Powers and roots

  • Surds
    problem

    Surds

    Age
    14 to 16
    Challenge level

    Find the exact values of x, y and a satisfying the following system of equations: 1/(a+1) = a - 1 x + y = 2a x = ay

  • Archimedes and numerical roots
    problem

    Archimedes and Numerical Roots

    Age
    14 to 16
    Challenge level

    The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

  • Number rules - OK
    problem

    Number Rules - OK

    Age
    14 to 16
    Challenge level

    Can you produce convincing arguments that a selection of statements about numbers are true?

  • Small pepper seedlings in orange pots.
    problem

    Near 10

    Age
    14 to 16
    Challenge level

    10 must remain within easy reach...

  • Small tomato seedlings in pink pots.
    problem

    Powerful Order

    Age
    14 to 16
    Challenge level

    Powers of numbers might look large, but which of these is the largest...

  • Small tomato seedlings in pink pots.
    problem

    Roots Near 9

    Age
    14 to 16
    Challenge level

    For how many integers n is the difference between √n and 9 less than 1?

  • Root to Poly
    problem

    Root to Poly

    Age
    14 to 16
    Challenge level

    Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

  • Equal Temperament
    problem

    Equal Temperament

    Age
    14 to 16
    Challenge level

    The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.

  • Small tomato seedlings in pink pots.
    problem

    Integer Indices

    Age
    14 to 16
    Challenge level

    From this sum of powers, can you find the sum of the indices?

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