Mathematics Extension 2 - 2016 Post-HSC Exam Thoughts (2 Viewers)

calamebe · Oct 21, 2016

InteGrand said:
$\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:$

$\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 $P$.$

$\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.

Paradoxica · Oct 21, 2016

bye sr

JAMLO · Oct 21, 2016

last year u need aorund 75 for e4

aoc · Oct 21, 2016

Glyde said:
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 · Oct 21, 2016

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.

Glyde · Oct 21, 2016

E3 cut off?

raghib483 · Oct 21, 2016

123ryoma12 said:
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 · Oct 21, 2016

123ryoma12 said:
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).

$\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.$

chickencoop · Oct 21, 2016

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 · Oct 21, 2016

chickencoop said:
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 · Oct 21, 2016

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

tommo727 · Oct 21, 2016

What would around 70 raw be?

Green Yoda · Oct 21, 2016

http://prnt.sc/cx2m65
Check Q5....seems familiar??

DatAtarLyfe · Oct 21, 2016

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.
FeelsBadMan

Chinese_taipei · Oct 21, 2016

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 · Oct 21, 2016

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

thomasdo1 · Oct 21, 2016

Chinese_taipei said:
Hmmm.. for 70, it'll probably be more like 92ish. I'm not expert at this

yup around 92 is my guess

Carrotsticks · Oct 22, 2016

Uploaded detailed solutions. First draft so feel free to let me know of any errors.

http://community.boredofstudies.org...ticks-2016-hsc-mx2-solutions.html#post7206077

eating · Oct 22, 2016

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

rulerpenkey · Oct 22, 2016

what do people think 87 would scale to?

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