Simultaneous equations

  • Graphs of changing areas
    problem

    Graphs of Changing Areas

    Age
    16 to 18
    Challenge level

    Use graphs to gain insights into an area and perimeter problem, or use your knowledge of area and perimeter to gain insights into the graphs...

  • Real(ly) numbers
    problem

    Real(ly) Numbers

    Age
    16 to 18
    Challenge level

    If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

  • Walls
    problem

    Walls

    Age
    16 to 18
    Challenge level

    Plane 1 contains points A, B and C and plane 2 contains points A and B. Find all the points on plane 2 such that the two planes are perpendicular.

  • Cobalt decay
    problem

    Cobalt Decay

    Age
    16 to 18
    Challenge level

    Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.

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