NOTE: Follow this link to understand the Australian Curriculum maths content for year 9 for all maths strands.
The additional resources located further down the page take the student on a journey through the Australian year 9 maths curriculum. I have split the resources out using the following textbook’s index as it is widely used throughout schools in Australia and is excellent.
Essential Mathematics for the Australian Curriculum 9
Third Edition
(They now have a fourth edition.)
The textbook, Essential Mathematics for the Australian Curriculum 9, is being used by many schools across Australia and I have found it to be an excellent resource. It can be purchased directly from the Cambridge Education website or through school booklists. If you buy the full textbook package, you will receive a print version, a downloadable offline version, and an interactive version powered by Cambridge’s HOTmaths tool. (At the time of writing, you get 12 months’ access to the nonprint resources designed to correspond to a year of schooling). IMPORTANTLY, the additional interactive resources give you access to online exercises with answers, walkthroughs and quizzes, and other supporting material. Often, schools don’t emphasise this so make sure you login using your special code that is located inside the front cover of your textbook and use the extra features. They could be the difference between an A or a B. Even if your school does not use this textbook, if you buy it yourself (for little more than the price of a couple of hours tutoring) you get many resources to help you excel in maths.
One of the key features of the Cambridge Essential Maths series is that they break out the key ideas of each chapter learning sequence into a simple summary box. Here is an example:
You should pay attention to these. Additionally, at the end of each chapter, they provide a chapter summary which is a onepage flow chart effectively summarising the above key ideas. I recommend you print them out in colour, laminate, and post them to a pinup board where you study. A snippet of the top of one is here.
As time permits, I will add links to instructional pages and videos including worked examples and practice worksheets with solutions as additional resources against the textbook’s learning sequence. The information below builds on the already fabulous resource with even more assistance. Importantly, with links to video instruction, combined with the textbook and the other resources below, you can effectively selflearn the entire year 9 content or use it to consolidate areas of content you may not have completely understood.
Chapter 1 Reviewing number and financial mathematics
1A Integer operations CONSOLIDATING
 Instruction: Video – What are integers? (2.3 mins) by Infinity Learn NEET.
 Instruction and examples: Video – Multiplying positive and negative number rules (2.5 mins) by Mr. Colin Dodds [For two numbers, if signs are different, answer is negative and if the signs are the same, the answer is positive.]
 Instruction and examples: Video – A Trick for Adding and Subtracting Negative Numbers (2 mins) by LearnFree.
 Instruction and examples: Video – What are square numbers? (2.33 mins) by Mr Bletcher Education.
 Instruction and examples: Video – How to cube a number (3.4 mins) by Math with Mr. J.
 Instruction and examples: Video – Square roots and cube roots (5 mins) by Math with Mr. J.
 Instruction: Video – What is a prime number? What are prime numbers used for? (1.8 mins) by Eye on Tech.
 Instruction: Video – Difference between prime and composite numbers (2.3 mins) by MooMooMath and Science.
 Instruction and examples: Video – Prime factorisation (6 mins) by 1st Class Maths.
 Instruction and examples: Video – Highest Common Factors (HCF), Lowest Common Multiple (LCM) and Primes (16 mins) by 1st Class Maths.
 Instruction and examples: Video – Order of operations explained. (4.75 mins) by Minity Maths.
 Instruction and examples: Video – How to evaluate expressions by substituting (5.5 mins) by Math with Mr J.
 Practice: Worksheets with answers: Web Page – Adding/Subtracting positive/negative integer worksheet generator by Mathaids.com
 Practice: Worksheets with answers: Web Page – LCM/HCF worksheet generator by Mathaids.com.
 Practice: Worksheets with answers: Web Page – Evaluating expressions using substitution worksheet generator by Mathaids.com.
 Practice: Worksheets with answers: Web Page – Operations with Perfect Squares and Cubes worksheet generator by Mathaids.com.
1B Decimals and significant figures
 Instruction and examples: Video – How to Round Decimals (6.5 mins) by Math with Mr. J.
