Real(ly) Numbers

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

How Many Solutions?

Find all the solutions to the this equation.

After Thought

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?

Graphic Biology

Age 16 to 18 Challenge Level:

The graph above has several plots representing biological processes. Can you assign as many possible solutions to each of these plots?

Can you model each one as a mathematical function?

What units and labels would be appropriate for each of the axes, considering each plot in turn?