101 Mathematical Projects by Brian Bolt, David Hobbs

By Brian Bolt, David Hobbs

This booklet for academics indicates tasks which cater for a variety of innovations and talents, and hyperlinks with different curriculum topics.

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101 Mathematical Projects

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To make these competitions fair the 1000 point standard must represent the same level of performance in each event. How can this be achieved? How are the points awarded to the other levels of performance arrived at? 2 School events (a) Make up a pentathlon of running, jumping and throwing events for your own age group. Take the school's age group athletic records as your standard or some other measure which you think gives the same level of performance in each of thefivedisciplines you choose and award that 100 points.

4 How accurately must a ball be struck to enter a pocket? The black ball is a frequent target for potting when it is on its spot at the head of the table. Find the range of angles through which it can be hit to enter a top pocket. 5 The amount a ball slows down (a) while rolling, (b) through hitting a cushion, are important factors which a player must take into account when hitting a ball. Design experiments to investigate the retardation. Red ball 6 How is spin important to a cue ball? What is its effect and how is it used?

However, a player who has analysed and understood the game should never lose. The analysis of this and related games, together with the invention of new versions, gives plenty of scope for an interesting project. 1 Ordinary noughts and crosses 3 Four in a line (a) How many ways can a line of three Xs be put on a board? How many lines are controlled by an X in (i) the centre, (ii) the corner, (iii) the middle of a side? What is the smallest number of Xs which could block all the possible lines so preventing O winning?

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