Centre for Continuing Education

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

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

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This new course is the first in a series of four Mathematics Extension 1 courses and provides review of key content and skills from the Mathematics Extension 1 Preliminary course. It also covers initial concepts from the Mathematics Extension 1 HSC course. The topics addressed include introduction to vectors, further operations with vectors and proof by mathematical induction. Study skills and examination techniques will also be emphasised.

Other courses in this series include HSC Mathematics Preparation – Extension 1 (Part 2) (April) and HSC Mathematics Preparation – Extension 1 (Part 3) (July). You do not need to attend all three parts in order to benefit.


By the end of this course, you should be able to:

  • sketch graphs that are reciprocals, square roots, absolute values, products or sums of given functions
  • solve inequalities using algebraic and graphical techniques
  • use algebraic and graphical concepts in the modelling and solving of problems involving to functions and their inverses
  • understand and use parametric representation of lines, parabolas and circles
  • use the remainder and factor theorems to solve problem involving polynomials
  • solve problems using the relationships between the roots and coefficients of polynomial equations, graph polynomials and determine the multiplicity of roots of a polynomial equation
  • define and use the inverse trigonometric functions and sketch their graphs
  • apply concepts and techniques of inverse trigonometric functions and simplifying expressions involving compound angles in the solution of problems
  • apply understanding of the concept of a derivative in the solution of problems, including rates of change, exponential growth and decay and related rates of change
  • use concepts of permutations and combinations to solve problems involving counting or ordering
  • prove results using mathematical induction
  • apply concepts and techniques involving vectors to solve problems
  • answer a range of questions based on the topics covered
  • critically evaluate your 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.


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

Preliminary course

  • ME-F1 Further Work with Functions
  • ME-F2 Polynomials
  • ME-T1 Inverse Trigonometric Functions
  • ME-T2 Further Trigonometric Identities
  • ME-C1 Rates of Change
  • ME-A1 Working With Combinatorics

HSC course

  • ME-V1.1 Introduction to Vectors
  • ME-V1.2 Further Operations with Vectors
  • ME-P1 Proof by Mathematical Induction

Intended audience

Year 12 students or accelerated Year 11 students who have already completed the previous topics.

Delivery style

Delivered as a two-day activity-based workshop where we will explore and apply mathematical knowledge and skills in a combination of lectures, tutorials and problem-solving sessions. Practice exercises are carefully graded and you will receive immediate feedback.


You will receive:

  • 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
  • relevant past examination questions from the previous Mathematics Extension 1 course, as well as from other educational jurisdictions, with sample answers provided.

Course evaluation

This course will be evaluated via an on-line 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.


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  • Free, expert advice
  • Course materials – yours to keep
  • CCE Statement of Completion

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