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Explore how matrices can fix vectors and vector directions.

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

Can you work out the parentage of the ancient hero Gilgamesh?

What groups of transformations map a regular pentagon to itself?

Can you find the pairs that represent the same amount of money?

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?

Investigate the normal distribution

Show that the edges $AD$ and $BC$ of a tetrahedron $ABCD$ are mutually perpendicular if and only if $AB^2 +CD^2 = AC^2+BD^2$. This problem uses the scalar product of two vectors.