November 2009, Stage 4&5

This month many of our problems focus on properties of number and calculating. 'Playing' with the mathematics of a situation is often a good way to get into a problem and several resources this month lend themselves to that approach.

Problems

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What's Possible?

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

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

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A Question of Scale

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

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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Plus Minus

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

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

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Farey Approximation

Stage: 5 Short Challenge Level: Challenge Level:1

Use Farey sequences to obtain rational approximations to irrational numbers.

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Farey Fibonacci

Stage: 5 Short Challenge Level: Challenge Level:1

Investigate Farey sequences of ratios of Fibonacci numbers.

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Implicitly

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find the maximum value of the curve defined by this expression?

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Aim High

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

How do you choose your planting levels to minimise the total loss at harvest time?

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Ford Circles

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

Small circles nestle under touching parent circles when they sit on the axis at neighbouring points in a Farey sequence.

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Cobalt Decay

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

Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.