# Beginner’s Guide to Year 11 Maths Extension 1

In this Guide, we're going to give you the lowdown on all the topics in Year 11 Extension 1 Maths so you have the foundations for an E4 in Year 12!

Need help acing Maths Extension 1? Struggling with some of the difficult concepts in Extension Maths? Don’t worry, you’re not alone! This Beginner’s Guide to Year 11 Maths Extension 1 will explain those difficult concepts in clear terms to help you lay strong foundations for Year 12!

## All about the Beginner’s Guide to Year 11 Maths Extension 1

Now that the new syllabus for the HSC has commenced, it’s essential that students build on their foundational knowledge from Years 7-10 and grow that knowledge moving forwards in Year 11. This will become an indispensable base for students as they progress into Year 12.

This Guide identifies the skills you need to master the Year 11 Maths Extension 1 HSC content, whilst also breaking down the different topics accessible and clear theory.

We’ve written this guide to help students navigate the new syllabus changes surrounding the Year 11 Mathematics Extension 1 topic and assist their preparation for their Year 11 exams.

## What’s in this Extension 1 Maths Guide?

### 1. Further Functions and Relations

1. Functions and Relations
2. Non-Linear Functions
3. Absolute Values and Inequalities
4. Polynomials
5. Parametric forms

### 2. Trigonometric Functions

1. Trigonometry and Inverse Trigonometry

### 3. Calculus

1. Introductory calculus
2. Rates of change
3. Applications of calculus

### 4. Exponentials and Logarithms

1. Applications
2. Exponentials and Logarithms
3. Motion in a straight line
4. Rates of change

### 6. Probability

1. Combinatorics
2. The pigeonhole principle
3. Binomial Expansions

## How will this Guide help me?

• 2020 is the first year which contains the new syllabus materials and content. Our goal in this article is to create clarity around the new areas of the new syllabus topics like Conditional Probability and provide challenging questions that will help prepare students for their HSC.
• In essence, your goal is to perform well in the HSC. to that end, this Guide contains the information and advice you need to equip yourself to prepare for the HSC.
• As we believe this will be beneficial to understanding Mathematics rather than just a list of steps, we examine the concepts behind the questions rather than pure calculations. This approach is the philosophy behind our Matrix method for Maths.

## What are some common student learning difficulties?

In Year 11 Maths Extension 1, students encounter the following Mathematical weaknesses:

• A poor understanding of Algebra. Students who have a poor understanding of Algebra will severely struggle with the topics explored in Year 11 Extension 1 Mathematics.

For example: Find the solutions of $$x$$ for the following quadratic equation:

$$y=x^2-6x-16$$.

Students would struggle with this question as many are familiar with factorising but are unfamiliar with the other methods like completing the square or quadratic formula which need to be applied in order to successfully solve the question.

• Inability to link concepts together. A lack of conceptual understanding of the various topics explored in Mathematics Extension 1 will eliminate a student’s ability to tackle questions involving multiple concepts.

For example: Find the values of $$m$$ for which the graph of the parabola $$y=x^2+5mx+m$$ is always above the $$x$$ – axis.

In this question, it’s important a student has a good conceptual understanding on the link between the discriminant and the parabola and solving quadratic inequalities. Without a good conceptual understanding, students would assume that “above the $$x$$ – axis” translates to solving the discriminant greater than zero rather than below zero.

• Students struggle to communicate properly the topics learnt, which is a reflection of rote learning and lack of conceptual understanding
• Unable to do difficult questions. Many students see a difficult question and give up without considering how to approach it. This doesn’t grow confidence and certainly won’t enable students to do later questions in the HSC paper!

## What do Band 6 students do differently?

• Have a good algebraic understanding. Rather than pushing through the Year 11 and 12 topics, band 6 students tend to have an awareness of their weaknesses and go back to previous years and practise their algebraic skills.
• Keep a logbook of mistakes. Many students enjoy practising questions, but when they reach a question too difficult to solve they skip it and do a question they can solve.

Outside of exam conditions, you have the freedom to do this but within an exam, it would be unwise to simply skip a question. To combat this, keep a logbook of all questions you are unable to do, and make the time to figure out how to answer it.
• Consistently give yourself feedback. How can you expect to improve if you don’t check your answers and don’t know where you went wrong? Keep a logbook of all questions you get incorrect, and make clear to yourself how you can correct it.

Remember this is year 11. You have plenty of time to formulate new and healthy habits which will ensure fewer mistakes.
• Be inquisitive. Ask questions about things you don’t understand! Remember, the better you understand a concept in mathematics, the easier it is to solve questions and remember the steps.
• Be disciplined. Consistently set aside time to understand one concept. Make it your mission to chip away at it.
• Communicate what you understand. Learn to explain to your peers how to do a question. It will help you remember and understand as well. It will also reveal to you things you don’t completely understand.

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