Here we collect some 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 to. |

More or less? | Assess your skills of estimation and understanding of measurement. This is a good overall workout in the basic equations of science. |

Graphic biology | This problem will hone your skills with the interpretation and use of graphs whilst drawing on all of your knowledge of biology. |

Natural shapes | 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 you. |

Chi-squared faker | 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. |

Blood buffers | This problem gives practice in the advanced used of logarithms and gives insights into titration curves. |

Drug stabiliser | 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 throughout.