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Prepare for university - mathematical biology
Helpful preparation for university for those intending to study biological sciences.
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problem
Pythagorean golden means
16 to 18
Show that the arithmetic mean, geometric mean and harmonic mean of
a and b can be the lengths of the sides of a right-angles triangle
if and only if a = bx^3, where x is the Golden Ratio.
problem
Quartics
16 to 18
Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the
parameter t varies.
article
On the importance of pedantry
A introduction to how patterns can be deceiving, and what is and is not a proof.
problem
Number pattern explorations
7 to 14
Investigate what happens if we create number patterns using some simple rules.
problem
Ideal gases
16 to 18
Problems which make you think about the kinetic ideas underlying
the ideal gas laws.
problem
Favourite
...on the wall
11 to 14
Explore the effect of reflecting in two intersecting mirror lines.
problem
Sort them out (2)
7 to 11
Can you each work out the number on your card? What do you notice?
How could you sort the cards?