Year 9 Mathematics in the Australian Curriculum

AC9M9N01

recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers using digital tools

AC9M9A01

apply the exponent laws to numerical expressions with integer exponents and extend to variables

AC9M9A02

simplify algebraic expressions, expand binomial products and factorise monic quadratic expressions

AC9M9A03

find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane

AC9M9A04

identify and graph quadratic functions, solve quadratic equations graphically and numerically, and solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate

AC9M9A05

use mathematical modelling to solve applied problems involving change including financial contexts; formulate problems, choosing to use either linear or quadratic functions; interpret solutions in terms of the situation; evaluate the model and report methods and findings

AC9M9A06

experiment with the effects of the variation of parameters on graphs of related functions, using digital tools, making connections between graphical and algebraic representations, and generalising emerging patterns

AC9M9M01

solve problems involving the volume and surface area of right prisms and cylinders using appropriate units

AC9M9M02

solve problems involving very small and very large measurements, time scales and intervals expressed in scientific notation

AC9M9M03

solve spatial problems, applying angle properties, scale, similarity, Pythagoras’ theorem and trigonometry in right-angled triangles

AC9M9M04

calculate and interpret absolute, relative and percentage errors in measurements, recognising that all measurements are estimates

AC9M9M05

use mathematical modelling to solve practical problems involving direct proportion, rates, ratio and scale, including financial contexts; formulate the problems and interpret solutions in terms of the situation; evaluate the model and report methods and findings

AC9M9SP01

recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity

AC9M9SP02

apply the enlargement transformation to shapes and objects using dynamic geometry software as appropriate; identify and explain aspects that remain the same and those that change

AC9M9SP03

design, test and refine algorithms involving a sequence of steps and decisions based on geometric constructions and theorems; discuss and evaluate refinements

AC9M9ST01

analyse reports of surveys in digital media and elsewhere for information on how data was obtained to estimate population means and medians

AC9M9ST02

analyse how different sampling methods can affect the results of surveys and how choice of representation can be used to support a particular point of view

AC9M9ST03

represent the distribution of multiple data sets for numerical variables using comparative representations; compare data distributions with consideration of centre, spread and shape, and the effect of outliers on these measures

AC9M9ST04

choose appropriate forms of display or visualisation for a given type of data; justify selections and interpret displays for a given context

AC9M9ST05

plan and conduct statistical investigations involving the collection and analysis of different kinds of data; report findings and discuss the strength of evidence to support any conclusions

AC9M9P01

list all outcomes for compound events both with and without replacement, using lists, tree diagrams, tables or arrays; assign probabilities to outcomes

AC9M9P02

calculate relative frequencies from given or collected data to estimate probabilities of events involving “and”, inclusive “or” and exclusive “or”

AC9M9P03

design and conduct repeated chance experiments and simulations, using digital tools to compare probabilities of simple events to related compound events, and describe results