October 2002, Stage 4&5

Problems

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LOGO Challenge 8 - Rhombi

Age 7 to 16 Challenge Level:

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

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Excel Technique: Using Paste Special to Lift a Copy of Values

Age 11 to 16 Challenge Level:

Learn how to use advanced pasting techniques to create interactive spreadsheets.

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Excel Technique: Inserting an Increment Button

Age 11 to 16 Challenge Level:

Learn how to use increment buttons and scroll bars to create interactive Excel resources.

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Excel Technique: Making a Table for a Function of Two Independent

Age 11 to 16 Challenge Level:

Learn how to make a simple table using Excel.

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Excel Interactive Resource: Make a Copy

Age 11 to 16 Challenge Level:

Investigate factors and multiples using this interactive Excel spreadsheet. Use the increment buttons for experimentation and feedback.

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Excel Investigation: Ring on a String

Age 11 to 16 Challenge Level:

This investigation uses Excel to optimise a characteristic of interest.

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Shopping Basket

Age 11 to 16 Challenge Level:

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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Number Rules - OK

Age 14 to 16 Challenge Level:

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...

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Back to Basics

Age 14 to 16 Challenge Level:

Find b where 3723(base 10) = 123(base b).

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Flexi Quads

Age 16 to 18 Challenge Level:

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?

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Diverging

Age 16 to 18 Challenge Level:

Show that for natural numbers x and y if x/y > 1 then x/y>(x+1)/(y+1}>1. Hence prove that the product for i=1 to n of [(2i)/(2i-1)] tends to infinity as n tends to infinity.

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Sine Problem

Age 16 to 18 Challenge Level:

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.

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Diagonals for Area

Age 16 to 18 Challenge Level:

Can you prove this formula for finding the area of a quadrilateral from its diagonals?