Maths Extension 1 is an advanced, challenging, and rewarding mathematics course available to high-achieving Year 11 and 12 students in New South Wales. Studying Extension 1 Maths opens doors to careers in STEM fields, demonstrates mathematical aptitude to employers and universities, and most importantly, fosters a lifelong passion for problem-solving, logical reasoning, and quantitative analysis. In this guide, we cover everything you need to know about HSC Maths Extension 1!

So, what is Maths Extension 1?

Maths Extension 1 is an advanced HSC mathematics course that goes beyond the standard 2U Mathematics course. Extension 1 builds upon and supplements the 2U course, introducing students to new and more complex mathematical concepts.

The Extension 1 course focuses heavily on theoretical mathematics and applying advanced mathematical techniques to solve intricate, multi-step problems.

Compared to the standard 2U maths course which teaches mathematical techniques for practical applications, the emphasis in Extension 1 is much more on abstract reasoning, logical deduction, and proofs. For example, students may be required to prove various mathematical theorems or properties.

Why do students study Maths Extension 1?

There are many excellent reasons for strong math students to enroll in the HSC Maths Extension 1 course:

Career Advantages‍

1. A high HSC Math Extension 1 score looks outstanding on university applications and CVs when applying for jobs, especially in fields related to:

• Engineering
• Finance and banking
• Information technology
• Physical, environmental, mathematical, and statistical sciences

2. Math Extension 1 is highly regarded by top universities as preparation for STEM degrees, giving students an edge for competitive program admission

3. Employers view Math Extension 1 on an HSC certificate as an indication of high-level quantitative capability

University Preparation

1. Extension 1 develops the advanced mathematical thinking and problem-solving skills needed for success in STEM degrees

2. Many university courses have 1st year math prerequisites that Extension 1 directly prepares students for, including:

• Calculus
• Linear algebra
• Discrete mathematics
• Statistics
• Quantitative reasoning

3. The abstract reasoning and formal proofs in the course help students transition to the more theoretical approach of university mathematics

Interest & Passion for Mathematics

• Students who enjoy exploring complex mathematical concepts can further indulge their interests
• Tackling new mathematical challenges builds confidence in university studies
• Working through multi-step problems is intellectually stimulating and improves general logical reasoning ability

What topics are covered in Maths Extension 1?

Year 11 topics

In Year 11, you will cover four major topics in Maths Extension 1 (source: Mathematics Extension 1 Stage 6 Syllabus 2017)

Functions

The Functions topic builds both algebraic and graphical skills to describe, analyse, and model relationships between changing quantities. Students develop a deeper conceptual understanding of function behaviour while strengthening their abilities to connect algebraic and graphical representations, determine solutions to equations, communicate mathematical ideas concisely, apply algebraic techniques to solve problems and predict outcomes in real-world contexts such as finance, economics, and weather modelling.

Trigonometric Functions

The Trigonometric Functions topic develops an understanding of periodic trigonometric functions through geometric, algebraic, numerical, and graphical approaches. Students explore inverse trigonometric functions, strengthening connections between algebraic and graphical representations. This supports solving problems involving inverse functions, modelling naturally occurring periodic phenomena such as waves and signals, making predictions, and broadening comprehension of how to apply trigonometry to theoretical situations as well as real-life scenarios.

Calculus

Combinatorics

Outcomes

Year 12 topics

In Year 12, you will cover five major topics in Maths Extension 1 (source: Mathematics Extension 1 Stage 6 Syllabus 2017).

Proofs

The Proof topic involves communicating and justifying mathematical statements through clear, concise, and precise reasoning. Students develop skills in constructing accurate justifications, critiquing arguments, and generalising patterns. Mastering proof methodology enables a higher level of mathematical thinking necessary for effective problem-solving.

Vectors

The Vectors topic introduces the mathematical representation of quantities with magnitude and direction, enabling the description of object behaviour in two dimensions using geometric and algebraic approaches. Students strengthen their conceptual understanding of position, displacement, and movement in 2D space while learning to effectively apply vector notations and analyse the geometry of scenarios. Mastering vectors supports the exploration of theoretical situations and real-world applications in areas like engineering, structural analysis, and navigation.

