AC9M9A04 Year 9 Mathematics

AC9M9A04 – Year 9 Mathematics: null

Strand

Algebra

Substrand

Algebra

This Content Descriptor from Year 9 Mathematics provides the specific knowledge and skills students should learn. Use it to plan lessons, create learning sequences, and design assessments that align with the Australian Curriculum v9.

Content Descriptor

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

Elaborations

• recognising that in a table of values, if the second difference between consecutive values of the dependent variable is constant, then it is a quadratic
• graphing quadratic functions using digital tools and comparing what is the same and what is different between these different functions and their respective graphs; interpreting features of the graphs such as symmetry, turning point, maximum and minimum values, and determining when values of the quadratic function lie within a given range
• solving quadratic equations algebraically and comparing these to graphical solutions
• using graphs to determine the solutions of quadratic equations; recognising that the roots of a quadratic function correspond to the \(x\)-intercepts of its graph and that if the graph has no \(x\)-intercepts, then the corresponding equation has no real solutions
• relating horizontal axis intercepts of the graph of a quadratic function to the factorised form of its rule using the null factor law; for example, the graph of the function \(y=x^2-5x+6\) can be represented as \(y=(x-2)(x-3)\) with \(x\)-axis intercepts where either \((x-2)=0\) or \((x-3)=0\)
• recognising that the equation \(x^2=a\), where \(a>0\), has \(2\) solutions, \(x=\sqrt a\) and \(x=\)-\(\sqrt a\); for example, if \(x^2=39\) then \(x=\sqrt{39}=6.245\) correct to \(3\) decimal places, or \(x=\)-\(\sqrt{39}=\)-\(6.245\) correct to \(3\) decimal places, and representing these graphically
• graphing percentages of illumination of moon phases in relation to First Nations Australians’ understandings that describe the different phases of the moon

Achievement Standard This Supports

This Content Descriptor contributes to the following Achievement Standard:

Year 9 ASMATY9

Year 9 Mathematics Achievement Standard

By the end of Year 9, students recognise and use rational and irrational numbers to solve problems. They extend and apply the exponent laws with positive integers to variables. Students expand binomial products, and factorise monic quadratic expressions. They find the distance between 2 points on the Cartesian plane, and the gradient and midpoint of a line segment. Students use mathematical modelling to solve problems involving change in financial and other applied contexts, choosing to use linear and quadratic functions. They graph quadratic functions and solve monic quadratic equations with integer roots algebraically. Students describe the effects of variation of parameters on functions and relations, using digital tools, and make connections between their graphical and algebraic representations. They apply formulas to solve problems involving the surface area and volume of right prisms and cylinders. Students solve problems involving ratio, similarity and scale in two-dimensional situations. They determine percentage errors in measurements. Students apply Pythagoras’ theorem and use trigonometric ratios to solve problems involving right-angled triangles. They use mathematical modelling to solve practical problems involving direct proportion, ratio and scale, evaluating the model and communicating their methods and findings. Students express small and large numbers in scientific notation. They apply the enlargement transformation to images of shapes and objects, and interpret results. Students design, use and test algorithms based on geometric constructions or theorems. They compare and analyse the distributions of multiple numerical data sets, choose representations, describe features of these data sets using summary statistics and the shape of distributions, and consider the effect of outliers. Students explain how sampling techniques and representation can be used to support or question conclusions or to promote a point of view. They determine sets of outcomes for compound events and represent these in various ways. Students assign probabilities to the outcomes of compound events. They design and conduct experiments or simulations for combined events using digital tools.