Visualising and representing

  • What's that graph?
    problem
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    What's That Graph?

    Age
    14 to 18
    Challenge level
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    Can you work out which processes are represented by the graphs?

  • Kite in a Square
    problem
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    Kite in a Square

    Age
    14 to 18
    Challenge level
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    Can you make sense of the three methods to work out what fraction of the total area is shaded?

  • Always Perfect
    problem
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    Always Perfect

    Age
    14 to 18
    Challenge level
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    Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

  • Parabella
    problem
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    Parabella

    Age
    16 to 18
    Challenge level
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    This is a beautiful result involving a parabola and parallels.

  • Three by One
    problem
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    Three by One

    Age
    16 to 18
    Challenge level
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    There are many different methods to solve this geometrical problem - how many can you find?

  • Circles ad infinitum
    problem
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    Circles Ad Infinitum

    Age
    16 to 18
    Challenge level
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    A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

  • Areas and Ratios
    problem
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    Areas and Ratios

    Age
    16 to 18
    Challenge level
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    Do you have enough information to work out the area of the shaded quadrilateral?

  • Orthogonal Circle
    problem
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    Orthogonal Circle

    Age
    16 to 18
    Challenge level
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    Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

  • Cubestick
    problem
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    Cubestick

    Age
    16 to 18
    Challenge level
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    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
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    Loch Ness

    Age
    16 to 18
    Challenge level
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    Draw graphs of the sine and modulus functions and explain the humps.