Geometry and Algebra - October 2006, Stage 3&4

Problems

problem icon

Decoding Transformations

Stage: 3 Challenge Level: Challenge Level:1

See the effects of some combined transformations on a shape. Can you describe what the individual transformations do?

problem icon

Combining Transformations

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

Does changing the order of transformations always/sometimes/never produce the same transformation?

problem icon

Simplifying Transformations

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

How many different transformations can you find made up from combinations of R, S and their inverses? Can you be sure that you have found them all?

problem icon

Points in Pairs

Stage: 4 Challenge Level: Challenge Level:1

In the diagram the radius length is 10 units, OP is 8 units and OQ is 6 units. If the distance PQ is 5 units what is the distance P'Q' ?

problem icon

The Line and Its Strange Pair

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

In the diagram the point P' can move to different places along the dotted line. Each position P' takes will fix a corresponding position for P. If P' moves along a straight line what does P do ?

problem icon

Mapping the Wandering Circle

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

In the diagram the point P can move to different places around the dotted circle. Each position P takes will fix a corresponding position for P'. As P moves around on that circle what will P' do?

problem icon

Intersections

Stage: 4 and 5 Challenge Level: Challenge Level:1

Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?