October 2002, Stage 4&5

Problems

LOGO Challenge 8 - Rhombi

Stage: 2, 3 and 4 Challenge Level:

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

Excel Technique: Inserting an Increment Button

Stage: 3 and 4 Challenge Level:

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

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

Stage: 3 and 4 Challenge Level:

Learn how to make a simple table using Excel.

Excel Interactive Resource: Make a Copy

Stage: 3 and 4 Challenge Level:

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

Excel Investigation: Ring on a String

Stage: 3 and 4 Challenge Level:

This investigation uses Excel to optimise a characteristic of interest.

Diagonals for Area

Stage: 4 Challenge Level:

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.

Number Rules - OK

Stage: 4 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...

Back to Basics

Stage: 4 Challenge Level:

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

Stage: 5 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?

Diverging

Stage: 5 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.

Sine Problem

Stage: 5 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.