Mathematics Extension 1 Predictions/Thoughts (5 Viewers)

Jamesssss10 · Nov 10, 2023

Interdice said:
I do Ext 1 + Advanced.

Lets say my HSC mark is 80. Let's say my internal mark is 66.

(80+66)/2 = 73

73 is a nice whole number. However since I'm doing 1 unit of extension, I'll get 36.5. Will it get brought up to 37, or brought down to 36?

But what if you were just of the next band, a 69 for example, would it show as 35 and band e2? Doesn’t make sense

Interdice · Nov 10, 2023

Jamesssss10 said:
But what if you were just of the next band, a 69 for example, would it show as 35 and band e2? Doesn’t make sense

The difference would be minuscule. not even worth thinking about

scaryshark09 · Nov 10, 2023

on your results page, after alignment, its rounded to the nearest whole number (or nearest even number ig for 3u kids who don't do 4u). this is purely just for display purposes

however, UAC gets given marks to 4dp, so rounding makes no difference for your atar

in regards to the 80 external, and 66 internal, your mark would be displayed as 37/50 for a 3u kid, however this rounding up is not a benefit when it comes to atar

tywebb · Nov 13, 2023

apex solutions: https://www.dropbox.com/scl/fi/2kia...Exam.pdf?rlkey=jp3u4wc1ddtsrcq7h14d8af7d&dl=0

Here is their youtube version:

tywebb · Nov 14, 2023

nesa's mg is up at https://educationstandards.nsw.edu....xam-pack+++++++++++++++++++++++++++++++++++++ now

harrowed2 · Nov 15, 2023

tywebb said:
matrix solutions: https://www.matrix.edu.au/wp-conten...MATHS_EXT1_HSC_Solutions_MATRIX-EDUCATION.pdf

I can't make this link work

carrotsss · Nov 15, 2023

harrowed2 said:
I can't make this link work

2023 HSC Maths Ext 1 Exam Paper Solutions

You've found the 2023 HSC Maths Extension 1 Paper Solutions complete with full explanations! Read here to see how you went.

www.matrix.edu.au

harrowed2 · Nov 15, 2023

carrotsss said:
2023 HSC Maths Ext 1 Exam Paper Solutions

You've found the 2023 HSC Maths Extension 1 Paper Solutions complete with full explanations! Read here to see how you went.

www.matrix.edu.au

Thank you!

tywebb · Nov 15, 2023

looks like they changed the filename from

2023_HSC_MATHS_EXT1_HSC_Solutions_MATRIX-EDUCATION.pdf

to

2023_MATHS_EXT1_HSC_Solutions_HSC-MATHS-EXTENSION-1-SOLUTIONS.pdf

I fixed the link in post #451

tywebb · Nov 16, 2023

They also seem to have changed 12e

2023_HSC_MATHS_EXT1_HSC_Solutions_MATRIX-EDUCATION.pdf had

2023_MATHS_EXT1_HSC_Solutions_HSC-MATHS-EXTENSION-1-SOLUTIONS.pdf has

Also in 13b 2023_HSC_MATHS_EXT1_HSC_Solutions_MATRIX-EDUCATION.pdf had

and 2023_MATHS_EXT1_HSC_Solutions_HSC-MATHS-EXTENSION-1-SOLUTIONS.pdf has

So 2023_MATHS_EXT1_HSC_Solutions_HSC-MATHS-EXTENSION-1-SOLUTIONS.pdf is the better version.

Also if you have both versions it might be better to rename this one

2023_HSC_MATHS_EXT1_HSC_Solutions_MATRIX-EDUCATION-version2.pdf or something like that.

tywebb · Dec 20, 2023

Terry Lee Solutions: https://advancedmathematics.com.au/Resources/2023 Ext1.pdf

tywebb · Feb 24, 2024

tywebb said:
So if you wrote it out in full it would be

$\text{Area of triangle spanned by } \overrightarrow{OA},\overrightarrow{OB}\text{ is}$

$\textstyle\frac{1}{2}|\overrightarrow{OA}\times\overrightarrow{OB}|=\frac{1}{2}\left|\begin{vmatrix}\bold i&\bold j&\bold k\\a_1&a_2&0\\b_1&b_2&0\end{vmatrix}\right|=\frac{1}{2}|(a_1b_2-a_2b_1)\bold k|=\frac{1}{2}|a_1b_2-a_2b_1|$

I've heard various stories about how many marks this would get - everything from 0 to full marks.

I didn't go to NESA's HSC feedback day today which was held at UTS - but I heard that at that the HSC markers confirmed it would get full marks.

Arguments for saying stick to the syllabus is seriously weakened when many students have not been in schools in NSW for 13 years, but rather in later years come to Australia to do the HSC - when they have already been educated elsewhere in determinants, vectors including cross product, matrices etc.

