Interpreting and evaluating - July 2009, Stage 5

This month our problems involve aspects of the process of interpreting the information in a question and examining in various ways the solution or methods used to get the solution. For example, are the assumptions and arguments made correct or appropriate? How does the solution relate to the initial problem? Can we make sense of someone else's finding? Can we compare strategies used?

Problems

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Whose Line Graph Is it Anyway?

Stage: 5 Challenge Level: Challenge Level:1

Which line graph, equations and physical processes go together?

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Succession in Randomia

Stage: 5 Challenge Level: Challenge Level:1

By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?

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Calculus Countdown

Stage: 5 Challenge Level: Challenge Level:1

Can you hit the target functions using a set of input functions and a little calculus and algebra?

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Operating Machines

Stage: 5 Challenge Level: Challenge Level:1

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

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Area L

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Draw the graph of a continuous increasing function in the first quadrant and horizontal and vertical lines through two points. The areas in your sketch lead to a useful formula for finding integrals.

Elsewhere...