This Durham Maths Mystery is designed to extend high achieving GCSE students and for use with students studying mathematics post-16.
Task 1A: students are presented with a blank three by three grid and twenty fact cards. Students have to use the clues on the fact cards to help them sketch the possible graphs in the correct place on the grid. The graphs described are all quadratic, cubic or quartic functions. Students are required to use facts about symmetry, where graphs cut the axes, maximum and minimum points and translations of given graphs to determine the missing graphs. Students are then asked to analyse their solution to determine which clues were used, which were not used and to determine whether they believe their solution to be unique
Task 1B: Students are presented with sixteen cards upon which are equations of quadratic, cubic and quartic functions. Students are requested to match cards which show equivalent equations.
Task 1C: Students use the equation cards from task 1B to match to the graphs produced in task 1A, and thereby refine their sketches, including the labeling of the coordinates of key points on the curves. Students are encouraged to use calculus to find maximum and minimum points in order to help justify their answers. Further Durham Maths Mysteries for Key Stage 3 and 4 can be found here.