Maths Advanced is one of the most popular HSC maths courses for students in New South Wales who want to maximise their ATAR. This blog post covers everything you need to know about the HSC Maths Advanced course, from the topics covered to how it's assessed. Keep reading for tips on succeeding in Maths Advanced and the resources available.
What is Maths Advanced?
Maths Advanced is an HSC course option for students in New South Wales who want to study maths at a more complex and abstract level.
It is considered more challenging than the standard HSC Mathematics course, covering advanced topics like calculus, vectors, and complex numbers. Maths Advanced also emphasises mathematical reasoning and problem-solving skills.
The Maths Advanced course is designed to provide students with a strong foundation for university studies in maths, science, engineering, finance and economics. It focuses on abstract mathematical concepts and aims to develop students' ability to solve complex, non-routine problems.
Some key features of the HSC Maths Advanced course are:
- It is the highest level of maths offered in the NSW HSC.
- The course covers more complex material than Standard HSC Mathematics.
- It focuses on abstract reasoning, proofs and problem-solving.
- It provides assumed knowledge and foundation for university maths courses.
Maths Advanced provides deep, rigorous mathematical knowledge to students wanting to maximise their ATAR and pursue maths-related fields. The advanced critical thinking and problem-solving skills developed are valuable for many university courses and careers.
Why study Maths Advanced?
There are many great reasons to study HSC Maths Advanced if you are a high school student in New South Wales looking to maximise your ATAR.
Boosts your ATAR
- Maths Advanced is generally considered one of the courses that gets strongly scaled upwards when calculating a student's ATAR.
- This means students taking Maths Advanced often get bonus aggregate points added to their raw exam marks during the scaling process overseen by state curriculum and assessment authorities.
Opens up opportunities for the future
Studying Maths Advanced shows universities and employers that you:
- Have advanced critical thinking and problem-solving skills
- Can understand complex mathematical concepts
- Have strong logic, reasoning and analytical abilities
This can open up opportunities to study mathematics, science, engineering, finance and economics at university.
Sets you up for success at university
Maths Advanced provides assumed knowledge for university maths, science and business courses. Studying it means:
- You are well prepared for the level of maths at university
- You won't have to do bridging courses to catch up on maths knowledge
- You will have an advantage over students who didn't study Maths Advanced
Develops highly valued skills
Studying Maths Advanced helps develop transferable skills like:
- Logical thinking
- Analytical abilities
- Problem-solving
- Attention to detail
These skills are valued in many university courses and careers.
💡 HSC Maths Advanced opens doors to the future by boosting your ATAR, preparing you for university and developing valuable skills. It's worth the extra effort!
What topics are covered in Maths Advanced?
Year 11 topics
In Year 11, you will cover five major topics in Maths Advanced (source: Mathematics Advanced Stage 6 Syllabus 2017)
Functions
Functions covers algebraic and graphical methods to model relationships between changing quantities. Studying functions develops skills in identifying patterns, clear communication, algebraic techniques, problem-solving, and predicting outcomes. This is useful in areas like finance, economics, data analysis, marketing, and weather forecasting.
Trigonometric Functions
Trigonometric Functions covers the study of periodic functions using geometric, algebraic, numerical and graphical methods. This allows for the modelling of periodic phenomena like waves and signals. Studying trigonometric functions develops an understanding of periodic behaviour not found in other functions. This is applied in models of naturally occurring oscillations like vibrations, pendulums, electric currents, and radio signals.
Calculus
Calculus covers frameworks for modelling quantitative change. It develops connections between a curve's gradient, instantaneous rate of change, and derivatives. Studying calculus improves skills in solving problems involving functions and rates of change, using algebraic and graphical methods. This is relevant to quantitative fields like physics, chemistry, medicine, engineering, computing, statistics, business, finance, economics, and construction.
