Year 9 is where algebra and functional thinking take a big step forward. Our structured programme builds expressions, linear and quadratic relations, trigonometry and probability with real NZ examples, like interest on savings.

Key Topics Covered:

Real numbers, exponent laws, scientific notation, binomials and factorising, gradient and coordinate geometry, quadratic relations, surface area and volume, trigonometry, measurement error, proportion, interest and probability.

Parent Tip:

Year 9 maths sets up every senior maths course. A strong grasp of linear and quadratic relations now carries straight into Year 10 and beyond. We make sure each idea clicks before moving on.

Apply exponent laws and work with real numbers and scientific notation

Expand and factorise polynomials and solve quadratic equations

Model linear and quadratic relations with tables, graphs and equations

Find surface area and volume and use right-angle trigonometry

Compare simple and compound interest in NZ dollars

Find probabilities of compound events and read scatter plots

Parent and child practising Year 9 maths at home in New Zealand

No.	Topic	What We Cover
01	The Real Number System	Tell natural numbers, integers, rational and irrational numbers apart and show exact and approximate values.
02	Integer Exponents and Exponent Laws	Apply exponent laws with positive, zero and negative integer exponents.
03	Scientific Notation	Write and calculate with very large and very small quantities, such as the distance from Earth to the Sun.
04	Simplifying Algebraic Expressions	Simplify expressions with constants, variables and exponent laws, showing each algebraic step.
05	Expanding Binomial Products	Expand products of binomials and see how factors connect to quadratic expressions.
06	Factorising Simple Quadratics	Factorise trinomials with integer factors and link factorising to expanding.
07	Slope of a Line	Calculate and interpret slope as a constant rate of change from graphs and equations.
08	Midpoint and Distance on the Grid	Find the midpoint and distance between points using coordinates and the Pythagoras' theorem.
09	Linear Relations and Modelling Change	Model real and financial situations with linear equations, tables and graphs, such as a gym fee in NZ dollars.
10	Term 1 Review	Revise number, algebra and coordinate geometry through multi-step problems. A termly mock test and parent report follow.

Try a Free Lesson to See the Full Programme

See our structured approach in action. Your child's first lesson is completely free, no credit card needed.

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 Relations	Spot quadratic relations through constant second differences and name key features of parabolas.
12	Graphing Quadratic Relations	Graph quadratics with digital tools and read symmetry, vertex and intercepts.
13	Solving Quadratics by Graphs and Tables	Use graphs and tables to solve quadratic equations and read x-intercepts as solutions.
14	Solving Quadratics by Factorising	Solve quadratic equations with integer roots by factorising and the zero product property.
15	Transformations of Linear Graphs	Change a and b in y = ax + b and describe the effect on slope and position.
16	Transformations of Parabolas	Explore how stretches and shifts change a parabola and link them to the equation.
17	Linear versus Quadratic Models	Choose between linear and quadratic models for a situation and justify the choice.
18	Surface Area of Prisms and Cylinders	Use nets and formulas to find surface area and solve practical problems.
19	Volume of Prisms and Cylinders	Find volume and capacity and solve design problems, such as a farm water tank.
20	Term 2 Review	Revise quadratics, transformations and measurement through mixed and modelling tasks. A termly mock test and parent report follow.

No.	Topic	What We Cover
21	Very Large and Very Small Measurements	Solve measurement problems with extreme scales, scientific notation and time scales.
22	Pythagoras' Theorem in Spatial Problems	Apply the Pythagoras' theorem to real spatial problems and coordinate distances.
23	Right-Angle Trigonometry	Use sine, cosine and tangent to find unknown sides and angles in right triangles.
24	Similarity, Scale and Angle Properties	Use similarity, scale factors and angle properties to solve spatial problems.
25	Measurement Error	Find absolute, relative and percentage error and see why measured values are approximate.
26	Bounds and Accuracy	Set upper and lower bounds for measurements and judge how errors build up.
27	Direct Proportion	Model direct variation and solve problems with pay rates, conversions and ratios.
28	Rates, Ratio and Scale Modelling	Model problems with rates, ratios and scale, such as fuel use, density and construction plans.
29	Financial Literacy: Simple and Compound Interest	Compare simple and compound interest on savings and loans in NZ dollars.
30	Term 3 Review	Revise trigonometry, proportion and financial modelling. A termly mock test and parent report follow.

No.	Topic	What We Cover
31	Compound Events and Sample Spaces	List outcomes of multi-step chance events with lists, tables, arrays and tree diagrams.
32	With and Without Replacement	Compare events with and without replacement and assign probabilities.
33	Tree Diagrams and Multi-Stage Probability	Build and read tree diagrams for two-stage and three-stage events.
34	Relative Frequency	Calculate relative frequencies from data and use them to estimate probabilities.
35	Probability of And Events	Use tables, diagrams and reasoning to find probabilities of events happening together.
36	Inclusive and Exclusive Or	Tell inclusive from exclusive or and calculate the matching probabilities.
37	Probability Simulations	Design and run repeated trials and digital simulations, and compare theoretical and experimental results.
38	Scatter Plots and Lines of Best Fit	Plot two-variable data, describe the relationship and draw a line of best fit.
39	Mixed Problems and Test-Style Practice	Practise multi-step problems and explain your thinking, with test-style questions to build exam confidence.
40	Year 9 Review and Year 10 Readiness	Revise the year's key skills and preview Year 10 maths, including trigonometry and analytic geometry. A termly mock test and parent report follow.

Year 9 Maths Tutoring Across New Zealand

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 Programme

Try a Free Lesson to See the Full Programme

Try a Free Lesson to See the Full Programme

Try a Free Lesson to See the Full Programme