 Instruction and examples: Video – How to Round Numbers to Significant Figures (5.25 mins) by Cognito.
 Practice: Worksheets with answers: Web Page – Rounding decimals by Mathaids.com.
 Practice: Worksheets with answers: Web Page – Links to various significant figures worksheet generators by Mathaids.com.
1C Rational numbers CONSOLIDATING
 Instruction and examples: Video – Rational, Irrational and Real Numbers (4.5 mins) by Let’s Do Math.
 Instruction and examples: Video – Simplifying Fractions (3.5 mins) by The Organic Chemistry Tutor.
 Instruction and examples: Video – Simplifying fractions using prime factorisation (3.3 mins) by Susan Warren.
 Instruction and examples: Video – Converting Base10 Fractions (fractions with a denominator of 10ths) (7 mins) by mathantics.
 Instruction and examples: Video – How to convert fractions to decimals using long division (8 mins) by The Organic Chemistry Tutor. This will work with any fraction.
 Alternate instruction and examples: Video – Convert any fraction to a decimal (6.75 mins) by Math Antics.
 Instruction and examples: Video – Comparing fractions with common denominators. (3 mins) by Maggie Bell Teaching.
 Practice: Worksheets with answers: Web Page – Adding and Subtracting Rational Numbers Worksheets by Mathaids.com.
 Practice: Worksheets with answers: Web Page – Converting between fractions and decimals worksheet generator by Mathaids.com.
 Practice: Worksheets with answers: Web Page – Convert decimal to fractions worksheets by K5 Learning.
 Practice: Worksheets with answers: Web Page – Links to various fraction worksheet generators by Mathaids.com.
 Practice: Worksheets with answers: Web Page – Rational and irrational number worksheets by Cuemath.
1D Operations with fractions CONSOLIDATING
 Instruction and examples: Video – Fraction overview (14 mins) by TabletClass Math.
 Instruction and examples: Video – Fraction review (7.25 mins) by Math with Mr J.
 Instruction and examples: Video – Why Do We Flip the Second Fraction & Multiply to Divide Fractions? (4.2 mins) by Midnight Math Tutor.
 Alternate Instruction and examples: Video – The Magic Behind Flipping Numbers When Dividing Fractions (2.5 mins) by Jason Walker.
 Instruction and examples: Video – How to Multiply and Divide Mixed Numbers (6.5 mins) by Math with Mr J.
 Practice: Worksheets with answers: Web Page – Links to various fraction worksheet generators by Mathaids.com.
1E Ratios, rates and best buys CONSOLIDATING
These areas of maths are some of the most practical you will learn as you will use them almost daily in real life.
 Instruction and examples: Video – Ratios, Rates, and Best Buys (14.25 mins) by Angles and Acid.
 Alternate Instruction and examples: Video – Ratios, Rates, and Best Buys (11.2 mins) by Darren Lam.
 Alternate Instruction and examples: Video – Ratios, Rates, and Best Buys (10.2 mins) by MysterE.
 Practice: Worksheets with answers: Web Page – Ratio Worksheets by Mathaids.com.
 Practice: Worksheets with answers: Web Page – This ratios and rates worksheet generator will produce problems where the students must write simple fractions, rates, and unit rates from word phrases by Mathaids.com.
 Practice: Worksheets with answers: Web Page – This worksheet generator will produce problems where the students must write rates and unit rates from word phrases by Mathaids.com.
 Practice: Worksheets with answers: Web Page – Dividing in a given ratio worksheet generator by Worksheet Math.
 Practice: Worksheets with answers: PDF – Best buys examstyle questions by Corbett Maths. Here are the answers.
1F Percentages and money CONSOLIDATING
 Instruction and examples: Video – Converting Between Fractions, Decimals, and Percentages (5.33 mina) by Professor Dave Explains.
 Instruction and examples: Video – Percentages and money (8.7 mins) by MysterE.
 Worked examples: Video – Percentages & money (5.5 mins) by Chris Burcin.
