Short courses

Course summary

This course is the second 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.

Topics covered in Part 2 include Further Calculus and Further Applications of Calculus. 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 1) (January), 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.

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.

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

• solve problems involving derivatives of functions defined parametrically
• differentiate inverse trigonometric functions
• use integration by substitution to evaluate definite and indefinite integrals
• use double-angle identities to find integrals
• integrate expressions where the primitive is an inverse trigonometric function
• apply calculus to solve problems involving polynomials, further rates of change, areas and volumes and differential equations.

• How to find the derivative of a function defined parametrically using the chain rule
• The relationship between the derivative of a function and the derivative of its inverse
• Types of integration by substitution including where the substitution is expressed as a function of the variable of integration and where the variable of integration is the subject of the substitution
• The Multiple Root Theorem
• Using the chain rule to solve problems involving related rates
• Practical situations where the rate of change of a quantity is proportional to the amount by which the quantity exceeds some fixed value
• Finding areas between curves and volumes of solids of revolution
• Drawing and interpreting slope fields
• Solving first-order differential equations, including those resulting in the logistics function.

Students need to have completed the Year 11 Mathematics Extension 1 topics and should currently be studying Mathematics Extension 1 in Stage 6.

This course is suitable for students studying Year 12 Mathematics Extension 1.

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 students will receive immediate feedback.

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.