Higher level maths.... quite a nasty paper one...

ecbyrne

yeah true 2c looked a shocker but once you factorised to I think it was" (a+b) squared over ab, then minus 2" it worked out fine.

If both A and B were opposite signs it would obviusly be less than -2.
Proving if A and B had the same signs was more difficult. I just gave a few expamples that (a+b) squared over ab would be always be greater than 4. so then greater than 2. might not get full marks but most of them...

eoin2nc

Did well enough , what did people get for Q4c ii I got some long winded thing. For the 2~r do you just treat it like a geometric sequence? I m usually good at Q8 but I couldnt do this years one at all I had to do Q4 instaed. Still thought it was a fair enough paper

ShogunWarrior

Alright I thought, I liked all the algebra except of course for the Q2(c), just got me.
Thankfully I'm seeing alot of my answers pop up, hopefully it goes well.

(My) Answers:

Q1.
(a) (-2) / (x+2)
(b) (i) 1.5, 1/3 and 3
(c) (x-p)(x+p)(x-k) = equation and equate coefficients.

Q2.
(a) (x+5)^2 + 6
(b) (i) 47 (ii) 322
(c) ??

Q3.
(a) Forget.
(b) (i) 1-i  (ii) z^5 = 8i
(c) De Moivre's

Q4.
(a) 3
(b) (i),(ii) Prove
(c) (i) (n/2)(n+1) and (n/6)(n+1)(2n+1)
(ii) 6(n/6)(n+1)(2n+1) + 2(n/2)(n+1) + 5n -2 + 2^(n+1) and simplify

Q6.
(a) (3x^2)/(2 sqrt(3) )
(b) Show
(c) (i) -12
(ii) Eek.

Q7.
(a) 2 + 2cos2x
(b) (i),(ii) Show.
(c) ?

Q8.
Didn't take answers.

Peleus

Okay guys. lets post answers!

1
(a): 2/(x+2)
(b): (3,1/3,3/2)
(c): bc=ad. got this in the dying minutes. p and -p are roots. factors are (x+p) and (x-p). multiply two factors together and divide into cubic. the remainders should equal 0 so you get an equality property thing at the end and bc=ad after a bit of messin around.

2
(a): (x+5)^2 + 7
(b): (i) 47 (ii) 322
(c): i got this right but it was hard to explain. key was: a/b+b/a = (a^2+b^2)/ ab. lowest non zero integer is 1 therefore, since (a^2+b^2)>2ab, (a^2+b^2)/ ab cannot be less than |2|.

3
(a):B= [clockwise from top left] (-7)(2)(5)(0)
(b): (i)z= 1-i (ii) 8i
(c): DE MOIVRE!!!!

6
(a):[3(root)x]/2
(b):quotient rule
(c): (i) b=-12 (ii) didnt get right answer for this

7
(a):2+2cos2x
(b): (i) -(10x+6y)/(10y+6x) (ii) sub two points into derivative to get slops of tangents and multiply answers together to get -1. QED.
(c):1/(1+x^2). right answer. my method was wrong apparently tho. i used inverse sine(x/a) formula. but let a (a constant)=root(1+x^2) (not a constant). oh well, hopefully he'll just see the answer and mark it right.

8
(a): x^2 + (1/3)sin3x +c
(b): (i) e-1 (ii): 12 -ln5. [divide (x^2-1) into (2x^3)]
(c):i got 53/6 but everybody got different aswers for that. attempt marks will do me. plus they might edit the marking scheme becuase people got so many different answers for this.

Okay, they're my answers. They're right to the best of my knowlege so if you got any of these tell me so i know its right and everybody else does. thanks

mahamageehad

Peleus wrote: »

(c): i got this right but it was hard to explain. key was: a/b+b/a = (a^2+b^2)/ ab. lowest non zero integer is 1 therefore, since (a^2+b^2)>2ab, (a^2+b^2)/ ab cannot be less than |2|.

thank you!!!!

Peleus

straight_As wrote: »

Ok guys, I'm only just finished 4th year.........I'll give 2c a go.

a>0, b>0, both positive.

a/b+b/a........must be positive to satisfy above, therefore, must be greater than 2 (positive again).

therefore,
a/b+b/a > 2
(a^2+b^2)/ab > 2 ab is positive as a>0, b>0.......multiply across and retain inequality sign.
a^2 - 2ab - b^2 > 0
(a-b)^2 > 0 ......true, therefor above statement must be true.

Different signs. a>0 and b<0 or vice versa
Therefore,
-(a/b)-(b/a) = -(a/b + b/a).........less than zero, prove less than -2.
-(a^2 + b^2)/ab < -2
therefore a^2 + b^2 -2ab > 0
(a-b)^2 > 0 therefore above statment is true

Not sure if I'm right, I still have two years to the LC to improve though!

yep thats what i wrote. it was a bit of a bitch to explain it tho. you're rly good for a fourth year!

