Visualising and representing

  • Polygon walk
    problem

    Polygon walk

    Age
    16 to 18
    Challenge level
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    Go on a vector walk and determine which points on the walk are closest to the origin.

  • Paintbrush and different coloured watercolour paint blocks.
    problem

    Painting by numbers

    Age
    16 to 18
    Challenge level
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    How many different colours of paint would be needed to paint these pictures by numbers?

  • Painting by functions
    problem

    Painting by functions

    Age
    16 to 18
    Challenge level
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    Use functions to create minimalist versions of works of art.
  • Thinking Mathematically - Short Problems
    problem

    Quick sum

    Age
    16 to 18
    Challenge level
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    Is this surd sum exactly 3?

  • Calculus analogies
    problem

    Calculus analogies

    Age
    16 to 18
    Challenge level
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    Consider these analogies for helping to understand key concepts in calculus.

  • Placeholder: several colourful numbers
    problem

    Speedo

    Age
    16 to 18
    Challenge level
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    Investigate the relationship between speeds recorded and the distance travelled in this kinematic scenario.

  • Polar Bearings
    problem

    Polar bearings

    Age
    16 to 18
    Challenge level
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    What on earth are polar coordinates, and why would you want to use them?
  • Trig reps
    problem

    Trig reps

    Age
    16 to 18
    Challenge level
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    Can you deduce the familiar properties of the sine and cosine functions starting from these three different mathematical representations?
  • Circles ad infinitum
    problem

    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

    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?