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• VC2M9A03

  sketch linear graphs of equations in various algebraic forms, using the coordinates of 2 points, and solve linear equations

  Elaborations

  • determining linear rules from suitable diagrams, tables of values and graphs, and describing them using both words and algebra

  VC2M9A03 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M9A05

  identify and graph quadratic functions, solve quadratic equations graphically and numerically, and use null factor law to 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=x2-5x+6 can be represented as y=x-2x-3 with x-axis intercepts where either x-2=0 or x-3=0
  • recognising that the equation x2=a, where a>0, has 2 solutions, x=a and x=-a (for example, if x2=39 then x=39=6.245 correct to 3 decimal places, or x=-39=-6.245 correct to 3 decimal places) and representing these graphically
  • graphing percentages of illumination of moon phases in relation to Aboriginal and Torres Strait Islander Peoples’ understandings that describe the different phases of the moon

  VC2M9A05 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M9A07

  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 

  Elaborations

  • investigating transformations of the graph of y=x to the graph of y=ax+b by systematic variation of a and b and interpreting the effects of these transformations using digital tools; for example,
    y=x→y=2x (vertical enlargement as a>1) →y=2x-1 (vertical translation) and
     y=x→y=12x (vertical compression as 0<a<1) →y=-12x (reflection in the horizontal axis) →y=-12x+3 (vertical translation)
  • investigating transformations of the parabola y=x2 to the graph of y=ax-h2+b in the Cartesian plane using digital tools to determine the relationship between graphical and algebraic representations of quadratic functions, including the completed square form; for example,
    y=x2→y=13x2 (vertical compression as 0<a<1) →y=13(x-5)2 (horizontal translation) →y=13(x-5)2+7 (vertical translation) or
    y=x2→y=2x2 (vertical enlargement as a>1) →y=-2x2 (reflection in the horizontal axis) →y=-2(x+6)2 (horizontal translation) →y=-2x+62+10 (vertical translation)
  • experimenting with digital tools by applying transformations to the graphs of functions, such as reciprocal y=1x, square root y=x, cubic y=x3 and exponential functions y=2x, y=(12)x, identifying patterns

  VC2M9A07 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M9A04

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

  Elaborations

  • recognising that the gradient of a line is calculated using the gradient of a line segment on that line and is independent of which 2 distinct points on the line are used for this calculation
  • using digital tools and transformations to illustrate that parallel lines in the Cartesian plane have the same gradient and that the relationship between the gradients of pairs of perpendicular lines is that their product is (−1)
  • using Pythagoras’ theorem to establish the distance between 2 points in the Cartesian plane and applying this using horizontal and vertical distances and coordinates
  • investigating graphical and algebraic techniques for finding the midpoint and gradient of the line segment between 2 points
  • using dynamic graphing software and superimposed images (for example, playground equipment, ramps and escalators) to investigate gradients in context and their relationship to rule of a linear function, and interpret gradient as a constant rate of change in linear modelling contexts

  VC2M9A04 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VCMNA310

  Sketch linear graphs using the coordinates of two points and solve linear equations

  Elaborations

  • determining linear rules from suitable diagrams, tables of values and graphs and describing them using both words and algebra

  VCMNA310 | Mathematics | Level 9 | Number and Algebra | Linear and non-linear relationships

• Mathematics Version 2.0: Level 9 achievement standards

  By the end of Level 9, students recognise and use rational and irrational numbers to solve problems.

  Students extend and apply the exponent laws with positive integers and the zero exponent to variables. They expand binomial products and factorise monic quadratic expressions. They...

  Level description | Mathematics | Mathematics Version 2.0 | Level 9

• VCMNA311

  Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations

  Elaborations

  • graphing parabolas, and circles connecting x-intercepts of a graph to a related equation

  VCMNA311 | Mathematics | Level 9 | Number and Algebra | Linear and non-linear relationships

• VCMNA309

  Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software

  Elaborations

  • investigating graphical and algebraic techniques for finding midpoint and gradient
  • recognising that the gradient of a line is the same as the gradient of any line segment on that line

  VCMNA309 | Mathematics | Level 9 | Number and Algebra | Linear and non-linear relationships

• VCMNA308

  Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software

  Elaborations

  • investigating graphical and algebraic techniques for finding distance between two points
  • using Pythagoras' theorem to calculate distance between two points

  VCMNA308 | Mathematics | Level 9 | Number and Algebra | Linear and non-linear relationships

• VCMNA301

  Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems

  Elaborations

  • identifying direct proportion in real-life contexts

  VCMNA301 | Mathematics | Level 9 | Number and Algebra | Real numbers

• VCSIS137

  Construct and use a range of representations, including graphs, keys, models and formulas, to record and summarise data from students’ own investigations and secondary sources, to represent qualitative and quantitative patterns or relationships, and distinguish between discrete and continuous data

  Elaborations

  • using spreadsheets to present data in tables and graphical forms and to carry out mathematical analyses of data
  • designing and constructing appropriate graphs to represent data and to look for trends and patterns

  VCSIS137 | Science | Levels 9 and 10 | Science Inquiry Skills | Recording and processing

• VC2M9M02

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

  Elaborations

  • representing very large and very small real numbers in scientific notation, converting real numbers expressed in scientific notation into decimal form; for example, the approximate geological age of Earth is 4.6 × 10⁹ years, and the mass of a glucose molecule is 2.99 × 10⁻²² grams
  • using knowledge of place value and applying exponent laws to operate with numbers expressed in scientific notation in applied contexts; for example, performing calculations involving extremely small numbers in scientific and other contexts
  • examining the degree of accuracy that different measurement instruments provide in a science laboratory, such as a measuring cylinder compared with a pipette, and recording data values to the correct degree of accuracy using appropriate scientific notation

