Recent content by tywebb

y 11 cambridge ext 1 16B Q8 (also y12 cambridge advanced 7F Q16)

y 11 cambridge ext 1 14G q3

amt have finally published the 2023 solutions: https://shop.amt.edu.au/products/amc-2023-solutions-pdf It’s about 4 months later than before when they used to come out in January

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}

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...

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. ;)

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...

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!

I don't think year 12 have a significant advantage over year 11 for the senior paper, or year 10 have a significant advantage over year 9 for the intermediate paper. But year 8 probably do have an advantage over year 7 for the junior paper. What do you think?

There was a typo in 28. - should have been x Correct version is up at same link if you got it 18 minutes ago, just use same link or refresh page. I'll check again tomorrow for any other typos and maybe start on the up and mp papers.

I put my 2023 AMC Junior solutions here: https://4unitmaths.com/amc-2023-jun-sol.pdf The AMT still haven't published their solutions. However I think my solutions concur with the answers in the answer key

Started watching Fibonacci A-Z+ Forex Trading Strategy with Fibonacci Cluster by Marko Cvjetićanin

Started watching the new 12-part series Fibonacci Numbers and the Golden Ratio by Arthur T. Benjamin

Extension 2 proofs project attached

Here is a new resource for proofs to be published on May 8, 2024: Kirkwood, J.R., Robeva, R. S., A Bridge to Higher Mathematics, CRC Press, 2024 However the ebook is already available.