# VCE Unit 1-2 Mathematical Methods: Polynomials

Understand and practice every type of question you will encounter in the Year 11 Unit 1-2 VCE Polynomials topic.

Students of VCE Units 1-2 Mathematical Methods – this course is for you!

What you’ll learn

• How Polynomials work.
• Algebra with Polynomials.
• Division of Polynomials.
• Factorising Polynomials.
• Factor and Remainder Theorems.
• Solving Polynomial Equations.
• Solving Inequalities.
• Sketching Polynomials.
• Sketching Cubic and Quartic Functions.
• Determining Polynomial Equations.
• Root Finding (Bisection Method).
• Applications and exam-style questions.
• Graphics CAS calculator tips.

Course Content

• Introduction –> 6 lectures • 13min.
• Polynomials Basics –> 17 lectures • 1hr 10min.
• Division of Polynomials –> 9 lectures • 1hr 10min.
• Factor and Remainder Theorems –> 7 lectures • 31min.
• Factorising Polynomials –> 7 lectures • 1hr 9min.
• Solving Polynomial Equations –> 7 lectures • 36min.
• Sketching Cubic Functions using Transformations –> 9 lectures • 48min.
• Sketching Cubic Functions using Factorisation –> 9 lectures • 1hr 6min.
• Solving Inequalities with Cubic Functions –> 5 lectures • 25min.
• Determining Cubic Equations (Families of Cubics) –> 8 lectures • 40min.
• Sketching and Understanding Quartics –> 12 lectures • 53min.
• Overall Behaviour of Polynomials –> 16 lectures • 1hr 43min.
• Root Finding with Bisection Method –> 3 lectures • 33min.
• Applications –> 16 lectures • 49min.

Requirements

Students of VCE Units 1-2 Mathematical Methods – this course is for you!

In this comprehensive course, I take you through over 120+ step-by-step worked examples of VCE Methods Unit 1-2 Polynomials questions. By the end you will be able to recognise, understand and answer any polynomial question that comes your way in homework or assessments – whether it be long division, solving, sketching or applications. I’ve included some graphics CAS calculator tips too!

120+ Bite-Sized Worked Examples

I don’t believe in teaching ‘theory’ when it comes to mathematics – only application. This is why this course has no separate theory videos. Instead, every piece of theory that you will need is explained through an illustrative example question, where you get to understand how the theory is applied in practice straight away.

With this approach, you can focus on learning how to answer problems – which is what you get assessed on in VCE Methods. After all, you’re not tested on theory but your actual ability to do the questions, right? The purpose of this course is to give you the tools to do just that.

The best thing about maths is that you can learn how to do a ‘type’ of question by understanding just one single example. If you can break one example down into the individual steps, you can then apply these same steps to any similar question – even if the context, numbers or equation is different. This is exactly the study strategy I used to nail my VCE Mathematical Methods and Specialist Maths exams and achieve a 99.70 ATAR.

So what’s the formula to success in maths?

1. Watch and understand the steps involved in an example problem.
2. Practice applying the steps on your own to similar questions.
3. Repeat for every type of question.

Let’s look at each of these one-by-one.

Step 1. Watch and understand the steps involved in an example problem.

This is taken care for you by the course videos! I’ve been tutoring these kinds of maths questions for over 5 years and I’ve learned a lot along the way – including ways that my students tend to understand explanations best, and the kinds of common mistakes they make in their understanding along the way. In this course, I demonstrate and explain the steps to each problem like I would be tutoring them. I might be biased, but I think self-paced study through a good video course can be a more effective solution than tutoring. Not only is it more convenient, but you can also always come back to the examples whenever you need them – even during that last-minute cram at midnight!

Step 2. Practice applying the steps on your own to similar questions.

This is where you come in – it’s time to do some independent study! In the course notes, I direct you to some relevant example questions from the VCE Unit 1&2 Methods Cambridge Textbook. If you want to succeed, do not skip out on this step!

Step 3. Repeat for every type of question in the topic.

Great news! This course takes care of making sure that you revise each question type and don’t miss anything. It thoroughly brings together a collection of the main types of questions I’ve seen in VCE Methods Unit 1-2 Polynomials homework, textbooks, tests, SACs and exams. You can use the course structure as a ‘checklist’ to make sure you’ve fully covered the Polynomials topic!

And that’s it! Once you can understand the examples covered in this course, I’m confident that you will be able to answer almost every polynomials question at Year 11 VCE level (and even get a head start on a large proportion of the Year 12 polynomials curriculum as well). All it takes is a bit of your time to watch and practice the examples.

Isn’t that too much work…?

I know that VCE is a stressful and busy time. I know you will likely have other subjects to think about too – trust me, I’ve also been there! With this in mind, I tried my best to ensure that all of the videos are as bite-sized as possible. Most are only a few minutes long!

And here is another really helpful tip: you don’t actually have to watch every single part of this course! You are free to jump around the content, or double the speed 😉 You can look into the course curriculum to find out which question types you are struggling with, and just work through those ones first (exactly like how you might come to a tutor and ask for help with a particular question)! In the Introduction section I’ve included some printable course materials and useful tips about how to optimally use your study time and get the most out of this course.

Disclaimer

VCE® is a registered trademark of the VCAA. The VCAA does not endorse or make any warranties regarding this study resource. Past VCE exams and related content can be accessed directly at the official VCAA website.

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