Functions and their inverses

  • Real-life equations
    problem
    Favourite

    Real-Life Equations

    Age
    16 to 18
    Challenge level

    Here are several equations from real life. Can you work out which measurements are possible from each equation?

  • Equation matcher
    problem
    Favourite

    Equation Matcher

    Age
    16 to 18
    Challenge level

    Can you match these equations to these graphs?

  • Area L
    problem
    Favourite

    Area L

    Age
    16 to 18
    Challenge level

    By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?

  • PCDF
    problem
    Favourite

    PCDF

    Age
    16 to 18
    Challenge level

    When can a pdf and a cdf coincide?

  • Machines
    problem

    Machines

    Age
    7 to 11
    Challenge level
    What is happening at each box in these machines?
  • Readme
    problem

    Readme

    Age
    16 to 18
    Challenge level
    Decipher a simple code based on the rule C=7P+17 (mod 26) where C is the code for the letter P from the alphabet. Rearrange the formula and use the inverse to decipher automatically.
  • Double time
    problem

    Double Time

    Age
    16 to 18
    Challenge level
    Crack this code which depends on taking pairs of letters and using two simultaneous relations and modulus arithmetic to encode the message.
  • Pitchfork
    problem

    Pitchfork

    Age
    16 to 18
    Challenge level
    Plot the graph of x^y = y^x in the first quadrant and explain its properties.
  • The Number Crunching Machine
    problem

    The Number Crunching Machine

    Age
    7 to 11
    Challenge level
    Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?
  • Curve match
    problem

    Curve Match

    Age
    16 to 18
    Challenge level

    Which curve is which, and how would you plan a route to pass between them?

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