Course summary
This course is the second 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 Integral Calculus and Random Variables. Prerequisite skills from the Mathematics Advanced Preliminary course will also 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 3) (July) 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:
- define a primitive function and recognise that integration is the reverse process of differentiation
- determine primitive functions (indefinite integrals) of polynomial, exponential, logarithmic and trigonometric functions, including composite functions using substitution
- apply the rules of integration, including the sum, scalar multiple and reverse chain rule, to find indefinite integrals of a variety of functions
- find a specific primitive function given an initial condition, by determining the constant of integration
- interpret the definite integral as the limit of a sum and connect it to the area under a curve using the Fundamental Theorem of Calculus
- evaluate definite integrals using primitive functions and apply the Fundamental Theorem of Calculus to solve problems
- calculate areas of regions bounded by curves and the x-axis or y-axis, including cases where the function changes sign over the interval
- use symmetry properties of even and odd functions to simplify integration problems
- apply numerical methods, including the trapezoidal rule, to approximate the value of definite integrals
- model and solve practical problems involving integration, including finding areas bounded by two curves or a curve and the coordinate axes
- define and interpret a discrete random variable and its probability distribution, including calculating expected value, variance and standard deviation
- construct and use probability distributions for discrete random variables in tabular and graphical form to solve problems
- distinguish between discrete and continuous random variables, and explain why the probability of a continuous random variable taking any specific value is zero
- define and apply the cumulative distribution function (CDF) and probability density function (PDF) for continuous random variables
- verify that a function satisfies the properties required of a probability density function and use it to calculate probabilities over given intervals
- calculate the expected value (mean) and variance of a continuous random variable using integration of the probability density function
- identify the normal distribution as a continuous probability distribution and recognise its bell-shaped curve, symmetry about the mean, and the relationship between mean, median and mode.
Content
The following topics from the Mathematics Advanced HSC (2024) syllabus will be covered:
- Integral calculus
- Random variables
Prerequisites
Students should have completed the Year 11 Mathematics Advanced Preliminary course before undertaking this course.
Who this course is for
This course is suitable for students studying Year 12 HSC 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 previous mathematics courses, as well as from other educational jurisdictions, with sample answers provided.
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.
