Mathematical challenges

Explore roots, eigenvectors, polar curves and Newton iteration

Make a prediction or construction, check it, then use the idea in an algebraic question.

Open the graph and construction studio

• Matrix transformation challenge

  Construct a matrix from the geometry of its image.

• Argand locus challenge

  Read the centre and boundary, then express the locus algebraically.

• Polar region challenge

  Choose limits that trace the boundary once, then calculate its area.

• Roots of unity construction

  Find the angle between neighbouring roots and list all the root indices.

• Differential equation matching

  Predict solution behaviour and apply an initial condition.

• Shortest path decisions

  Find the shortest route through a weighted graph and check its total length.