Australia · ACARA Content Descriptions
Year 9 Mathematics
This course bridges the gap between arithmetic and abstract reasoning through algebraic modelling and geometric proof. Students investigate proportional reasoning and data analysis to make sense of the world while developing fluency in non linear relationships.
01The Language of Algebra
Students expand their algebraic repertoire by simplifying expressions, expanding binomials, and solving complex linear equations.
Students will identify and define key components of algebraic expressions, including variables, coefficients, constants, and terms, and practice writing simple expressions from verbal descriptions.
Students will combine like terms and apply the order of operations to simplify algebraic expressions, focusing on efficiency and accuracy.
Students will apply the distributive law to expand algebraic expressions, including single term multiplication and basic binomial products.
Students will master the distributive law to expand binomial products, including perfect squares and difference of two squares, using visual models and the FOIL method.
Students will reverse the expansion process by factorising algebraic expressions, focusing on finding the highest common factor.
Students will factorise expressions using grouping and recognize special products like difference of two squares and perfect squares.
Students will solve one-step linear equations using inverse operations, building foundational skills for more complex equations.
Students will solve multi-step linear equations involving distributive property and variables on both sides, applying systematic problem-solving strategies.
Students will understand the concept of inequalities, represent solutions on a number line, and solve simple linear inequalities.
Students will solve multi-step linear inequalities, including those requiring multiplication or division by negative numbers, and interpret their solutions.
Students will apply index laws to simplify expressions involving multiplication and division of terms with the same base.
02Linear and Non Linear Relationships
Exploring the geometry of the Cartesian plane through gradients, intercepts, and an introduction to parabolas.
Students will review the Cartesian coordinate system, plot points, and identify coordinates in all four quadrants.
Students will calculate the gradient (slope) of a line given two points, interpreting its meaning in various contexts.
Students will sketch linear functions using the gradient-intercept form, identifying the y-intercept and gradient.
Students will derive the equation of a straight line given two points, a point and a gradient, or its intercepts.
Students will identify and graph horizontal and vertical lines, understanding their unique equations and gradients.
Students will use the distance formula to calculate the length of a line segment between two given points.
Students will apply the midpoint formula to find the coordinates of the midpoint of a line segment.
Students will identify quadratic relationships from tables of values and understand their non-linear nature.
Students will generate tables of values for simple quadratic functions (e.g., y=x^2, y=-x^2) and plot points to observe the parabolic shape, without formal graphing of y=ax^2.
Students will explore the effect of adding a constant 'c' to y=x^2 by comparing tables of values and observing vertical shifts in plotted points, focusing on the vertex.
Students will solve pairs of linear equations by graphing them and identifying their point of intersection.
03Geometric Reasoning and Trigonometry
Applying Pythagoras' Theorem and basic trigonometric ratios to solve problems involving right-angled triangles.
Students will understand the concept of geometric proofs, identifying postulates, theorems, and logical reasoning.
Students will apply Pythagoras' Theorem to find the length of the hypotenuse in right-angled triangles.
Students will apply Pythagoras' Theorem to find the length of a shorter side in right-angled triangles.
Students will use the converse of Pythagoras' Theorem to determine if a triangle is right-angled.
Students will define sine, cosine, and tangent as ratios of sides in right-angled triangles relative to a given angle.
Students will apply sine, cosine, and tangent ratios to calculate unknown side lengths in right-angled triangles.
Students will use inverse trigonometric functions to calculate unknown angles in right-angled triangles.
Students will solve problems involving angles of elevation and depression in real-world contexts.
Students will understand the concept of similar figures, identifying corresponding angles and proportional sides.
Students will use the properties of similar triangles to find unknown side lengths and angles.
Students will understand the concept of congruent figures and the conditions (SSS, SAS, ASA, RHS) for proving triangle congruence.
04Measurement and Surface Area
Calculating the surface area and volume of composite shapes, prisms, and cylinders.
Students will review and apply formulas for the area of rectangles, triangles, parallelograms, and trapezoids.
Students will review and apply formulas for the circumference and area of circles, solving problems involving circular shapes.
Students will decompose complex 2D shapes into simpler components and add their areas to find the total area.
Students will calculate the area of composite shapes by subtracting smaller areas from larger boundary shapes.
Students will identify common 3D objects and draw their nets to visualize their surfaces.
Students will develop and apply formulas to find the total surface area of rectangular and triangular prisms.
Students will develop and apply formulas to find the total surface area of cylinders.
Students will calculate the volume of rectangular and triangular prisms using the base area times height principle.
05Financial Mathematics and Proportion
Applying percentage increases and decreases to financial contexts including simple interest and profit/loss.
Students will review converting between percentages, fractions, and decimals, and calculating percentages of amounts.
Students will calculate percentage increases and decreases, applying them to various contexts like sales and growth.
Students will calculate percentage profit and loss, and determine original values after a percentage change in business scenarios.
Students will calculate interest earned or paid over time using the simple interest formula (I=PRN).
Students will rearrange the simple interest formula to find unknown principal, interest rate, or time.
Students will understand and simplify ratios, expressing them in their simplest form and using them to compare quantities.
Students will divide a given quantity into parts according to a specified ratio.
Students will understand rates, calculate unit rates, and use them to compare different quantities.
Students will identify and solve problems involving direct proportion, understanding the constant of proportionality.
Students will apply their understanding of direct proportion to solve more complex real-world problems, including those involving scaling and unit conversions.
06Statistics and Probability
Analysing data sets using measures of center and spread, and exploring multi-step probability events.
Students will review methods of data collection and various ways to represent data, including frequency tables and histograms.
Students will calculate and interpret the mean, median, and mode for various data sets, understanding their strengths and weaknesses.
Students will calculate and interpret the range and interquartile range (IQR) as measures of data spread.
Students will construct five-point summaries and draw box-and-whisker plots to visually represent and compare data distributions.
Students will compare the distributions of two or more data sets using measures of central tendency, spread, and appropriate graphical representations (e.g., back-to-back stem-and-leaf plots, parallel box plots).
Students will interpret various data displays (histograms, box plots, stem-and-leaf plots) to describe data shape, identify outliers, and draw conclusions.
Students will review basic probability concepts, including sample space, events, and calculating theoretical probability.
Students will calculate the probability of two independent events occurring, using multiplication rule.