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

View on Australian Curriculum website Australian Curriculum, Assessment and Reporting Authority
Curriculum content descriptions

Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267)

Elaborations
  • applying transformations, including translations, reflections in the axes and stretches to help graph parabolas, rectangular hyperbolas, circles and exponential functions
General capabilities
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Transformation (Geometry),  Exponential functions,  Hyperbolic functions,  Parabolic functions

Video

Using exponents in real-life contexts

This animated presentation provides four examples of the use of exponential functions to model real-life practical situations. The examples highlight the manipulation of indices (exponents) and the index laws.

Interactive resource

EagleCat: parabola

Explore the graphs of quadratic equations in two forms: (a) the turning point form, y = a(x – h)² + k, and (b) the intercept form, y = (x – a)(x – b). Observe changes to the turning point and the shape of parabolic graphs through various transformations. Alternately, change the equation and observe changes in the x-intercepts ...

Teacher resource

Secondary mathematics: different representations

These seven learning activities, which focus on 'representations' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use different representations ...

Teacher resource

Exponential growth and doubling time

This resource aims to guide and support a mathematics teacher of Year 10 across three main areas as the class explores the mathematics of exponential growth. The contexts used are compound interest, animal and human population growth, and the growth (and decay) of bacteria populations.

Teacher resource

TIMES Module 35: Number and Algebra: the quadratic function - teacher guide

This is a 29-page guide for teachers. It introduces graphing of quadratic functions.

Interactive Resource

Rotational Transformations

An animated tutorial, describing the process of drawing the resulting image after rotation of a triangle, followed by an interactive quiz.

Interactive resource

Congruent triangles

Find out about congruent and non-congruent triangles and the conditions required to make them. Use line segments and angles to build two congruent triangles for three different combinations of sides and angles. Explore the SSS case (side, side, side), the SAS case (two sides and the included angle) and the ASA case (two ...

Teacher resource

reSolve: Mechanical Linkages: Geometry Proofs

This series of six lessons explores geometry proofs using real world contexts focused on the dynamics of linkages and moving joints. Students use physical models and computer simulations, the lessons move from a view of geometry as a study to static diagrams to encompass movement. Each lesson is outlined in detail including ...

Teacher resource

reSolve: Real World Algebra: Exponential Functions

This sequence of two lessons explores exponential functions as seen in the real world, linking the representations of function rules, graphs and tables of values. Students consider real world objects and data that can be described using exponential functions. They use simulations and modelling to investigate transformations, ...

Teacher resource

TIMES Module 22: Number and Algebra: consumer arithmetic - teacher guide

This is a 23-page guide for teachers, providing an introduction to the financial mathematics component of the number and algebra strands for years 9 and 10. A brief history of the concept of money concludes the module.

Text

In a spin

This resource is a web page containing a short task to explore volume of a solid shape. The task involves calculating the volume of the solid formed by rotating a right angled triangle about its hypotenuse A printable resource and solution is also available to support the task. This resource is an activity from the NRICH website.

Interactive resource

Trig degrees: sine tool

Use a unit circle tool to explore sine values for angles between 0° and 360°. Observe the graph being drawn as each sine value is plotted. This learning object is one in a series of nine objects. Three objects in the series are also packaged as a combined learning object.

Interactive resource

Trig degrees: cosine tool

Use a unit circle tool to explore cosine values for angles between 0° and 360°. Observe the graph being drawn as each cosine value is plotted. This learning object is one in a series of nine objects. Three objects in the series are also packaged as a combined learning object.

Moving Image

Maths of mouse plagues

How do pests such as mice reach plague proportions? The answer is that they can grow at an exponential rate. Watch this clip to see how that happens, but first enjoy (or squirm at) some footage of a real mouse plague.

Text

Volume of a Pyramid and a Cone

This resource is a web page containing an investigative task to explore volume. Derive the formulae for the volumes of a square-based pyramid and a cone, using mathematical concepts. A printable resource is also available to support the task. This resource is an activity from the NRICH website.

Teacher resource

TIMES Module 22: Measurement and Geometry: scale drawings and similarity - teacher guide

This is a 41-page guide for teachers. It contains an introduction to scale drawings and similarity, and in particular the tests for triangles to be considered similar. Applications of similarity are included throughout the module.

Assessment resource

Trigonometry: assessment

Test your understanding of angles and their sine, cosine and tangent values. Use a unit circle tool to find sine, cosine and tangent values in different quadrants. Use the tool to find the angle when given sine, cosine or tangent values. Determine the values for angles between 0° and 360°. Solve problems by using the unit ...

Interactive resource

Trig degrees: sine to 360

Use a unit circle tool to explore sine values in different quadrants. Determine the sin Ø values for angles between 0° and 360°. Observe the symmetry and patterns of the functions to predict the behaviour of sin Ø in different quadrants. Observe the graph animate and visually connect it with the unit circle tool and table ...

Moving Image

Calculations involving exponential growth: world population

Recently the world's population passed seven billion and it continues to grow by 200,000 people every day. Listen to some reasons why our population is growing at such a rate, and the strain this will put on resources such as food and water. This clip provides context for calculations involving exponential growth.

Interactive resource

Trig degrees

Use a unit circle tool to explore sine, cosine and tangent values in different quadrants. Determine the values for angles between 0° and 360°. Observe the symmetry and patterns of the functions to predict the behaviour of the graphs and the values for the functions in different quadrants. Observe the graphs animate and ...