Compound transformations

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.

What happens to these capital letters when they are rotated through one half turn, or flipped sideways and from top to bottom?

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

Sort the frieze patterns into seven pairs according to the way in which the motif is repeated.

A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

Can you find a way to turn a rectangle into a square?

Make a footprint pattern using only reflections.

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?

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