Interpreting and Evaluating - January 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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OK! Now Prove It

Stage: 5 Challenge Level: Challenge Level:1

Make a conjecture about the sum of the squares of the odd positive integers and prove your conjecture.

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Rain or Shine

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

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.

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So Big

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

One side of a triangle is divided into segments of length a and b by the inscribed circle, with radius r. Prove that the area is: abr(a+b)/ab-r^2

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Chi-squared Faker

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

How would you massage the data in this Chi-squared test to both accept and reject the hypothesis?

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Mind Your Ps and Qs

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

Sort these mathematical propositions into a series of 8 correct statements.

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