Thoughts on 2020 Maths Extension 1 HSC paper
by Martin Gossow, publised 14 November 2020
Last week, students of the 2020 cohort sat the first Mathematics Extension 1 examination following the largest change to the syllabus in a few decades. After a tumultuous and anxious year, students were probably hoping that NESA would take it easy and remedy their stress. For students who have just entered Year 12 (and tutors/teachers like me instructing the cohort) are eager to get their hands on an exam to gauge the new difficulty level.
Look’s like NESA was willing to throw in some surprises. In contrast to the Mathematics Advanced exam—meticulously crafted to cover every topic in equal weighting—this exam goes all-out on a few topics and leaves others completely ignored. Most notably was the lack of vector geometry proofs or applications of differential equations.
The 10-mark multiple choice was reasonably straight forward, sticking to routine algebraic calculations and process-of-elimination questions. The last of these looks scary at first but just requires some substitution. Question 11 is all routine calculation as expected. The given induction (appearing in Question 12) is reasonably nice, and the pigeonhole principle is very explicitly given. Question 13 focuses heavily on calculus and integration, involving a reasonably involved substitution and a tricky double-chain-rule that was sure to lead to some elementary mistakes.
At this point, I expect students were feeling a little exhausted after Question 13 but somewhat confident they could knock out a proof about the orthogonality of rhombus diagonals. Instead, NESA throws an eight-mark curveball interweaving the binomial theorem with combinatorics. While a beautiful question in its own right, this topic got only a one-sentence (and rather vague) mention in the syllabus, and it is was unclear that a question of this type would be given in the exam. I had written questions of this sort into the Prime booklets, although they will be sure to receive a greater focus in the revision of this Year 11 topic (which a lot of students may be lacking in). The final question is a reasonable trigonometry palette-cleanser although involves a few different topics.
All students taking Extension 1 mathematics should take at least a cursory glance at this paper, especially trying Question 13a (which only needs Year 11 knowledge). We will also look at this exam more closely when the date of next year’s HSC approaches, but this was for sure a strong start to the new syllabus.