Course summary

This course is the first in a series of four Mathematics Extension 1 courses designed to consolidate knowledge and skills, build confidence in solving unfamiliar problems and maximise examination results. It includes succinct summaries of topics to help solidify foundations, and a broad range of examination-style questions to demonstrate the application of these. Students are given time to apply their knowledge and receive individual assistance and feedback. Study skills and examination techniques will also be addressed.

Part 1 provides a review of key content from the Year 11 Mathematics Extension 1 course, as well as initial concepts from the Year 12 Mathematics Extension 1 course. Topics addressed include Permutations and Combinations, The Binomial Theorem, Further Work with Functions, Polynomials, Further Trigonometry, Proof by Mathematical Induction, Introduction to Vectors and Inverse Trigonometric Functions. There are a range of questions provided to ensure all students are able to engage with the content, even if they have not previously studied these topics.

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

Aims

The aim of this course is to improve students’ knowledge of the Stage 6 Mathematics Extension 1 course. We want students to leave with a deeper understanding of the topics covered, and feeling confident that they have the skills required to interpret and answer examination questions.

Learning outcomes

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

• solve problems involving inequalities, functions and their inverses, graphical relationships between functions, and parametric equations
• apply the remainder and factor theorem and sums and products of zeroes to solve problems involving polynomials
• solve problems in three dimensions using trigonometry and simplifies expressions, proves results and solves problems involving compound angles using trigonometric identities
• use permutations and combinations to solve problems involving counting, ordering and probability
• use the binomial theorem to solve problems and prove identities
• use mathematical induction to prove results involving sums and divisibility
• operate with 2D and 3D vectors
• solve problems involving inverse trigonometric functions.

Content

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

• Graphs of reciprocal and absolute value functions, as well as graphs arising from the sum or difference of functions
• The algebraic and graphical relationships between a function and its inverse
• Factorising and graphing polynomials, solving polynomial equations and the relationship between the roots and coefficients of polynomials
• The sum and difference expansions for trigonometric functions and how these can be applied to solve trigonometric equations
• The multiplication principle and how it can be applied to solve problems involving ordered and unordered selections, including those with additional restrictions
• The properties of Pascal’s Triangle and its application to the expansion of binomial expressions
• The nature of inductive proof, including the statement to be proved, the base case and the inductive step, and the use of mathematical induction in proving sum and divisibility results
• The definition of vectors as having direction and magnitude, and the notation used to describe vectors
• The scalar product of vectors and its application to geometric reasoning and vector projections
• The graphs and properties of inverse trigonometric functions

Prerequisites

Students need to have completed the Advanced Pathway in Year 10 Mathematics course and should be currently studying or intending to study Mathematics Extension 1 in Stage 6.

Who this course is for

This course is suitable for students in Year 11 and 12 who are currently studying Year 12 Mathematics Extension 1.

Delivery style

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

Materials

The course materials contain topic summaries, examples that illustrate key ideas, and a range of examination style questions. Worked solutions to all examples and practice problems are included. All course materials are provided electronically.

Bring your own device

Please bring a device to access the course materials, along with a NESA-approved calculator.

Course evaluation

This course will be evaluated through an online questionnaire, which will be sent via email and SMS during 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.