*belle*

oh thank god thats over!
they were either really easy or very hard and no in between.
q2 c ....hmmm that was a mean q
i seem to be getting a lot of the same answers,so im happy enough. got an a1last year so hopefully i wont go down a grade.that would be depressing!

if you can do that in 4th year ,well done,you will be sorted for the leaving if you keep that up.now paper two! hopefully that wont be too hard.;)

ZorbaTehZ

Wow, that was quite a nasty paper, some difficult part c's in there. Part ii of c, of question 6 is a very difficult question imo. The way I'd go about solving it, is by finding the maxima/minima of 2x^3+3x^2-12x, and then by judging the distances between those maxima/minima, you'd find a value for C that would push it up/down far enough that it doesn't cross the x-axis in 3 places.

ShogunWarrior

Re Q2. (c):

Surely the solution involving a,b > 0 is not valid because it states a and b are non-zero not greater than zero

Also, a and b are not necessarily integers, it states they are real numbers

So a and b could be -1, -0.5, 0.1, 0.2 etc. etc. just not zero (must be stated since there is division in the equation).

Anyway it really didn't click with me so that's those marks gone.

ZorbaTehZ

ShogunWarrior wrote: »

Surely the solution involving a,b > 0 is not valid because it states a and b are non-zero not greater than zero

Yes, so there's 4 possibilities: both greater than zero, both less than zero, a>0 b<0 and a<0 b>0. The 2 latter can be taken together since the signs cancel out, and vice versa with the 2 former. Straight_As was considering the different situations.

Peslo

What was the story with there being no part (i) or (ii) in b or c of Q1!!!!!!! That was bang out of order! I mean, they've ALWAYS done that and they have done with EVERY other question on the paper!
If they had of broken up 1c into to parts, i think more people could have managed it.

Peleus

woo, going by the answers on this site, i got an A1! YES!!! that may turn out the be an A2 two if they change the marking scheme. oh well

Peslo

Peleus wrote: »

woo, going by the answers on this site, i got an A1! YES!!! that may turn out the be an A2 two if they change the marking scheme. oh well

Eh, hang on, by the looks of things they'll be changin the marking scheme for everyone else's benefit, not for your demise!!

orangetictac

I think i got 32/3

Did it twice and got same answer.
What u get for 8b)ii)

daggy

6,7,8 were savaiste cabbaiste in my opinion..
2(c) made me burst out laughing! the most abstract yolk i've ever seen..im kinda regretting not even attempting it cause i know how i would have started it and judging by this thread i may have been on the right track ah well sure.

6(c) not sure, was it c>-20 and c<7 or something like that?! i could have the signs wrong.. i cant remember. it was def 7 and 20 though.

blanked on 1 (c) and it was so simple really.. very annoyed at myself. ah well sure!
hopefully i'll manage a B? did it in "irish" too... used so much irish just so they couldnt take the bonus from me... hahah. paper 2 will be a nuclear disaster !

Fuascailt

daggy wrote: »

paper 2 will be a nuclear disaster !

A disaster ? You sound like you did well

muffinman

I'm pretty disappointed.. Was hoping for an A1 but that seems unlikely now..
Q1 and Q3 were definitely 50m each for me.. Did them in 10 mins each.. But 2c, 7c, 8bii and 8cii lost me marks.. I'll get attempts but nothing major

Peslo

What was the story with there being no part (i) or (ii) in b or c of Q1!!!!!!! That was bang out of order! I mean, they've ALWAYS done that and they have done with EVERY other question on the paper!
If they had of broken up 1c into to parts, i think more people could have managed it.

hippety-pippety

did anyone get 9 for 8(c)?

i think that paper wasnt too bad. Im pleased enough with it, bt this thread is freaking me out, so many people got all the hard bits lik 1(c) & 2 (c).. i'll def only get attempt marks for about 3 of my part (c)s.
bt being slightly generous with attempt marks & assuming the q.s that went well were correct, i got something like 86%, not bad eh

jennyq

Just wondering if anybody at all at all (doesn't seem like it) did 5(c)? I did it & I think what I did made sense (or at least I hope :rolleyes:) & I'm just wondering if anyone else had anything different.

I made them each (going in the order they were written) u n-1, u n & u n+1

Then I said for a geometric sequence that u n+1/u n is equal to u n/u n-1

Then I did out both of those, made the two answers equal to each other, & I got n= -1. I said that wouldn't be possible as n can't be a negative. Dunno if you had to go on to prove something for r too.

Anyone else do anything different? Sorry if the terms of series is kinda hard to read, typing maths problems out is impossible

Nanaki

jennyq wrote: »

Just wondering if anybody at all at all (doesn't seem like it) did 5(c)? I did it & I think what I did made sense (or at least I hope :rolleyes:) & I'm just wondering if anyone else had anything different.

I made them each (going in the order they were written) u n-1, u n & u n+1

Then I said for a geometric sequence that u n+1/u n is equal to u n/u n-1

Then I did out both of those, made the two answers equal to each other, & I got n= -1. I said that wouldn't be possible as n can't be a negative. Dunno if you had to go on to prove something for r too.

