Coordinates - February 2005, Stage 4&5

Problems

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Lost on Alpha Prime

Stage: 4 Challenge Level: Challenge Level:1

On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?

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Tracking Points

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

Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?

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Something in Common

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

A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.

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Exponential Trend

Stage: 5 Challenge Level: Challenge Level:1

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.

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Pitchfork

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

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

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Polar Flower

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

This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.