Simultaneous equations

  • 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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