Area - July 2006, Stage 4&5

Problems

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Two Shapes & Printer Ink

Stage: 4 Challenge Level: Challenge Level:1

If I print this page which shape will require the more yellow ink?

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Trapezium Four

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

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

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Areas of Parallelograms

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

Can you find the area of a parallelogram defined by two vectors?

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Peeling the Apple or the Cone That Lost Its Head

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

How much peel does an apple have?

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Integral Equation

Stage: 5 Challenge Level: Challenge Level:1

Solve this integral equation.

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Integral Sandwich

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

Generalise this inequality involving integrals.

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Integral Inequality

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

An inequality involving integrals of squares of functions.