So when they see a question like this it is obvious to them to use the cross product - and now according to the HSC markers would not be penalised for doing so - especially when the question said "or otherwise".

Luukas.2 · Feb 24, 2024

tywebb said:
I've heard various stories about how many marks this would get - everything from 0 to full marks.

I didn't go to NESA's HSC feedback day today which was held at UTS - but I heard that at that the HSC markers confirmed it would get full marks.

Arguments for saying stick to the syllabus is seriously weakened when many students have not been in schools in NSW for 13 years, but rather in later years come to Australia to do the HSC - when they have already been educated elsewhere in determinants, vectors including cross product, matrices etc.

So when they see a question like this it is obvious to them to use the cross product - and now according to the HSC markers would not be penalised for doing so - especially when the question said "or otherwise".

They could have just come from Victoria, the VCE specialist maths course includes vector cross products!

tywebb · Feb 24, 2024

Luukas.2 said:
They could have just come from Victoria, the VCE specialist maths course includes vector cross products!

So do you think it's fair to give full marks for the obviously much shorter solution - compared to these which obviously take much longer time and effort?

(from nesa mg)

scaryshark09 · Feb 24, 2024

tywebb said:
So do you think it's fair to give full marks for the obviously much shorter solution - compared to these which obviously take much longer time and effort?

View attachment 42564
(from nesa mg)

yeah no, i dont think that's fair
the simpler solution (3 posts ago) doesn't assess anything from the actual NSW syllabus pretty much. theres no way someone should be getting 3/3 for that.

tywebb · Feb 24, 2024

scaryshark09 said:
yeah no, i dont think that's fair
the simpler solution (3 posts ago) doesn't assess anything from the actual NSW syllabus pretty much. theres no way someone should be getting 3/3 for that.

Well they said because the question said "or otherwise" they would have no choice but to award full marks for the cross product solution, however short that may be - and regardless of anyone's opinions on the matter.

epicmaths · Feb 24, 2024

Love the cross products solution - another reflection of how poorly conceived the new HSC syllabus is, bring back circle geometry!

Luukas.2 · Feb 24, 2024

@tywebb, the cross-product solution is mathematically flawless. The question did not include any direction that the cross-product method contravenes. I struggle to see any reason why it should be penalised - and especially if the solution included a statement as to what the cross-product is and how the solution thus follows. The question did strike me as strange, in that I saw multiple 'otherwise' approaches before I recognised the hence approach being suggested, but students who can see alternatives that weren't considered in advance shouldn't be penalised for greater knowledge or insight than was anticipated.

Having said that, the following question was on the 2021 MX2 HSC, q15(d), and worth 2 marks:

$\text{Prove that $2^n + 3^n \neq 5^n$ for all integers $n \ge 2$.$

Would you give full marks for the following solution? It is valid, but also surely not what the examiners intended...

$\begin{align*} \text{When $n = 2$:} \qquad \text{RHS} &= 5^n = 5^2 = 25 \\ \text{LHS} &= 2^n + 3^n = 2^2 + 3^2 = 4 + 9 = 13 \\ \\ \text{Since $13 \neq 25$} \quad \text{LHS} &\neq \text{RHS} \quad \text{when $n = 2$} \end{align*}$

Fermat's Last Theorem, which was proved in 1999 by Andrew Wiles, states:

$\text{The equation $a^n + b^n = c^n$, where $a$, $b$, and $c \in \mathbb{Z}^+$, has no solutions for integers $n > 2$.}$

$\text{Hence, taking $a = 2$, $b = 3$, and $c = 5$, the equation $2^n + 3^n = 5^n$ cannot have any solutions for integers $n > 2$.}$

$\text{Combining the results from the $n = 2$ and $n > 2$ cases, it follows that $2^n + 3^n \neq 5^n$ for all integers $n \ge 2$.}$

In general, questions being solvable by valid methods beyond the syllabus are a potential problem that should be considered / addressed while drafting the exams, not as a marking problem after the exams have been sat.

tywebb · Feb 24, 2024

Luukas.2 said:
...Fermat's Last Theorem, which was proved in 1999 by Andrew Wiles, states:..

No because it wasn't. It was proved in 1994 and published in 1995.

tywebb · Feb 24, 2024

But generally if one can give a reference for a theorem that was proved, one can go on to use it to prove other things without having to prove it again. That's how maths works.

Maybe a more succinct solution would simply be

Screen Shot 2024-02-24 at 10.32.07 pm.png

follows as a corollary of Fermat's Last Theorem

Reference:

Wiles, Andrew (1995). "Modular elliptic curves and Fermat's Last Theorem" Annals of Mathematics. 141 (3): 443–551.

Mathematics Extension 1 Predictions/Thoughts (5 Viewers)

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