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
• develop a pair of simultaneous linear equations to model a practical situation
• 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
• A3.2: Graphs of practical situations
• Students:
• construct a graph from a table of values both with and without digital technology
• 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
• determine the best model (linear or exponential) to approximate a graph by considering its shape, using technology where appropriate
• identify the strengths and limitations of linear and non-linear models in given practical contexts