Find the longest diagonal of a box measuring 6 cm by 8 cm by 24 cm.

√(36 + 64 + 576) = √676 = 26 cm

Year 9 · Australian Curriculum

Year 9 maths: what's covered and how to help

Year 9 is where algebra gets serious and trigonometry begins. Here's every topic in the Australian Curriculum for Year 9, where students get stuck, and free worksheets and tests for each one.

Year 9 worksheets Year 9 maths test Every topic ↓

What’s new in Year 9

Algebra steps up: expanding binomial products, factorising and the first quadratics.
Trigonometry starts, building on Pythagoras from Year 8.
Linear graphs become coordinate geometry: gradient, midpoint and distance.
Index laws extend to pronumerals, and scientific notation is used for very large and very small numbers.

Where students get stuck

Index laws with pronumerals and negative numbers. Practise it →
Setting up the right trigonometric ratio. Practise it →
Finding the equation of a line from two points. Practise it →
Multi-step Pythagoras problems in context. Practise it →

Every Year 9 maths topic

Grouped by strand, as in the Australian Curriculum. Each topic has worked examples, a question to try and a free worksheet.

Algebra

6 topics

QuadraticsGraphing parabolas, null factor law, solving quadratic equations.
AlgebraBinomial expansion, monic quadratic factorising, simplifying.
Linear equations and graphsSketch from gradient/intercept, solve from any form.
Coordinate geometryGradient, midpoint, distance between two points.
Exponent lawsIndex laws extended to variables and longer expressions.
Simple interestI = PRT: the Year 9 financial maths foundation.

Measurement

5 topics

Pythagoras (applied)Combine Pythagoras with similarity, ratio and trig.
Surface area and volumeCylinders, prisms, composite 3D objects.
Scientific notationStandard form, conversions, calculations with very large and very small numbers.
Measurement errorCalculate absolute, relative and percentage errors, and learn what they actually mean.
Direct proportion, rates and scaleModel real situations with ratios, rates and scale.

Space

2 topics

TrigonometrySOHCAHTOA: find missing sides and angles in right-angled triangles.
Enlargements and scale factorsScale shapes up and down, spot what changes and what stays the same.

Statistics

2 topics

StatisticsChoosing displays, comparing distributions, describing skew.
Comparing data setsRead, draw and describe comparative displays.

Probability

2 topics

ProbabilityWith/without replacement, multi-step events, relative frequency.
Venn diagrams and two-way tablesUse real data to find probabilities with and, or and not.

Quick check

3 Year 9 questions

One from each of these topics. Try each one, then open the answer.

Linear equations and graphs
State the gradient and $y$ -intercept of $y = 4x - 7$ .
Answer
Gradient $4$ , $y$ -intercept $-7$
Pythagoras (applied)
Find the longest diagonal of a box measuring $6$ cm by $8$ cm by $24$ cm.
Answer
$\sqrt{36 + 64 + 576} = \sqrt{676} = 26$ cm
Exponent laws
Simplify $b^5 \times b^2$ .
Answer
$b^7$

Try the full Year 9 sample test →

How to help with Year 9 maths at home

Year 9 results shape the maths choices that come next, so fix gaps now rather than in Year 10.
Year 9s sit NAPLAN numeracy from 10 to 22 March 2027, which covers everything up to Year 9.
Before a topic test, have them do a practice test under time, then redo every question they got wrong.
If algebra is shaky, go back to Year 8 expanding and factorising before pushing on with quadratics.

Year 9 maths questions

What maths do Year 9 students learn in Australia?

Algebra (binomial products, factorising, quadratics, index laws, linear graphs and coordinate geometry, simple interest), measurement (Pythagoras, surface area and volume, scientific notation, measurement error), space (trigonometry and enlargements), statistics and probability.

Does Year 9 maths affect senior subject choices?

Often, yes. Schools usually use Year 9 and 10 results to place students into the harder senior maths courses, which assume Year 9 algebra and trigonometry are automatic.

Do Year 9 students do NAPLAN?

Yes. Year 9 students sit the NAPLAN numeracy test, from 10 to 22 March 2027.

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