Course summary

This course is the third 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 3 include Introduction to Vectors (Applications to Motion) and The Binomial Distribution and Sampling Distribution of the Mean. 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 2) (April) 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:

• use 2D vectors to solve problems involving motion in two dimensions
• represent the motion of a projectile using vectors
• solve problems relating to the path of a projectile in which the initial velocity and/or angle of projection may be unknown, in a variety of contexts
• solve practical problems involving Bernoulli random variables
• solve practical problems involving binomial distributions and binomial probabilities
• apply the central limit theorem to estimate the probability that the sample mean lies within given bounds.

Content

• Describing the changing positions of an object by expressing its vector as a function of time
• Finding the velocity and acceleration vectors of an object using differential calculus
• Finding the position and velocity vector of an object using integral calculus
• Solving motion problems involving constant and non-constant velocity using vectors
• The horizontal and vertical equations of motion of a projectile
• The features of the flight of a projectile, including time of flight, maximum height, range, instantaneous velocity and impact velocity
• Bernoulli random variables and representing binomial experiments as a fixed number of Bernoulli trials
• The mean and variance of a binomial distribution
• Calculating the expected frequencies of the various possible outcomes from a binomial experiment
• The relationship between a population and a sample, and the role of sampling in gathering information about a population
• Finding the mean and variance of the sampling distribution of the mean
• The Central Limit Theorem. 

Prerequisites

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

Who this course is for

This course is suitable for students 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 carefully graded, and students 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.