Beginner’s Guide to Year 12 Maths Advanced

Are you struggling to keep up with your class? In this Beginner's Guide to Year 12 Maths Advanced, we're going to give you all the tools you need to catch up and excel at school.

year 12 Maths Adv Guide overview mobile

Confused about all the new changes in the HSC Syllabus? Trying to wrap your head around all the difficult concepts explored? Well, you’ve come to the right place! This Beginner’s Guide to Year 12 Maths Advanced will break down these tricky concepts and create clarity around all the grey areas!

All about the Beginner’s Guide to Year 12 Maths Advanced

Now that the new syllabus for the HSC has commenced, it’s essential that students build on their foundational knowledge from Years 7-10 and grow that knowledge moving forwards in Year 12. Now you are in Year 12, you will draw upon this past knowledge..

This Guide identifies the skills required to develop mastery over the Year 12 Maths Advanced HSC content, whilst also breaking down each concept into clear and concise theory.

Our purpose for writing this guide is to create clarity around the new syllabus changes surrounding the Year 12 Mathematics Advanced topic and help students prepare for their Trial HSC and HSC exams.


What’s in this Guide?

1. Applications of differentiation

2. Integration

3. Graphing Techniques (coming soon)

4. Calculus of Trigonometric Functions (coming soon)

5. Descriptive Statistics (coming soon)

6. Bivariate Data Analysis

Linear regression

7. Continuous Random Variables

Normal Distribution

8. Series and sequences

9. Financial Applications


How will this Guide help me?

2020 is the first year which contains the new syllabus materials and content. Our goal in this article is to create clarity around the new areas of the new syllabus topics like Statistics and to curate challenging questions which will help prepare you for the HSC.

Ultimately, your goal is to perform well in the HSC. So, this article will have information which will adequately equip you to prepare for the HSC.

We examine the concepts behind the questions rather than pure calculations as we believe this will be beneficial to understanding mathematics rather than just a list of steps. This is the philosophy behind our Matrix method for Maths.

The Matrix Method for Maths is our proven process to ensure you develop knowledge and skills.
Step Matrix Method
1 Theory Developing a thorough understanding of concepts is the first step to mastering Maths. Learn from Matrix Theory Books that are carefully structured to help you understand even the most complex stuff!
2 Application Memorising formulas will only get you so far. Consolidate your understanding by learning how to apply concepts and techniques to solve problems.
3 Examples Work through examples that will actually be in your exam. You’ll learn how to present your solution for maximum marks in exams.
4 Concept Checks Learn the most efficient problem-solving techniques with different types of exam-style questions.
5 Workbook Practice sharpening your skills with hundreds of exam-style questions. It’s important to keep practising as this is the only way to find the right balance between speed and accuracy.
6 Quiz and Feedback Weekly quizzes and feedback provide you with opportunities to identify your gaps and address them ASAP.
7 Topic Test Working under exam conditions will boost your confidence for the real thing. Learn from your mistakes and fill your gaps so you are continually improving.


What are some common student learning difficulties?

In Year 12 Maths, students encounter the following Mathematical weaknesses:

  • A poor understanding of Algebra. Students who have a poor understanding of Algebra will severely struggle with the topics explored in Year 11 mathematics.

For example: Find the solutions of \(x\) for the following quadratic equation:


Students would struggle with this question as many are familiar with factorising but are unfamiliar with the other methods like completing the square or quadratic formula which need to be applied in order to successfully solve the question.

  • Inability to link concepts together. A lack of conceptual understanding in the various topics explored in Advanced Mathematics will eliminate a students ability to tackle questions involving multiple concepts.

For example: Find the values of \(m\) for which the graph of the parabola \(y=x^2+5mx+m\) is always above the \(x\) – axis.

In this question, it’s important a student has a good conceptual understanding on the link between the discriminant and the parabola and solving quadratic inequalities. Without a good conceptual understanding, students would assume that “above the \(x\) – axis” translates to solving the discriminant greater than zero rather than below zero.

  • Students struggle to communicate properly the topics learnt, which is a reflection of rote learning and lack of conceptual understanding
  • Unable to do difficult questions. Many students see a difficult question and give up without considering how to approach it. This doesn’t grow confidence and certainly won’t enable students to do later questions in the HSC paper!


What do Band 6 students do differently?

  • Have a good algebraic understanding. Rather than pushing through the Year 12 topics, band 6 students tend to have an awareness of their weaknesses and go back to previous years and practice their algebraic skills.
  • Keep a logbook of mistakes. Many students enjoy practising questions, but when they reach a question too difficult to solve they skip it and do a question they can solve.



    Outside of exam conditions, you have the freedom to do this but within an exam, it would be unwise to simply skip a question. To combat this, keep a logbook of all questions you are unable to do, and make the time to figure out how to answer it


  • Consistently give yourself feedback. How can you expect to improve if you don’t check your answers and don’t know where you went wrong? Keep a logbook of all questions you get incorrect, and make clear to yourself how you can correct it.



    Remember this is year 11. You have plenty of time to formulate new and healthy habits which will ensure fewer mistakes.


  • Be inquisitive. Ask questions about things you don’t understand! Remember, the better you understand a concept in mathematics, the easier it is to solve questions and remember the steps.
  • Be disciplined. Consistently set aside time to understand one concept. Make it your mission to chip away at it.
  • Communicate what you understand. Learn to explain to your peers how to do a question. It will help you remember and understand as well. It will also reveal to you things you don’t completely understand.


Last chance to get HSC exam ready!

It’s your last chance to boost your skills and confidence. Revise all Maths Adv core topics with our HSC experts and practise your exam skills with our mock exam. Learn more about our Year 12 Maths Adv Course now!

Start HSC Maths confidently

Expert teachers, weekly quizzes, one-to-one help! Ace your next assessment with Matrix+ Online.

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