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Mastering HSC Mathematics
Insider Tips On How to Master Mathematics


Millions saw the apple fall, but Newton asked why.

— Bernard Baruch


From the Golden ratio, present in all nature, to the Burj Khalifa towering 830m over the Dubai skyline, and from counting change at the cash register, to budgeting out your trip. 


Mathematics is everywhere. Almost all careers use skills learned in Mathematics on a daily basis. It’s no surprise that almost all students study some level of maths for the HSC, whether it be Standard, Advanced, Extension 1 or Extension 2 Mathematics. 


As a senior student, you may have many questions about HSC Maths. What level of Maths should I take? Is Extension 2 Mathematics worth it? How do I improve my marks? And most commonly, how do I stop making careless mistakes? 


At Marquis Education, we understand the HSC Mathematics syllabus and journey in microscopic detail.


We, too, had asked those countless questions about HSC Maths. As Educators at Marquis, we believe in supporting students to achieve their best results. So, here are our insider tips on choosing which level of Maths to study at, improving marks, and stop making those careless errors. 


Choosing your Maths level for the HSC


Our quick tips on selecting your Math level:

 

  • Research and understand all the available Math levels 
  • Consider the importance of scaling 
  • Mathematics Extension courses are the highest scaling subjects in the entire HSC 

 


The first question you may ask yourself is: “What level of Maths should I study?” When making your choice, you should take into account your own Mathematical confidence, interest, abilities, as well as the subject’s scaling. 


Mathematical Ability 

Each Mathematics subject requires different levels of Mathematical competency and ability. We have created a flowchart to show a brief overview of the different Math levels that can be chosen in Year 11 and Year 12. 


Your Year 10 Mathematics performance should help determine your choice.

  • If you are not confident in your abilities, consider taking Year 11 Mathematics Standard. However, the scaling for Mathematics Advanced is significantly higher than for Standard, so if you are willing to study hard, please seriously consider taking Advanced. 
  • If you have demonstrated a general competency, consider taking Year 11 Mathematics Advanced. 
  • If you have performed well, consider taking the Year 11 Mathematics Extension 1 course. This will also include the Advanced course, so you will be taking three units of Mathematics altogether, and you will be required to sit both exams. 
  • If you are in Year 11 and have performed well in your Mathematics Advanced & Extension 1 course, consider taking up Year 12 Mathematics Extension 2. Although the difficulty of the content and questions will be of the highest calibre, you will no longer need to complete the Advanced exam and both your Extension 1 and 2 results will count as two units each. 


We recommend you do some thorough research into the syllabus for each course, assess your own mathematical abilities, and be aware of any prerequisites you may need for your desired University course. 


Understanding Scaling


Scaling is an essential factor in your choice, as subjects are not treated equally. The raw marks from certain high-scaling subjects are ‘scaled’ upwards while the raw marks from low-scaling subjects are ‘scaled’ downwards. This allows marks to be compared over different subjects. The scaling of your chosen subjects will significantly influence the calculation of your ATAR. The Mathematics Extension courses, both Ext 1 & Ext 2, are the highest scaling subjects in the entire HSC. Therefore, if you are reasonably confident in Maths, we recommend that you study at an Extension level. Even if you are average in the Year 11 Extension 1 course, consider taking up Extension 2 in Year 12, it may definitely be worthwhile simply due its high-scaling. 


It is also vital that you don't underestimate your own abilities. If you are willing to put the time and effort in, a more challenging level can be worthwhile. So, don’t sell yourselves short by not trying a harder subject and finding out your ultimate potential.


Insider Maths Tips

Whichever level you study at, we have five key tips that we have learnt from personal experience. Incorporate this advice into your studies to maximise your Math marks.

1 Understand why you are studying Maths

  • Ability to problem solve is important 
  • Maths helps you develop a resilience 
  • Almost all careers need Mathematics, you are learning for your future 
  • Reframe your perspective on Maths to increase your motivation


The ability to solve problems is vital in all aspects of your life. Mathematics may teach you formulae and abstract concepts, but it also gives you the ability and motivation to try and try again – to be ready to fail in order to get the right solution. Learning Maths also develops your ‘lateral thinking’ techniques, encouraging you to look at problems in innovative and creative ways. It encourages you to become open to new ideas, challenge assumptions, and generate a variety of potential alternative solutions. Therefore, it enhances your creative problem-solving abilities whilst also helping you develop personal resilience and strength. 


These beliefs are ingrained in all we do at Marquis Education. At Marquis, we educate to transform. Part of the transformation is teaching you to work hard and smart, so that you can reap rewards through your results and own personal growth. 


