The Beginner’s Guide to Year 10 Maths

Welcome to our Beginner's Guide to Acing Year 10 Maths. In this Guide, we're going to walk you through the core subjects of Year 10 Maths with easy to follow overviews and concept checks where you can test your knowledge and skills.

guide-maths-year-10-beginners-guide-to-year-10-maths-overview-banner-e-Fixed Mobile Banners

All about the Beginner’s Guide to Year 10 Maths

The Beginner’s Guide to Year 10 Maths is your trusted Guide for acing Year 10 Maths. Year 10 is an important year for Maths students. Students in Year Maths consolidate their learning and begin acquiring the advanced knowledge and skills they will need for 2 Unit maths and beyond.

The concepts and skills learned in Year 10 prepare students for the complex and rigorous ideas they will encounter in Years 11 and 12. Students who fall behind in Year 10 have a difficult time catching back up.

We wrote the Beginner’s Guide to Year 10 Maths to help students get the right foundations before they start Year 11 and Stage 6.

Each of these articles in the Beginner’s Guide addresses the NSW Syllabus Outcomes. A complete list of these Outcomes can be found here on the NESA website.

What’s in this Guide?

1. Quadratic Equations

2. Probability

3. Trigonometric Ratios

4. Further Trigonometry

5. Non-Linear Equations (Curve Sketching)

6. Functions

7. Logarithms


How will this Guide help me?

In this guide, each article will explain the theory to you and show you how to apply it.

Throughout each article, we’ve provided some worked examples so that you can see how to apply the theory. We’ve also provided a number of questions for each subject. These will let you test your knowledge.

Finally, we’ve provided you with worked solutions so that you can check your skills and understand your mistakes.

Developing a strong understanding of the theory is the first step in our Matrix Method for MathsTM .


The Matrix Method for Maths is our proven process to ensure you develop knowledge and skills.
Step Matrix Method
1 Theory Developing a thorough understanding of concepts is the first step to mastering Maths. Learn from Matrix Theory Books that are carefully structured to help you understand even the most complex stuff!
2 Application Memorising formulas will only get you so far. Consolidate your understanding by learning how to apply concepts and techniques to solve problems.
3 Examples Work through examples that will actually be in your exam. You’ll learn how to present your solution for maximum marks in exams.
4 Concept Checks Learn the most efficient problem solving techniques with different types of exam-style questions.
5 Workbook Practice sharpening your skills with hundreds of exam-style questions. It’s important to keep practising as this is the only way to find the right balance between speed and accuracy.
6 Quiz and Feedback Weekly quizzes and feedback provide you with opportunities to identify your gaps and address them ASAP.
7 Topic Test Working under exam conditions will boost your confidence for the real thing. Learn from your mistakes and fill your gaps so you are continually improving.

What are the common issues faced by Year 10 students?

Some common problems that students face are:

  • Difficulty solving quadratic equations (Monic and Non-Monic) because they don’t understand the Year 9 factorisation techniques.

For example: Find the \(x\) – intercepts of the parabola \(y=x^2+6x+5\).

Unless students know how to factorise, there is no way of finding the \(x\) – intercepts of this equation. They must make sure the equation is in the form \(0=(x+5)(x+1)\) before finding the \(x\) – intercepts.

  • Difficulty applying basic trigonometric concepts to harder applications, such as 3D Trigonometry. This has always been a topic that students struggle with as it is an entirely new concept with many types of functions introduced at the same time.
  • Students also struggle with visualising trigonometric problems.
  • Difficulty representing bearing problems as diagrams because of the language used in the question.
  • Students also struggle to understand the relevance and importance of related angles.
  • Students who struggle with solving simple quadratic equations (Polynomial Degree 2) will usually find it difficult to cope with Polynomials with higher degrees.
  • Understanding the concept of logarithms being related to indices. This is particularly true of students who struggle with the fundamentals.

For example: Solve the equation \(3^x=12\)

Students must be able to manipulate this equation into logarithmic form in order to find the value of \(x\).

The answer would be \(x=log_312\)

Why do students struggle with Maths in Year 10?

Many students struggle in Year 10 Maths because they take the wrong approach to learning. Mathematics requires the application of logic, not rote learning.

Here are some of the common reasons we’ve found that students struggle:

  • Students fail to read questions carefully – When presented with complex questions they are left confused with what steps to take.
  • Students should not rote learn trigonometry – Instead, they need to understand what each trigonometric ratios means and how they are derived.
  • Students do not clarify their problems when doubts arise – This only piles up to more problems that are left unresolved. When students have difficulty, they should ask questions early so they don’t fall behind.
  • Students don’t see the real life applications of the concepts taught. When students don’t see the relationship between Maths and real life, they begin to think that Maths is unimportant. This means that they will become unmotivated to learn Maths.

What should I do to improve my marks in Maths?

Students should set up a consistent study rhythm where they have time set aside each week for:

  • Learning theory
  • Practising methods
  • Testing themselves
  • Logging their mistakes


It is important that you keep track of your mistakes. Keeping a journal of mistakes will allow students to reflect on their errors and develop strategies to avoid making mistakes in the future.


Take your Maths to the next level

Matrix+ gives you clear and structured online lesson videos, quality resources, and forums to ask your Matrix teachers questions and for feedback, wherever you are. Learn more.

Get ahead with Matrix+ Online

Expert teachers, detailed feedback and one-to-one help. Learn at your own pace, wherever you are.

Review consistently to build your understanding

Now it is time to familiarise yourself with the content of this Guide. This is a resource that you should come back to consistently when you encounter the subjects at school during the year.

First up, we’ll look at quadratic equations in Part of this Guide.

© Matrix Education and, 2023. Unauthorised use and/or duplication of this material without express and written permission from this site’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Matrix Education and with appropriate and specific direction to the original content.


Get free study tips and resources delivered to your inbox.

Join 75,893 students who already have a head start.

Our website uses cookies to provide you with a better browsing experience. If you continue to use this site, you consent to our use of cookies. Read our cookies statement.

OK, I understand