Appendix B: Maths requirements and examples
To develop their skills, knowledge and understanding in Environmental Science, students must have been taught, and to be competent in, the appropriate areas of maths indicated below.
Overall at least 10% of the marks in assessments for Environmental Science will require the use of maths skills. These skills will be applied in the context of environmental science and will be at least the standard of higher tier GCSE mathematics.
The following tables illustrate where these maths skills may be developed during teaching or could be assessed.
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 given throughout this specification.
Arithmetic and numerical computation
Maths skill number  Skill  Example 

MS 0.1  Recognise and make use of appropriate units in calculations 
Students should demonstrate their ability to:

MS 0.2  Recognise and use expressions in decimal and standard form 
Students should demonstrate their ability to:

MS 0.3  Use ratios, fractions and percentages 
Students should demonstrate their ability to:

MS 0.4  Estimate results 
Students should demonstrate their ability to estimate results to sense check that the calculated values are appropriate, such as when calculating residence times in different water reservoirs. 
MS 0.5  Use calculators to find and use power, exponential and logarithmic functions 
Students should demonstrate their ability to:

Handling data
Maths skill number  Skill  Example 

MS 1.1  Use an appropriate number of significant figures 
Students should demonstrate their ability to:

MS 1.2  Find arithmetic means 
Students should demonstrate their ability to find the mean of a range of data, eg mean power output of a wind farm. 
MS 1.3  Construct and interpret frequency tables and diagrams, bar charts and histograms 
Students should demonstrate their ability to:

MS 1.4  Understand simple probability  Students should demonstrate their ability to use the term probability appropriately when investigating causal relationships such as the link between human health problems and urban pollutants. 
MS 1.5  Understand the principles of sampling as applied to scientific data 
Students should demonstrate their ability to:

MS1.6  Understand the terms mean, median and mode 
Students should demonstrate their ability to calculate or compare the mean, median and mode of a set of data, eg of yields of fish farmed under different conditions or fish from commercial catches. 
MS 1.7 
Use a scatter diagram to identify a correlation between two variables 
Students should demonstrate their ability to interpret a scatter graph, eg to compare human development index with environmental footprint of different countries. 
MS 1.8  Make order of magnitude calculations 
Students should demonstrate their ability to:

MS 1.10 
Understand measures of dispersion, including standard deviation and range 
Students should demonstrate their ability to:

MS 1.11  Identify uncertainties in measurements and use simple techniques to determine uncertainty when data are combined 
Students should demonstrate their ability to calculate percentage error where there are uncertainties in measurement, eg estimating total population using subsamples in a preliminary study. 
Algebra
Maths skill number  Skill  Example  

MS 2.1  Understand and use the symbols : = < << >> > and ~.  No example required.  
MS 2.2  Change the subject of an equation 
Students should demonstrate their ability to use and manipulate equations, eg nutrient transfer rates, energy conversion efficiencies and fish maximum sustainable yields. 

MS 2.3  Substitute numerical values into algebraic equations using appropriate units for physical quantities 
Students should demonstrate their ability to use a given equation, eg Simpson’s index of diversity:
to assess the impact of a new habitat management regime. 

MS 2.4  Solve algebraic equations 
Students should demonstrate their ability to solve equations in an environmental context, eg calculations using the universal soil loss equation to assess the effectiveness of soil conservation programmes. 
Graphs
Maths skill number  Skill  Example 

MS 3.1  Understand data presented in a variety of graphical forms 
Students should demonstrate their ability to interpret data in a range of graphical forms, including line graphs, which may involve logarithmic scales, bar charts, stacked bar charts, histograms, kite diagrams, pie graphs, scatter graphs, 3dimensional graphs, flow diagrams, Sankey diagrams and circular (radar) diagrams to enable a wide variety of data to be analysed. 
MS 3.2  Translate information between graphical numerical and algebraic forms 
Students should demonstrate their ability to understand that data may be presented in a number of formats and be able to use these data, eg dissolved oxygen levels, soil erosion rates. 
MS 3.3  Plot two variables from experimental or other data 
Students should demonstrate their ability to select an appropriate format for presenting data, bar charts, histograms, graphs and scattergraphs, eg organic matter and oxygen depletion, nutrient inputs and yield increase. 
MS 3.4 
Understand that y = m x + c represents a linear relationship 
Students should demonstrate their ability to predict/sketch the shape of a graph with a linear relationship, whether with a positive or negative correlation, eg the relationship between insolation and solar panel output 
MS 3.6  Calculate rate of change from a graph showing a linear relationship 
Students should demonstrate their ability to calculate a rate from a graph, eg rate of infiltration through rocks with different permeabilities. 
MS 3.7 
Draw and use the slope of a tangent to a curve as a measure of rate of change 
Students should demonstrate their ability to use this method to measure the gradient of a point on a curve, eg rate of heat loss through double glazing with varying gaps. 
Geometry and trigonometry
Maths skill number  Skill  Example 

MS 4.1 
Calculate the circumferences, surface areas and volumes of regular and irregular shapes 
Students should demonstrate their ability to:
