the total value of the jeweller’s stock?


Does anyone know the answer to this Project Maths question?

That's only the part a of the question, that's meant to be the easy bit!!!
From what I remember it went on to a part h/j.
Project maths is an absolute joke!!! Wish I could've done the normal course:mad:

AnneElizabeth

< 0........(negative).......................C

I didn't think it was that good tbh... Not liking this whole "it was brilliant"

TimeToShine

Easiest paper 2 i've ever seen tbh

what.to.do

< 0........(negative).......................C

Very happy with this paper.
Probably because I was expecting HELL after Friday, and I'm not the strongest of maths students..
But I could give the a and b parts a good run, and most of the c parts, so happy out!

When I got 4c out, i actually did the little "woo-woo!" dance in my seat.

nommm

∈of C....(complex)........................D

Way better than the other one. I wouldn't call it 'easy' tho!

FreshTillDeath

Paper 2 is my worse of the two papers but i did put a good bit of work into it and generally i'm very happy with it ( Besides Q3 ). Its after making me more optimistic that i didn't fail the whole thing anyway All questions were accessible and didn't make me cringe!

LilMissCiara

∈ of N...(positive).........................B

TimeToShine wrote: »

Easiest paper 2 i've ever seen tbh

I concur..!

I think I have done a near perfect paper.

I am almost certain that Paper 1 and Paper 2 will give me an A2, or at least a B1!

polka dot

< 0........(negative).......................C

Happy out with questions 6 and 7! Loved them. Glad I wasn't relying on question 4, I have never seen that circle yoke before in my life. (Though I vaguely remember it being called a concentric circle...? Maybe?) Didn't touch it.

Question 5 was okay, got the proof out. Couldn't get the next part out. Got the c part all out.

Question 1. Good god. Screwed it up so badly that I'd be surprised if I got more than 15 marks (got part a out...)

Vectors was lovely, except for part a. Have a feeling that was some formula or triangle I was meant to know and didn't. My own fault.


Group theory. WHAT the heck was that?! Goddamn tetrahedron made no sense to me. The A part was like... heaven. But the b part 1 and 2 just no. Also made up part 5. Can't wait to see the solutions for that anyway

madmax92

Ive done like 1 a+b, 2a+b, 3 a+ b1, 4 a(att) + b, 5 a+b+c (att) + 8 a+b and I passed away 1hour before the end! FAIL

LilMissCiara

∈ of N...(positive).........................B

polka dot wrote: »

Vectors was lovely, except for part a. Have a feeling that was some formula or triangle I was meant to know and didn't. My own fault.

Nope, multiply it out and let the i parts equal each other and the same for the js. You'll have a simultaneous equation then!

ChloeElla

< 0........(negative).......................C

Wow.. I thought it was a nice paper, pretty straightforward, but most girls in my class were complaining majorly about it!

madmax92

ChloeElla wrote: »

Wow.. I thought it was a nice paper, pretty straightforward, but most girls in my class were complaining majorly about it!

As I could never understand vectors, here I done them in 10mins so it was pretty easy. They ballanced 2 papers, so I hope just to pass it.

NotExactly

ChloeElla wrote: »

Wow.. I thought it was a nice paper, pretty straightforward, but most girls in my class were complaining majorly about it!

Ara sure, you'll always have that :rolleyes:

kahf1_01

< 0........(negative).......................C

well it was a relieft when I opened the paper and read it. At least it was "normal"

It wasn't too difficult. It was more familiar and common. I did Q 1,2,3,4,5,8

Q1. Part was A was great. B perfect. Part C I couldn't remember, attempt at most.
Q2. Part A was fine, as was B (I hope) C i was easy. though C ii wasn't
Q3. A was fine, I hope it was + instead of - the B part was a nightmare! bar i
Q4. A fine. B I think I got it. C another nightmare!
Q5. Well, I was getting tried at this stage. A was fine. B was impossible. and C was a real project maths question. I couldn't get it in surd form. kinda weird.
Q8. Part A was lovely. B little harder. and C was good.

Overall, paper 1 and 2 combined. I'd LOVE a B, although C looks likely. phew least it's all over, btw I get really tried at the end, my concentration drops off.

electrictrad

∈ of N...(positive).........................B

LilMissCiara wrote: »

To prove it I did the thing with the proof slopes of a line but switched it so it was opposite.. :L

Couldn't get 7Cii out.. I used 3 pages and all..! :P

7 cii in 5 lines!. . .Standard Deviation = 1, as the SD from part i cancels out with the upper line

. . .Loved the probability, especially the Pascals Triangle problem. . .

. . .Anyone else get a decimal BD on 5 c ii , and 300root3 for 5c part 1?

River Song

I predicted right again I said last night the tan^-1 pi approximation would be great to come up

Oh my, what a LOVELY paper. I might be on track to get my B again Eeeep

electrictrad

∈ of N...(positive).........................B

Catacomb wrote: »

I turned Tan(A+B) into Tan(A-(-B)) used the "Tan(A-B)" formula for it and then turned all the resulting Tan(-B)'s into -Tan(B)?

:rolleyes: I wonder if that will get marks, it just seemed to easy for my liking?

Unfortunately, probably just the attempt. . .but I could be wrong. . .

you've to let tan(a+b)=sin(a+b)/cos(a+b), expand, and divide up and below by cosacosb. . .at least thats the book proof. . .

LilMissCiara

∈ of N...(positive).........................B

electrictrad wrote: »

7 cii in 5 lines!. . .Standard Deviation = 1, as the SD from part i cancels out with the upper line

. . .Loved the probability, especially the Pascals Triangle problem. . .

. . .Anyone else get a decimal BD on 5 c ii , and 300root3 for 5c part 1?

Haha.. It took all of 2 seconds..! :P

And yes I got a decimal... 992.32m?

nightdream

augmented reality wrote: »

That's only the part a of the question, that's meant to be the easy bit!!!
From what I remember it went on to a part h/j.
Project maths is an absolute joke!!! Wish I could've done the normal course:mad:

True, the hard part is the last few questions!!!! These one here are meant to be easy:/
Paper 2 was alright today, although the roof top question took me a long time. And still couldn't get it out:/

electrictrad

∈ of N...(positive).........................B

LilMissCiara wrote: »

Haha.. It took all of 2 seconds..! :P

And yes I got a decimal... 992.32m?

Youre probably right

I think I was about 1536.05, ar something in that range. . .probably not right, but anyway. . .

Loved Q4 with the 2 circles. . .pix^2 for part i anyone?

partyatmygaff

Pretty good Paper compared to Paper 1.

Q1: I got some extremely strange answers for nearly every section of this question but nothing I couldn't get out.
Q2: Only had enough time to get to 2bii (Not counting it anyway)
Q3: Part a was quite alright. Part B was a bit strange, I got some very strange answers near the end.
Q4: Loved this question. L'Hopital's rule in part A, trig equation and a lovely question concentric circles.
Q5: My favourite question on the paper. The simple trig equation was fine. The tan(A+B) identity proof was fine and getting part bii out was surprisingly pleasant. The 3D trig question went perfectly fine as well.
Q6: Lovely question from start to finish.
Q7: Lovely question apart from Cii which I managed to answer but i'm not quite sure if I went about it the right way.
Q8: Int by parts was fine. The max/man question was also quite nice except I may have made a blunder somewhere throughout. Part C was quite nice too.


All in all, far better than Paper I anyway. I just hope the Marking scheme isn't too harsh on this paper...

BeanbagBallbag

for anyone who wants a solution to the tan question..

5 B i)

Tan (A + = tanA + tanB
....................1- tanAtanB

tan (A + = sin(A +
..................cos(A +

=sinAcosB +cosAsinB
...cosAcosB + sinAsinB

divide above and below by cosB

= sinAcosB/cosB + cosAsinB/cosB
....... cosAcosB/cosB + sinAsinB/cosB

=sinA + cosAtanB
...cosA + sinAtanB

divide above and below by cosA

= sinA/cosA +cosAtanB/cosA
...cosA/cosA + sinAtanB/cosA

= tanA + tanB
...1 +tanAtanB


ii) A + B= 90'

tan2A = -1
tan2B

tan2A
tan2(90-A)

= tan2A
...tan(180-2A)

=tan2A
(tan180-tan2A)/1 +tan180tan2A .......................tan180 = 0



= tan2A
....-tan2A

= -1

jumpguy

In the question on the Line, (b) (iv) (the last part), wasn't the angle AOB = 90 degrees and the angle A'OB' = 90 degrees?

Hence both angles were equal?

A very nice paper. So sickened I got the (c) (iii) of Q8 wrong. I bet that'll be the difference between a grade, and it was so simple! I realised that it was only a sub-in question as I was sealing the paper. :mad:

Probability and stats Q7 (b) was strange, but quite manageable (required thought though - was a bit deceptive).

polka dot

< 0........(negative).......................C

LilMissCiara wrote: »

Nope, multiply it out and let the i parts equal each other and the same for the js. You'll have a simultaneous equation then!

Ohhhhhhhhhhhh.

Well I was on the right track (...baby I was born this way :rolleyes:) Yeah. I multiplied it out, put i = i and j=j ...

And that's where the similarities end I'm afraid. Half marks maybe!