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by Martin Gossow - Prime Education

This article gives a brief summary regarding some statistics about the Mathematics Advanced HSC Exam of 2021. There will also be some comments on new trends which are emerging since the change in syllabus in 2019, and how to best prepare for the next HSC exam.

**Mark Distribution**

To start, we look at the number of marks per question. It is especially interesting to see the general distribution of marks. Questions worth 7-8 marks usually incorporate a number of different topics, and involve synthesising your knowledge.

The exam starts with 10 multiple choice questions, and then has two short-answer writing sections. Most questions are worth about 3 marks, meaning you have just over 5 minutes to complete each question.

**Topic Distribution**

Next, we give the distribution of questions broken down into their respective topics. Of course, no question only covers a single topic, but usually each part will have a main *theme* or *idea* that they want you to use.

The Statistics topic is the only topic which was introduced after the syllabus change. It makes up a surprisingly large portion of this exam, and a number of questions marked under other topics also had aspects of statistics. Many of these questions have a lot of setup and information, even though they might not be worth many marks in the end.

The Functions and Calculus topics have been staples of the HSC exam for years, and there are plenty of examinable areas here. You should make sure that you can complete questions in this topic efficiently and confidently.

Although it may not be a trend, it is noteworth that many of the functions questions were to do with finding tangent lines to curve. This allows the examiners to blend algebraic and geometric ways of thinking.

**Year 11 vs Year 12 Content**

In this exam, **48%** of questions were based on content that was learnt in Year 11. This is also the proportion of marks that came from Year 11 content. Understanding of this content also provides you with a solid foundation for the Year 12 content which builds on top of it, especially in mathematics.

However, note that just because a question comes from the topics that form the Year 11 syllabus, these questions may be slightly harder to the ones you have seen before. A useful study tip is to attempt the *challenge* or *extension* questions from your Year 11 textbooks, especially once you have gone through the Year 12 syllabus and are studying for your final exams.

In this graph, we see a reasonably clear divide between the Year 11 and Year 12 topics. The only crossover is in calculus (differential vs integral), statistics and functions.

Here are the main takeaways that I see from looking at this data, although feel free to make your own conclusions.

- Over a three hour exam, you have 1.8 minutes per mark of the paper. This is approximately 5 minutes per question on average.
- The last third of the paper makes up many of the marks, so you must maintain consistent focus throughout the exam.
- Statistics is being tested very heavily at the moment, followed by Functions and Calculus. Make sure these topics are well-understood!
- Geometry is becoming less important, but is still part of the syllabus. Much of this comes from Year 10 and before, so brush up on this if you need to.
- About half of the exam comes from Year 11 content, so you must revise these topics. The syllabus will tell you precisely which types of questions can be tested.
- Many questions from Year 11 appear in more difficult forms and may require knowledge from Year 12. Hence, you need to practice all topics in tadem, which is best done through past papers.

Overall, practice your foundations! Make sure you are confident with Year 11 topics, particularly with Calculus and Functions. This can secure you a majority of the marks in the exam.