Year 9 Maths — The Practical Guide to the Australian Curriculum

What do Year 9 learn in Maths?

Year 9 Maths students in Australia learn a broad range of new mathematical skills and knowledge. There is a significant jump in the level of difficulty from what was required in Year 8, especially in the core strands of Algebra, Measurement and Geometry.

Students are faced with new concepts in the areas of equations, financial mathematics, surface area, volume and probability (just to name a few).

The Year 9 Maths Curriculum is divided into 6 strands:

• Number

• Algebra

• Measurement

• Space

• Statistics

• Probability

Number and Algebra

These strands focus on helping students develop a deep understanding of numbers and their relationships. In Year 9, students will learn how to use advanced algebraic techniques to solve and graph linear equations as well as some simple non-linear relations. Midpoint, the distance between 2 points and finding the equation of a line are also covered in this strand.

By the end of Year 9, students must be confident in simplifying algebraic expressions, expanding brackets, factorising and applying all six index laws.

Real numbers

• Apply index laws

• Express numbers in scientific notation

• Identify direct proportion

Key skill:

• Simplifying negative indices

• Zero Index law

Money and financial mathematics

• Solve problems involving simple interest

Key skill:

• Calculating compound interest

Patterns and algebra

• Expand and factorise algebraic expressions

• Simplify algebraic expressions

Key skill:

• Use the distributive law

• Binomial expansion

• DOPS & trinomials

Linear and non-linear relationships

• Distance between 2 points

• Midpoint and gradient of a line segment

• Solving linear equations

• Sketching linear and simple non-linear graphs

Key skill:

• Find the rule from a table of values, a graph or a real-world scenario

• Intercept method and Gradient-intercept method to sketch a graph

• Point-intercept form

• Graphing parabolas and circles

Measurement and Space

The Measurement and Space strands in Year 9 Maths introduce students to a variety of new units and topics. Pythagoras' Theorem and Trig ratios are just some of the skills that students will learn this year.

Students build on their knowledge of 2D shapes from previous years to develop a greater understanding of 3D objects. New surface area and volume formulas are covered, with an emphasis on application to real-world scenarios.

Units of measurement and Shape

• Area of composite shapes

• Volume and surface area

Key skill:

• Calculate the volume and surface areas of both prisms and cylinders

Geometric reasoning

• Establish properties of similarity

• Congruence conditions (SSS, SAS, ASA and RHS)

• Scale factors and ratios

Key skill:

• Solve problems using the properties of congruency and similarity

Pythagoras and Trigonometry

• Apply Pythagoras theorem

• Trigonometric ratios of right-angled triangles

Key skill:

• Calculate unknown side lengths and angles using the 3 trigonometric ratios

• Pythagoras in 3D

Statistics and Probability

Year 9 Maths sees students learning about chance, data and statistical concepts at a higher level than ever before. They will continue to develop their ability to analyse and describe the distribution of data.

For the first time, students are introduced to advanced probability notation and terms such as 'union' and 'intersection'. Venn diagrams are also used to help students visualise these concepts.

Chance

• Identify complementary and independent events

• Two-step experiments with tree diagrams and arrays

• Calculate probabilities involving 'and' & 'or'

Key skill:

• Fluency in the language of probability ('at least', 'or', 'and' & 'mutually exclusive')

• Convert a Venn diagram into a two-way table (and vice versa)

Data representation and interpretation

• Compare a range of data types

• Describe data as skewed, bi-modal or symmetrical

• Population vs Sample

• Construct frequency tables, histograms, stem-and-leaf plots and dot plots

Key skill:

• Calculate mean, median, mode and range for sets of data with decimals

• Use measures of centre to make sense of and explain data

• Understand the effect of outliers and bias in surveys

What they don't teach you at school

There's a large chunk of "optional" work in year 9 that sets the stage nicely for year 10 and beyond. Unfortunately, as schools rush through the curriculum, this work often gets neglected.

