Centre for Continuing Education

HSC Mathematics Preparation Course - Extension 1 (Part 1) (January)

HSC Mathematics. The smart way to prepare for your HSC.

Prepare for HSC Mathematics the smart way with HSC Mathematics preparation courses at CCE, the University of Sydney.

This course is the first in a series of three Mathematics Extension 1 courses and provides consolidation of key content and skills from fundamental topics in the Mathematics Extension 1 course. The program covers circle geometry, polynomials, further trigonometry, applications of differential calculus (including harder curve sketching), and harder inequalities and coordinate geometry. Study skills and examination techniques will also be emphasised.

This course is part of a 3-part series covering key areas from within this subject’s syllabus. Other courses include HSC Mathematics Preparation Course – Extension 1 (Part 2) (April) and HSC Mathematics Preparation Course – Extension 1 (Part 3) (July). Students do not need to attend all three parts in order to benefit.


Upon successful completion of this course, students should be able to:

  • Apply properties of circles to prove geometric results.
  • Use a variety of methods to solve polynomial equations.
  • Solve problems involving harder applications of trigonometric principles, including using trigonometric functions of sums and differences of angles.
  • Sketch curves involving both horizontal and vertical asymptotes.
  • Solve inequalities involving unknowns in the denominator.
  • Find the angle between two lines and divide an interval in a given ratio.
  • Answer a range of questions based on the topics covered.
  • Critically evaluate their own and others' solutions to improve the quality of responses in assessment tasks.
  • Interpret mathematical language of examination questions to better understand the steps required in a quality solution.


(Aligned to NESA Syllabus Reference Points)

The following topics from the Mathematics Extension 1 syllabus will be covered:

  • Circle geometry (2.6-2.10)
  • Polynomials (16.1-16.4)
  • Further trigonometry (5.6-5.9)
  • Applications of differential calculus (10.1-10.8, including 10.5E)
  • Angle between two lines (6.6)
  • Internal and external division of lines (6.7E)

Delivery Style

This Mathematics Extension 1 course is delivered as activity-based workshops where students explore and apply mathematical knowledge and skills in a combination of lectures, tutorials and problem-solving sessions. Practice exercises are carefully graded and students receive immediate feedback.


  • A Course Booklet including theory and worked examples, covering all syllabus dot points from the relevant topics.
  • Solutions to all questions in the course notes.
  • HSC Questions from recent years on the relevant topics, with sample answers provided.

Course Evaluation

This course will be evaluated via an online student questionnaire delivered in class.

Getting Through Your HSC: A Practical Guide

While you progress through this journey and also the conclusion of your schooling life, we know you’ll have a lot on your mind – exams, future study, careers – but remember, while keeping focused on these bigger goals and aspirations, it’s also important not to forget your own health and well-being.

For tips on staying motivated and keeping focused, dealing with anxiety, keeping healthy, relaxation, pre-study exercise and more, read our article Getting Through Your HSC: A Practical Guide.


  • Expert trainers
  • Central locations
  • Small class sizes
  • Free, expert advice
  • Student materials – yours to keep
  • Statement of completion