Being curious

  • Napkin
    problem
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    Napkin

    Age
    14 to 16
    Challenge level
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    A napkin is folded so that a corner coincides with the midpoint of an opposite edge. Investigate the three triangles formed.

  • Hexy-Metry
    problem
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    Hexy-Metry

    Age
    14 to 16
    Challenge level
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    A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

  • Dating made Easier
    problem
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    Dating Made Easier

    Age
    14 to 16
    Challenge level
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    If a sum invested gains 10% each year how long before it has doubled its value?

  • Fit for photocopying
    problem
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    Fit for Photocopying

    Age
    14 to 16
    Challenge level
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    Explore the relationships between different paper sizes.

  • Parabolic Patterns
    problem
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    Parabolic Patterns

    Age
    14 to 18
    Challenge level
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    The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.

  • Vector journeys
    problem
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    Vector Journeys

    Age
    14 to 18
    Challenge level
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    Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

  • Which spinners?
    problem
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    Which Spinners?

    Age
    14 to 18
    Challenge level
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    Can you work out which spinners were used to generate the frequency charts?

  • Summing geometric progressions
    problem
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    Summing Geometric Progressions

    Age
    14 to 18
    Challenge level
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    Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

  • Perception versus reality
    problem
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    Perception Versus Reality

    Age
    14 to 18
    Challenge level
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    Infographics are a powerful way of communicating statistical information. Can you come up with your own?

  • Iff
    problem
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    Iff

    Age
    14 to 18
    Challenge level
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    Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?