Exploring and noticing

Explore a new way of multiplying with matrices.

What happens when you find the powers of this matrix?

Explore the shape of a square after it is transformed by the action of a matrix.

Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?

Which curve is which, and how would you plan a route to pass between them?

What can you deduce about the gradients of curves linking (0,0), (8,8) and (4,6)?

Get started with calculus by exploring the connections between the sign of a curve and the sign of its gradient.

Find the location of the point of inflection of this cubic.

Here you have an opportunity to explore the proofs of the laws of logarithms.