Anyone else do anything different? Sorry if the terms of series is kinda hard to read, typing maths problems out is impossible

my class didn't even cover seqs & series!
wasn't too happy about it being in Q5, would have liked to see some induction, it hasn't come up in a while, and its not too bad.
What do ye think of induction?

daggy

Fuascailt wrote: »

A disaster ? You sound like you did well

pahhaha! Definate disaster on the way... i am depending on questions 1 to 5 and i suck balls at most of them.. got a C in it for the mocks, in fact the exact same mark as in p1 but man oh man.. The circle is my favourite. Then mapping is so straight forward think.. vectors next.. trig is pot luck for me. hit and miss. I really am serious when i say this - nuclear disaster! I can never do part (c) ! crrud..
as for today, i have no idea how i did really. The only part (c) i think i may have gotten right was 7.. and as for the rest, well who knows!?


The other thing is, i always end up doing questions completely arse ways.. i once did a vector question using the Cosine rule and i was too dense to see the much easier vector method (even with the word vector in front of me..)

I never really know. Tá sé thart, ar aon nós...hup!

Rich89

I thought it was alright to tell the truth.

Q1. Was fine, nothing bad there.

Q2. (c.) was the only thing i hadnt a clue about

Q3. Grand again, De Moivre's thereom was a guaranteed 20 marks . I noticed somebody said a while back that its never been asked before and it has just not in Q3 but Q5.

Q6. Didnt get (c.) (ii.)...ill read back, someone probably posted an answer.

Q7. (c.) again, took ages, I think I spent about 20mins doing it! Dont think I got it out though.

Q8. (b.) parts kinda confused me but attempted and got an answer out for them so I should get some marks!

Davidius

Had I sat that paper, I definitely wouldn't have been able to do 2(c) due to the fact that it's nearly impossible to explain clearly. I'm doing it now, and I just can't get any clear explanation down at all.

EDIT:
Never mind I was going about it the wrong way, then I realised and it became simple. Well I think it's correct anyway.

How I did it:
a > 0
b > 0
or
a < 0
b < 0
(negatives cancel into positive in a/b + b/a )

a/b + b/a > 0 ... (Positive+Positive = Positive)
Given -2 and + 2. Use +2.

a/b + b/a >= 2
(a^2+b^2)/ab >= 2 (Note: ab is positive*positive = positive)
(a^2+b^2) >= 2ab ... (No change in inequality sign, ab is positive)
a^2 - 2ab + b^2 >= 0
(a-b)^2 >= 0 ... True
Thus a/b + b/a >= 2 is true for a, b > 0 or a, b < 0

For:
a > 0
b < 0
or vice versa

Both a/b and b/a are negative because +/- or -/+ make a negative.
Thus:
a/b + b/a < 0 (Negative + negative = negative)

Use -2:
a/b + b/a <= - 2
(a^2+b^2)/ab <= -2 (Note: ab is negative as + times - = - )
(a^2+b^2) >= -2ab (ab is negative, thus you multiply by negative, the sign changes)
a^2 + 2ab + b^2 >= 0
(a+b)^2 >= 0 ...True
Thus the statement a/b + b/a <= -2 is also true for a > 0, b < 0 or vice versa.

It has been shown that when there is a non-zero value for a and b then a/b + b/a >= 2 or a/b + b/a <= -2. Thus -2 < a/b + b/a < 2 is false.

shockingpinkdna

Burner- wrote: »

I think I got 21 1/6 for Q8 C , that sound right to anyone?

Everyone seems to be getting 32/3 (10 and 2/3)

There's a thread discussing it: http://www.boards.ie/vbulletin/showthread.php?t=2055308582&goto=newpost

stillwater10

How many marks would i lose if i left Q1 part a as 2(x+2)/x^2-4

dyle123

stillwater10 wrote: »

How many marks would i lose if i left Q1 part a as 2(x+2)/x^2-4

I'm wondering the same because I stopped there as well. No more than 3 I'd say.

shockingpinkdna

Yuugib wrote: »

i tried to work the qs 8 out just now.. and got 10/1/6

then for qs 1 a i got 2/(x+2)

qs b i = 47 and ii = 233 O_o

3 (a) got the same

3 b i got 1 - i
b ii = o + 8i

5 a got -2<x<5

b i = 9 and -3
ii = 11 and -2

qs 6 a (3x^2/2root x^3)
c i = -12
ii = c<-20 and c>7

qs 8 B i = e - 1
ii = 1/4 ln 5

can anybody confirm?

I got the same as you for 1(a), and (b)(i) but for (b)(ii) i got 322 not 233!
I think I got the same for 5 (a) as well.
I can't remember anything else!

Peleus

Peslo wrote: »

Eh, hang on, by the looks of things they'll be changin the marking scheme for everyone else's benefit, not for your demise!!

i just got the impression from most people i talked to that it was a pretty easy test. i was probably only talking to a small minority. hopefully i am cos that means more marks for all! judging by what it was like in the Junior Cert i'd say ill get what i expect to.

louise-x

I thought it was a handy paper.
didn't get 2(c) or 8(c) but that's it...