problem Agile Algebra Age 16 to 18 Challenge level Observe symmetries and engage the power of substitution to solve complicated equations.
problem Painting by functions Age 16 to 18 Challenge level Use functions to create minimalist versions of works of art.
problem Operating machines Age 16 to 18 Challenge level What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
problem 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?
problem Loch Ness Age 16 to 18 Challenge level Draw graphs of the sine and modulus functions and explain the humps.
problem Exploring cubic functions Age 14 to 18 Challenge level Quadratic graphs are very familiar, but what patterns can you explore with cubics?
problem Parabolas Again Age 14 to 18 Challenge level Here is a pattern composed of the graphs of 14 parabolas. Can you find their equations?
problem Ellipses Age 14 to 18 Challenge level Here is a pattern for you to experiment with using graph drawing software. Find the equations of the graphs in the pattern.
problem More Parabolic Patterns Age 14 to 18 Challenge level The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.
problem 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.