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Mathematical Skills - A-Levels Biology

Mathematical skills

(i) A.0 – arithmetic and numerical computation

Mathematical skillsExemplification of mathematical skill in the context of A Level biology (assessment is not limited to the examples given below)
A.0.1Recognise and make use of appropriate units in calculationsCandidates may be tested on their ability to:
• convert between units, e.g. mm3 to cm3 as part of volumetric calculations
• work out the unit for a rate, e.g. breathing rate
A.0.2Recognise and use expressions in decimal and standard formCandidates may be tested on their ability to:
• use an appropriate number of decimal places in calculations, e.g. for a mean
• carry out calculations using numbers in standard and ordinary form, e.g. 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, e.g. 0.0050 mol dm-3 is equivalent to 5.0 × 10-3 mol dm-3
A.0.3Use ratios, fractions and percentagesCandidates may be tested on their ability to:
• calculate percentage yields
• calculate surface area to volume ratio
• use scales for measuring
• represent phenotypic (monohybrid and dihybrid crosses)
A.0.4Estimate resultsCandidates may be tested on their ability to:
• estimate results to sense check that the calculated values are appropriate
A.0.5Use calculators to find and use power, exponential and logarithmic functionsCandidates may be tested on their ability to:
estimate the number of bacteria grown over a certain length of time

(ii) A.1 – handling data

Mathematical skillsExemplification of mathematical skill in the context of A Level biology (assessment is not limited to the examples given below)
A.1.1Use an appropriate number of significant figuresCandidates 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 be reported only to the limits of the least accurate measurement
A.1.2Find arithmetic meansCandidates may be tested on their ability to:
• find the mean of a range of data, e.g. the mean number of stomata in the leaves of a plant
A.1.3Construct and interpret frequency tables and diagrams, bar charts and histogramsCandidates 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, e.g. data relating to organ function
• plot a range of data in an appropriate format, e.g. enzyme activity over time represented on a graph
• interpret data for a variety of graphs, e.g. explain electrocardiogram traces
A.1.4Understand simple probabilityCandidates may be tested on their ability to:
• use the terms probability and chance appropriately
• understand the probability associated with genetic inheritance
A.1.5Understand the principles of sampling as applied to scientific dataCandidates may be tested on their ability to:
• analyse random data collected by an appropriate means, e.g. calculate an index of diversity to compare the biodiversity of a habitat
A.1.6Understand the terms mean, median and modeCandidates may be tested on their ability to:
• calculate or compare the mean, median and mode of a set of data, e.g. height/mass/size of a group of organisms
A.1.7Use a scatter diagram to identify a correlation between two variablesCandidates may be tested on their ability to:
• interpret a scattergram, e.g. the effect of life style factors on health
A.1.8Make order of magnitude calculationsCandidates may be tested on their ability to:
• use and manipulate the magnification formula

magnification=size of imagesize of real object\text{magnification} = \frac{\text{size of image}}{\text{size of real object}}
A.1.9Select and use a statistical testCandidates 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
A.1.10Understand measures of dispersion, including standard deviation and rangeCandidates 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, e.g. where there is an outlying result
A.1.11Identify uncertainties in measurements and use simple techniques to determine uncertainty when data are combinedCandidates may be tested on their ability to:
• calculate percentage error where there are uncertainties in measurement

(iii) A.2 – algebra

Mathematical skillsExemplification of mathematical skill in the context of A Level biology (assessment is not limited to the examples given below)
A.2.1Understand and use the symbols: =, <, <<, >>, >, ∝, ~No exemplification required
A.2.2Change the subject of an equationCandidates may be tested on their ability to:
• use and manipulate equations, e.g. magnification
A.2.3Substitute numerical values into algebraic equations using appropriate units for physical quantitiesCandidates may be tested on their ability to:
• use a given equation e.g. a formula to calculate an index of diversity

D=N(N1)n(n1)D = \frac{N(N-1)}{\sum n(n-1)}
A.2.4Solve algebraic equationsCandidates may be tested on their ability to:
• solve equations in a biological context, e.g. cardiac output = stroke volume × heart rate
A.2.5Use logarithms in relation to quantities that range over several orders of magnitudeCandidates may be tested on their ability to:
use a logarithmic scale in the context of microbiology, e.g. growth rate of a microorganism such as yeast

(iv) A.3 – graphs

Mathematical skillsExemplification of mathematical skill in the context of A Level biology (assessment is not limited to the examples given below)
A.3.1Translate information between graphical, numerical and algebraic formsCandidates 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, e.g. dissociation curves
A.3.2Plot two variables from experimental or other dataCandidates may be tested on their ability to:
• select an appropriate format for presenting data, bar charts, histograms, graphs and scattergrams
A.3.3Understand that y = mx + c represents a linear relationshipCandidates may be tested on their ability to:
• predict/sketch the shape of a graph with a linear relationship, e.g. the effect of substrate concentration on the rate of an enzyme-controlled reaction with excess enzyme
A.3.4Determine the intercept of a graphCandidates may be tested on their ability to:
read off an intercept point from a graph, e.g. compensation point in plants
A.3.5Calculate rate of change from a graph showing a linear relationshipCandidates may be tested on their ability to:
• calculate a rate from a graph, e.g. rate of transpiration
A.3.6Draw and use the slope of a tangent to a curve as a measure of rate of changeCandidates may be tested on their ability to:
• use this method to measure the gradient of a point on a curve, e.g. amount of product formed plotted against time when the concentration of enzyme is fixed

(v) A.4 – geometry and trigonometry

Mathematical skillsExemplification of mathematical skill in the context of A Level biology (assessment is not limited to the examples given below)
A.4.1Calculate the circumferences, surface areas and volumes of regular shapesCandidates 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
• e.g. calculate the surface area or volume of a cell