Trigonometric Functions

The Trigonometric Functions topic develops an understanding of periodic trigonometric functions through geometric, algebraic, numerical, and graphical approaches, as students strengthen skills in manipulating expressions to prove identities and solve equations. Students explore algebraic and geometric methods for solving trigonometric problems, deepening connections between algebraic and graphical representations, and enhancing their ability to apply trigonometry to solve theoretical problems or real-world scenario issues involving waves and signals. This builds conceptual knowledge of how trigonometric functions can model periodic phenomena while improving proficiency with trigonometric manipulations and computations.

Calculus

The Calculus topic develops a conceptual understanding of change and skills in using analytical and numerical integration techniques to model situations involving change, solve problems, and predict outcomes relevant to science, engineering, finance, economics and construction. Studying calculus allows students to quantify models of change, deduce their consequences, and strengthen their capacities to describe problems algebraically and graphically as well as solve them.

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Statistical Analysis

The Statistical Analysis topic develops skills in exploring, displaying, and interpreting data through modelling to identify and communicate key information, as students build an understanding of reliability when analysing situations and predicting outcomes. Studying statistics improves abilities to carefully interpret data, consider misrepresentation issues, and inform decisions made by scientific, business, and policy groups.

Outcomes

Are there any prerequisites for Maths Extension 1?

Maths Extension 1 builds directly on the standard Year 11 Mathematics Advanced and Year 12 Mathematics 2 Unit courses. To enrol, students must meet certain prerequisites:

Performance Requirements

• Achieved Band E4 (80-100%) or higher in Year 10 Mathematics 5.3 (accelerated course) or
• Band E3 (75-79%) or higher in Year 10 Mathematics 5.2
• Currently achieving a high level of competence in the Year 11 Mathematics Advanced course

The Year 11 Mathematics Advanced course covers assumed knowledge for Extension 1 including:

• Basic calculus (differentiation and integration)
• Trigonometric identities
• Polynomials
• Surds and logarithms
• Quadratics

Other Capabilities

• Strong algebraic skills - rearranging complex formulas, solving equations etc.
• Abstract reasoning and logic - make generalisations and prove mathematical arguments
• Problem-solving aptitude - break down multi-step problems
• Attention to detail - precision with mathematical working
• Work ethic - Extension 1 moves at a fast pace and has high course demands

In summary, a strong foundation in Year 10 accelerated math and currently excelling in Year 11 Advanced Mathematics are the key prerequisites. Extension 1 will greatly extend students' mathematical knowledge and problem-solving abilities.

What skills/capabilities are required to do Maths Extension 1?

Maths Extension 1 requires and further develops a specialised skill set beyond basic numeracy. Students should possess strong capabilities in:

1. Algebraic Techniques: Rearranging complex formulas, factorising expressions, making substitutions - for example:

• Using the quadratic formula
• Manipulating trigonometric identities
• Simplifying logarithmic and exponential expressions

2. Multi-Step Problem Solving: Breaking down problems and persisting through multiple stages of working to reach a solution. For example:

• Optimising surface areas and volumes of rectangular prisms
• Proving various trigonometric identities
• Using integration by parts twice to evaluate a complex integral

3. Mathematical Reasoning: Making generalisations based on specific examples and providing deductive logical arguments. For instance:

• Noticing a pattern in solutions to quadratic equations and forming a conjecture
• Constructing proofs involving triangle properties using prior theorems and results

4. Attention to Detail: Precision with mathematical notation, working, and language. Dropping negative signs or miscopying formulas leads to incorrect solutions.

What type of students should do Maths Extension 1?

Maths Extension 1 best suits students who:

• Have a natural flair, interest in, and enthusiasm for mathematics - finding satisfaction in solving tricky problems
• Achieved a high level of competence in accelerated Year 10 math courses
• Are currently excelling (E4 Band 6 or higher) in Year 11 Advanced Mathematics
• Learn mathematical concepts quickly and can independently consolidate their knowledge
• Have persistence and resilience when tackling multi-step problems - not giving up easily
• Pay close attention to mathematical detail and precision in their working
• Have a strong work ethic for handling challenging content and fast course pace

How is Maths Extension 1 assessed?

