Visualising and representing

  • Hypotenuse Lattice points
    problem

    Hypotenuse Lattice Points

    Age
    14 to 16
    Challenge level

    The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

  • AMGM
    problem

    AMGM

    Age
    14 to 16
    Challenge level

    Can you use the diagram to prove the AM-GM inequality?

  • A Tilted Square
    problem

    A Tilted Square

    Age
    14 to 16
    Challenge level

    The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

  • Triangles within Pentagons
    problem

    Triangles Within Pentagons

    Age
    14 to 16
    Challenge level

    Show that all pentagonal numbers are one third of a triangular number.

  • Packing 3D shapes
    problem

    Packing 3D Shapes

    Age
    14 to 16
    Challenge level

    What 3D shapes occur in nature. How efficiently can you pack these shapes together?

  • Small pepper seedlings in turquoise pots.
    problem

    Centre Square

    Age
    14 to 16
    Challenge level

    What does Pythagoras' Theorem tell you about the radius of these circles?

  • Small pepper seedlings in turquoise pots.
    problem

    In or Out?

    Age
    14 to 16
    Challenge level

    Weekly Problem 52 - 2014
    Four arcs are drawn in a circle to create a shaded area. What fraction of the area of the circle is shaded?

  • Can you traverse it?
    problem

    Can You Traverse It?

    Age
    14 to 18
    Challenge level

    How can you decide if a graph is traversable?

  • Data matching
    problem

    Data Matching

    Age
    14 to 18
    Challenge level

    Use your skill and judgement to match the sets of random data.

  • Grass-covered hills beneath a blue sky.
    problem

    Curve Hunter

    Age
    14 to 18
    Challenge level

    This problem challenges you to sketch curves with different properties.

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