Quadratic equations

  • How old am I?
    problem
    Favourite

    How Old Am I?

    Age
    14 to 16
    Challenge level

    In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

  • Quadratic Patterns
    problem
    Favourite

    Quadratic Patterns

    Age
    14 to 16
    Challenge level

    Surprising numerical patterns can be explained using algebra and diagrams...

  • Partly Circles
    problem
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    Partly Circles

    Age
    14 to 16
    Challenge level

    What is the same and what is different about these circle questions? What connections can you make?

  • Mega Quadratic Equations
    problem
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    Mega Quadratic Equations

    Age
    14 to 18
    Challenge level

    What do you get when you raise a quadratic to the power of a quadratic?

  • Always Two
    problem
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    Always Two

    Age
    14 to 18
    Challenge level

    Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

  • In Between
    problem
    Favourite

    In Between

    Age
    16 to 18
    Challenge level

    Can you find the solution to this algebraic inequality?

  • Good Approximations
    problem

    Good Approximations

    Age
    16 to 18
    Challenge level
    Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.
  • Darts and Kites
    problem

    Darts and Kites

    Age
    14 to 16
    Challenge level
    Explore the geometry of these dart and kite shapes!
  • Golden Construction
    problem

    Golden Construction

    Age
    16 to 18
    Challenge level
    Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.
  • Symmetrically So
    problem

    Symmetrically So

    Age
    16 to 18
    Challenge level
    Exploit the symmetry and turn this quartic into a quadratic.
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