Visualising and representing

  • Areas and Ratios
    problem
    Favourite

    Areas and Ratios

    Age
    16 to 18
    Challenge level
    2 out of 3

    Do you have enough information to work out the area of the shaded quadrilateral?

  • Orthogonal Circle
    problem
    Favourite

    Orthogonal Circle

    Age
    16 to 18
    Challenge level
    2 out of 3

    Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

  • Cubestick
    problem
    Favourite

    Cubestick

    Age
    16 to 18
    Challenge level
    2 out of 3

    Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.

  • Loch Ness
    problem
    Favourite

    Loch Ness

    Age
    16 to 18
    Challenge level
    2 out of 3

    Draw graphs of the sine and modulus functions and explain the humps.

  • Differential equation matcher
    problem
    Favourite

    Differential Equation Matcher

    Age
    16 to 18
    Challenge level
    2 out of 3

    Match the descriptions of physical processes to these differential equations.

  • Aim high
    problem
    Favourite

    Aim High

    Age
    16 to 18
    Challenge level
    2 out of 3

    How do you choose your planting levels to minimise the total loss at harvest time?

  • Folium of Descartes
    problem
    Favourite

    Folium of Descartes

    Age
    16 to 18
    Challenge level
    3 out of 3

    Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.

  • Matchsticks
    problem

    Matchsticks

    Age
    7 to 11
    Challenge level
    1 out of 3
    Reasoning about the number of matches needed to build squares that share their sides.
  • Coke machine
    problem

    Coke Machine

    Age
    14 to 16
    Challenge level
    1 out of 3
    The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
  • Wrapping Gifts
    problem

    Wrapping Gifts

    Age
    16 to 18
    Challenge level
    1 out of 3
    A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?