# 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

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: =, <, <<, >>, >, , .

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

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 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 