Creating and manipulating expressions and formulae

  • Ball bearings in a metal wheel.
    problem

    Ball Bearings

    Age
    16 to 18
    Challenge level
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    If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

  • Particularly general
    problem

    Particularly General

    Age
    16 to 18
    Challenge level
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    By proving these particular identities, prove the existence of general cases.
  • Operating machines
    problem

    Operating Machines

    Age
    16 to 18
    Challenge level
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    What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
  • Interpolating polynomials
    problem

    Interpolating Polynomials

    Age
    16 to 18
    Challenge level
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    Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.
  • Telescoping Functions
    article

    Telescoping Functions

    Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.
  • Magic squares for special occasions
    article

    Magic Squares for Special Occasions

    This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
  • Reaction rates!
    article

    Reaction Rates!

    Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...
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