Explore the two quadratic functions and find out how their graphs are related.
Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?
Here are some more quadratic functions to explore. How are their graphs related?
The NRICH Stage 5 weekly challenges are shorter problems aimed at Post-16 students or enthusiastic younger students. There are 52 of them.
Find the relationship between the locations of points of inflection, maxima and minima of functions.
Consider these analogies for helping to understand key concepts in calculus.
Observe symmetries and engage the power of substitution to solve complicated equations.
Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!
When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?