Year 11+ Working systematically

  • problem
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    Shopping Basket

    Age
    11 to 16
    Challenge level
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    The items in the shopping basket add and multiply to give the same amount. What could their prices be?

  • Expenses
    problem
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    Expenses

    Age
    14 to 16
    Challenge level
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    What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?

  • Mathsland National Lottery
    problem
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    Mathsland National Lottery

    Age
    14 to 16
    Challenge level
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    Can you work out the probability of winning the Mathsland National Lottery?

  • Bendy Quad
    problem
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    Bendy Quad

    Age
    14 to 16
    Challenge level
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    Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

  • Squirty
    problem
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    Squirty

    Age
    14 to 16
    Challenge level
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    Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

  • Difference Sudoku
    problem
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    Difference Sudoku

    Age
    14 to 16
    Challenge level
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    Use the differences to find the solution to this Sudoku.

  • problem
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    Funnel

    Age
    14 to 16
    Challenge level
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    A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

  • 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 walk
    problem
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    Vector Walk

    Age
    14 to 18
    Challenge level
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    Starting with two basic vector steps, which destinations can you reach on a vector walk?