Maths PP1

Gangsta

T-b0n3 wrote:

Was plus or minis (4 + i) if i remember right..

ya that's right. then you sub that in for the square root malarky and solve.

seems like most people did well on the forum fair play. The reaction is a lot better than last year.

Your Man

in the height of it i forgot to write down the make/model of my calculator...doesnt actualy matter does it?

colm-ccfc84

Your Man wrote:

in the height of it i forgot to write down the make/model of my calculator...doesnt actualy matter does it?

I would doubt it. I didn't even use a calculator I think.

Nehpets

Hmm could paper 2 be harder because this one, to be fair, was a lot easier than last year. (where the **** do I put the question mark in that sentence? haha, ah well english is over )

Gangsta

lads i don't think it matters if you write down 0 or a 2x2 0 matrix because i think in Oliver Murphy's book (excellent book btw, best out there) that he writes down zero. I'll have a look, hopefully he does

I didn't use a calculator either lol.

Gangsta

JC 2K3 wrote:

Q6:
Can't believe I didn't get (c)(iii). I'm so annoyed I didn't realise that as it was a constant you could put any number in in place of x and work it out. As for part (ii), I proved it like:
f'(x) = -g'(x)
integ(f'(x)) = -integ(g'(x))
f(x) = -g(x) + c
f(x) + g(x) = c
c being a constant(constant of integration)

You sly man you did it the applied maths way!!

Sure what am I saying.... I did it that way too;)

KnifeWRENCH

i shouldnt have read this thread..its made me realise how badly i did i did enough to pass (i hope) but some questions went totally against me.
question 4: sequences and series.48 out of 50 in my pre,a question very like the 2006 one...and then,for 2007,they throw in induction,logs and factorial notation. i got about 10/50...
differentiation did not go nearly as well as expected.i messed up BOTH equation of tangents (put dy/dx directly into equation formula,without evaluating it at the point x1,y1 first)
the integration area i got somethinglike 145/6....which i thought was okay until i realised no-one else got an answer anything near that.
the two algebra were okay but overall im disappointed...and paper 2 is my weaker paper by far.
i got a C2 in my pre....somehow i think i'll be getting a D2 in august

analyse this

Its beyond me why we are still talking about the exam three days later! Its over...we cannot change it now! Post mortems merely cause distress and aggravation which will hinder your performance in the next exams!

ZorbaTehZ

Gangsta wrote:

You sly man you did it the applied maths way!!

Sure what am I saying.... I did it that way too;)

Are you sure they will accept that since the question says: "Hence show that ... is a constant"

JC 2K3

In the first part you find out that f'(x) = -g'(x).....

Nehpets

How did I not see that?

sd123

JC 2K3 wrote:

Easy, except for the last part I just put y=0 and it worked out like e^3x = 3x, which I said could not be true.....

I'm fairly sure I haven't dropped more than 10-20 marks here, so still on course for the A1

yea, i did the same but then thought that there might be some value of x for which e^3x might be equal to 3x so i tried to proove that they could never be equal by induction because the question said DEDUCE that it doesn't cut the x axis. didn't realise you had to use the 3 c i to solve c ii. o well, same as you, lost bout 20 marks so still on course for an A1.:D

Tomlowe

0 represents any zero matrix by the way, just found that out, up 3 marks

JC 2K3

sd123 wrote:

yea, i did the same but then thought that there might be some value of x for which e^3x might be equal to 3x so i tried to proove that they could never be equal by induction because the question said DEDUCE that it doesn't cut the x axis.

If the question said DEDUCE, then surely you couldn't INDUCE to prove it

sd123

JC 2K3 wrote:

If the question said DEDUCE, then surely you couldn't INDUCE to prove it

i thought they said DEDUCE to try to make you think of INDUCE. thats what i thought anyway cos they're trying to bring q 4 and 5 theory throughout the entire papers eg 06 q7 c. anyway when i got to lnx = e^3x i didn't know what else to do to show that they're not equal for ALL values of x. makes sense though. BTW im not great at induction and wasn't able to prove it for (k+1) so it doesn' really matter tbh. in your way how do u know its true for all values of x???:rolleyes:

JC 2K3

Well, I don't think I got it right, I just wrote:
@y=0
ln3x = 3x
e^3x = 3x
which isn't true
therefore, it does not hit the x-axis.

But, in response to your reasoning, deduction and induction are two different methods of proving something. If the question says deduce or prove by deduction then you have to use deduction, if it says induce or prove by induction, you have to use induction.

sd123

i said that as well, before trying to proove by induction, do u think that's sufficent to get full marks?

JC 2K3

Nah, attempt marks, ie. 2/5

sd123

did many people attempt/do well in q 4 or 5

JC 2K3

Yeah, if I hadn't forgotten to prove the series was arithmetic in 4(c) I'd have gotten 100% in 4 and 5.

