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Listed under:  Arts  >  Backstage

### 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 ...

### 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 ...

### 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 ...

### 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 ...

### 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 ...

### 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 ...

### 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. ...

### 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 ...

### 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 ...

### 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 ...

### Sea rescue: plotting the course

Help a rescue crew to reach a sinking boat. Make a chart to guide the crew. Check the meaning of symbols, place them on a map and complete a key. Mark danger spots such as an oyster bed and submerged rock. Use the map to steer a safe course.

### Ready to race: wheels, jets, tyres and gears

Go to a race track and collect information from different kinds of visual texts to make your kart the fastest on the track. First, add important kart parts and choose the style of kart you want. Then collect information about the time and place of your race. Next, go to the garage to set up your kart before doing a starting ...

### Storyboard: Flutter-by friends!

Explore the title and picture on the cover of 'Flutter-by friends!' Then make a prediction about the storyline. Listen to the story and follow as each word is underlined. Find out if your prediction matches the storyline. Put the jumbled events of the story in the right order.

### 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 ...

### Biography: Federation people: Charles Todd

Investigate the role played in Federation by astronomer and engineer Charles Todd and his Overland Telegraph. Examine two different types of biographies of Todd: one short and the other more detailed. Inspect examples of how he was visually depicted in his time. This learning object is one in a series of objects in the ...

### Dice duels: two dice: assessment

Test your understanding of what occurs when dice are biased and your ability to distinguish between biased and uneven distributions. Interpret graphical representations of the results of rolls of dice to determine whether or not dice have been biased. Predict results when dice have been biased and faces are combined. Bias ...

### Dice duels: one dice: assessment

Test your understanding of what occurs when a dice is biased. Interpret graphical representations of the results of rolls of a dice to determine whether or not the dice has been biased. Use your understanding of even distributions, sample size and random variation to identify which face has been biased. This assessment ...

### Data - Years 5 and 6

The 11 learning objects in this collection relate to the use, collection, display, comparison and interpretation of statistical data. Objects in the first category, statistical graphs, enable students to compare and use a broad range of statistical graphs appropriately. Objects in the second category, surveys, explore and ...

### The cruise of the Kormoran, 1940-41

This is a nautical chart showing the route of the German auxiliary cruiser Kormoran, which was known as 'Raider G'. The chart shows the route the ship took across the Atlantic and Indian oceans during its operations between December 1940 and November 1941. The circles represent the locations of ships the Kormoran either ...

### 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 ...