Exploring and noticing

  • Flipping Twisty Matrices
    problem

    Flipping Twisty Matrices

    Age
    14 to 18
    Challenge level

    Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.

  • Road maker
    problem

    Road Maker

    Age
    14 to 18
    Challenge level

    Which of these roads will satisfy a Munchkin builder?

  • A brief introduction to complex numbers
    problem

    A Brief Introduction to Complex Numbers

    Age
    14 to 18
    Challenge level

    In this problem, we define complex numbers and invite you to explore what happens when you add and multiply them.

  • Where are you flying?
    problem

    Where Are You Flying?

    Age
    14 to 18
    Challenge level

    Where do people fly to from London? What is good and bad about these representations?

  • Grass-covered hills beneath a blue sky.
    problem

    Curve Hunter

    Age
    14 to 18
    Challenge level

    This problem challenges you to sketch curves with different properties.

  • The Matrix
    problem

    The Matrix

    Age
    14 to 18
    Challenge level

    Explore a new way of multiplying with matrices.

  • A powerful Matrix
    problem

    A Powerful Matrix

    Age
    14 to 18
    Challenge level

    What happens when you find the powers of this matrix?

  • Square Pair
    problem

    Square Pair

    Age
    14 to 18
    Challenge level

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

  • Napoleon's Hat
    problem

    Napoleon's Hat

    Age
    16 to 18
    Challenge level

    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?

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