Esteemed reader: Appended to problem 42 is a dialogue highlighting an unsettling outcome of a limited (and limiting) approach to mathematics education.


212. Circle shard


In the diagram is a semicircle (half disk) with radius 5 cm.  The semicircle is divided into five equal arcs, as shown by the ().  Determine the area of the shaded region (coloured region).

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211. Saline system

There are 6% and 10% saline solutions.  By combining some of each of these solutions, and adding an extra 20 g of water, you want to make 200 g of an 8% saline solution.  Determine how many grams of the 6% and 10% solutions are needed.


210. December dodecagons


In the diagram is a regular dodecagon with sides 1 cm, with line segments connecting pairs of vertices to form a 12-pointed star.  Determine the area of the smaller dodecagon formed at the center.