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VCE 11 Methods 2023

4.11 Average and instantaneous rates of change

Interactive practice questions

A bucket containing water has a hole through which the water leaks. The graph shows the amount of water remaining in the bucket after a certain number of minutes.

Loading Graph...

a

What is the slope of the line?

b

What does the slope tell you?

The amount of water in the bucket increases by $1$1 litre every $\frac{1}{2}$12 minute.

A

The amount of water in the bucket decreases by $\frac{1}{2}$12 litre every minute.

B

The amount of water in the bucket decreases by $1$1 litre every $\frac{1}{2}$12 minute.

C

The amount of water in the bucket increases by $\frac{1}{2}$12 litre every minute.

D
Easy
3min

The graph shows the cost, in dollars, of a phone call for different call durations.

Easy
2min

The table shows Skye's progress through a four-hour ultramarathon.

Easy
3min

The table shows the linear relationship between the temperature on a particular day and the net profit of a store. Find the rate of change of net profit.

Easy
2min
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Outcomes

U1.AoS3.1

average and instantaneous rates of change in a variety of practical contexts and informal treatment of instantaneous rate of change as a limiting case of the average rate of change

U1.AoS3.4

average and instantaneous rates of change and their interpretation with respect to the graphs of functions

U1.AoS3.3

use of gradient of a tangent at a point on the graph of a function to describe and measure instantaneous rate of change of the function, including consideration of where the rate of change is positive, negative or zero, and the relationship of the gradient function to features of the graph of the original function.

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