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Excel in NZ Year 9 Mathematics

Build a strong foundation in number operations, algebra, geometry, and statistics. Prepare for NCEA success with clear, engaging lessons and practice problems.

Start Your math Journey

Start with number operations to strengthen your calculation skills. Then dive into algebra, where you'll learn to solve equations and graph functions. Geometry will teach you about shapes and spatial reasoning, while statistics and probability round out your mathematical toolkit. Each topic builds on the last, preparing you for more advanced concepts in Year 10 and beyond.

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Maths is my weakest subject and I am always looking for help. One day, I came across StudyPug online and after I tried out the free maths lessons, I really liked it and signed up right away. Your lessons are very easy to understand even on some of the toughest questions. That's the maths help I have been looking for.

Isla Brown - Year 7 maths student, Hamilton, New Zealand

Year 9 Maths Topics

Number Theory

Divisibility Rules

Prime factors

Determining Common Factors

Determining Common Multiples

Introduction to exponents

Adding and Subtracting Integers

Introduction to integer addition

Adding integers

Introduction to integer subtraction

Subtracting integers

Application of integer operations

Multiplying and Dividing Integers

Understanding integer multiplication

Multiplying integers

Understanding integer division

Dividing integers

Applications of integer operations

Rational Numbers

Comparing and ordering rational numbers

Solving problems with rational numbers in decimal form

Solving problems with rational numbers in fraction form

Determine square roots of rational numbers

Powers and Exponents

Using exponents to describe numbers

Exponent rules

Order of operations with exponents

Using exponents to solve problems

Ratios, Rates, and Proportions

Ratios

Rates

Proportions

Proportional Relationships

Identifying proportional relationships

Understanding graphs of proportional relationships

Understanding tables of values of proportional relationships

Applications of linear relationships

Percents

Representing percents

Percents, fractions, and decimals

Percent of a number

Adding and multiplying percents

Taxes, discounts, tips and more

Simple interest

Radicals

Square and square roots

Cubic and cube roots

Evaluating and simplifying radicals

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding and subtracting radicals

Multiplying and dividing radicals

Rationalize the denominator

Measuring Systems

Metric systems

Imperial systems

Conversions between metric and imperial systems

Conversions involve squares and cubic

Coordinates, Quadrants, and Transformations

Cartesian plane

Draw on coordinate planes

Introduction to transformations

Horizontal and vertical distances

Angles, Lines, and Transversals

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Symmetry and Surface Area

Line symmetry

Rotational symmetry and transformations

Surface area of 3-dimensional shapes

Properties of triangles

Classifying triangles

Isosceles and equilateral triangles

Circles

Circles and circumference

Angles in a circle

Arcs of a circle

Areas and sectors of circles

Scale Factors and Similarity

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Pythagorean Theorem

Squares and square roots

Pythagorean theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

Introduction to 3-Dimensional Figures

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface area of cylinders

Volume

Introduction to volume

Volume of prisms

Volume of cylinders

Word problems relating volume of prisms and cylinders

Linear Equations (Basic)

Model and solve one-step linear equations: ax = b, x/a = b

Solving two-step linear equations using addition and subtraction: ax + b = c

Solving two-step linear equations using multiplication and division: x/a + b = c

Solving two-step linear equations using distributive property: a(x + b) = c

Solving Linear Equations

Solving linear equations using multiplication and division

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Solving literal equations

Linear Inequalities

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Solving multi-step linear inequalities

Compound inequalities

Introduction to Relations and Functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Linear Functions

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Midpoint formula: \(M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)\)

Gradient equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Gradient intercept form: y = mx + b

General form: Ax + By + C = 0

Gradient-point form: \(y - y_1 = m (x - x_1)\)

Rate of change

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from gradient-intercept form y=mx+b

Graphing linear functions using a single point and gradient

Word problems of graphing linear functions

Parallel and perpendicular lines in linear functions

Applications of linear relations

Multiplication and Division of Polynomials

Common factors of polynomials

Factorising polynomials by grouping

Solving polynomials with the unknown "b" from x^2 + bx + c

Solving polynomials with the unknown "c" from x^2 + bx + c

Factorising polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

Solving polynomials with the unknown "b" from \(ax^2 + bx + c\)

Factorising polynomials: \(ax^2 + bx + c\)

Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Evaluating polynomials

Using algebra tiles to factorise polynomials

Solving polynomial equations

Word problems of polynomials

Data and Graphs

Reading and drawing bar graphs

Reading and drawing histograms

Reading and drawing line graphs

Box-and-whisker plots and scatter plots

Stem-and-leaf plots

Pie charts

Reading and drawing Venn diagrams

Frequency tables and dot plots

Statistics

Median and mode

Mean

Range and outliers

Application of averages

Probability

Determining probabilities using tree diagrams and tables

Probability of independent events

Probability with Venn diagrams

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