Master Year 9 Maths

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Year 9 Maths Topics

Number Theory

Divisibility Rules

Determining Common Factors

Determining Common Multiples

Introduction to Exponents

Number Systems

Understanding the number systems

Prime factorisation

Greatest common factors (GCF)

Least common multiple (LCM)

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Adding and Subtracting Integers

Introduction to integer addition

Adding integers

Introduction to integer subtraction

Subtracting integers

Word problems on adding and subtracting integers

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

Operations with Decimals

Adding and subtracting decimal numbers

Multiplying decimal numbers

Dividing decimal numbers

Order of operations (BIDMAS)

Adding and Subtracting Fractions

Using model to add and subtract fractions

Adding fractions with like denominators

Subtracting fractions with like denominators

Adding and subtracting fractions with unlike denominators

Adding and subtracting mixed numbers

Multiplying and Dividing Fractions

Multiplying fractions and whole numbers

Dividing fractions with whole numbers

Multiplying proper fractions

Multiplying improper fractions and mixed numbers

Dividing fractions and mixed numbers

Applications of fraction operations

Powers and Exponents

Using exponents to describe numbers

Order of operations with exponents

Using exponents to solve problems

Surds

Square and square roots

Cubic and cube roots

Evaluating and simplifying surds

Converting radicals to mixed surds

Converting radicals to entire surds

Adding and subtracting surds

Multiplying and dividing surds

Rationalize the denominator

Ratios, Rates, and Proportions

Proportional Relationships

Identifying proportional relationships

Understanding graphs of linear relationships

Understanding tables of values of linear 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

Measuring 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

Scale Factors and Similarity

Enlargements and reductions with scale factors

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

Circles

Circles and circumference

Arcs of a circle

Areas and sectors of circles

Patterns and Solving Equations

Evaluating algebraic expressions

Evaluating polynomials

Introduction to Polynomials

Characteristics of polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Solving Linear Equations

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 (Advanced)

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

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)

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

Multiplying and dividing monomials

Multiplying polynomials by monomials

Dividing polynomials by monomials

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

Reading and drawing Venn diagrams

Statistics

Median and mode

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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