Interpreting and evaluating - July 2009, Stage 4&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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Back Fitter

Stage: 4 Challenge Level: Challenge Level:1

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

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Four on the Road

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Four vehicles travel along a road one afternoon. Can you make sense of the graphs showing their motion?

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Rationals Between

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What fractions can you find between the square roots of 56 and 58?

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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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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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Tangled Trig Graphs

Stage: 5 Challenge Level: Challenge Level:1

Can you work out the equations of the trig graphs I used to make my pattern?

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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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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.

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Operating Machines

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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