Picturing Mathematics and Graph Sketching - September 2004, Stage 4&5

Problems

Changing Places

Stage: 4 Challenge Level:

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

Inside Out

Stage: 4 Challenge Level:

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

Bus Stop

Stage: 4 Challenge Level:

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .

Climbing

Stage: 5 Challenge Level:

Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.

Area L

Stage: 5 Challenge Level:

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?

Thousand Words

Stage: 5 Challenge Level:

Here the diagram says it all. Can you find the diagram?