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Broad Topics > Information and Communications Technology > Graphical calculators

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Limiting Probabilities

Age 16 to 18 Challenge Level:

Given probabilities of taking paths in a graph from each node, use matrix multiplication to find the probability of going from one vertex to another in 2 stages, or 3, or 4 or even 100.

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Pitchfork

Age 16 to 18 Challenge Level:

Plot the graph of x^y = y^x in the first quadrant and explain its properties.

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Climbing

Age 16 to 18 Challenge Level:

Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.

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Quartics

Age 16 to 18 Challenge Level:

Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.