Maths Extension 2 is an advanced, highly challenging mathematics course available to students in the HSC in New South Wales. It builds on topics introduced in Maths Advanced and Maths Extension 1. Keep reading to learn everything you need to know about succeeding in Extension 2 Maths.
What is Maths Extension 2?
Maths Extension 2 is an elective course typically taken in Year 12 by students who have already completed Maths Advanced and Maths Extension 1. It focuses on furthering conceptual understanding and complex problem-solving skills in mathematics.
Maths Extension 2 is a 1-unit course. HSC students need to complete at a minimum 10 units. Your ATAR will only comprise of scores from your top 10 units.
The course goes into mathematical rigour, proofs, and enrichment well beyond the standard HSC mathematics curriculum.
The aim of Maths Extension 2 is to provide stimulus and challenge for capable maths students, allowing them to develop mastery in abstract mathematical concepts at the highest level available in high school. It also encourages complex problem-solving and divergent mathematical thinking.
Why study Maths Extension 2?
There are many great reasons to take on the challenge of HSC Maths Extension 2 if you have an aptitude for mathematics:
Career Advantages
Studying Extension 2 demonstrates mathematical maturity to universities and future employers. It shows you can grasp complex concepts and think critically.
Intellectual Stimulation
- Opportunity to push mathematical abilities to the limit
- Discover advanced theoretical mathematics
- Develop the ability to provide mathematical proofs
- Enjoy enrichment well beyond the standard curriculum
Personal Growth
- Builds logical thinking and problem-solving skills
- Gains a sense of achievement from tackling considerable mathematical challenges
- Learn independent research and self-directed learning
The advanced critical thinking and analysis skills developed in Maths Extensions 2 are valuable for many future pursuits. It provides an exceptionally strong foundation for further mathematics study at the university level.
What topics are covered in Maths Extension 2?
Year 12 topics
In Year 12, you will cover five major topics in Maths Advanced (source: Mathematics Extension 2 Stage 6 Syllabus 2017)
Proof
Proof entails effectively communicating and justifying arguments for mathematical statements with clarity and precision. Understanding proof fosters accurate reasoning and communication, crucial for comprehending mathematical arguments' structures. Proficiency in proof cultivates critical thinking, communication, and problem-solving skills essential for generalising patterns and effectively critiquing mathematical arguments.
Vectors
Vectors represent quantities with magnitude and direction, crucial for understanding object behaviour in various contexts. This mathematical concept aids in analysing objects in two or three dimensions, encompassing position, location, and movement. Its applicability spans across disciplines like engineering, structural analysis, and navigation, offering a versatile toolset for theoretical and real-world scenarios.
Complex Numbers
Complex Numbers, integral in various fields including electronics, extend the real number system. Studying them enhances comprehension of algebra, geometry, and their real-world applications. This knowledge fosters mathematical inter-connectedness, preparing students for advanced mathematics and practical use of technology.
Calculus
Calculus explores change through differential equations and integration, offering techniques to solve complex problems in fields like Chemistry, Physics, and construction. It enhances students' capacity to model diverse functions, predict future outcomes, and utilise algebraic and graphical methods. Essential for understanding and navigating dynamic situations, calculus fosters analytical skills crucial across various industries.
Mechanics
Mechanics explores how objects' motion changes when subjected to forces, utilising mathematical representations of magnitude and direction. Understanding mechanics aids in modelling physical systems, predicting object behaviour under forces like gravity and air resistance, and fostering comprehension of motion changes. It is crucial for students to grasp mechanics for applying mathematical techniques, solving problems, and predicting outcomes, especially in physics contexts.
Outcomes
Are there any prerequisites for Maths Extension 2?
Maths Extension 2 builds on the concepts and skills developed in Mathematics Advanced. Here are the specific prerequisites:
Formal prerequisites
To study Maths Extension 2, you must:
- Be enrolled concurrently in Mathematics Advanced
- Be enrolled in Maths Extension 1
Some schools may also require a minimum grade in Mathematics Advanced, such as Band E4 or higher.
Recommended level of mathematical skill and knowledge
To be well-prepared for success in Maths Extension 2, you should have:
- A strong grasp of advanced mathematical concepts from topics like trigonometry, calculus, statistics and networks
- Well-developed problem-solving and mathematical reasoning ability
- Confidence in communicating mathematical ideas and justifying solutions
💡 Head here for additional study techniques to enhance your understanding and excel in Maths Extension 2.
Here is an overview of the mathematical skills you are expected to have mastered prior to Maths Extension 2:
Algebra
- Manipulating and factorising algebraic expressions
- Using logarithmic and exponential functions
- Applying coordinate geometry techniques
Trigonometry
- Solving trigonometric equations
- Using trigonometric identities and formulas
- Applying trigonometry in 3D problems
Calculus
- Differentiating and integrating a variety of functions
- Solving problems using differentiation and integration
- Working with kinematics problems
Statistics
- Statistical descriptions and distributions
- Identifying and using models for data, including lines of best-fit
- Applying statistical tests
If you need to revise any mathematics from earlier years, take the time to consolidate these skills. A strong foundation will help you tackle the advanced concepts introduced in Maths Extension 2.
What skills/capabilities are required to do Maths Extension 2?
Mathematics Extension 2 extends students' mathematical knowledge in new and complex ways. To succeed, you need:
Mathematical thinking and problem-solving ability: You will tackle open-ended, unfamiliar problems. You need advanced reasoning skills to create structured solutions.
