Mathematical Requirements - A-Levels Biology
In order to be able to develop their skills, knowledge and understanding in Biology, students need to have been taught, and to have acquired competence in, the appropriate areas of mathematics as indicated in the table of coverage below.
Overall, at least 10% of the marks in assessments for biology will require the use of mathematical skills. These skills will be applied in the context of biology and will be at least the standard of higher tier GCSE mathematics.
The following tables illustrate where these mathematical skills may be developed during teaching or could be assessed. Those shown in bold type would only be tested in the full A-level course.
This list of examples is not exhaustive. These skills could be developed or assessed in other areas of specification content. Other areas where these skills could be developed have been exemplified throughout these specifications.
6.1 Arithmetic and numerical computation
| Mathematical skills | Exemplification of mathematical skill in the context of Biology | |
|---|---|---|
| MS 0.1 | Recognise and make use of appropriate units in calculations | Students may be tested on their ability to: • convert between units, eg mm3 to cm3 as part of volumetric calculations • work out the unit for a rate, eg breathing rate |
| MS 0.2 | Recognise and use expressions in decimal and standard form | Students may be tested on their ability to: • use an appropriate number of decimal places in calculations, eg for a mean • carry out calculations using numbers in standard and ordinary form, eg use of magnification • understand standard form when applied to areas such as size of organelles • convert between numbers in standard and ordinary form • understand that significant figures need retaining when making conversions between standard and ordinary form, eg 0.0050 mol dm−3 is equivalent to 5.0 × 10−3 mol dm−3 |
| MS 0.3 | Use ratios, fractions and percentages | Students may be tested on their ability to: • calculate percentage yields • calculate surface area to volume ratio • use scales for measuring • represent phenotypic ratios (monohybrid and dihybrid crosses) |
| MS 0.4 | Estimate results | Students may be tested on their ability to: • estimate results to sense check that the calculated values are appropriate |
| MS 0.5 | Use calculators to find and use power, exponential and logarithmic functions | Students may be tested on their ability to: • estimate the number of bacteria grown over a certain length of time |
6.2 Handling data
| Mathematical skills | Exemplification of mathematical skill in the context of Biology | |
|---|---|---|
| MS 1.1 | Use an appropriate number of significant figures | Students may be tested on their ability to: • report calculations to an appropriate number of significant figures given raw data quoted to varying numbers of significant figures • understand that calculated results can only be reported to the limits of the least accurate measurement |
| MS 1.2 | Find arithmetic means | Students may be tested on their ability to: • find the mean of a range of data, eg the mean number of stomata in the leaves of a plant |
| MS 1.3 | Construct and interpret frequency tables and diagrams, bar charts and histograms | Students may be tested on their ability to: • represent a range of data in a table with clear headings, units and consistent decimal places • interpret data from a variety of tables, eg data relating to organ function • plot a range of data in an appropriate format, eg enzyme activity over time represented on a graph • interpret data for a variety of graphs, eg explain electrocardiogram traces |
| MS 1.4 | Understand simple probability | Students may be tested on their ability to: • use the terms probability and chance appropriately • understand the probability associated with genetic inheritance |
| MS 1.5 | Understand the principles of sampling as applied to scientific data | Students may be tested on their ability to: • analyse random data collected by an appropriate means, eg use Simpson’s index of diversity to calculate the biodiversity of a habitat |
| MS 1.6 | Understand the terms mean, median and mode | Students may be tested on their ability to: • calculate or compare the mean, median and mode of a set of data, eg height/mass/size of a group of organisms |
| MS 1.7 | Use a scatter diagram to identify a correlation between two variables | Students may be tested on their ability to: • interpret a scattergram, eg the effect of lifestyle factors on health |
| MS 1.8 | Make order of magnitude calculations | Students may be tested on their ability to: • use and manipulate the magnification formula |
| MS 1.9 | Select and use a statistical test | Students may be tested on their ability to select and use: • the chi-squared test to test the significance of the difference between observed and expected results • the Student’s t-test • the correlation coefficient |
| MS 1.10 | Understand measures of dispersion, including standard deviation and range | Students may be tested on their ability to: • calculate the standard deviation • understand why standard deviation might be a more useful measure of dispersion for a given set of data, eg where there is an outlying result |
| MS 1.11 | Identify uncertainties in measurements and use simple techniques to determine uncertainty when data are combined | Students may be tested on their ability to: • calculate percentage error where there are uncertainties in measurement |
6.3 Algebra
| Mathematical skills | Exemplification of mathematical skill in the context of Biology | |
|---|---|---|
| MS 2.1 | Understand and use the symbols: =, <, <<, >>, >, ∝, ~ | No exemplification required. |
| MS 2.2 | Change the subject of an equation | Students may be tested on their ability to: • use and manipulate equations, eg magnification |
| MS 2.3 | Substitute numerical values into algebraic equations using appropriate units for physical quantities | Students may be tested on their ability to: • use a given equation, eg Simpson’s index of diversity |
| MS 2.4 | Solve algebraic equations | Students may be tested on their ability to: • solve equations in a biological context, eg cardiac output = stroke volume × heart rate |
| MS 2.5 | Use logarithms in relation to quantities that range over several orders of magnitude | Students may be tested on their ability to: • use a logarithmic scale in the context of microbiology, eg growth rate of a microorganism such as yeast |
6.4 Graphs
| Mathematical skills | Exemplification of mathematical skill in the context of Biology | |
|---|---|---|
| MS 3.1 | Translate information between graphical, numerical and algebraic forms | Students may be tested on their ability to: • understand that data may be presented in a number of formats and be able to use these data, eg dissociation curves |
| MS 3.2 | Plot two variables from experimental or other data | Students may be tested on their ability to: • select an appropriate format for presenting data, bar charts, histograms, graphs and scattergrams |
| MS 3.3 | Understand that represents a linear relationship | Students may be tested on their ability to: • predict/sketch the shape of a graph with a linear relationship, eg the effect of substrate concentration on the rate of an enzyme-controlled reaction with excess enzyme |
| MS 3.4 | Determine the intercept of a graph | Students may be tested on their ability to: • read off an intercept point from a graph, eg compensation point in plants |
| MS 3.5 | Calculate rate of change from a graph showing a linear relationship | Students may be tested on their ability to: • calculate a rate from a graph, eg rate of transpiration |
| MS 3.6 | Draw and use the slope of a tangent to a curve as a measure of rate of change | Students may be tested on their ability to: • use this method to measure the gradient of a point on a curve, eg amount of product formed plotted against time when the concentration of enzyme is fixed |
6.5 Geometry and trigonometry
| Mathematical skills | Exemplification of mathematical skill in the context of Biology | |
|---|---|---|
| MS 4.1 | Calculate the circumferences, surface areas and volumes of regular shapes | Students may be tested on their ability to: • calculate the circumference and area of a circle • calculate the surface area and volume of rectangular prisms, of cylindrical prisms and of spheres • eg calculate the surface area or volume of a cell |