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NSW Syllabuses

Mathematics Standard Stage 6 - Year 12 Standard 1 - Algebra MS-A3 Types of Relationships 📎

Outcomes

A student:

  • MS1-12-1

    uses algebraic and graphical techniques to evaluate and construct arguments in a range of familiar and unfamiliar contexts

  • MS1-12-6

    represents the relationships between changing quantities in algebraic and graphical forms

  • MS1-12-9

    chooses and uses appropriate technology effectively and recognises appropriate times for such use

  • MS1-12-10

    uses mathematical argument and reasoning to evaluate conclusions, communicating a position clearly to others

Related Life Skills outcomes: MALS6-1, MALS6-7, MALS6-8, MALS6-13, MALS6-14

 

  • Subtopic Focus

  • The principal focus of this subtopic is the graphing and interpretation of relationships, and the use of simultaneous linear equations in solving practical problems.
  • Students develop their ability to communicate concisely, use equations to describe and solve practical problems, and use algebraic or graphical representations of relationships to predict future outcomes.
  • Within this subtopic, schools have the opportunity to identify areas of Stage 5 content which may need to be reviewed to meet the needs of students.
  • Content

  • A3.1: Simultaneous linear equations
  • Students:
  • solve a pair of simultaneous linear equations graphically, by finding the point of intersection between two straight-line graphs, using technology  PC ICT
  • develop a pair of simultaneous linear equations to model a practical situation AAMPC CCTICT
  • solve practical problems that involve finding the point of intersection of two straight-line graphs, for example determine and interpret the break-even point of a simple business problem where cost and revenue are represented by linear equations AAMPC WE
  • A3.2: Graphs of practical situations
  • Students:
  • construct a graph from a table of values both with and without digital technology ICT
  • use values of physical phenomena, eg the growth of algae in a pond over time, or the rise and fall of the tide against a harbour wall over time to plot graphs and make predictions
  • sketch the shape of a graph from a description of a situation, for example the time passed and the depth of water in different shaped containers, or the speed of a race car as it moves around different shaped tracks CCT
  • determine the best model (linear or exponential) to approximate a graph by considering its shape, using technology where appropriate AAMPC CCTICT
  • identify the strengths and limitations of linear and non-linear models in given practical contexts AAM CCT