Here we collect 10 essential problems to get you thinking before
you embark on your degree course. We recommend that you try them
over the summer before starting university. We have also included a
short explanation of why each problem might be useful to you.
Remember, these problems are designed to make you think and there
is not necessarily a 'right' answer. Approach them in a thoughtful
way; it is to be hoped that they are both interesting and
stimulating. What questions do they raise in you mind? Where do
these questions lead you? Take them to a level that feels
comfortable for you.
Finally, once you have done the problems, study the solutions.
These will give you additional insights into the problems and the
underlying mathematics and science.
Big and small numbers in biology
||This problem will refine your skills at estimation and
approximation. There are several parts for you to come back
Using the haemocytometer
||This interactive page will give you practice in the sort of
proportional reasoning calculation routinely used in
More or less?
||Assess your skills of estimation and understanding of
measurement. This is a good overall workout in the basic equations
||This problem will hone your skills with the interpretation and
use of graphs whilst drawing on all of your knowledge of
||This interactive page lets you play with the basic ideas
concerning the modelling of disease dynamics.
||Here you can think about the shapes occurring in nature. This
is the sort of problem which you can take to any level and will get
you thinking about the geometrical properties of the world around
||Gets you thinking about statistical tests and how and why they
might, or might not, be as straightforward as they may seem.
Is your DNA unique?
||You will need to be clear with your probability and
combinatorics as you work through this fascinating problem.
||This problem gives practice in the advanced used of logarithms
and gives insights into titration curves.
||This problem will give you a problem-solving workout and
reinforce your understanding of decay processes.
You are also advised to read our interactive article which takes
you through a fascinating area of biology: genetics. You will need
a pencil and paper to hand as calculations are required