Mathematical Modelling - November 2007, Stage 4&5

Problems

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Under the Ribbon

Stage: 4 Challenge Level: Challenge Level:1

A ribbon is nailed down with a small amount of slack. What is the largest cube that can pass under the ribbon ?

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The Legacy

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

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

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The Fire-fighter's Car Keys

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

A fire-fighter needs to fill a bucket of water from the river and take it to a fire. What is the best point on the river bank for the fire-fighter to fill the bucket ?.

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The Invertible Trefoil

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

When is a knot invertible ?

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Funnel

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

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

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Cola Can

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

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

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Bridge Builder

Stage: 5 Challenge Level: Challenge Level:1

In this short problem we investigate the tensions and compressions in a framework made from springs and ropes.

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Overarch 1

Stage: 5 Short Challenge Level: Challenge Level:1

This short question asks if you can work out the most precarious way to balance four tiles.

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Odd One Out

Stage: 5 Short Challenge Level: Challenge Level:1

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

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Making More Tracks

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

Given the equation for the path followed by the back wheel of a bike, can you solve to find the equation followed by the front wheel?

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More Bridge Building

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

Which parts of these framework bridges are in tension and which parts are in compression?