October 2002, Stage 4&5

Problems

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LOGO Challenge 8 - Rhombi

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

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

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Excel Technique: Inserting an Increment Button

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Learn how to make a simple table using Excel.

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Excel Interactive Resource: Make a Copy

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

This investigation uses Excel to optimise a characteristic of interest.

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Diagonals for Area

Stage: 4 Challenge Level: Challenge Level:1

Prove that the area of a quadrilateral is given by half the product of the lengths of the diagonals multiplied by the sine of the angle between the diagonals.

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Number Rules - OK

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

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

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

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

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Flexi Quads

Stage: 5 Challenge Level: Challenge Level:1

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

Stage: 5 Challenge Level: Challenge Level:1

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

Stage: 5 Challenge Level: Challenge Level:1

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.