Course summary
This course is the third in a series of four Mathematics Advanced courses designed to consolidate key content and skills from specific topics in the Mathematics Advanced HSC Course. Topics covered include Applications of Calculus, Sequences and Series, and Financial Mathematics. Prerequisite skills from the Year 11 Mathematics Advanced course will be reviewed. Study skills, problem-solving strategies, and examination techniques are also emphasised.
Other courses in this series include HSC Mathematics Preparation - Advanced (Part 1) (January), HSC Mathematics Preparation - Advanced (Part 2) (April) and HSC Mathematics Advanced - Exam Preparation Course (September). You do not need to attend all parts in order to benefit.
Learning outcomes
By the end of this course, you should be able to:
- use first and second derivatives to find stationary points, determine concavity, and locate points of inflection
- use calculus techniques to sketch a wide variety of functions by identifying their key structural features
- construct mathematical models and apply differentiation to solve real-world optimisation problems under given constraints
- model and solve rectilinear motion problems by relating displacement, velocity, and acceleration as derivatives over time
- interpret and evaluate the derivative as an instantaneous rate of change across physical, economic, and scientific contexts
- define arithmetic and geometric sequences using both recursive and explicit formulas to find specific terms
- apply the formulas for the sum of arithmetic and geometric series to model linear and exponential growth or decay
- understand the condition required for a geometric series to converge and calculate its limiting sum
- recognise pattern characteristics in abstract and practical scenarios to select and deploy the correct sequence model
- calculate the future and present value of single investments and depreciating assets using compound interest frameworks
- define an annuity and use geometric series to derive and calculate its value over regular intervals
- model reducing-balance loans using recurrence relations to track and analyse the outstanding balance over time
- calculate loan repayments, evaluate total interest paid, and determine the financial impact of changing payment frequencies.
Content
The following topics from the Mathematics Advanced HSC (2024) syllabus will be covered:
- Applications of calculus
- Sequences and series
- Financial mathematics
Prerequisites
Students should have completed the Year 11 Mathematics Advanced course before undertaking this course.
Who this course is for
This course is suitable for students studying Year 12 Mathematics Advanced.
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. Past HSC exam-style questions will be explored and completed both individually and collaboratively in groups.
Materials
You will receive electronic copies of the following:
- a course booklet including theory and worked examples, covering all syllabus dot points from the relevant topics
- solutions to all questions in the course booklet
- a selection of relevant past examination questions from the previous mathematics course, as well as from other educational jurisdictions, with sample answers.
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.