They're such easy questions, I've no idea why more people don't attempt them. Algebra is such a bitch in comparison.

sd123

not much use of formulae in q 4 though. i did all question, except 5.
to show, by inspection what Un was in q 4 b, were they just looking for a straight answer?

i found the two algebra qs to be easy except for the STRANGE twist at the end of c ii, which i got after a while:D

Gangsta

ZorbaTehZ wrote:

Are you sure they will accept that since the question says: "Hence show that ... is a constant"

Yes because I used my result in C (i)

Tomlowe wrote:

0 represents any zero matrix by the way, just found that out, up 3 marks

Are you sure? Where did you get that from? hopeully another 3marks for me, I was really dreading that.

JC 2K3 wrote:

They're such easy questions, I've no idea why more people don't attempt them. Algebra is such a bitch in comparison.

I actually think algebra is really soft, especially this years. Most teachers put the emphasis on differentiation and integration and spend less time on Q4 and Q5 which is why I think students do likewise.

JC 2K3

Gangsta wrote:

I actually think algebra is really soft, especially this years. Most teachers put the emphasis on differentiation and integration and spend less time on Q4 and Q5 which is why I think students do likewise.

Well, I agree with you that it hasn't been too bad in recent years, but they've thrown some horrible questions in in the past. It takes longer to do than series also.

JC 2K3

sd123 wrote:

not much use of formulae in q 4 though. i did all question, except 5.
to show, by inspection what Un was in q 4 b, were they just looking for a straight answer?

Sure series are much mor than using formulae...

in q 4 b you worked out the first few terms and got 5, 5/2, 5/3. 5/4 which meant the general term was obviously 5/n(you just had to write it down as an observation).

eZe^

JC 2K3 wrote:

Yeah, if I hadn't forgotten to prove the series was arithmetic in 4(c) I'd have gotten 100% in 4 and 5.

They're such easy questions, I've no idea why more people don't attempt them. Algebra is such a bitch in comparison.

Agreed, although algebra is really easy, question 4 and 5 are always more straight forward, but instead of making a mistake with proving the sequence is arithmetic I didnt see that the number line question was about integers, so I marked all the bloody values! hahah, hopefully only a minus 3 job. Guess thats why my teacher always stressed the importance of reading the question!

KnifeWRENCH

JC 2K3 wrote:

Yeah, if I hadn't forgotten to prove the series was arithmetic in 4(c) I'd have gotten 100% in 4 and 5.
They're such easy questions, I've no idea why more people don't attempt them.

thats what i had always thought about Q.4...until i saw the one on thursday i had always banked on Q.4 being one of my better questions,i found sequences and series way easier than complex numbers....but Q.4 was an absolute disaster for me:(
i had never concentrated on Q.5 coz i dont like induction or binomial expansion...they've mixed questions 4 and 5 for the last 2 years.i was hoping 4 would be entirely sequences and series,and that all the stuff i didnt like (induction,logs,factorial notation) would be in Q.5
alas,it was not to be:(

JC 2K3

Induction and binominal expansion questions are giving away marks IMO.

A binominal expansion is just a series with Un = (n r) x^(n-r).y(r). And they very often have an expansion like (x + 1/x)^n and you have get which term is independant of x, piece of cake.

Induction, you just learn the rules, apply them, and there're your marks.

Useless talking about it now I guess....

charlie1234

Crumbs wrote:

Q.5
(a) -3, -2, -1, 0, 1

(b)
(i) ur+1 = (9Cr).(-1)^r.(2)^9-r.(x)^9-3r
(ii) -5376

(c)
(i) Sn = x(1-x^n)/(1-x)^2 - n.x^n+1/1-x (probably possible to simplify further)
(ii) s(infinity) = x/(1-x)^2

5(C) (i) would Sn not be = to x(1-x^n)/(1-x)^2 only as the terms are upto n, not n+1, i got that and got part ii right, although i think i started at n = 1 not 0.

We had a very similar question on our mocks, but it was nx^n-1 if i remember correctly, the answers were the same though.

cocoa

charlie1234 wrote:

5(C) (i) would Sn not be = to x(1-x^n)/(1-x)^2 only as the terms are upto n, not n+1, i got that and got part ii right, although i think i started at n = 1 not 0.

We had a very similar question on our mocks, but it was nx^n-1 if i remember correctly, the answers were the same though.

put simply, no. have a look in your book at the questions on "arithmetico geometric" series. I'll be posting a solution in a couple hours anyway but if you can't wait...

charlie1234

cocoa wrote:

put simply, no. have a look in your book at the questions on "arithmetico geometric" series. I'll be posting a solution in a couple hours anyway but if you can't wait...

never mind, its ok, checked the answers they were one term smaller