Explaining, convincing and proving

  • 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?

  • Logical Cards
    problem

    Logical Cards

    Age
    16 to 18
    Challenge level
    1 out of 3

    Which of the cards provides the counter example?

  • Two Cubic Equations
    problem

    Two Cubic Equations

    Age
    16 to 18
    Challenge level
    1 out of 3

    Which statement correctly describes the real roots of the equation?

  • Fred's Maths Problems
    problem

    Fred's Maths Problems

    Age
    16 to 18
    Challenge level
    1 out of 3

    If the statement is not true, what can we say will be true?

  • Adding odd numbers (part 2)
    problem

    Adding Odd Numbers (part 2)

    Age
    16 to 18
    Challenge level
    1 out of 3

    Can you use Proof by Induction to establish what will happen when you add more and more odd numbers?

  • Tetra Slice
    problem

    Tetra Slice

    Age
    16 to 18
    Challenge level
    1 out of 3

    Can you prove that a quadrilateral drawn inside a tetrahedron is a parallelogram?

  • Be reasonable
    problem

    Be Reasonable

    Age
    16 to 18
    Challenge level
    2 out of 3

    Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.