Visualising and representing

  • Orthogonal Circle
    problem

    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.

  • Five circuits, seven spins
    problem

    Five circuits, seven spins

    Age
    16 to 18
    Challenge level
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    A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.
  • Cubestick
    problem

    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

    Loch Ness

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

  • Differential equation matcher
    problem

    Differential equation matcher

    Age
    16 to 18
    Challenge level
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    Match the descriptions of physical processes to these differential equations.

  • Maths Shop Window
    problem

    Maths shop window

    Age
    16 to 18
    Challenge level
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    Make a functional window display which will both satisfy the manager and make sense to the shoppers
  • Hyperbolic thinking
    problem

    Hyperbolic thinking

    Age
    16 to 18
    Challenge level
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    Explore the properties of these two fascinating functions using trigonometry as a guide.
  • Gosh Cosh
    problem

    Gosh cosh

    Age
    16 to 18
    Challenge level
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    Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.

  • Curvy Equation
    problem

    Curvy equation

    Age
    16 to 18
    Challenge level
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    This problem asks you to use your curve sketching knowledge to find all the solutions to an equation.

  • To swim or to run?
    problem

    To swim or to run?

    Age
    16 to 18
    Challenge level
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    The famous film star Birkhoff Maclane wants to reach her refreshing drink. Should she run around the pool or swim across?