Explaining, convincing and proving

  • Repetitiously
    problem
    Favourite

    Repetitiously

    Age
    14 to 16
    Challenge level
    2 out of 3

    Can you express every recurring decimal as a fraction?

  • Small pepper seedlings in orange pots.
    problem
    Favourite

    Terminology

    Age
    14 to 16
    Challenge level
    2 out of 3

    Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

  • Semi-detached
    problem
    Favourite

    Semi-Detached

    Age
    14 to 16
    Challenge level
    2 out of 3

    A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

  • problem
    Favourite

    Triangles and Petals

    Age
    14 to 16
    Challenge level
    2 out of 3

    An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

  • Inscribed in a Circle
    problem
    Favourite

    Inscribed in a Circle

    Age
    14 to 16
    Challenge level
    2 out of 3

    The area of a square inscribed in a circle with a unit radius is 2. What is the area of these other regular polygons inscribed in a circle with a unit radius?

  • Painted Cube
    problem
    Favourite

    Painted Cube

    Age
    14 to 16
    Challenge level
    2 out of 3

    Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

  • The Spider and the Fly
    problem
    Favourite

    The Spider and the Fly

    Age
    14 to 16
    Challenge level
    2 out of 3

    A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

  • Multiplication square
    problem
    Favourite

    Multiplication Square

    Age
    14 to 16
    Challenge level
    2 out of 3

    Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

  • Triangle in a Triangle
    problem
    Favourite

    Triangle in a Triangle

    Age
    14 to 16
    Challenge level
    2 out of 3

    Can you work out the fraction of the original triangle that is covered by the inner triangle?

  • Trapezium Four
    problem
    Favourite

    Trapezium Four

    Age
    14 to 16
    Challenge level
    2 out of 3

    The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?