Explaining, convincing and proving

  • Gradient match
    problem

    Gradient Match

    Age
    16 to 18
    Challenge level
    1 out of 3

    What can you deduce about the gradients of curves linking (0,0), (8,8) and (4,6)?

  • Turning to calculus
    problem

    Turning to Calculus

    Age
    16 to 18
    Challenge level
    1 out of 3

    Get started with calculus by exploring the connections between the sign of a curve and the sign of its gradient.

  • Inner equality
    problem

    Inner Equality

    Age
    16 to 18
    Challenge level
    1 out of 3

    Can you solve this inequalities challenge?

  • Archimedes Numerical Roots
    problem

    Archimedes Numerical Roots

    Age
    16 to 18
    Challenge level
    1 out of 3

    How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

  • More Dicey Decisions
    problem

    More Dicey Decisions

    Age
    16 to 18
    Challenge level
    1 out of 3

    The twelve edge totals of a standard six-sided die are distributed symmetrically. Will the same symmetry emerge with a dodecahedral die?

  • Seriesly
    problem

    Seriesly

    Age
    16 to 18
    Challenge level
    1 out of 3

    Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!

  • Patterns of inflection
    problem

    Patterns of Inflection

    Age
    16 to 18
    Challenge level
    1 out of 3

    Find the relationship between the locations of points of inflection, maxima and minima of functions.

  • Polynomial interpolation
    problem

    Polynomial Interpolation

    Age
    16 to 18
    Challenge level
    1 out of 3

    Can you fit polynomials through these points?

  • Proving the Laws of Logarithms
    problem

    Proving the Laws of Logarithms

    Age
    16 to 18
    Challenge level
    1 out of 3

    Here you have an opportunity to explore the proofs of the laws of logarithms.

  • Solving by squaring
    problem

    Solving by Squaring

    Age
    16 to 18
    Challenge level
    1 out of 3

    Which of the statements is true?