Estimating and approximating

  • Ladder and Cube
    problem
    Favourite

    Ladder and Cube

    Age
    14 to 16
    Challenge level

    A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

  • Back fitter
    problem
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    Back Fitter

    Age
    14 to 18
    Challenge level

    10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

  • Equation Attack
    problem
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    Equation Attack

    Age
    16 to 18
    Challenge level

    The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.

  • Root hunter
    problem
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    Root Hunter

    Age
    16 to 18
    Challenge level

    In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

  • The not-so-simple pendulum 1
    problem
    Favourite

    The Not-So-Simple Pendulum 1

    Age
    16 to 18
    Challenge level

    See how the motion of the simple pendulum is not-so-simple after all.

  • Shedding Some Light
    problem

    Shedding Some Light

    Age
    7 to 11
    Challenge level
    Make an estimate of how many light fittings you can see. Was your estimate a good one? How can you decide?
  • Placeholder: several colourful numbers
    problem

    Counting Sweets

    Age
    7 to 14
    Challenge level
    How might you use mathematics to improve your chances of guessing the number of sweets in a jar?
  • Growing
    problem

    Growing

    Age
    16 to 18
    Challenge level
    Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)
  • Squaring the circle
    problem

    Squaring the Circle

    Age
    11 to 14
    Challenge level
    Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make an estimate.
  • 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?
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