 Instruction and examples: Video – How to Express One Number as a Percentage of Another (5 mins) by Cognito.
 Instruction and examples: Video – Solving percentage problems with the unitary method (5.25 mins) by Scott Smith.
 Practice: Worksheets with answers: Web Page – Converting between percents, decimals, and fractions worksheet generator by Mathaids.com.
 Instruction and Practice: Worksheets with answers: Web Page – Expressing one number as a percentage of another by RadfordMathematics.com
 Practice: Worksheets with answers: Web Page – Percent of an amount list of worksheets by Mr Barton Maths.
 Practice: Worksheets with answers: Web Page – Percentage Worksheets by Math Salamanders.
 Practice: Worksheets with answers: Web Page – All sorts of percentage type worksheets by MathDrills.com.
1G Percentage increase and decrease CONSOLIDATING
 Instruction with examples: Video – Percentage Increase and Decrease (Multiplier Method) (7.33 mins) by Cognito.
 Instruction and examples: Video – Percentage Increase/Decrease (1 of 2: The Potato Paradox) (7.5 mins) by Eddie Woo.
 Instruction and examples: Video – Percentage Increase/Decrease (2 of 2: Example question) (7.5 mins) by Eddie Woo.
 Instruction and examples: Video – How to Calculate Percentage Change (Increase or Decrease) (4 mins) by Cognito.
 Instruction and examples: Video – Reverse Percentages – Calculating The Cost Before The Discount (8.25 mins) by Cognito.
 Instruction, examples and practice: Web page – Reverse percentages – finding the original amount by Third Space Learning.
 Practice: Worksheets with answers: PDF – Increasing/decreasing by a percentage worksheet by Corbett Maths. Here are the answers.
 Practice: Worksheets with answers: PDF – Exam style percentage change by Corbett Maths. Here are the answers.
 Practice: Worksheets with answers: Web Page – Finding the original after a percentage change by StudyMaths.co.uk.
1H Profits and discounts
Another area of maths that is very practical: profits, discounts, selling price and markup is something you really need to understand. Don’t memorise, try to understand.
 Instruction: Video – What is profit? (1 min) by StudentForce.
 Instruction: Video – Discount and selling price (1.7 mins) by Homeschool Flashcards.
 Instruction: Video – What is markup? (3 mins) by Two Teachers.
 Instruction with worked examples: Video – How to Find Selling Price – Easy Trick – With Cost Price and Markup (4.75 mins) by Sam Tube.
 Instruction with worked examples: Video – Markup examples (5.75 mins) by Joshua Emmanuel.
 Instruction with worked examples: Video – Markup and Markdown + Solved Problems (6 mins) by Joshua Emmanuel.
 Instruction with worked examples: Video – Find cost if selling price and percent markup is given (5 mins) by Anil Kumar.
 Instruction, examples and practice: Web Page – Financial decisions by Mathspace.
 Practice: Worksheets with answers: Web Page – Various profit and loss worksheets by Math Worksheet 4 Kids.
 Practice: Worksheets with answers: PDF – Calculating sales price, cost of sales, markup and profit by EdUpStairs. (R stands for the South African Rand currency.)
1l Income and taxation
 Instruction: Video – Getting paid in Australia – calculating salary (4.2 mins) by Joel Speranza Math.
 Instruction: Video – Getting paid in Australia: calculating wages, overtime, penalty rates and more (9 mins) by Joel Speranza Math.
 Instruction: Video – Getting paid in Australia: commission (5 mins) by Joel Speranza Math.
 Instruction: Video – Gross income versus net income. (1.4 mins) by One Minute Economics.
 Instruction: Video – Australian income tax (5.25 mins) by Jason de Nys.
 Instruction with examples: Video – Payasyougo (PAYG) taxation in Australia and how to calculate taxable income. (14 mins) by Miss D Maths.
