2023 School Trial Papers (1 Viewer)

C_master · Oct 30, 2023

Aeonium said:
optimistic naive starting year 12 perspective: not very but like i've put in a bunch of work in doing qns making notes and [other stuff] so it feels easy (and i have to teach my friends which also helps identify gaps)
just note that the collective hsc physics experience is that there are like 0 good physics teachers so enjoy

I agree the teachers here are so ass; I cant imagine the teachers Im gonna get when I start physics

carrotsss · Oct 30, 2023

C_master said:
How hard does Physics get? Im in year 10 and Im curious

I wouldn’t call it super hard, the difficulty mostly comes from the super content heavy second half where you just have to know lots of random niche details. If you don’t cover all that garbage thoroughly (or have a bad teacher like 99% of physics students) it’s pretty tough to catch up on at the last minute.

mmmmmmmmaaaaaaa · Oct 30, 2023

Aeonium said:
just note that the collective hsc physics experience is that there are like 0 good physics teachers so enjoy

yep agree

C_master · Oct 30, 2023

carrotsss said:
I wouldn’t call it super hard, the difficulty mostly comes from the super content heavy second half where you just have to know lots of random niche details. If you don’t cover all that garbage thoroughly (or have a bad teacher like 99% of physics students) it’s pretty tough to catch up on at the last minute.

Is yr 11 Physics ez coz rn for me it is

carrotsss · Oct 30, 2023

C_master said:
Is yr 11 Physics ez coz rn for me it is

yeah

none of phys is super hard just annoying

carrotsss · Oct 30, 2023

Rattlehead15 said:
Is it weird that I have a great physics teacher? Probably my 2nd best teacher overall

i used to have a good phys teacher then she left 🫡

C_master · Oct 30, 2023

tywebb · Nov 4, 2023

Sydney Grammar 2023 Chemistry trial: https://community.boredofstudies.org/resources/sydney-grammar-2023-chemistry-trial.20400/

now added to post #11

tywebb · May 1, 2024

tywebb said:
6 extension 2 trials from 2023 (too big for BOS server): https://www.mediafire.com/file/e9f1zocy20mqlp4/6-ext-2-trials-2023updated.zip/file - and I'm too lazy to upload separately to BOS.

They are Ascham, NSBHS, NSGHS, Sydney Tech, Sydney Grammar and Fort Street

Here is an alternative solution to the 2023 Sydney Grammar Q16b using properties of beta and gamma functions

which is much shorter than their 4 page solution!

tywebb · May 1, 2024

oos?

Yeah - BUT if they put the beta function in the exam then it is going to be much better to use properties of beta functions and sometimes gamma functions in the solution rather than a hopelessly inefficient solution.

And it's not just SGS with the oos stuff.

HSC exams have put beta functions in the exam too. Like 2020 and 2023 HSC exams.

I think there are other beta function questions in other trials too but there are hundreds of them so maybe later I'll compile a beta function extravaganza with uncomfortably efficient solutions maybe fitting it in 10 pages where the official solutions are 100 pages!

There are also some covert beta function questions in extension 1 where there is a worded binomial distribution question requiring a page of complicated arguments in the official soluition, but can be solved in 1 line via a regularised incomplete beta function! I'll try to hunt them down too but they are not as easy to find as they are not so obvious. An example is in the 2023 CSSA ext. 1

ilovemangos · May 1, 2024

if you did this in internal exams, you would probably have to appeal to teachers right? and it should be fine for hsc though i assume

tywebb · May 1, 2024

ilovemangos said:
if you did this in internal exams, you would probably have to appeal to teachers right? and it should be fine for hsc though i assume

If the teacher is competent enough to put a beta function question in the exam then they should be competent enough to cope with a beta function solution - without the need for appeal.

tywebb · Friday at 7:47 PM

To get started, here are 12 examples from 1945-2023 LC and HSC exams where you can use beta functions

$\textstyle\text{1945. Find }\int_0^\frac{\pi}{2}\cos^3x\ \!dx$

$\textstyle\text{1951. Find }\int_0^a\frac{x^\frac{3}{2}}{\sqrt{a-x}}\ \!dx$

$\textstyle\text{1956. Find }\int_0^tx^2(t-x)^\frac{3}{2}\ \!dx$

$\textstyle\text{1962. Find }\int_0^\frac{\pi}{2}\sin^6\theta\ \!d\theta$

$\textstyle\text{1980. Find }\int_0^1x(1-x)^{20}\ \!dx$

$\textstyle\text{1980. Find }\int_0^\frac{\pi}{2}\cos^2x\ \!dx$

$\textstyle\text{1985. Find }\int_0^1x(1-x)^{99}\ \!dx$

$\textstyle\text{1987. Find }\int_0^\frac{\pi}{2}\cos^5x\ \!dx$

$\textstyle\text{1991. Find }\int_0^\frac{\pi}{2}\sin^4x\ \!dx$

$\textstyle\text{1995. Show that }\int_0^\frac{\pi}{2}\sin^{2n}\ \!dx=\frac{2n-1}{2n}\cdot\frac{2n-3}{2n-2}\cdots\frac{3}{4}\cdot\frac{1}{2}\cdot\frac{\pi}{2}\text{ and}$

$\textstyle\int_0^\frac{\pi}{2}\sin^{2n+1}x\ \!dx=\frac{2n}{2n+1}\cdot\frac{2n-2}{2n-1}\cdots\cdot\frac{4}{5}\cdot\frac{2}{3}\cdot1$

$\textstyle\text{2020. Show that }\int_0^1x^n(1-x)^n\ \!dx=\frac{(n!)^2}{(2n+1)!}$

$\textstyle\text{2023. Show that }\int_0^1x^n(1-x)^n\ \!dx=\frac{1}{2^{2n}}\int_0^\frac{\pi}{2}\sin^{2n+1}x\ \!dx$

https://4unitmaths.com/beta-functions-in-past-papers.pdf

tywebb · Friday at 7:59 PM

Incidentally looking at all the past papers back to 1916, it wasn't till 1945 that integrals appeared.

The other integral in 1945 was $\textstyle\int\frac{dx}{3x+4}$

2023 School Trial Papers (1 Viewer)

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