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Listed under:  Mathematics  >  Algebra  >  Equations  >  Differentiation (Functions)
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.

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

TIMES Module 8: Statistics and Probability: data investigation and interpretation, year 10 - teacher guide

This is a 29-page guide for teachers. Box plots are introduced as another graphical tool and are used for comparisons of data. Scatter plots are used to explore relationships between quantitative (usually continuous) variables.

Dataset

Daily extremes

This resource is a Bureau of Meteorology (BOM) web page that provides tables of data for the top ten temperature and rainfall records around Australia on the day, month, season or year selected. Highest and lowest maximum and minimum temperatures, as well as the highest rainfall totals, are displayed and ranked. The tables ...

Dataset

Daily maximum temperature extremes graphs

This resource is a Bureau of Meteorology (BOM) web page that provides graphs that show the percentage area of the selected state or territory and the percentage area of Australia that experienced extremely hot, cold or wet conditions on each day of the month selected. Graphs on this page are available for the previous seven ...

Dataset

Daily maximum temperature extremes graph for Australia

This resource is a Bureau of Meteorology (BOM) web page providing graphs that show the percentage area of the selected state or territory, or the whole of Australia, that experienced extremely hot, cold or wet conditions on each day of the year selected. The graphs are available for the previous seven years and are based ...

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

reSolve: Real World Algebra: Quadratic Functions

This sequence of three lessons explores different representations of quadratic functions, with particular emphasis on turning points in quadratic graphs. Students use images of trajectories, inscribe their own curves using Geogebra and then further explore the algebraic representation of their curves. Each lesson is outlined ...

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: 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: 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 ...

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

Circuits - upper primary

This collection of 11 digital curriculum resources is organised in three categories - types of circuits; circuit applications; and conductors and insulators. Interactive learning objects enable students to build and manipulate simple series and parallel electric circuits. Students investigate how current flows, effects ...