Area - July 2006, Stage 4&5

Problems

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Two Shapes & Printer Ink

Age 14 to 16 Challenge Level:

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

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Trapezium Four

Age 14 to 16 Challenge Level:

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

Age 14 to 16 Challenge Level:

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

Age 14 to 16 Challenge Level:

How much peel does an apple have?

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Integral Equation

Age 16 to 18 Challenge Level:

Solve this integral equation.

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Integral Sandwich

Age 16 to 18 Challenge Level:

Generalise this inequality involving integrals.

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Integral Inequality

Age 16 to 18 Challenge Level:

An inequality involving integrals of squares of functions.