The following document contains effective questions for introducing calculus. Each question has a sample answer provided. Students should use these questions alongside the other resources highlighted within the document.
(i) will sketch a graph to show the rate at which the height of the water level changes with time for two cylindrical containers of different radii and an inverted cone of given radius.
(ii) investigate constant speed
A Teaching & Learning plan to help students
• understand what is meant by, and the difference between, average and instantaneous rates of change
• recognise the need for differential calculus in terms of real-world problems
• understand the concept of the derivative of a function
• understand that differentiation (differential calculus) is used to calculate instantaneous rates of change
• understand how to apply differentiation to calculate instantaneous rates of change
Introduce students to the average rate of change with this Khan Academy video. By watching the video, your students will be able to answer the following question:
What's the average rate of change of a function over an interval?
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