Exponential and Logarithmic Functions
Exponential and Logarithmic Functions covers the properties and manipulation of exponential and logarithmic expressions. It introduces exponential functions through derivatives. Studying these functions develops an understanding of exponential growth and decay models. It also enables solving practical problems involving rates of change, like population growth and compound interest. This builds skills in applying calculus concepts to real-world contexts.
Statistical Analysis
Statistical Analysis covers exploring, displaying, analysing, and interpreting data to identify and communicate key information. Studying statistical analysis develops skills in carefully interpreting data and being aware of potential misrepresentation. It improves the ability to recognise, describe, and apply statistical techniques to analyse situations and predict outcomes. This builds awareness of how data-driven conclusions inform decisions made by groups like scientists, businesses, and policy-makers.
Outcomes
Year 12 topics
In Year 12, you will cover five major topics in Maths Advanced (source: Mathematics Advanced Stage 6 Syllabus 2017)
Functions
Functions teaches students to model relationships between changing quantities using algebraic and graphical techniques. Studying functions builds skills in identifying connections between algebraic and graphical representations, describing interactions between variables, finding patterns, precise communication, algebraic manipulation, solving problems, and predicting outcomes in fields like finance, economics, and meteorology.
Trigonometric Functions
Trigonometric Functions covers studying periodic functions using geometric, algebraic, numerical and graphical methods. This enables solving practical problems by modelling naturally occurring oscillations like waves and signals to predict outcomes. Studying trigonometric functions builds an understanding of periodic behaviour not found in other functions. Properties of periodic functions are applied in models of vibrations, waves, pendulums, electric currents, and radio signals.
Calculus
Calculus covers frameworks for modelling and analysing quantitative change. It develops differentiation and integration methods. Studying calculus improves skills in operating with and modelling changing situations using algebraic and graphical techniques. This aids in describing, and solving problems involving change, and predicting outcomes in fields like biomathematics, economics, engineering, and construction. Overall, calculus develops the ability to quantify, model, and deduce the consequences of change.
💡 Head here for additional study techniques to enhance your understanding and excel in Maths Advanced.
Financial Mathematics
Financial Mathematics covers sequences, series, and their financial applications. Studying financial mathematics develops skills in analysing and interpreting financial situations, calculating optimal choices, and solving money-related problems. This builds abilities to make informed financial decisions, understand their consequences, and prudently manage personal finances. Overall, it enables mathematically-grounded financial analysis and decision-making.
Statistical Analysis
Statistical Analysis covers exploring, displaying, analysing, and interpreting data to identify and communicate key information. Studying statistical analysis develops skills in carefully interpreting data and being aware of potential misrepresentation. It improves the ability to recognise, describe, and apply statistical techniques to analyse situations and predict outcomes. This builds awareness of how data-driven conclusions inform decisions made by groups like scientists, businesses, and policy-makers.
Outcomes
Are there any prerequisites for Maths Advanced?
To study HSC Maths Advanced in New South Wales, you first need to complete certain prerequisite courses.
There are no prerequisites, but students who do Maths Advanced should have done well in their previous maths classes.
You should also have strong skills in:
- Algebraic manipulation
- Mathematical reasoning and problem-solving
- Using technology like graphics calculators
What skills/capabilities are required to do Maths Advanced?
HSC Maths Advanced covers complex conceptual material and multi-step problems. To be successful, you need:
- Strong algebraic skills - rearranging complex formulas, advanced factorisation, completing the square, etc.
- Advanced problem-solving abilities - breaking down multi-layered problems into logical steps.
- Mathematical reasoning skills - construct proofs, and provide reasoning to justify solutions.
- Technology skills - accurately use graphics calculators and math software like GeoGebra.
- Analytical thinking - critically evaluate mathematical arguments and models.
- Abstract thinking - understand theoretical concepts like vectors and complex numbers.
- Attention to detail - solve problems accurately avoiding careless errors.
- Persistence - keep trying when faced with challenging multi-step problems.
Developing these mathematical capabilities takes time and effort. Being actively engaged in class and practising regularly is key.
Discover tips and tricks on note-taking here to enhance your understanding and retention of complex mathematical concepts.
