Linear and Non-Linear Equations: Level K

Solve linear equations

  • Solve problems involving linear equations, including those derived from formulas (ACMNA235)
  • Solve linear equations involving simple algebraic fractions (ACMNA240)
  • Solve problems involving parallel and perpendicular lines (ACMNA238)

Video: The Coordinate Geometry of Typography Page

Computers use mathematical expressions to display points, lines, curves and shapes to represent images.

Task: Graphing letters

Find the coordinates and gradients of the letters A and K before choosing your own letters to represent using linear and non-linear equations. One should include two lines that are parallel and two that are perpendicular – how do their gradients relate?


Solve simultaneous equations

  • Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology (ACMNA237)

Video: Solving linear simultaneous equations

Use number plumber and algebra to find the cheapest rental truck.

Task: Find the cheapest rental truck

Use number plumber (load theĀ Hiring-a-moving-truck example) and algebra to find the cheapest rental truck.


Solve inequalities

  • Solve linear inequalities and graph their solutions on a number line (ACMNA236)

Video: Graphing inequalities Page

Using Geogebra to graph inequalities

Task: “You sunk my inequality!”

Choose coordinates for your battleship and use inequalities to plot your opponent’s destruction! Optional game board.


Non-linear relationships

  • Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate (ACMNA239)
  • Solve simple quadratic equations using a range of strategies (ACMNA241)

Interactive: Graphing parabolas

Graph parabolas using Geogebra.

Interactive: Throwing a ball

Apply quadratic equations to projectile motion.