Welcome to the bioNRICH problems. These are mathematical activities designed to complement and enhance the study of biology at A-level and undergraduate level.

The questions are broken down into key areas of mathematical activity. In each area, the activities are arranged roughly in order of difficulty / depth. To assist you in using the problems, we have a simple key:




The problem contains a flash interactive resource. Good for use on interactive whiteboards as a group activity or on individual computers.
The problem can be used as a quick starter or lesson filler. There might be several smaller pieces to the problem or it might quickly generate thought or discussion. This does not mean that the full potential of the problem will quickly be exhausted: you may wish to return to the problem several times or analyse the resulting issues in detail.
The problem quickly raises many interesting ideas and is particularly well suited to group discussion.




Area of Maths Question Description
Numbers Big and small numbers in biology 10 individual questions using numbers big and small to estimate and calculate various quantities in biological contexts.
A question of scale This interactive page allows you to test your knowledge and skill using powers of 10 to place physical quantities in order of size.
Measurement and estimation More or less? 10 individual questions asking you to assess the accuracy of a variety of biological estimates.
Scientific measurement This interactive page allows you to test your skills of measurement with a sequences of scientific images.
Using the haemocytometer This problem gives an interactive version of a haemocytometer, a tool used to measure cell counts in fluid samples. You can keep practising with new samples until you have cracked the maths.
Growth processes Bio-graphs Various graphs without labels are shown. What physical processes of situations might the graphs relate to?
Time to evolve Practice estimation in the context of evolution.
Catalyse that! Explore rates of a temperature dependent reaction.
Graphs and equations Real-life equations Relate these commonly used equations to points on a series of graphs. Which are possible and which are not?
Equation matching A series of graphs are given containing just 2 or 3 points. Which equations do the points rule out?
Units Bigger or smaller? Develop your intuition for changing units by asking the simple question: will a unit change give me a larger or smaller number?
Choose your units Which would be the most sensible units in which to measure these objects?
New units for old Give yourself an in-depth units workout by matching up these physical phenomena with their dimensions and standard units.
Data handling Stats Statements This question gives you 10 statistical statements. Develop your statistical intuition by asking yourself are they sometimes, always, nearly always, almost never or never true?
Very Old Man Is it likely someone could have lived to 200 years old? Use statistics to investigate.
Chi squared faker How could you massage this $\chi^2$-squared test to reject the hypothesis?
Moles and molarity Conversion sorter A molarity calculation has been written out and broken up into several pieces. Can you use the interactive tool to rearrange the pieces of the calculation into their logical order?
Mixed up mixtures A standard calibration for a spectrophotometric assay for lysozyme was performed and the data tabulated. The date has become mixed up. Can you reassemble it using the interactive card sorter?
Percentage, ratio and dilutions Dilution series calculator In this interactive tool a bacterial solution is diluted in four stages. Can you work out what the final concentration will be? Practice with new questions until you understand the process.
Exact dilutions Save on the washing up! Using just three beakers can you create dilutions of certain concentrations?
Investigating dilution series Follow on from the previous question by choosing the dilutions in each of four stages to try to match certain final targets.
Fractions and decimals The genes of Gilgamesh It is possible to create a genetic stock of the type that the hero Gilgamesh was said to possess?
Shapes Natural Shapes Think about the shapes that occur naturally in nature. Can you describe and group them according to their mathematical properties?
Fitting flat shapes Develop your understanding of area by visualising the best way in which you can pack various shapes together most efficiently. Does Nature pack shapes efficiently?
Efficient packing Go further that the previous question with a calculation to pack small circles into a large square.
Packing 3D shapes Can you visualise or sketch the packing of the sorts of 3D shapes which occur in nature?
Logarithms Power Match Get to grips with the meaning of logarithms by pinning the flags onto the logarithmic targets.
Temperature pH From a table of data for the dissociation constant of water at various temperatures, work out how hot water must be to have different pH values.
Mixing pH Use the pH formula to calculate the pH and concentrations of dilutions.
Extreme dissociation Take the pH formula to its theoretical limits in these extreme calculations.
Blood buffers In this extended question explore how blood buffers keep the pH levels balanced in the human body.
Calculus Differential equation matcher Can you match these physical processes with their underlying differential equations?


The problems on the bioNRICH site were created by Steve Hewson. Please send feedback to post16.nrich@maths.org . We welcome any feedback on both the parts you like and the parts you feel need further development. This will help us to create a really strong, FREE resource for all budding biologists.