What type of students should do Maths Advanced?
Maths Advanced is suited to New South Wales students who:
- Achieved high marks in Maths
- Enjoy abstract mathematics and problem-solving.
- Are self-motivated with good independent study habits.
- Are aiming for mathematics related university courses like engineering, computer science, physics, economics etc.
- Want to boost their ATAR with maths scaling.
- Are willing to put in the time and effort required. Maths Advanced has a challenging workload.
While it is an advantage to have natural mathematical ability, a very strong work ethic can compensate if you have the passion for advanced maths. Discuss your options with teachers.
How is Maths Advanced assessed?
There are two components to the HSC assessment for Maths Advanced in New South Wales:
1. School-based Assessment
- Worth 50% of your final mark
- Includes tests, assignments and an investigation project
- Assesses mathematical techniques, reasoning, and communication skills
- Examiners look for demonstrated understanding of concepts and ability to apply skills
source: Assessment and Reporting Stage 6 Mathematics Advanced November 2018
2. HSC Exam
- Worth 50% of your final mark
- 3-hour written paper with 2 sections
- Section I (15 marks) - objective response questions
- Section II (85 marks) - long answer multi-step problems
- Examiners look for correct working and reasoning in applying mathematical techniques
The HSC exam aims to differentiate student ability in advanced calculus, algebra, functions, statistics and trigonometry.
source: Assessment and Reporting Stage 6 Mathematics Advanced November 2018
Scaling
- Maths Advanced marks are scaled up as it is considered more challenging than standard Mathematics
- In 2021, un-scaled exam marks were scaled up by 15 marks on average
- Scaling ensures Maths Advanced students are fairly rewarded for the higher workload and difficulty
Aim to perform consistently well in both school and exam assessments. This gives you the best shot at a top-scaled mark.
Here are some links to past HSC exams:
Tips to succeed in Maths Advanced
Maths Advanced covers complex concepts and multi-step problems. Here are some tips to help you succeed:
1. Actively participate in class
- Pay close attention to teacher explanations and ask questions
- Contribute to discussions and share your thinking
- Connect new concepts to your prior knowledge
2. Consolidate your learning
- Review material and attempt practice questions soon after they are taught
- Identify gaps in your understanding and seek help early
3. Refine your problem-solving skills
- Break complex problems into logical steps before attempting solutions
- Estimate solutions before calculating to check your working
- Verify solutions make sense in the given context
4. Invest time in developing mathematical thinking
- Read mathematical arguments and proofs carefully
- Practise providing reasoned justifications for solutions
5. Use technology effectively
- Become adept using your graphics calculator for complex calculations
- Use math software like Geogebra for visualising concepts
6. Prepare thoroughly for assessments
- Ensure you cover all syllabus content in your revision
- Attempt past papers under timed conditions
- Reflect on where you can improve your exam technique
Putting in consistent effort is key to excelling in this demanding course. Stay motivated by focusing on your future goals.
What resources are available for Maths Advanced?
There are many useful resources to help you study for HSC Maths Advanced:
- Textbooks - Check with your teacher on the recommended text. Excel Maths Advanced has good exam practice questions.
- NESA syllabus - Details all course content, outcomes and assessment requirements. Download from the NESA website.
- Past papers - NESA provides official past exams and mark schemes for revision.
- Maths Online - Online course materials, tutorial videos and practice quizzes from NESA.
- Wolfram Alpha - Useful for worked solutions to complex problems.
- Graphics calculator - Invest in a TI-Nspire CX II or Casio ClassPad for the exam.
Apex Tuition Australia
Getting a Maths Advanced tutor can give you the edge to maximise your marks. Apex Tuition Australia matches students with tutors who achieved Band 6 results and E4 rankings in the HSC. Their expert knowledge of syllabus content, exam techniques and study methods ensures you have the right strategies to succeed. With personalised feedback and support, Apex empowers students to reach their full potential in Maths Advanced.
