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Coke Machine

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design. Coins inserted into the machine slide down a chute into the machine and a drink is duly released. How many more revolutions does the foreign coin make over the 50 pence piece going down the chute? N.B. A 50 pence piece is a 7 sided polygon ABCDEFG with rounded edges, obtained by replacing AB with arc centred at E and radius EA; replacing BC with arc centred at F radius FB ...etc..

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Just Opposite

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

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Get Cross

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?

Wedge on Wedge

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

This problem, based on a structure that includes a compound angle, could be a standard post-16 trigonometry question, but offered here, with side lengths selected to make ratio calculations easy, we hope to encourage students to explore the construction on which the compound angle formulae rest.

The numbers were chosen to make calculation as easy as possible. It seemed that once students reached for a calculator to help them multiply or divide, they would think that the SIN, COS or TAN buttons were the answer here and this is not a terribly useful directon to take.

But there may be value in asking students how they might solve the problem with numbers that they make up for themselves (or for each other). Can they describe ageneral strategy? It is also useful at this point to ask whether all the side length data is necessary.

A short distance beyond Stage 4 students will have a range of formulae to apply to problems like this, our aim at this stage is to help them spend some time exploring the constructions that make those formulae possible or valid.