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Listed under:  Mathematics  >  Algebra  >  Equations
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

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.

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 ...

Interactive resource

What's the problem: nature: level 1

Star as a contestant in a quiz show! Select three worded mathematical problems, about nature, from two categories: 'plants' or 'animals'. Identify the correct answer for each step in the problem-solving process. Examine the suggestions made by the panel to help you. Collect a prize based on your score. This is the first ...

Interactive resource

What's the problem: planets: level 1

Star as a contestant in a quiz show! Select three worded mathematical problems, about planets, from two categories: 'Earth and moon' or 'solar system'. Identify the correct answer for each step in the problem-solving process. Examine the suggestions made by the panel to help you. Collect a prize based on your score. This ...

Interactive resource

What's the problem: sports: level 1

Star as a contestant in a quiz show! Select three worded mathematical problems, about sports, from two categories: 'school sport' or 'world sport'. Identify the correct answer for each step in the problem-solving process. Examine the suggestions made by the panel to help you. Collect a prize based on your score. This is ...

Interactive resource

The take-away bar: make your own easy subtractions

Solve subtractions such as 58-9. Use a linear partitioning tool to help solve your own subtractions. Learn strategies to do complex arithmetic in your head. Split a subtraction into parts that are easy to work with, work out each part and then solve the original calculation. This learning object is one in a series of five objects.

Interactive resource

The take-away bar: make your own hard subtractions

Solve subtractions such as 93-47. Use a linear partitioning tool to help solve your own subtractions. Learn strategies to do complex arithmetic in your head. Split a subtraction into parts that are easy to work with, work out each part and then solve the original calculation. This learning object is one in a series of five ...

Interactive resource

The take-away bar: generate easy subtractions

Solve subtractions such as 28-9. Use a linear partitioning tool to help solve randomly generated subtractions. Learn strategies to do complex arithmetic in your head. Split a subtraction into parts that are easy to work with, work out each part and then solve the original calculation. This learning object is one in a series ...

Assessment resource

Thinking addition: 2-digit plus 2-digit: assessment

Test your ability to turn a word problem into an equation. Solve the equation without a calculator. For example, use a partitioning tool to help solve the sum 38+19. Choose which strategy you used to solve the problem. View and print a report of your results. This assessment object is the second in a series of two objects ...

Video

Moulin Rouge!, 2001: Love

This clip shows Christian, a love-struck writer, stealing a private moment with Satine, a courtesan, on the rooftops of the Moulin Rouge to convince her of the power of love. To counter Satine's belief that she cannot afford to fall in love with him, Christian speaks and sings lines from popular love songs. The lyrics, ...

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 ...