Mathematical Skills - A-Levels Biology
Mathematical skills
(i) A.0 – arithmetic and numerical computation
| Mathematical skills | Exemplification of mathematical skill in the context of A Level biology (assessment is not limited to the examples given below) | |
|---|---|---|
| A.0.1 | Recognise and make use of appropriate units in calculations | Candidates 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.0.2 | Recognise and use expressions in decimal and standard form | Candidates 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.0.3 | Use ratios, fractions and percentages | Candidates 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.0.4 | Estimate results | Candidates may be tested on their ability to: • estimate results to sense check that the calculated values are appropriate |
| A.0.5 | Use calculators to find and use power, exponential and logarithmic functions | Candidates 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 skills | Exemplification of mathematical skill in the context of A Level biology (assessment is not limited to the examples given below) | |
|---|---|---|
| A.1.1 | Use an appropriate number of significant figures | Candidates 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.1.2 | Find arithmetic means | Candidates 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.1.3 | Construct and interpret frequency tables and diagrams, bar charts and histograms | Candidates 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.1.4 | Understand simple probability | Candidates may be tested on their ability to: • use the terms probability and chance appropriately • understand the probability associated with genetic inheritance |
| A.1.5 | Understand the principles of sampling as applied to scientific data | Candidates 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.1.6 | Understand the terms mean, median and mode | Candidates 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.1.7 | Use a scatter diagram to identify a correlation between two variables | Candidates may be tested on their ability to: • interpret a scattergram, e.g. the effect of life style factors on health |
| A.1.8 | Make order of magnitude calculations | Candidates may be tested on their ability to: • use and manipulate the magnification formula |
| A.1.9 | Select and use a statistical test | Candidates 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.1.10 | Understand measures of dispersion, including standard deviation and range | Candidates 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.1.11 | Identify uncertainties in measurements and use simple techniques to determine uncertainty when data are combined | Candidates may be tested on their ability to: • calculate percentage error where there are uncertainties in measurement |
(iii) A.2 – algebra
| Mathematical skills | Exemplification of mathematical skill in the context of A Level biology (assessment is not limited to the examples given below) | |
|---|---|---|
| A.2.1 | Understand and use the symbols: =, <, <<, >>, >, ∝, ~ | No exemplification required |
| A.2.2 | Change the subject of an equation | Candidates may be tested on their ability to: • use and manipulate equations, e.g. magnification |
| A.2.3 | Substitute numerical values into algebraic equations using appropriate units for physical quantities | Candidates may be tested on their ability to: • use a given equation e.g. a formula to calculate an index of diversity |
| A.2.4 | Solve algebraic equations | Candidates may be tested on their ability to: • solve equations in a biological context, e.g. cardiac output = stroke volume × heart rate |
| A.2.5 | Use logarithms in relation to quantities that range over several orders of magnitude | Candidates 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 skills | Exemplification of mathematical skill in the context of A Level biology (assessment is not limited to the examples given below) | |
|---|---|---|
| A.3.1 | Translate information between graphical, numerical and algebraic forms | Candidates 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.3.2 | Plot two variables from experimental or other data | Candidates may be tested on their ability to: • select an appropriate format for presenting data, bar charts, histograms, graphs and scattergrams |
| A.3.3 | Understand that y = mx + c represents a linear relationship | Candidates 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.3.4 | Determine the intercept of a graph | Candidates may be tested on their ability to: • read off an intercept point from a graph, e.g. compensation point in plants |
| A.3.5 | Calculate rate of change from a graph showing a linear relationship | Candidates may be tested on their ability to: • calculate a rate from a graph, e.g. rate of transpiration |
| A.3.6 | Draw and use the slope of a tangent to a curve as a measure of rate of change | Candidates 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 skills | Exemplification of mathematical skill in the context of A Level biology (assessment is not limited to the examples given below) | |
|---|---|---|
| A.4.1 | Calculate the circumferences, surface areas and volumes of regular shapes | Candidates 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 |