Mathematics / Year 10 / Number and Algebra / Linear and non-linear relationships

Curriculum content descriptions

Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation (ACMNA268)

Elaborations
  • investigating the features of graphs of polynomials including axes intercepts and the effect of repeated factors
General capabilities
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Curves,  Polynomials

Interactive

Desmos Graphing Calculator - Google Play app

Plot functions, create tables, add sliders and animate your graphs. Touch points of interest on the graph to show maximums, minimums and points of intersection. Type in an equation and watch the calculator solve the problem.

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TIMES Module 39: Number and Algebra: polynomials - teacher guide

This is a 27-page guide for teachers. This module introduces addition, subtraction, multiplication and division of polynomials. Factorisation of polynomials and the solution of polynomial equations are also discussed.

Interactive

Laptop wrap: Parallelendicular

Students construct a series of GeoGebra applets that investigate the parameters gradient and intercepts of straight lines. They reinforce this knowledge with Microsoft Math 3.0. 

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TIMES Module 33: Number and Algebra: factorisation - teacher guide

This is a 17-page guide for teachers. It continues the discussion of factorisation. In particular, the techniques for the factorisation of quadratic expressions are presented.

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Solving Linear Equations - Calculate

This unit of work focuses on solving linear equations. It includes an AMSI Interactive online module, a range of other AMSI Schools and external links and video tutorials and some extension or enrichment ideas. A short quiz at the end of the AMSI Interactive will help students to test their understanding at the completion ...

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Factorising Quadratics and Solving - Calculate

This activity explores the properties of the family of functions and their graphs known as parabolas. The unit includes an AMSI Interactive online module, a range of other AMSI Schools and external links and video tutorials and some extension or enrichment ideas to take their understanding further. A short quiz at the end ...

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Linear Relationships (and how Maths can help you choose a great car) - Calculate

The activity has students collecting their own information from a well-known Australia car buying website and using this to find an estimated relationship between the ‘asking price’ for a used car and the distance it has traveled in kilometres.

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Trade and Investment at a Glance

Using an illustrated report from the Department of Foreign Affairs and Trade, this Teacher guide provides ten learning sequences that engage students in the analysis and interpretation of data about Australian imports and exports. Students: identify Australia's major exports and imports; investigate international trade ...

Interactive

Algebra four

This is an interactive game for two students in which they solve algebraic equations, similar to 'Connect four'. The players can choose from problems that are one- or two-step, quadratic, have distributive properties or have variables on both sides, and more than one problem type can be chosen. The length of time each player ...

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Voronoi Diagrams - Calculate

This unit of work explores coordinate geometry in the context of Voronoi diagrams. Students use linear coordinate geometry to construct Voronoi diagrams by finding the gradient of a line segment, then finding the midpoint, a perpendicular line and finally the perpendicular bisector.

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The Mathematics of Projectiles - Calculate

This activity provides a practical introduction to the motion of projectiles with a focus on angles. It is designed as a lead in to parabolic and quadratic functions.