Advice from the Top of the State Extension 2 Mathematics
Prime graduate, Stanley Luk has achieved Rank 1 of Extension 2 Mathematics from the State NSW from his 2017 HSC Exams.

Who am I?
My name is Stanley Luk; a student of Shore School with an ATAR of 99.70 and the good fortune to place 1^{st} in the state for Extension 2 Mathematics. Now although it took a lot of effort during my time in year 12 to get there, I feel that shooting for success in Extension 2 Mathematics is not as hard as people think, provided that you do the right things. The following advice I’m giving was what I felt help me improve my mathematics, so I’m hoping it can be of use to all of you as well.

My HSC Results
Mathematics Extension 2 100/100 Mathematics Extension 1 99/100 English Extension 2 96/100 English Extension 1 46/50 English Advanced 41/50 Physics 92/100 Chemistry 89/100 
How can I better learn and understand the concepts?
I find that it is common to go over the topics at least two to three times before you feel very confident with them. Some topics are smaller and easier, like Curve Sketching, but some others like Complex Number, Conics and Mechanics often require a lot of depth to your knowledge as well.
Ideally, you should learn your content for the first time before you cover it in school. Now, this does not mean accelerating a year, even doing them just a month or a week before your school teacher should give you a preliminary understanding that can be built on, making it far easier to understand later.
Often, most people turn towards tutoring centre like Prime Education for this. Hitting the books to learn yourself is hard, but not impossible, however, don’t be afraid to seek a secondary teacher as they can really boost your game.
When you cover your content a second time, all the ‘hard’ parts will hopefully start to click with you, or you won’t be as daunted, ideally the second time you see a topic should be during school, allowing you to stay ahead of your peers. At this stage, you can revise the content again, and again, but that is not necessary. You should now a lot of it by now but may still be rough around the edges, that’s okay, this is where practicing questions become useful.

What can do before an exam?
Through a quick google search, you should easily be able to access all the past Extension 2 Mathematics papers back to 1960 as well as selective and private school trial papers. Before starting timed practice exams, it is important to understand the structure of HSC questions as you will find examiners tend to ask the same styles of questions with little variations across the years. Use the HSC papers from 1990 to 2005 as well as any other school trial exams for this. Page through the paper, stop to do questions you find slightly difficult, or that require lots of working. Don’t do what you can easily get full marks with, attempt and understand what is difficult first. Basically, you should build your knowledge of the HSC exam before you start trying for speed and accuracy.
You should leave the HSC papers from 2006 to 2017 for timed practice. There is also a large availability of school trial exams so you won’t run out. When doing timed practice, do the entire paper in one sitting as 3 hours is a long exam and you will need to get a feel for it. I find it helpful to place time constraints on myself as well. Start with 95% of the time and see if you can slowly but surely drop it to 90% or even 85%.
Marking your papers properly is a necessity. Always be harsh and always make a note of any mistakes. I like to write on the front of each paper exactly; where I went wrong, what topic it was, and what type of mistake it was (i.e. ‘forgetting a negative’ or ‘not realising a symmetrical case in combinatorics’). This should give you a heightened awareness of what’s hard or not for you, as well as document your improvement as you make less and less.

What can do during an exam?
Not panicking during an exam is easier said than done, and the best piece of advice I can give for this is that practice mostly builds confidence. Realise that the exam before you is exactly the same as a practice exam with similar difficulty so you should be confident in your preparations.
Examiners put the different variations on the same thing in a 4U paper because they need to test to a syllabus. Remember that and try not to be fazed by anything that seems ‘new’ because the chances are that it isn’t.
As for finishing with time to check your paper, I’m torn between the advice for this. As for me, I always aimed for 2030 minutes of checking time, but I know others who perform best by taking it more slowly through the exam to reduce careless errors and finishing the paper close to the time limit. Basically, do whatever works for you.

Any other recommendations or advice?
Don’t be Daunted, people will tell you Extension 2 Mathematics is hard, you will find difficulty with questions, but remember that the vast majority of the paper, namely Questions 114 will simply routine work with variations on algebra or calculations. The difficult parts are questions 15 and 16 but you should be confident in getting almost all the marks for the earlier parts of the exam. Hard work, practice, and dedication will take you very far in all HSC subjects, Extension 2 Mathematics is no different.

Do you have a good maths question?
Yes, this may seem beyond the course at first glance, but a little simplification goes a long way in helping you solve a problem. See if you understand your trigonometry well, or better yet, find the neat geometric solution to this.
Question
Let \( D = \sqrt{(\sin x – \cos y)^2 + (\sin y – \cos x)^2} \) for real \( x \) and \( y \). What is the maximum value that \( D \) can take?
(A) \( \sqrt{2} \)
(B) \( 2 \)
(C) \( \sqrt{6} \)
(D) \( 2\sqrt{2} \)