Inequalities

  • Integral Sandwich
    problem

    Integral Sandwich

    Age
    16 to 18
    Challenge level

    Generalise this inequality involving integrals.

  • Farey Neighbours
    problem

    Farey Neighbours

    Age
    16 to 18
    Challenge level

    Farey sequences are lists of fractions in ascending order of magnitude. Can you prove that in every Farey sequence there is a special relationship between Farey neighbours?

  • Erratic quadratic
    problem

    Erratic Quadratic

    Age
    16 to 18
    Challenge level

    Can you find a quadratic equation which passes close to these points?

  • Making Waves
    problem

    Making Waves

    Age
    16 to 18
    Challenge level

    Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?

  • Thousand Words
    problem

    Thousand Words

    Age
    16 to 18
    Challenge level

    Here the diagram says it all. Can you find the diagram?

  • Integral Inequality
    problem

    Integral Inequality

    Age
    16 to 18
    Challenge level

    An inequality involving integrals of squares of functions.

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