Nobody fails Biology because the maths is hard. The sums here are the ones you did at 14. People lose marks because they pick the wrong average, use the wrong percentage formula, or forget what the number is actually telling them about the organism.
Every one of these turns up somewhere in the course. It helps to know where, because then the maths stops feeling random.
| Type of number | Where it shows up in Biology |
|---|---|
| Decimals | Almost every measurement — the length of a bacterial cell, the mass of a seedling |
| Fractions | Your calculator often gives an answer as a fraction. Find the button that flips it to a decimal before the exam, not during it |
| Percentages | Percentage change in mass in an osmosis practical, percentage cover in a quadrat |
| Ratios | Surface area to volume ratio — the one ratio you must be fluent with |
| Proportions | Scaling a drawing up or down from a micrograph so the shape stays true |
| Frequencies | Allele frequency in a population, and how it shifts over generations |
| Densities | Population density in ecology, stomatal density on a leaf |
| Approximations | Quick estimates, such as checking a magnification answer looks sensible |
| Reciprocals | Turning a time into a rate: rate = 1 ÷ time taken |
These three all try to answer the same question — “what is a typical value here?” — but they answer it in different ways.
| Average | How you find it | What it is good for |
|---|---|---|
| Mean | Add up all the values, divide by how many there are | Summing up a whole data set in one number. It uses every value, so every value affects it |
| Median | Put the values in order and take the middle one | Data with an odd result that would drag the mean off. Half the values sit below it, half above |
| Mode | The value that appears most often | Categories, where a mean makes no sense — the most common blood group, the most common eye colour |
A mean on its own is only half a story. Two sets of results can have exactly the same mean and still be nothing alike. That is what the measures of dispersion are for.
| Measure | What it tells you | Watch out for |
|---|---|---|
| Standard deviation (SD) | How far the values sit from the mean on average. Small SD means the results are consistent | You must work out the mean first. Useful for comparing how consistent two data sets are |
| Standard error (SE) | How far your sample mean is likely to be from the true mean of the whole population | It is about how good your sample is, not how varied the organisms are. SE is always smaller than SD |
| Interquartile range (IQR) | The difference between the 75th and 25th percentiles — the range of the middle half of the data | Quartiles cut the ordered data into four equal parts. The IQR ignores extreme values completely |
SD = how Different the individuals are from each other. SE = how Exact your estimate of the mean is. If you sample more organisms, SE shrinks, but SD does not have to.
Biology jumps between the size of a ribosome and the size of a rainforest, so you need a tidy way to write very big and very small numbers. Scientific notation, also called standard form, does that.
These two words sound identical and get used loosely, but the exam treats them as different jobs.
A rate tells you how fast something changes. In Biology it is nearly always “how much, per unit of time”.
If you have a table, subtract one row from another. If you have a graph, the rate is the gradient. Both give the same thing, so use whichever the question hands you.
Calculate a rate from a table
A respirometer measured the oxygen used by germinating seeds. At 2 minutes, 0.8 cm3 had been used. At 10 minutes, 3.2 cm3 had been used. Calculate the average rate of oxygen uptake. (2 marks)
Examiners are fussy about these words, so use them precisely.
| Term | What it means |
|---|---|
| Directly proportional | A straight-line relationship: if x doubles, y doubles. As one goes up, so does the other, by the same factor |
| Inversely proportional | If x doubles, y halves. As one goes up, the other comes down |
| Positive correlation | The graph slopes upwards: as x increases, y increases. It does not have to be a straight line |
| Negative correlation | The graph slopes downwards: as x increases, y decreases |
This is where most of the lost marks live. Both compare two numbers, but they answer different questions, and they use different formulas.
Use this when one value came before the other — a starting mass and a final mass, a count before treatment and after.
Divide by the initial value, because that is the thing you are comparing against. A negative answer simply means it went down, and you should say so.
Use this when you are comparing two values that are just… two values. There are two versions, and the question decides which one you need.
Method 1 treats A as the baseline, so it answers “how much bigger is B compared with A?”. Method 2 divides by the mean of the two numbers instead, so it does not matter which one you call A. Use it when neither value is a starting point.
Percentage change in an osmosis practical
A potato cylinder had a mass of 5.20 g. After 30 minutes in a sucrose solution its mass was 4.42 g. Calculate the percentage change in mass. (2 marks)
Symmetrical percentage difference
A student counted stomata on two leaf surfaces. The mean was 12 stomata per mm2 on the upper surface and 68 per mm2 on the lower surface. Calculate the percentage difference between them, to three significant figures. (3 marks)
Which type you have decides how you graph it and which test you can use, so sort this out early.
| Type | What it is | Biological examples |
|---|---|---|
| Discrete | Quantitative data made of separate, countable values. You cannot have half of one | Number of woodlice in a sample, number of offspring in a litter |
| Continuous | Quantitative data from measuring. It can take any value in a range, including decimals | Temperature of an enzyme reaction over time, volume of oxygen released by pondweed |
You will be given the formulas in the exam. What you have to supply is the judgement about which one fits.
| Test or index | Use it when you want to… |
|---|---|
| t-test | Compare the means of two sets of data and decide whether the difference is significant. The data should be continuous, roughly normally distributed, with similar standard deviations |
| Chi-squared test | Compare observed results with expected results — the outcome of a genetic cross, or whether two species are associated |
| Correlation test | Find out whether two variables are related, and how strongly |
| Simpson’s reciprocal index | Measure the biodiversity of a community. It takes in both the number of species (richness) and how many individuals of each (evenness). A higher value means more biodiversity |
| Lincoln index | Estimate the size of an animal population by capture, mark, release and recapture |
Three things push you towards one test rather than another: the size of the sample, whether the data is discrete or continuous, and what the question is actually asking.
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