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 Practice: Worksheets with answers: Web Page –
 Practice: Worksheets with answers: PDF –
1J Simple interest
 Instruction: Video –
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 Instruction and examples: Video –
 Practice: Worksheets with answers: Web Page –
 Practice: Worksheets with answers: PDF –
1K Compound interest EXTENDING
 Instruction: Video –
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 Instruction and examples: Video –
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 Practice: Worksheets with answers: Web Page –
 Practice: Worksheets with answers: PDF –
Chapter 2 – Linear and simultaneous equations
2A Algebraic expressions CONSOLIDATING
 Instruction and examples: Video –
 Instruction and examples: Video –
 Instruction and examples: Video –
 Practice: Worksheets with answers:PDF –
 Practice: Worksheets with answers:PDF –
2B Simplifying algebraic expressions
2C Expanding algebraic expressions
2D Solving linear equations
2E Equations with brackets and pronumerals on both sides
2F Solving word problems
2G Inequalities
2H Using formulas
2I Simultaneous equations using substitution EXTENDING
2J Simultaneous equations using elimination EXTENDING
2K Applications of simultaneous equations EXTENDING
Chapter 3 – Pythagoras’ theorem and trigonometry
3A Pythagoras’ theorem
 Instruction and examples: Video –
 Instruction and examples: Video –
 Instruction and examples: Video –
 Practice: Worksheets with answers:PDF –
 Practice: Worksheets with answers:PDF –
3B Finding the length of the shorter sides
3C Applying Pythagoras’ theorem
3D Pythagoras in three dimensions EXTENDING
3E Trigonometric ratios
3F Finding side lengths
3G Solving for the denominator
3H Finding an angle
3I Applying trigonometry EXTENDING
3J Bearings EXTENDING
Chapter 4 – Linear relations
4A Introduction to linear relations CONSOLIDATING
 Instruction and examples: Video –
 Instruction and examples: Video –
 Instruction and examples: Video –
 Practice: Worksheets with answers:PDF –
 Practice: Worksheets with answers:PDF –
4B Graphing straight lines using intercepts
4C Lines with one intercept
4D Gradient
4E Gradient and direct proportion
4F Gradient–intercept form
4G Finding the equation of a line
4H Midpoint and length of a line segment
4I Perpendicular and parallel lines EXTENDING
4J Linear modelling
4K Graphical solutions to simultaneous equations
Chapter 5 – Measurement
5A Length and perimeter CONSOLIDATING
The following diagram is useful when converting between length units:
 Instruction and examples: Video – Perimeter – year 9 – and examples (14.5 mins) by Maffsguru.
 Instruction and examples: Video – Tick marks in geometry (3.6 mins) by Shigehito Tanaka.
 Instruction and examples: Web Page – Perimeter Of Compound Shapes by Third Space Learning.
 Practice: Worksheets with answers: Web Page – Area and perimeter of complex shapes by MathDrills.com.
 Practice: Worksheets with answers: Web Page – Area and perimeter of complex shapes by K5 Learning.
5B Circumference and perimeter of a sector
 Instruction: Video – How did pi get discovered? (9 mins) by Shoo Rayner Drawing.
 Instruction and examples: Video – How to Calculate the Circumference of a Circle (1 min) by WikiHow.
 Instruction and examples: Video – Year 9 5B Circumference of a circle and perimeter of a sector (6.75 mins) by Jayme Rafferty.
 Worked examples: Video – Circumference and perimeter of sectors (Approx 6 mins) by Ms Crawford.
 Worked example: Video – Perimeter of Sector Quick Question (2 mins) by Hegarty Maths.
 Practice: Worksheets with answers: Web Page – Arc length and perimeter by Maths4Everyone.com.
5C Area
 Instruction and examples: Video – Area Video for Kids: Finding the Square Measurement of a Space (3.2 mins) by Star Toaster.
 Instruction and examples: Video – Area of a sector (4.25 mins) by Ms. Smith’s Math Tutorials. Year 9 focuses on using degrees generally so the radians part of this video is only relevant if your teacher has been discussing using radians.
 Instruction and examples: Web Page: Area of sectors by Third Space Learning.
