Interpreting and evaluating - July 2009, Stage 3&4

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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Parallel Lines

Stage: 3 Challenge Level: Challenge Level:1

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

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How Steep Is the Slope?

Stage: 3 Challenge Level: Challenge Level:1

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

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At Right Angles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

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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?