Functions and Graphs: Age 14-16

This is part of our collection of favourite rich tasks arranged by topic.

If you are a teacher, you can find the whole collection on our Secondary Curriculum teacher page.
Alternatively, if you are a student, you'll find the same problems on our Secondary Curriculum student page.


  • Five green equilateral triangles, arranged to almost make a complete pentagon.
    problem
    Favourite

    Doesn't Add Up

    Age
    14 to 16
    Challenge level

    In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

  • Perpendicular lines
    problem
    Favourite

    Perpendicular Lines

    Age
    14 to 16
    Challenge level

    Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

  • Small pepper seedlings in orange pots.
    problem
    Favourite

    Negatively Triangular

    Age
    14 to 16
    Challenge level

    How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

  • problem
    Favourite

    At Right Angles

    Age
    14 to 16
    Challenge level

    Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

  • Surprising Transformations
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    Favourite

    Surprising Transformations

    Age
    14 to 16
    Challenge level

    I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

  • Parabolic Patterns
    problem
    Favourite

    Parabolic Patterns

    Age
    14 to 18
    Challenge level

    The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.

  • Exploring cubic functions
    problem
    Favourite

    Exploring Cubic Functions

    Age
    14 to 18
    Challenge level

    Quadratic graphs are very familiar, but what patterns can you explore with cubics?

  • Curve fitter
    problem
    Favourite

    Curve Fitter

    Age
    14 to 18
    Challenge level

    This problem challenges you to find cubic equations which satisfy different conditions.

  • Back fitter
    problem
    Favourite

    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?

  • What's that graph?
    problem
    Favourite

    What's That Graph?

    Age
    14 to 18
    Challenge level

    Can you work out which processes are represented by the graphs?

  • Tangled Trig Graphs
    problem
    Favourite

    Tangled Trig Graphs

    Age
    16 to 18
    Challenge level

    Can you work out the equations of the trig graphs I used to make my pattern?

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