Inverse functions

For the final lesson in the three week plan in maths we have been looking at Inverse Functions. If you missed the lesson or just didn’t get it, here is a video by a very good but very american teacher. For what is required for Core 3, you don’t need to watch any further than about 7 minutes 13 seconds.

If you find the style a bit too much and you require something a bit more sober then here are some notes.

Combined Transformations and Composite Functions

For the second week of the year twelve three week plan, here are some supporting materials on Combined Transformations and Composite Functions.

First of all a nice animation on which order to do composite functions in.

Then some extra notes on combined transformations.

Domain and Range

Following on from the year twelve lessons this week, here are some supporting materials on domain and range.

First of all, a clear and concise video explaining domain and range:

Next a link to some notes and examples on Domain and Range.

Finally a link to an activity for finding the domain and range of a function using its graph.

Freaky Maths trick

Thanks to my mate Rob for putting me onto this.

Knight Moves

Knight Moves is a mildly enjoyable thriller from the early nineties. It is also the name of one my favourite maths puzzles/investigations. The only prior knowledge required for this problem is the moves a knight can make in chess. The idea is for the knight to make it around every square on a empty board without revisiting a square. The board does not have to be a standard chess board, my favourite incarnation involves a cross shaped board.

Two of my year eleven students have produced a fantastic environment for investigating this puzzle. The environment allows you to choose the shape of your board as well as the number of players – you can either try to find the route around the board by yourself or try to trap an opponent (or opponents) into being unable to make a legal move.

The problem has been around for hundreds of years, Wikipedia seems to think it has been around since the 9th Century. A quick Google (try Knight Tour as well as Knight Moves) will reveal that quite a few people have spent quite a lot of time dedicated to this puzzle.