 Instruction and examples: Video – Area of a Rectangle, Triangle, Circle & Sector, Trapezoid, Square, Parallelogram, Rhombus, Geometry (20.5 mins) by The Organic Chemistry Tutor.
 Worked example: Video – Area of a sector given a central angle  Circles (2.5 mins ) by Khan Academy.
 Worked examples: Video – Area of 2 Dimensional (2D)Shapes (12 mins) by Visual Learning Portal.
 Formulae: Sheet – 2D shape area formulae sheet by Cazoom Maths.
 Practice: Worksheets with answers: PDF – Area, arc length and perimeter of sectors of circles by TES. (Needs a free login set up.
 Practice: Worksheets with answers: PDF – Area of sectors by Spring Ford.
 Practice: Worksheets with answers: Web Page – Various links to area worksheets by Math Worksheets 4 Kids.
5D Composite shapes
 Instruction and examples: Video – Perimeter and Area of composite shapes (10.5 mins) by MathTutorMe.
 Instruction and examples: Video – Composite shapes – area and perimeter (20.33 mins) by Mr Coulter’s Math Class.
 Worked example: Video – Perimeter and Area of a Complex Figure 1 (4 mins) by G5Life.
 Worked example: Video – Area of Composite Figures with Triangle Shapes (2 mins) by MooMooMath and Science.
 Worked examples: Video – Some complex examples of the area of composite shapes (6.2 mins) by Isaac Education.
 Lesson, examples and problems: Web Page – This is a good lesson with some tricky questions by MathSpace.
 Practice: Worksheets with answers: Web Page – A page with links to various excellent worksheets by CueMath.
5E Surface area of prisms and pyramids
 Instruction and examples: Video – Ex5E Surface Area of Prisms and Pyramids (9 mins) by Darren Lam.
 Instruction and examples: Video – 5E Surface Area of Prisms and Pyramids (6.9 mins) by Bianca.
 Worked examples: Video – Surface Area of Prisms and Pyramids (14 mins) by djdmath.
 Worked examples: Video – Surface area of prisms (6.8 mins) by gwatt50.
 Practice: Worksheets with answers: PDF – Surface area of prisms and pyramids by Eric Sever.
 Practice: Worksheets with answers: PDF – Surface area of prisms and pyramids by Mr Wellwood.
5F Surface area of a cylinder
 Instruction and examples: Video – Surface Area of Cylinder (Simplifying Math) (10.5 mins) by Mr Buffington.
 Alternate: Instruction and examples: Video – Surface area of a cylinder (5 mins) by mathstrix.
 Worked example: Video – Surface area of an open cylinder (4.66 mins) by Mathematics Pro.
 Worked example: Video – Surface area of a hollow cylinder (6.25 mins) by Mathematics Pro.
 Practice: Worksheets with answers: PDF – Surface area of cylinders by Mr Broden.
 Practice: Worksheets with answers: PDF – Surface area of cylinders by Corbett Maths. And here are the answers.
5G Volume of a prism
 Instruction and examples: Video – What is volume? (1.5 mins) by WCLN.
 Instruction and examples: Video – Reminder about the connection between volume and capacity (3.8 mins) by iiTutor.
 Instruction and examples: Video – Volume of Prisms Introduction (8.5 mins) by Work with Burke.
 Instruction and examples: Video – Finding the volume of prisms (7 mins) by Work with Burke.
 Worked example: Video – Volume of a trapezoidal prism part 1 (3.8 mins) by Mr Q Teaches Geometry.
 Worked example: Video – Volume of a trapezoidal prism part 2 (7.8 mins) by Mr Q Teaches Geometry.
 Worked example: Video – Volume of an LShape Prism (1.75 mins) by Corbett Maths.
 Worked example: Video – Volume of Regular Pentagonal Prism (2.5 mins) by Rachel Briscoe.
 Practice: Worksheets with answers: Web Page – Volume of prisms by Mr Barton Maths.
 Practice: Worksheets with answers: PDF – Volume of a prism by Edexcel GCSE via MathsGenie. Here are the answers.
