Exploring and noticing

  • Which spinners?
    problem
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    Which Spinners?

    Age
    14 to 18
    Challenge level
    1 out of 3

    Can you work out which spinners were used to generate the frequency charts?

  • Trapezium made of wooden tangram pieces, including a square and a parallelogram.
    problem
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    Quad in Quad

    Age
    14 to 18
    Challenge level
    2 out of 3

    Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

  • Exploring cubic functions
    problem
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    Exploring Cubic Functions

    Age
    14 to 18
    Challenge level
    2 out of 3

    Quadratic graphs are very familiar, but what patterns can you explore with cubics?

  • Negative 3 to the power of negative 3.
    problem
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    Negative Powers

    Age
    14 to 18
    Challenge level
    2 out of 3

    What does this number mean? Which order of 1, 2, 3 and 4 makes the highest value? Which makes the lowest?

  • Back fitter
    problem
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    Back Fitter

    Age
    14 to 18
    Challenge level
    2 out of 3

    10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

  • Three by One
    problem
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    Three by One

    Age
    16 to 18
    Challenge level
    1 out of 3

    There are many different methods to solve this geometrical problem - how many can you find?

  • Equation Attack
    problem
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    Equation Attack

    Age
    16 to 18
    Challenge level
    1 out of 3

    The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.

  • Root hunter
    problem
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    Root Hunter

    Age
    16 to 18
    Challenge level
    1 out of 3

    In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

  • Climbing Powers
    problem
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    Climbing Powers

    Age
    16 to 18
    Challenge level
    2 out of 3

    Does it make any difference how we write powers of powers? 

  • It's only a minus sign
    problem
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    It's Only a Minus Sign

    Age
    16 to 18
    Challenge level
    2 out of 3

    Solve these differential equations to see how a minus sign can change the answer