In this feature we have collected together some problems about quadratic equations and sequences. We invite you to explore the problems, and explain and justify your conjectures using algebraic and diagrammatic representations.
problem
Quadratic patterns
Age
14 to 16
Challenge level
Surprising numerical patterns can be explained using algebra and diagrams...
problem
Hollow squares
Age
14 to 16
Challenge level
Which armies can be arranged in hollow square fighting formations?
problem
Difference of two squares
Age
14 to 16
Challenge level
What is special about the difference between squares of numbers adjacent to multiples of three?
problem
Pythagoras perimeters
Age
14 to 16
Challenge level
If you know the perimeter of a right angled triangle, what can you say about the area?