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Listed under:  Mathematics  >  Algebra  >  Mathematical expressions  >  Polynomials
Teacher resource

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.

Teacher resource

TIMES Module 34: Number and Algebra: quadratic equations - teacher guide

This is a 19-page guide for teachers. It introduces quadratic equations and methods for solving them.

Teacher resource

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.

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 ...

Moving Image

Solving equations with the distributive property

This is a video demonstration of solving a linear equation by algebraic means. In the commentary, the presenter carefully explains the step-by-step method used to solve this example, which includes use of the distributive law and collecting like terms to simplify the equation. Having found the solution, the presenter verifies ...

Teacher resource

Coordinate geometry

This is a teacher resource for coordinate geometry consisting of a website and a PDF with identical content. The website contains a screencast discussing the solution of an exercise. The resource contains the distance formula; methods for finding the midpoint of two points and dividing an interval in a given ratio; determining ...

Moving Image

Nautical Robots

How might you find out how much and where the Earth's oceans are warming? Watch the report by Ruben Meerman and discover how more than 3000 'nautical robots', known as argo floats, have been placed in the oceans to collect data on variations in temperature, pressure and salinity.

Interactive Resource

Graphing calculator by Desmos - iTunes 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. Free when reviewed on 12/5/2015.

Interactive Resource

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. Free when reviewed on 12/5/2015.

Teacher resource

reSolve: Algebra: Sums & Differences of Squares

This sequence of three lessons explores sums and differences of two squares. Students are introduced to the historical context of using lookup tables for multiplications and challenged to investigate and generalise the underlying process using algebraic means. In subsequent lessons students use visual and algebraic methods ...

Video

Using linear equations to model population growth, Hooke's Law and parcel shipping charges

In this animated presentation students are provided with three examples of mathematical modelling in real-world settings. Linear functions are used to model population growth, Hooke's Law and parcel shipping charges.

Interactive resource

Differential calculus: linear graphs

Observe the linear distance–time graph of a rocket travelling at a constant velocity. Calculate the average and instantaneous velocity of the rocket over different time intervals. Notice how as each time interval becomes smaller the rocket's average velocity is equivalent to its instantaneous velocity. Work out how the ...

Interactive resource

Differential calculus: power functions

Observe the non-linear graphs of various power functions (such as f(x) = x², or f(x) = x³) and select the expressions for finding the gradient of the secant between small changes in x represented by Δx. Tabulate the values of f'(x) and plot the derivative of each function. Determine the pattern between the graphs for each ...

Interactive resource

Differential calculus: cubic function

Observe the non-linear distance–time graph of a rocket travelling at a changing velocity. The distance, s, travelled by the rocket after t seconds is determined by the formula s(t) = t³ – 2. Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results and look ...

Interactive resource

Differential calculus: derivatives graphing tool

Use this revision tool to examine the relationship between functions and their derivatives by observing their graphs. Select a polynomial function (for example, f(x) = x³ – 3x²) from the menu. Estimate the gradients of the given tangents and position them on the graph of the function. Draw the graph of the derivative function. ...

Interactive resource

Differential calculus: linear and non-linear graphs

Observe the linear and non-linear distance–time graphs of a rocket travelling at both constant and changing velocities. Calculate the average and instantaneous velocities of the rocket over different time intervals. Notice what happens to the average and instantaneous velocities as the time intervals become smaller. Work ...

Interactive resource

Differential calculus: derivatives and power functions

Observe the non-linear distance-time graph of a rocket travelling at a changing velocity. Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results and derive a formula for finding the instantaneous velocity at a given point. In the second activity, observe ...

Interactive resource

Differential calculus: cubic and quartic functions

Observe the non-linear time graph of a rocket travelling at a changing velocity. The distance, s, travelled by the rocket after t seconds is determined by the formulas: s(t) = t³ – 2 and s(t) = t⁴ + t². Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results ...

Assessment resource

Lights, camera, action: camera: assessment

Test your understanding of how camera shots are used to tell a story in films. For instance, you have been enrolled at the Spellberg School of Film, where you are assessed on your camera work skills. First, immerse yourself in basic film terms, then do a quiz on them. Next, choose five shots for a horror film. You select ...

Assessment resource

Picture story: outdoor adventure: assessment

Test your ability to create a movie from a still picture by choosing shots and camera moves. As a practice task, use software tools to recreate a movie about horseriding. See how combinations of camera shots hide things from, or reveal things to, the audience and create mood. Apply these skills to an assessment by telling ...