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Listed under:  Mathematics  >  Algebra  >  Functions and relations
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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

EagleCat: trig-G

Explore the graphs of trigonometric equations in the form: (a) y = a sin[n(x - h)] + k, (b) y = a cos[n(x - h)] + k and (c) y = a tan[n(x - h)] + k. Use sliders or enter values to dilate, reflect and translate the basic trigonometric equations y = sin(x), y = cos(x) and y = tan(x), and observe the changes in the amplitude, ...

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: 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 ...

Teacher resource

Applications of differentiation

This is a teacher resource for applications of differentiation consisting of a website and a PDF with identical content. It contains a discussion of graph sketching, related rates of change and the solution of maxima and minima questions.

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 ...

Interactive resource

Differential calculus: non-linear graphs

Observe the non-linear distance–time graph of a rocket travelling at a changing 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 approaches its instantaneous velocity. Use the slider to ...

Interactive resource

Differential calculus: the derivative

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) = t². Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results and look for ...

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: quartic 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) = t⁴ + t². Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results and look ...

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 ...

Collection

Introduction to differential calculus

This collection of 17 digital curriculum resources (all learning objects) is organised into three sections: rates of change; differential calculus; and review of differential calculus via three learning objects. Students explore rates of change through liquid-pouring activities, and are introduced to the gradient of secants ...

Collection

Graphing functions

This collection contains five digital curriculum resources (all interactive learning objects) that introduce students to graphing linear, parabolic, cubic and trigonometric functions. Through exercises, students investigate how the constants in each function equation influence relevant aspects of graphing, such as dilations ...

Teacher resource

Starting Smart: what is next in the pattern? - years 6-8

This curriculum resource package is a ten-week middle years teaching plan and set of supporting resources to extend students' understanding of patterns and sequences. Students: identify, describe and extend patterns; construct tables of values; plot graphs; and develop skills to describe algebraically the relationships ...

Teacher resource

Integration

This is a teacher resource for integration consisting of a website and a PDF with identical content. The website contains a number of screencasts discussing the solutions of exercises, four interactives demonstrating estimations of area under curves, and accompanying screencasts describing the interactives. The resource ...

Teacher resource

Polynomials

This is a teacher resource for polynomials consisting of a website and a PDF with identical content. The website contains a number of screencasts discussing the solutions of exercises, a number of interactives demonstrating properties of polynomials and accompanying screencasts describing the interactives. The resource ...

Teacher resource

Quadratics

This is a teacher resource for quadratics consisting of a website and a PDF with identical content. The website contains a number of screencasts discussing the solutions of exercises, a number of interactives demonstrating properties of quadratics and accompanying screencasts describing the interactives. The resource contains ...

Teacher resource

Limits and continuity

This is a teacher resource for limits and continuity consisting of a website, a PDF with identical content and a number of screencasts discussing the solutions of exercises. An informal understanding of limits and continuity is important for secondary school calculus. This module provides this informal treatment and indicates ...