Mathematical requirements and exemplifications

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.

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

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 $m a g n i f i c a t i o n = \frac{s i z e o f i m a g e}{s i z e o f r e a l o b j e c t}$
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

Algebra

	Mathematical skills	Exemplification of mathematical skill in the context of Biology
MS 2.1	Understand and use the symbols: =, <, <<, >>, >, $\propto$ , $~$ .	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 $[D = 1 - (\sum ({n / N)}^{2}]$
MS 2.4	Solve algebraic equations	Students may be tested on their ability to: solve equations in a biological context, eg $cardiac output = s t r o k e v o l u m e \times h e a r t r a t e$
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

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 $y = m x + c$ 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

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

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

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