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Broad Topics >

Advanced Algebra > Relations

##### Age 16 to 18 Challenge Level:

Given any two polynomials in a single variable it is always
possible to eliminate the variable and obtain a formula showing the
relationship between the two polynomials. Try this one.

##### Age 16 to 18 Challenge Level:

Find relationships between the polynomials a, b and c which are
polynomials in n giving the sums of the first n natural numbers,
squares and cubes respectively.

##### Age 16 to 18 Short Challenge Level:

If you plot these graphs they may look the same, but are they?

##### Age 16 to 18 Challenge Level:

The family of graphs of x^n + y^n =1 (for even n) includes the
circle. Why do the graphs look more and more square as n increases?

##### Age 16 to 18 Challenge Level:

Can you work out what simple structures have been dressed up in these advanced mathematical representations?