Maths Extension 1 has both school-based assessments and a final external examination which are used to calculate students' HSC marks:

School Assessments (50%)

• These assessments are set by teachers and usually include assignments, investigations, homework tasks and class tests.
• Assessable work is marked according to NESA guidelines - examiners look for a demonstrated understanding of course content, correct mathematical working, clear communication and reasoning.
• School assessments aim to assess students' ongoing learning, mathematical thinking, and problem-solving process.

The school-based assessments are marked by looking at two main criteria (source: Assessment and Reporting in Mathematics Extension 1 Stage 6)

HSC Exam (50%)

• The Extension 1 exam is 2.5 hours long held at the end of Year 12
• The Maths Extension 1 exams contain two sections (source: Assessment and Reporting in Mathematics Extension 1 Stage 6):

• Typically includes short answer conceptual questions as well as multi-step mathematical problems.
• Marking focuses on the final solutions but working out is also assessed - solutions without working usually receive minimal or no marks.
• The exam tests the full range of students' mathematical knowledge and skills developed in the course.

The Extension 1 exam is often statistically scaled to account for annual variations in difficulty and student cohort ability.
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Here are some links to past HSC exams:                                       

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So in summary, the course uses both school and exam marks, rewards demonstrated understanding over purely correct solutions, and scales exam marks to provide adjusted student rankings every year.

How to succeed in Maths Extension 1?

Here are key pieces of advice for HSC students to maximise their performance in the demanding Maths Extension 1 course:

Get Conceptual Understanding

• Don't just memorise formulas and mechanically apply methods - deeply understand the theory behind mathematical concepts and results. This allows adapting approaches to novel problems.
• When learning new content like arithmetic/geometric sequences, visualise number patterns rather than just substituting them into formulas.
• For complex concepts like partial derivatives, use multiple representations - words, diagrams, numerical examples, symbolic notation etc.

Refine Algebraic Technique

• Fluently applying skills like factorising, substituting variables, manipulating surds, using logarithm rules etc. saves time on exams allowing focus on complex steps.
• Identify weaknesses around rearranging formulas or solving quadratics and do targeted practice questions.

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Head here for additional study techniques to enhance your understanding and excel in Maths Extensions 1.

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Attempt Practice Exam Papers

• Repeatedly working through past papers under timed conditions - builds speed, resilience, and familiarity with exam-style questions.
• Mark papers rigorously, and identify knowledge gaps revealed by incorrect answers and areas where poor algebraic or reasoning skills cost marks.

Consolidate Learning

• Annotate class notes, verbalise concepts taught out loud in your own words, and maintain summary formula/definitions sheets.
• Space out revision over weeks, actively thinking about and applying concepts so understanding shifts into long-term memory.

What resources are available for Maths Extension 1?

Many great print and online resources exist to supplement classroom learning for Maths Extension 1 including:

Textbooks

• Excel Mathematics Extension 1 Year 11 by S. Marjanovic provides comprehensive coverage of the course with exam practice questions.
• Mathematics Extension 1 NESA Edition from Oxford University Press breaks content into modules with topic tests for self-assessment.

Online Resources

• HSC Maths Ext 1 online course at Khan Academy has lessons and mastery quizzes for all parts of the syllabus.
• ExamSolutions on YouTube works through solutions for past Extension 1 exam papers question-by-question.
• NESA website hosts scope of study documents, sample exam papers, and marking guidelines.

Tutoring

Getting a personalised Maths Extension 1 tutor can greatly accelerate exam preparation. Apex Tuition Australia provides expert HSC math tutors who scored in the top 1% of NSW and have in-depth understanding of what it takes to achieve an E4. Lessons are structured around comprehending challenging concepts, honing problem-solving skills, and building exam technique. This targeted coaching delivers confidence and results when it matters most.

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