From our tutor who scored 100 for Extension 2 Mathematics and 99 for Extension 1 Mathematics:

– Make sure you know how to integrate and differentiate all your basic functions, and use product and quotient rules; this will form the base of many questions like volumes and motion.
– Brush up on your algebra: many questions especially in 3U and 4U require you to do some complex and tedious algebra; many students lose marks here because of careless errors. The best way to minimise these mistakes is to practice.

Understanding is key:
– Make sure you know where your concepts and formulas are derived from; for example, knowing how Newton’s root approximations actually work, or where inverse functions come from. Many questions, especially in 3U and 4U, will test your understanding of these concepts by asking you tricky questions (for example, why doesn’t Newton’s root approximations if you find the roots to (x-1)(x+1) starting from x=0).
What’s even better about understanding these things is that you’ll never forget how to do these questions in the exam, because if you forget the formula, just derive it during the exam!
– At all levels of mathematics, the HSC will throw you a few “out there” questions, usually in question 16 for 2U and 4U, and question 14 for 3U. The key to solving these questions is understanding your basic formulas and concepts: all these “strange” questions will require you to have a deep understanding of your basics, which will let you apply these concepts in different and more creative ways.

Problem solving:
– Many students will struggle for 1 or 2 parts in question 15 for 2U and 4U, and question 13 for 3U. That’s because these specific questions will have the most difficult question in the exam. The final question of your exam will always test your understanding by requiring you to apply concepts you already know in a creative way, or it will introduce a new concept or formula and get you to try to learn on the spot. Strictly speaking, the final question is actually EASIER than the second last one as long as you have a good understanding of the concepts.
– The second last question will have parts that need you to find an inspired solution: i.e. you either see it or you don’t.

Scrounging those marks:
Make sure you attempt every question if you have the time. Students tend to look at a question with multiple parts, and if some of these parts look difficult, or impossible to solve, they just give up on the entire question. Well, that’s a terrible idea and will probably cost you at least 3 or 4 marks in the exam. The hardest questions have a tendency to have 1 or 2 free marks embedded in them. This might be any of the parts, so have a read of all of them and see if you can solve them. The biggest type of this is the “Hence, using this formula, find x”, where in the earlier question, it was a “prove that the formula for x is x=y+1”. Just sub in y and solve the question! Don’t just skip it, it’s a free mark!

Practice exams and time management:
– Finally, make sure you practice. I cannot stress this enough. For obvious reasons, the more you practice, the higher your marks will be.
Aim to finish all the past papers available to you on the HSC website. Of course, since you will probably be doing the new syllabus by the time you read this, that means the old HSC past papers aren’t completely relevant. Here’s where you’ll need to get past papers from other schools, from their trials. These are the next best thing!
– When you do these papers, you should know each one is a precious resource. So don’t waste it! Do each paper timed, and in exam conditions, and then make sure you mark, and redo any questions that you get wrong.
The biggest mistake students make is that they finish a paper, mark it, and maybe even redo the questions they get wrong, but then they don’t bother practicing areas that they’re clearly lacking in.
– If you do a paper, and you can’t do an integration question in maybe question 11-12 of the paper, what should this tell you? It would tell me that you’re clearly missing some fundamental skills in integration, so maybe go reread your textbook chapter on it, and do a few questions from there.

– This is a bit different from 4U: For 4U, the questions tend to be ordered in terms of topic from question 11-14, so if you get a poor mark (say 70% or less) for one of these questions, redo the textbook chapter on it. This is the biggest part of improving! You do a paper, work out your weakness, and FIX IT! This is how you go from a 50% to an 85%! Remember, the bulk of your paper will consist of easy questions, where as long as you have the fundamentals of each topic down, you can get full marks for these questions. Specifically, q11-14 for 2U, 4U and q11-12 for 3U are these types of questions. Aim to lose not a single mark here, as it is definitely doable.

“The reason why not all students get above 75% for these papers is because they haven’t done this process. This means they might go into the exam, and get tested on, say, motion, and realise “Oh dear, I can’t do any of these questions, because I didn’t revise them. Whoops.”. This will instantly make you lose 5 marks, or 5%. If there’s more than one topic where this happens for you, well, you lose more than 5%. So please, make sure you do the past papers, and work on areas of weakness for you. This is probably the best way to ace your exams.”

Written by Doug. W | Sirius Learning | Maths tutor

Previously graduated from James Ruse Agricultural high school, Doug has tutoring experiences with young students in primary up to HSC students doing Mathematics Extension 2. Doug has achieved outstanding HSC results: 100 for Mathematics 4U, 99 for Maths 3U and 96 for Physics. Doug is a very intuitive speaker who explains underlying concepts extremely well and particularly good at explaining commonly mistakes made in maths questions. Doug is passionate about logic and numbers and will strive to help you achieve your best.

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