5H Volume of a cylinder
 Instruction and examples: Video – 5H Volume of a Cylinder Introduction (3 mins) by Work with Burke.
 Instruction and examples: Video – Finding the volume of cylinders continued (5.4 mins) by Work with Burke.
 Alternate Instruction and examples: Video – Volume of cylinders (3.5 mins) by Tutoring Hour.
 Worked examples: Video – Calculating the Volume of Composite Shapes by Miss Gill Teaches Maths.
 Practice: Worksheets with answers: PDF – Volume of cylinders by Kuta Software.
 Practice: Worksheets with answers: PDF – Volume of composite solids (inc. cylinders) by Edia.
Additional resources
Volume of a cone

 Instruction and examples: Video – Volume of a cone (2.5 mins) by MooMooMath and Science.
Other
 Practice: Worksheets with answers: PDF – Various perimeter and area worksheets by The Grange Academy.
Chapter 6 – Indices and surds
6A Index notation CONSOLIDATING
 Instruction and examples: Video –
 Instruction and examples: Video –
 Instruction and examples: Video –
 Practice: Worksheets with answers:PDF –
 Practice: Worksheets with answers:PDF –
6B Index laws 1 and 2
6C Index law 3 and the zero power
6D Index laws 4 and 5
6E Negative indices
6F Scientific notation
6G Scientific notation using significant figures
6H Fractional indices and surds EXTENDING
6I Simple operations with surds EXTENDING
Chapter 7 – Geometry
7A Angles and triangles CONSOLIDATING
 Instruction and examples: Video –
 Instruction and examples: Video –
 Instruction and examples: Video –
 Practice: Worksheets with answers:PDF –
 Practice: Worksheets with answers:PDF –
7B Parallel lines CONSOLIDATING
7C Quadrilaterals and other polygons
7D Congruent triangles
7E Using congruence in proof EXTENDING
7F Enlargement and similar figures
7G Similar triangles
7H Proving and applying similar triangles
Chapter 8 – Algebraic techniques
8A Expanding binomial products
 Instruction and examples: Video –
 Instruction and examples: Video –
 Instruction and examples: Video –
 Practice: Worksheets with answers:PDF –
 Practice: Worksheets with answers:PDF –
8B Perfect squares and difference of perfect squares
8C Factorising algebraic expressions
8D Factorising the difference of perfect squares
8E Factorising by grouping
8F Factorising quadratic trinomials EXTENDING
8G Factorising trinomials of the form ax2 + bx + c EXTENDING
8H Simplifying algebraic fractions: Multiplication and division
8I Simplifying algebraic fractions: Addition and subtraction
8J Further simplification of algebraic fractions EXTENDING
8K Equations with algebraic fractions EXTENDING
Chapter 9 – Probability and statistics
9A Review of probability CONSOLIDATING
 Instruction and examples: Video –
 Instruction and examples: Video –
 Instruction and examples: Video –
 Practice: Worksheets with answers:PDF –
 Practice: Worksheets with answers:PDF –
9B Venn diagrams and twoway tables
9C Using set notation
9D Using arrays for twostep experiments
9E Tree diagrams
9F Experimental probability
9G Summarising data: Measures of centre
9H Stemandleaf plots
9I Grouped data
9J Measures of spread
9K Box plots EXTENDING
Chapter 10 – Introduction to quadratic equations and graphs
10A Quadratic equations EXTENDING
 Instruction and examples: Video –
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 Instruction and examples: Video –
 Practice: Worksheets with answers:PDF –
 Practice: Worksheets with answers:PDF –
10B Solving ax 2 + bx = 0 and x 2 = d EXTENDING
10C Solving x 2 + bx + c = 0 EXTENDING
10D Applications of quadratic equations EXTENDING
10E The parabola
10F Sketching y = ax 2 with dilations and reflections
10G Sketching translations of y = x 2
10H Sketching parabolas using intercept form EXTENDING
10I Modelling
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