Study Guide For 2/3 Unit HSC Maths

HSC Maths help, tutorials and quizzes for harder HSC maths.

Improve your performance at HSC Maths. Give yourself access to simple and effective methods to improve your marks and confidence.

Maths Coach is designed from the ground up for interactive learning.

Check your knowledge as you go. All you need to do is work through the Guided Examples. Because the next step is initially hidden from you it will be obvious whether you know the topic.

Students

Have you ever sat through a maths lesson, followed each step of the argument, and yet at the end felt you did not understand what it was about? If so, you have experienced a feeling common to most mathematics students. This is because

Learning Maths Is Different.

The first difference is that mathematical knowledge is cumulative - being able to master one topic often depends on your knowlege of a previous topic. The second difference is that Mathematics is not just a collection of facts you need to memorise. You need to be able to apply those facts. This is very much like learning a foreign language. It's not a coincidence that students from Non-English speaking backgrounds perform relatively better at maths.

When most people think of remote maths help they are asking the question: What's on the Internet that you can use to teach maths? The answer everyone comes up with is videos and PDFs. But that's an answer to the wrong question.

We started with the question: What do students need to do to learn Maths? The unsurprising answer is they need to

1. Learn the facts, and
2. Learn how to work the problems.

The two most effective learning methods are:

1. Interactive Worked Examples for learning how to work the problems, and
2. Flashcards for learning the facts.

Craig Barton's 'How I wish I Had Taught Maths' devotes zero space to the benefits of videos. That's right, zero.

New 2024 Edition

The latest update includes:

• Enhanced Guided Examples - most guided examples now come with a final section which challenges the student to work through a problem very similar to the one explained. This provides instant reinforcement of the ideas covered in the example.
• Lessons now include Active Reading Points. An Active Reading Point is a point in the lesson where the student is prompted to stop reading, pick up a pen and write out the response to a question. Read more about Active Reading Points below.
• A new course - Victoria QCE Mathematical Methods course is now available for Victorian students.

Proven Methods

Terence Tao, a Fields Medal winning mathematician is a fan of multiple choice questions for testing certain types of mathematical knowledge. This site's Flashcards feature does just that.

Barbara Oakley's 'A Mind For Numbers', summarises the current state of knowledge of the psychology and methods for learning Maths and Science subjects.

The most important methods mentioned in the book have been implemented as tools on this site. The chapters on chunking are especially relevant. The book gives you the 'what'. This site also gives you the 'how'.

Guided Examples

Maths Coach's Guided Example technology has been developed to mimic the interaction between student and tutor.

Your text book can't do this.

To see examples of the process and work through some yourself, click on the Samples link below. Each sample presents topic content and a link to the associated guided examples.

 

Samples

 

Guided Examples are a very effective way to increase your problem solving confidence.

There is another benefit of Guided Examples. Using worked solutions, it is natural to sneak a peek at the next line (we all do it). But this only increases your dependence on worked solutions. On the other hand, working a problem without a worked solution can be very frustrating, especially if you make a mistake in the first step. Guided Examples are a compromise between completely visible worked solutions and none at all.

The single most effective thing you can do to improve your marks is to work through Math Coach's Guided Examples.

Active Reading Points

Active Reading Points are designed to dissuade students from engaging in that widely used (but useless) study technique of staring at / rereading the page in the hope that something will click. They also help to keep you focused on the lesson.

Active Reading Points are indicated by a icon.

How To ...

The How to ... feature will show you how to perform a particular task. You start by selecting a task from a list.

This will take you to generally two or more example problems for the selected task. If you're still lost you can click to view the lesson that discusses that task.

To see the complete list of tasks, click on the How To link below.

 

How To ...

 

For the 2 Unit course there are more than 180 tasks. For the 3 Unit course there are an additional 90 or more tasks.

 

 

Flashcards to Practise Learning Formulas

There is no getting around the fact that you need to have a large number of formulas, definitions and facts at your fingertips if you intend to do well. Craig Barton's 'How I wish I Had Taught Maths' spends a chapter and more on the benefits of well designed multiple choice questions. The reason is simple:

Recall supercharges your learning.

To test your knowledge of course facts, click on the Cards link below.

 

Cards

 

Open Ended Questions (OEQs)

OEQs explore facts about a topic that don't fit into a worked example format.

Many questions will not have a single 'correct' answer. For example, you may be asked to provide examples of a mathematical object having specified properties. Sometimes no answer is provided.

Some questions will ask you to find the error in a sequence of statements. Other questions ask you to explain a result. This means you should make a written explanation which in most cases will be more than a single sentence.

Test Your Exam Readiness

Test your knowledge under exam conditions. The Test feature gives you random selections of a specified number of questions over a specified selection of topics. Sort of like the Cards tool but with worked examples.

An Effective Tutor's Aid

If you are a tutor the tools on this site will increase your teaching effectiveness. Students can learn the the mechanics of the problems relating to a topic by working through the guided examples on their own.

Which means you can spend more time working to improve the competence and confidence of your students.

Need Year 10 Maths Help?

If students need help with year 10 Maths, you can go to AC Maths.

14 Day Free Trial

Go to the Contact Us page, type the phrase 'Free Trial' and provide your name, a valid email address and the course you are studying. We'll get back to you with a trial login. No credit card required.

12 Months Access for $39.95

Get 12 months access for a one off payment of $39.95

An Easier Way To Learn HSC Maths.

Get the help your text book doesn't give you. Upgrade to Interactive Learning.