We were just as shocked as this little guy when we learnt how much gets left out!

We highly recommend all year 9 Maths students focus on the content listed below, even if their school teachers don't. You can easily find these topics under the 'extending' chapters in your year 9 maths textbook.

Under each topic, we've also shared some simple maths strategies that you can use to give yourself that competitive edge.

Financial Maths

Many schools will skim through financial maths. Make sure you take the time to understand both simple and compound interest, conceptually, as well as their formulas. Once you have a strong grasp of them, try tackling some of the harder questions in your textbook.

Whenever you try a financial problem, the best approach is to start by writing out what is given and what is unknown. This will help you to see exactly what information you have to work with and what you need to find.

Simultaneous Equations

Another topic that is often overlooked by school teachers in Year 9 Maths is simultaneous equations. This is a shame, as it is actually a really important topic that students will need to know, regardless of which VCE maths course they choose.

Aim to wrap your head around the concept first. What are simultaneous equations? Why are they useful? From here learn the methods to solve them. You must be able to use 'elimination' and 'substitution' with confidence so that you can then apply these processes to real-world examples.

The key to solving simultaneous equations is to make sure that you have two clear equations with two unknowns! If you only have one equation, then you won't be able to solve for both unknowns.

Algebraic techniques

This is where it starts to get a bit more challenging—and exciting! Algebra is the common language of maths, and being able to fluently manipulate algebraic expressions is crucial for success.

Due to limited time, many Year 9 Maths teachers will not cover these advanced modules in depth. Don't fall into this trap! Work through these at home so that you're ahead of the game for your final years of high school.

If it means copying out multiple worked examples on your own—do it. Watch youtube videos. Seek help from an online maths tutor. Make sure that you understand the following algebraic topics:

• Factorising trinomials (monic and non-monic)

• Factorising by grouping (using HCF)

• Completing the square

• Difference of perfect squares

• Algebraic fractions (simplifying and solving equations)

Trigonometry

When it comes to trigonometry, the focus in Year 9 is usually on SOHCAHTOA and learning how to use a scientific calculator to find angles and side lengths in right-angled triangles. The critical chapter which sometimes gets left out is the one on Bearings.

You must learn both compass and true bearings. These are not too difficult to master. Attempt some practice questions from your textbook and focus on word problems that require you to draw out the situation.

Surds and Fractional Indices

This is one of the most challenging areas of Year 9 Maths, but also one of the most overlooked. If you can master these concepts, you'll be well on your way to success in VCE.

To start with, make sure that you understand what a surd is and how to simplify expressions containing surds and fractional indices. You need to be able to articulate the difference between irrational and rational numbers, as well as re-write expressions as a single surd.

Quadratics

The final topic on our lists, which doesn't get enough love in year 9, is the graphing of Quadratics. This is a really important area as it will form the basis for a lot of the work you'll do later on.

You should understand what a quadratic equation is and how to solve them using the null factor law. Take your time to plot some basic quadratic graphs. Then see how various parts of the equation relate to the shape of a parabola.

Familiarise yourself with the intercept-method, the turning point form and the axis of symmetry. These concepts are essential for anyone thinking of doing maths methods.

Final Thoughts

There is a lot of ground to cover in Year 9 Maths, but don't let that overwhelm you. While it might seem like a lot of new information to take in, the Australian Curriculum is designed so that each concept builds on the last. As long as you take the time to understand the basics and master the core skills, you'll be in good shape for whatever VCE throws your way.

If you really want to fly through your final years of school, pay close attention to the 'extension' topics in each chapter. These are usually only covered in detail in later years, but if you can understand them early on you'll have a big advantage over most students.

Finally, don't forget to practise, practise, practise! If you want to learn how to get better at math, or are looking for some extra help with your studies, book a free assessment today. We'll tailor a learning plan specifically for your needs and help you make this year, your best yet!