Therefore, it is important to reframe your understanding of Maths as a problem that is yet to be solved. Math teaches you to appreciate the simplicity of an equation, to work hard and assess your own strengths and weaknesses so that you can achieve your goals. With this understanding, you will be more motivated to tackle those Math problems. 



Almost all careers need Mathematics, even in everyday life. It is an essential process we use daily to decode and rationalise our surroundings. After all, it is the most powerful creation of the human spirit. So, it is important to understand that you are learning for your own future.

2. Setting out your work clearly and correctly 

  • Set your work clearly to avoid careless errors, make it easier to review, and work from 
  • Markers look at the process, as well as the answer

One of the most important ways to maximise your marks is setting out your work in a clear, concise and methodical fashion. Having clear working out will help you avoid making careless mistakes, make your response easier for you to review, and provide a more robust platform for when you continue solving more complex questions. 


Well-defined and elegant setting out will allow your markers to better understand the logic and flow of your argument. Markers often give marks out for the process and explanation on how you arrive at your answer, not just the final numerical answer. For instance, in the Extension 2 exam you should include all your working out and set it out so that it is easy to understand, as many marks are allocated for the process over the answer. 


Here are some of my top tips when writing out Math solutions:

  • Write down the key information from the question 
  • When introducing variables, state “let x be…” or label this clearly in your diagram 
  • Label equations and pro-numerals appropriately 
  • Take up as many lines or pages as you need to communicate your process 
  • Write one equation per line
  • Draw large diagrams so that you can indicate important features accurately
  • Avoid skipping steps and take the care and time to write a few extra lines of working 
  • If possible, explain the steps in your proof, communicate with the marker when you are substituting, using assumptions, or making conclusions 


Write neatly so as to not confuse your symbols, numbers or letters.

3 Understanding your content and formulae

  • Understand the applications and circumstances you should use the formulae
  • Understand the derivations and logic of the concepts 
  • Repeatedly apply your learnings 


Maths is much more than just memorising a formula. You need to understand your formulae, know when and where to apply it, and how to use it. To build familiarity with your formulae, you should start by understanding its derivation and logic. Additionally, you can strengthen your understanding of mathematical concepts by consistently and constantly applying them to problems, questions and exercises on each topic. Through practice, you will learn when and how to apply the formulae in a variety of circumstances until it becomes second nature. 


Therefore, at Marquis Education, each time we teach a new formula or concept we always derive and explain the ideas, and then test our students with a series of HSC-style questions.

4. Practice, practice and more practice!

  • Use past papers to familiarise yourself with the format, style, and possible methods when tackling questions 
  • Practise under timed exam conditions 


It has been said, time and time again, but it’s true. We can’t stress this enough, but mastery of Mathematics can only be developed through regular practice of all content and tested topics. 


Once you understand the key concepts, the most effective way to consolidate your knowledge is to do as many past exam papers as possible. Use past papers to familiarise yourself with the format of questions, style of problems, and how you are able to use different methods to tackle these questions. Try completing the papers under exam conditions, to ensure that you are aware of the time limit and exam mindset. When completing papers, be on the lookout for any careless errors you may make, especially in the easier questions in earlier sections. 


Here at Marquis Education, we offer Maths Tutoring Programs for Years 6, 7, 8, 9, 10, 11 and 12 which include countless exam-style questions and problems in our assigned homework, quizzes, and module exams. This way, students have an abundance of practice, and know exactly how to approach their exams. 

5. Ask for help when you need it

  • Ensure you have a strong network to rely on 


Your senior years can be some of your most stressful yet, so do not be afraid to speak up and ask for help – whether it be about a specific Math question or something more. 


That is why you should be aware of the importance in establishing a strong support network. Speak to the educators and mentors at Marquis Education, relatives, friends, teachers and careers advisers for their advice and experiences. Remember, there is no such thing as self-made success; you will reach your goals with the help of others. 


We hope you keep all these tips in mind and wish you the best of luck for your senior Maths journey. Don’t forget, your educators and mentors here at Marquis Education are here to assist and guide you throughout the process. Remember, do not study Maths for the sake of being admired or for attracting attention. Study for the pleasure and passion derived from the feeling of energy that arises in the mind from the keen exercise of its powers in metaphysical, scientific and mathematical reasoning. 


Master HSC Mathematics and you will be one step closer to transforming yourself and your future.



We hope you will find this blog useful and insightful along with our Facebook and Instagram channels as we continue to share more updates and stories across Marquis Education, our innovative Educators and inspiring students journeys.


Did you know you can book a consultation with our team to discuss your study goals and learn more about our tailored learning programs that guide students to HSC success in English, Maths and the UCAT. Enquire online here.

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