# Mathematics Extension 2 - 2016 Post-HSC Exam Thoughts (1 Viewer)

#### calamebe

##### Active Member
$\bg_white \noindent For 13(d), p(x) = ax^{3} + bx^2 + cx + d, p'(x) = 3ax^2 + 2bx + c. Roots of p' are \frac{-2b\pm \sqrt{4b^2 - 3 \times 3ac}}{2\times 3a} = \frac{-b \pm \sqrt{b^2 - 3ac}}{3a}. So if b^{2} -3ac = 0 and p\left(x_{0}\right) = 0, where x_{0} = - \frac{b}{3a}, we have that x_{0} is a double root of p' and a root of p. Hence x_{0} is a triple root of p, following from the following general fact:$

$\bg_white \noindent \textbf{Fact.} Let P(x) be a polynomial of degree n \geq 2. Suppose x_{0} is a root of multiplicity m of the derivative P' and a root of P. Then x_{0} is a root of multiplicity m+1 of P.$

$\bg_white \noindent This result follows from if a is a root of multiplicity \mu of P, then a is a root of multiplicity \mu -1 of P''' as follows. Since x_{0} is a root of P, it has some multiplicity \mu \geq 1. Then x_{0} is a root of multiplicity \mu -1 of P'. But we are given it is a root of multiplicity m of P'. So \mu -1 = m \Rightarrow \mu = m+1, proving the claim.$

Edit: realised calamebe said this above.
Eh you said it much more in depth than me anyway, plus you proved the general case.

bye sr

#### JAMLO

##### Member
last year u need aorund 75 for e4

#### aoc

##### Active Member
this was so hard wtf yall think it was easy ? how lmao....im looking at about 55% raw what will this come back as a hsc mark as? i skipped almost all of 16 and 15
only response i can agree with haha

#### 4025808

##### Well-Known Member
Yeah, this was quite difficult imo, compared to previous years. Not too insane but doable overall I'd say.

The derangements question though. Perhaps looks like examiners have been getting ideas from BoS trials.

E3 cut off?

#### raghib483

##### New Member
Is derangements even in the syllabus???
Pretty sure it's not seeing as they had to give us the definition.
It's interesting you make that point - I think the course has been static for so long and is getting so old that the only way they can make 'new' questions are to introduce new concepts and work with them. Last year it was the introduction of Bernoulli polynomials, this year derangements.

But yes I definitely think this exam was harder than 2015, the raw-mark cutoff for e4 should be lower than the 75 it was last year

#### InteGrand

##### Well-Known Member
Is derangements even in the syllabus???
Pretty sure it's not seeing as they had to give us the definition.
It's really stupid to put that in the exam because the only ones able to answer it are those that luckily studied it. Unless someone's a genius and understood everything he needed to do from a 1 line definition and answered everything with the amount of time we were given.
There's Q's about it in an extension section of the 3U Year 12 Pender textbook. Also, the question explained everything needed to do it (i.e. no prior knowledge of derangements was prerequisite).

$\bg_white \noindent Incidentally, the last three parts of that Q. had essentially nothing to do with derangements/combinatorics (in terms of just being able to do them). Part (iii) is just rearranging the result of (ii), part (iv) follows from the geometric sequence fact that u_{n} = ru_{n-1} implies u_{n} = u_{2}r^{n-2} (which you can prove easily by induction or repeatedly plugging into this recurrence), with part (iv) having r = -1 and u_{n} = D(n) - nD(n-1) (the given initial conditions let us find u_{2}). Then part (v) is an induction question.$

Last edited:

#### chickencoop

##### Active Member
I really cannot be the only person who found this years dramatically harder than the previous years papers, can i...?

I dont even think i passed at this point and ive been avging high 70's for the previous years, tested under exam conditions and etc... but this year omg, i really want to call kids helpline rn (all jokes aside) because this is the first ever test i am ever going to fail in my life... AND ITS THE EFFING HSC

#### thomasdo1

##### Member
I really cannot be the only person who found this years dramatically harder than the previous years papers, can i...?

I dont even think i passed at this point and ive been avging high 70's for the previous years, tested under exam conditions and etc... but this year omg, i really want to call kids helpline rn (all jokes aside) because this is the first ever test i am ever going to fail in my life... AND ITS THE EFFING HSC
same ...

#### petermaniah198

##### New Member
for q 16ai, i found the imaginary and real parts. do i get one mark? lol

#### tommo727

##### Member
What would around 70 raw be?

Moderator

#### DatAtarLyfe

##### Booty Connoisseur
When you work your ass off for the past 1.5 years on 4u, doing heaps of past papers and having covered most exam style questions under the sun and averaging 90+ in most past papers. And then you go into the exam and nerves take over and you freeze.
1.5 years of working so that i can get 97+.
Now i'm not even sure i'll get an e4.

#### Chinese_taipei

##### New Member
Reckon I could get around 90 tops. Couldn't do Q16aii for some reason due to mind blank. F*ck

Raw marks conversion maths ext2 2016 (my estimate)
49-78
55ish-83
70-90
Remember your school assessment counts as well ay. Good luck peeps and swing yourselves back to home base

#### Chinese_taipei

##### New Member
Hmmm.. for 70, it'll probably be more like 92ish. I'm not expert at this

#### thomasdo1

##### Member
Hmmm.. for 70, it'll probably be more like 92ish. I'm not expert at this
yup around 92 is my guess

#### eating

##### Wannabe COMP god
HAHAHAHAHAHAHAHA

raw mark of 45-50, assuming a couple of marks for incomplete answers and no silly mistakes (>implying)

hope that can grasp me a high 70's mark.

EDIT: checked carrotstick's solutions; make that a 40-45 raw

Last edited:

#### rulerpenkey

##### New Member
what do people think 87 would scale to?