Year 9 Maths introduces students to more advanced algebraic and functional thinking. Students work with real numbers, negative exponents, quadratics, coordinate geometry, trigonometry, measurement error, proportional modelling and compound probability, with increasing emphasis on interpreting mathematics in authentic situations.

Key Topics Covered:

Real numbers, integer exponents, scientific notation, binomial expansion and quadratic factorisation, gradient and coordinate geometry, quadratic functions, linear and quadratic modelling, surface area and volume, trigonometry, measurement error, direct proportion, rates and compound probability.

Parent Tip:

Year 9 is where algebra becomes substantially more demanding. Strong understanding of quadratics, coordinate geometry and right-angled trigonometry is especially important because these ideas continue directly into Year 10 and senior mathematics. NAPLAN numeracy is also sat in March.

Apply exponent laws and work accurately with real numbers and scientific notation

Expand and factorise algebraic expressions and solve monic quadratic equations

Analyse linear and quadratic functions using algebra, tables, graphs and digital tools

Solve surface-area, volume, similarity, Pythagoras and right-triangle trigonometry problems

Evaluate measurement error and build models involving proportion, rates, scale and finance

Represent and analyse compound chance events using trees, relative frequency and simulations

Student working on quadratic graphs for Year 9 maths online with a tutor in Australia

No.	Topic	What We Cover
01	The Real Number System	Distinguish natural numbers, integers, rational and irrational numbers; represent exact and approximate real numbers and solve applied problems.
02	Integer Exponents and Exponent Laws	Apply exponent laws to numerical expressions with positive, zero and negative integer exponents and extend the laws to variables.
03	Scientific Notation	Represent very large and very small quantities in scientific notation and calculate with powers of 10 in measurement contexts.
04	Simplifying Algebraic Expressions	Simplify algebraic expressions involving constants, variables and exponent laws with clear algebraic reasoning.
05	Expanding Binomial Products	Expand products of binomials and recognise patterns connecting factors to quadratic expressions.
06	Factorising Monic Quadratics	Factorise monic quadratic expressions with integer factors and connect factorisation to expansion.
07	Gradient of a Line	Calculate and interpret gradient as a constant rate of change and connect graphical and algebraic representations.
08	Midpoint and Distance on the Cartesian Plane	Find midpoint and distance between two points, using coordinate methods and Pythagoras' theorem where appropriate.
09	Linear Functions and Modelling Change	Model practical and financial contexts using linear functions, tables, graphs and algebra; interpret solutions in context.
10	Term 1 Number and Algebra Review	Integrate real numbers, exponent laws, algebraic manipulation and coordinate geometry in multi-step problems.

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Student in a tutoring session with their tutor

Warm-up (5 min)

Quick mental maths and a review of the previous session

Core Teaching (25 min)

New concept from the lesson eBook, with examples and guided practice

Guided Practice (15 min)

Student works through problems with tutor support

Independent Practice (10 min)

Student completes the in-class quiz independently

Wrap-up (5 min)

Summary, 2 take-home quizzes and a preview of the next session

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No.	Topic	What We Cover
11	Introduction to Quadratic Functions	Recognise quadratic relations through constant second differences and identify key features of parabolic graphs.
12	Graphing Quadratic Functions	Graph quadratic functions using digital tools and interpret symmetry, turning points, intercepts, maxima and minima.
13	Solving Quadratics Graphically and Numerically	Use graphs and numerical approaches to solve quadratic equations and interpret x-intercepts as roots.
14	Solving Monic Quadratics Algebraically	Solve monic quadratic equations with integer roots using factorisation and the null factor law.
15	Transformations of Linear Graphs	Experiment with parameter changes in y = ax + b and generalise effects on gradient, direction and vertical translation.
16	Transformations of Quadratic and Other Functions	Use digital tools to explore transformations of parabolas and other related functions and connect algebraic changes to graphical effects.
17	Linear vs Quadratic Modelling	Choose between linear and quadratic models for applied problems, interpret graph features and evaluate the model.
18	Surface Area of Right Prisms and Cylinders	Develop and apply surface-area formulas using nets and solve practical problems with appropriate units.
19	Volume of Right Prisms and Cylinders	Calculate volumes of prisms and cylinders and solve optimisation and capacity problems in context.
20	Term 2 Algebra and Measurement Review	Apply quadratic reasoning, function transformations, surface area and volume in mixed and modelling problems.

No.	Topic	What We Cover
21	Very Large and Small Measurements	Solve measurement problems involving extreme scales, scientific notation, time scales and appropriate accuracy.
22	Pythagoras in Spatial Problems	Apply Pythagoras' theorem to authentic spatial problems and coordinate distances.
23	Right-Angled Trigonometry	Use trigonometric ratios to determine unknown sides and angles in right-angled triangles.
24	Similarity, Scale and Angle Properties	Apply similarity, scale factors and angle properties to solve spatial problems and reason about corresponding lengths and areas.
25	Measurement Error	Calculate and interpret absolute, relative and percentage error and recognise that measured quantities are estimates.
26	Bounds and Accuracy	Determine suitable upper and lower bounds for measurements and evaluate the impact of measurement precision.
27	Direct Proportion	Model direct-proportion relationships and solve problems involving pro rata pay, conversions and scientific contexts.
28	Rates, Ratio and Scale Modelling	Model practical problems involving rates, ratios and scale, including construction, density, flow and financial situations.
29	Financial Modelling	Use rates, ratio, linear relationships and other appropriate methods to analyse realistic financial decisions and report findings.
30	Term 3 Measurement and Modelling Review	Integrate trigonometry, similarity, error, proportion, rates and financial modelling in complex applications.

No.	Topic	What We Cover
31	Compound Events and Sample Spaces	List outcomes for multi-step chance events using systematic lists, tables, arrays and tree diagrams.
32	With and Without Replacement	Compare compound events with and without replacement and assign probabilities to outcomes.
33	Tree Diagrams and Multi-Stage Probability	Construct and interpret tree diagrams for two- and three-stage chance events.
34	Relative Frequency	Calculate relative frequencies from observed or supplied data and use them to estimate probabilities.
35	Probability of "And" Events	Use data, tables, diagrams and probability reasoning to estimate or calculate probabilities involving "and".
36	Inclusive and Exclusive "Or"	Distinguish inclusive and exclusive "or" and calculate or estimate associated probabilities.
37	Probability Simulations	Design and conduct repeated chance experiments and digital simulations for simple and compound events.
38	Comparing Theoretical and Experimental Probability	Compare expected probabilities with simulation results and explain variation across different numbers of trials.
39	Integrated Probability Investigation	Design a chance investigation, organise outcomes, analyse relative frequencies and communicate conclusions.
40	End-of-Year Year 9 Mathematics Assessment	Complete an integrated assessment across real numbers, algebra, functions, measurement, modelling and probability.

Year 9 Maths Tutoring in Australia

By Term 4 of Year 9 Maths, Your Child Will...

Year 9 Maths Curriculum, Term by Term

Try a Free Lesson to See the Full Program

Try a Free Lesson to See the Full Program

Try a Free Lesson to See the Full Program

Try a Free Lesson to See the Full Program