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Walls

Plane 1 contains points A, B and C and plane 2 contains points A and B. Find all the points on plane 2 such that the two planes are perpendicular.

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Maximum Scattering

Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?

Cut Cube

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

Points P, Q and R are drawn on a cube, one third of the way along the edges AB, GH and ED respectively, as shown in the diagram. The cube is then cut along the plane PQR. Which slice, if any, has the greater volume? Describe the shape and symmetries of the pieces obtained.