This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.
Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.
Parabolic patterns
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.
Doesn't add up
In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
Exploring cubic functions
Quadratic graphs are very familiar, but what patterns can you explore with cubics?
Perpendicular lines
Negatively triangular
How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
At right angles
Back fitter
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?
Surprising transformations
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?
What's that graph?
Can you work out which processes are represented by the graphs?
Tangled trig graphs
Can you work out the equations of the trig graphs I used to make my pattern?
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.