Mathematical Modelling - Lower Secondary

Where to Land

Stage: 4 Challenge Level: Challenge Level:1

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?

Slippage

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

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance up the wall which the ladder can reach?

Friday 13th

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

This month there is a Friday the thirteenth and this year there are three. Can you explain why every year must contain at least one Friday the thirteenth?

Christmas Trees

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Christmas trees are planted in a rectangular array of 10 rows and 12 columns. The farmer chooses the shortest tree in each of the columns... the tallest tree from each of the rows ... Which is the taller tree, A or B?

Hands Together

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

Sometime during every hour the minute hand lies directly above the hour hand. At what time between 4 and 5 o'clock does this happen?