Thoughts on 2020 Maths Advanced HSC paper
by Martin Gossow, publised 1 November 2020
Last week, students in the 2020 cohort were the first to complete a mathematics exam with the new syllabus, the first overhaul of the syllabus in many years. As of yet, there has been limited information in how NESA would choose to test this content, so understanding the structure and content of this exam will be very valuable to future students, especially those in Year 12 this year.
The most glaring change is the new format, with 31 (relatively) short-answer questions given in two writing booklets, rather than the usual questions 11-16 broken into parts that have previously featured. The main disadvantage of this is a loss of the sense of increasing difficulty throughout the exam. This can result in difficult questions early in the paper throwing students off. Furthermore, there is a content switching between topics. The best way to prepare for this is through mixed revision of topics, and a good practice of exam technique. These are gained through practice, and it is a major reason that we are introducing more exam-style testing into the Prime curriculum.
Calculus—as usual—features heavily in the exam, although less so than in the previous syllabus. Students need to be able to compute derivatives and integrals quickly and correctly. NESA seems to be shifting their focus to a testing of geometric reasoning, for example in Questions 15, 22 and 25. Again, these skills are best learnt through practice and by practicing a broad scope of questions. The more difficult type of questions usually requires a synthesis of geometric and algebraic approaches. This is best seen in Question 10, where students must recall the formula for the derivative of a chain rule and then use the geometric understanding of derivatives and function composition to identify the correct number of solutions.
Statistical analysis is the newcomer to the syllabus, and it was tested somewhat infrequently. However, each of the main topics were covered and they mainly focused on students being able to interpret the question correctly and apply the valid formulae. The former of these is often a difficulty for students, especially when first encountering the topic. Question 27 in particular has almost an entire page of writing just to give the question itself, and students have to interpret all of this data which they end up substitution into a relatively simple formula. NESA seems happy to provide students with explanation and formulae, focusing more on testing whether students understand the relationship between components of the topic rather than simply memorising a method.
All said, this exam did not offer too many surprises and it will make a good base of study for the next HSC. The new format allows for a considerable scope of questions to be asked, meaning students who want to achieve high marks require a solid understanding in every single topic and subtopic. This exemplifies the importance of the advice that I always give to students at any level: 1) Read the syllabus, 2) Practice exam-style questions, 3) Correct your mistakes.