Honours maths paper 1

sully88

how are you all feeling about this? Do ye believe all the talk about how the paper is going to be easier this year because of last years trouble?
Any body have any tips for what could be asked?
I heard that something like this could be up in differenciation:

y=ax^3+bx^2+cx+d has max at x=X1 and min at x=X2 and pt of inflection at x=X3

PROVE: 2x3-x1-x2=0

Apart from de moivres which most people seem to think will be on the paper, what prrofs do ye think will be asked?

Lucas10101

1. DeMoivres Theorem
2. Defo one of the Differential Theorems

Hope Areas dont come on Integration.

y = ax3+bx2+cx+d
dy/dx = 3ax2 +2bx +c
At Max = x1

If all the integers are positive, why is the answer full of Negatives, is this due to the Maximum value which is Negative??

sully88

ye i hope areas i integration dont come up either.

d2y/dx^2=6ax+2b=0.......at point of inflection

x=x3 is a soln....X3=-2b/6a=-b/3a

max at x1, min at x2
x1 and x2 are the roots of 3ax^2+2bx+c=0
alpha+beta=-b/a=-2b/3a
therfore x1+x2=-2b/3a
x3=-b/3a


2x3-x1-x2=2x3-(x1+x2)

=2(-b/3a)-(-2b/3a)
= 0
Its what some tachers would refer to as a "nice question"!

ninebeanrows

I would tip an alpha beta type question in Algebra.

An easy Sequence and Series Question, to get people to do it next year and so on. Difficult Calculus Question 7. And i think they will mix things up abit. Also reckon indices type question and inequality in q1 and q2

sully88

I think seq+series will be handy enough, im considering leaving out one of the differentiation q's which seem to be getting harder every year! If question 5 is nice I might leave out complex numbers.

Raphael

sully88 wrote:

how are you all feeling about this? Do ye believe all the talk about how the paper is going to be easier this year because of last years trouble?

Since they said the same thing this tikme last year, I sincerely doubt it. And "last years trouble" me arse, the only problem with last years paper was that you needed to be able to think rather than learn. How terribly shocking.

sully88

well im a repeat student and i assure you if you were in an exam hall with that paper last june you would think the same!

ninebeanrows

sully88 wrote:

well im a repeat student and i assure you if you were in an exam hall with that paper last june you would think the same!

It was marked easy though, so it shouldnt have made a difference once you gave the questions an attempt.

lisajane

If ur doing higher level in maths maybe u can answer this question for me. My brother is doing his junior cert and he's a bit clueless himself. I had a look at it myself and for the life of me i can't do it, even though it wasn't long ago i was there.

Here's the question, it was pass level in last years maths.

2 jumpers and 3 shirts cost 84 euro.
4 jumpers and 1 shirt cost 78 euro.

If the jumpers were x and the shirts were y , find the equations and the price of the jumpers and shirts.

The only thing i could do was this and im not sure if its even right:
2x + 3y = 84
4x + 1y = 78

how much are those jumpers and shirts

Lucas10101

lisajane wrote:

2 jumpers and 3 shirts cost 84 euro.
4 jumpers and 1 shirt cost 78 euro.

If the jumpers were x and the shirts were y , find the equations and the price of the jumpers and shirts.

The only thing i could do was this and im not sure if its even right:
2x + 3y = 84
4x + 1y = 78

how much are those jumpers and shirts

I think that's right:

2x + 3y = 84 (multiply by -2)
4x + y = 78

---

-4x -6y = -168
4x + y = 78

---

-5y = -90
y = 18
Implies y=18...x=> 2x + 3(18) = 84
2x +54 = 84
2x = 30
x = 15

Jumpers cost $15 and Shirts cost $18.:)

NB : 2 Jumpers + 3 Shirts cost 84
2(15) + 3(18) => 30+54 => 84 which verifies it.

lisajane

Thanx, im getting flash backs now. I remember the type of question from school. I remember something had to be cancelled out but i forgot how it was done. I pity all of ye doing exams now. Good luck!

Raphael

sully88 wrote:

well im a repeat student and i assure you if you were in an exam hall with that paper last june you would think the same!

I was, just finished first year. Hence having an opinion about it.

chas_88

i'd say those modulus inequality graphs (i think that's what they're called) are a certainty in question 1 or 2, they haven't come up since 1996.

colm-ccfc84

I hope there are no proofs. Maths should be about doing questions, not learning off proofs.

Lucas10101

I hope LOADS of proofs come up as I'm superb at remembering them. I can see DeMoivres, a Differential from Principals and an Integration Proof, Heaven on Earth if the Factor Theorem comes.

colm-ccfc84

First principals isn't a proof though, but yes that is easy, as is the factor theorem.

ninebeanrows

Lucas10101 wrote:

I hope LOADS of proofs come up as I'm superb at remembering them. I can see DeMoivres, a Differential from Principals and an Integration Proof, Heaven on Earth if the Factor Theorem comes.

Integration proof? Please explain, i thought there was no such thing?

colm-ccfc84

Area of cone, sphere by integration (presumeably!)