  VC2M9M02 | Mathematics | Mathematics Version 2.0 | Level 9 | Measurement

• VC2M9P01

  list all outcomes for two-step chance experiments both with and without replacement, using lists, tree diagrams, tables or arrays; assign probabilities to outcomes and events

  Elaborations

  • discussing two-step chance experiments, such as the game of heads and tails, describing the different outcomes and their related probabilities 
  • using systematic methods such as lists or arrays to record outcomes and assign probabilities, such as drawing the names of students from a bag to appoint 2 team leaders
  • using a tree diagram to represent a three-stage event and assigning probabilities to these events; for example, selecting 3 cards from a deck, assigning the probability of drawing an ace, then a king, then a queen of the same suit, with and without replacing the cards after every draw
  • assigning probabilities to compound events involving the random selection of people from a given population; for example, selecting 2 names at random from all of the students at a high school and assigning the probability that they are both in Year 9

  VC2M9P01 | Mathematics | Mathematics Version 2.0 | Level 9 | Probability

• Mathematics: Level 9 description

  In Level 9, students develop familiarity with a broader range of non-linear and linear functions and relations, and related algebra and graphs.

  Students apply index laws with integer indices to a range of numerical expressions and extend this to algebraic expressions involving numbers and pro-numerals...

  Level description | Mathematics

• VC2M9ST03

  represent the distribution of multiple data sets for numerical variables using comparative representations such as back-to-back stem-and-leaf plots and histograms; describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi-modal’; compare data distributions using mean, median and range...

  Elaborations

  • describing the shape of the distribution of data using terms such as ‘positive skew’, ‘negative skew’, ‘symmetric’ and ‘bi-modal’
  • using stem-and-leaf plots to compare 2 like sets of data such as the heights of girls and the heights of boys in a class
  • constructing grouped histograms that show trends in health issues such as lung cancer, leukaemia, stroke and diabetes, and using the graph to justify, verify or invalidate claims
  • exploring comparative data presented in reports by the National Indigenous Australians Agency in regard to ‘Closing the Gap’, discussing the comparative distributions within the context of the data, for example, comparative data presented in the ‘Closing the Gap – Prime Minister’s Report’ 
  • comparing means, medians and ranges of 2 sets of numerical data that have been displayed using histograms, dot plots or stem-and-leaf plots

  VC2M9ST03 | Mathematics | Mathematics Version 2.0 | Level 9 | Statistics

• VC2M9A06

  use mathematical modelling to solve applied problems involving change, including financial contexts involving simple interest; formulate problems, choosing to use either linear or quadratic functions or other simple variations; interpret solutions in terms of the context; evaluate the model and...

  Elaborations

  • modelling practical contexts using linear functions such as cooking times that include resting or cooling times, or water leakage from water tanks, using tables and graphs or digital tools and algebraically
  • modelling measurement situations and determining the perimeter and areas of rectangles where the length, l, of the rectangle is a linear function of its width, w; for example, l=w,  l=w+5,  l=3w,  l=2w+7
  • modelling practical contexts (for example, area, paths of projectiles, parabolic mirrors, satellite dishes) using simple quadratic functions, tables and graphs (hand drawn or using digital tools) and, algebraically, interpreting features of the graphs such as the turning point and intercepts in context; for example, area, paths of projectiles, parabolic mirrors, satellite dishes
  • modelling and solving problems involving financial contexts using linear functions, for example, combinations of purchases of different items when they have a set amount of money to spend, profit/loss situations and trade quotes involving call-out fees
  • modelling situations involving change, for example, change in daily temperature during the ski season, fluctuation of speed above and below the speed limit, and acceleration and deceleration of a car coming to and moving off from a set of traffic lights
  • modelling the hunting techniques of Aboriginal and Torres Strait Islander Peoples using quadratic functions and exploring the effect of increasing the number of hunters to catch more prey 

  VC2M9A06 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VCSIS138

  Analyse patterns and trends in data, including describing relationships between variables, identifying inconsistencies in data and sources of uncertainty, and drawing conclusions that are consistent with evidence

  Elaborations

  • exploring relationships between variables using spreadsheets, databases, tables, charts, graphs and statistics
  • describing data properties (for example mean, median, range, outliers, large gaps visible on a graph) and their significance for a particular investigation sample, acknowledging uncertainties

  VCSIS138 | Science | Levels 9 and 10 | Science Inquiry Skills | Analysing and evaluating

• Chinese - Background Language Learner - 7–10 Sequence: Levels 9 and 10 achievement standards

  By the end of Year 10, students use spoken and written Chinese to initiate and sustain extended interactions with others in their social world and in the Chinese-speaking community, for example, 我的学校生活，澳大利亚的运动，我最喜欢的春节活动. They ask questions (for example, 你真的认为…吗？请想一想…) and adapt language...

  Level description | Languages | Chinese | Background Language Learner | 7–10 Sequence | Levels 9 and 10

• Civics and Citizenship: Levels 9 and 10 description

  The Level 9 and 10 curriculum builds students’ understanding of Australia’s political system and how it enables change. Students examine the ways political parties, interest groups, media and individuals influence government and decision-making processes. They compare Australia’s system of government...

  Level description | The Humanities | Civics and Citizenship

• VCMSP323

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

  Elaborations

  • investigating a range of data and its sources. For example, the age of residents in Australia, Cambodia and Tonga, or the number of subjects studied at school by 14-year-old students in Australia, Japan and Timor-Leste

  VCMSP323 | Mathematics | Level 9 | Statistics and Probability | Chance