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### 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 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 ...

### 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 ...

This is an excerpt from a six-minute silent documentary dating from 1921 and entitled 'Korumburra, South Gippsland, Vic'. It begins with an intertitle which reads 'Unloading the Cream.' and shows two covered carts or wagons, each pulled by four horses, delivering cream to the Korumburra Cooperative Butter Factory. The wagons ...

### Working at the Nissan factory, Melbourne, 1979

This is a colour photograph taken on 14 September 1979 inside the Nissan car company's manufacturing plant in the south-eastern Melbourne suburb of Clayton. It shows an unidentified male refugee from Vietnam working in the body shop, a subassembly area before parts were taken to the full assembly line. He is using an electric-powered ...

### Astor television factory, Melbourne, 1956

This is a black-and-white photograph taken in 1956 of the Astor television factory. At the end of a row of identical television sets, a man can be seen assembling a television set. The image is titled, 'Assembling components of TV sets at the Radio Corporation of Australia 'Astor' factory in Grant Street, South Melbourne'.

### Car production line, 1928

This is a black-and-white photograph of car bodies being built at Holden's Motor Body Builders in Woodville, South Australia in 1928. It shows unfinished car bodies (mainly open-topped tourers) on stands that could be slid along a track. In the background men can be seen working on tourer car bodies. Sedan bodies, in which ...

### Sugar production, c1962 - asset 5

This is a clip taken from silent colour film footage, shot in about 1962, illustrating aspects of sugar production in the Maryborough district of south-east Queensland. A sequence of medium and close-up shots shows three men working in a section of the Maryborough Sugar Factory. Hessian bags are being filled with raw sugar ...

### A Day in a Biscuit Factory, 1932: 'Served by discerning hostesses'

This clip shows a range of manufacturing activities taking place at the Swallow and Ariell biscuit factory in Melbourne in 1932. Almost all the scenes in the clip depict female workers engaged in the production or decoration of biscuits, cakes or other 'dainty confectionary'. The tasks include operating light machinery, ...

### Birth of a Car, c1948: 'An Australian car is born'

This black-and-white clip shows a Holden FX, the first mass-produced Australian-made car, being assembled on a production line at the Holden plant at Fishermens Bend in Victoria in 1948. It shows the sedan body being fitted with the front and rear axles and components such as the six-cylinder motor, before the car goes ...

### GeogSpace: year 2 - exemplar

This is a web page consisting of an overview and two illustrations of practice on the GeogSpace website, a resource for teachers. The focus is on a student's understanding of the earth, as represented by a world map and a globe. Illustration 1 is a set of activities using a globe of the world as a model of the earth. Illustration ...