Ability to understand and use abstract concepts: Many concepts in Networks, Mechanics and Combinatorics are highly abstract. You need to move flexibly between abstract representations and practical contexts.
Communication and justification skills: You must justify mathematical solutions completely and concisely. This includes using clear mathematical language, logical argument and precise working.
Self-directed learning capability: Extension 2 is not fully prescribed in a textbook. To explore some concepts deeply, you need to take responsibility for sourcing and integrating information.
Persistence and resilience: The content is challenging. You need a determination to keep trying different mathematical approaches until you make progress. Seeking help is also a key skill.
Time management and organisation: The workload is significant. Careful planning and efficient use of study time are essential to complete the coursework and prepare thoroughly for the final HSC exam.
What type of students should do Mathematics Extension 2?
Mathematics Extension 2 best suits students who:
- Have a passion for mathematics and want to be challenged
- Achieved a high level of mastery in Mathematics Advanced topics
- Are independent and motivated learners
- Enjoy exploring mathematical ideas and proofs
- Are interested in tertiary study pathways that are maths-related like engineering, science, data analytics and finance
The best preparation is to achieve a strong understanding of all content in Mathematics Advanced. This gives you the foundation to apply that knowledge in advanced problem-solving contexts.
💡 If you found Mathematics Advanced engaging and interesting, you are well suited for the deeper exploration of mathematical concepts offered in Maths Extension 2. It provides an opportunity to truly stretch yourself mathematically before commencing advanced tertiary studies.
How is Maths Extension 2 assessed?
Maths Extension 2 involves both school-based assessments and an external HSC examination.
School-based assessment
- Worth 50% of your overall Extension 2 mark
- Includes two extended modelling tasks completed during the year
For these assessments, examiners are looking for:
- Creativity and complexity in applying mathematical techniques to open-ended, practical situations
- Logical reasoning in developing a model and solutions
- Clear explanations and justification of the methods, models and solutions developed
- Concise and accurate working and use of mathematical language
source: Assessment and Reporting in Mathematics Extension 2 Stage 6
HSC examination
- Worth 50% of your overall Extension 2 mark
- Includes a written examination with 2 sections:
- Short response questions (worth 10 marks)
- Extended response questions (worth 90 marks)
The exam tests your knowledge, understanding and skills across the Modules - Complex Numbers, Mechanics, Networks and Combinatorics.
source: Assessment and Reporting in Mathematics Extension 2 Stage 6
Examiners look for:
- Accuracy in applying techniques and mathematical understanding
- Valid processes in solving mathematical problems
- Clear diagrams, working and verbal explanations of reasoning
- Concise, structured and logical communication style
The exam itself is quite difficult. Student's raw exam marks are moderated based on school assessments. This process aims to provide a fair comparison of student achievement across the state.
Careful preparation and integration of the course content are key to maximise exam performance. The school assessments also provide an opportunity to receive detailed feedback to guide your exam preparation.
Here are some links to past HSC exams:
Tips to Succeed in Maths Extension 2
1. Consolidate advanced mathematics knowledge
- Revise key mathematical concepts from Methods and Advanced e.g. trigonometric identities, differentiation techniques
- Practise applying concepts in advanced problem-solving questions from past papers
- Clear up any gaps in understanding from earlier topics
2. Develop mathematical thinking habits
- Break down complex problems into smaller logical steps
- Verify solutions by working back through solve steps
- Link mathematical solutions back to practical contexts
3. Improve justification and communication skills
- Annotate working and solutions clearly
- Highlight how each step links to prior working
- Define key terms when explaining solutions
- Structure explanations logically and concisely
4. Attempt a range of practice questions
- Seek out questions that apply mathematics in real-world contexts
- Try questions from past HSC exams and different textbooks
- Use practice questions to identify knowledge gaps
5. Establish a study routine early
- Extension 2 content builds gradually
- Regular shorter sessions are better than cramming
- Stay on top of homework and seek help quickly on tricky concepts
6. Take care of yourself
- This course is intellectually demanding
- Maintain balance through rest, relationships and extracurricular activities
- Believe in your ability to improve and respond positively to feedback
By consolidating prior knowledge, developing key mathematical skills and habits, utilising different practice resources and keeping balance in life, you will be on track for success in this challenging but rewarding course.
What resources are available for Maths Extension 2?
There are a variety of useful resources to help you learn and revise Extension 2 content:
Textbooks
- Excel Mathematics Extension 2 by D. Huntley and G. Diskin
- Extreme Mathematics Extension 2 by P. Ferro and R. Ferro
These textbooks provide explanations and practice questions across all modules.
Past HSC Exam Papers
- NSW Education Standards Authority (NESA) Exam Papers
- Excel Past HSC Papers
Attempting actual past exams is critical exam preparation.
Videos
- HSC Maths Ext 2 online course by Art of Smart Education
- HSC Maths Australia Extension 2 YouTube playlist
Video tutorials can help explain difficult concepts visually.
Tutoring
Apex Tuition Australia provides exceptional HSC Maths tutors who ranked in the state's Top 50 Maths Extension 2 students themselves. Their mentors guide you through advanced concepts and share proven strategies for acing exams and assessments. Classes are structured based on each student's needs in the crucial months leading up to the HSC.
With individualised support from high-calibre tutors, quality resources to supplement your learning, and a strategic approach to exam preparation, you will be well set up to fulfil your potential in this rewarding advanced mathematics course.
