# Mathematical requirements and exemplifications

In order to be able to develop their skills, knowledge and understanding in chemistry, 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 20% of the marks in assessments for chemistry will require the use of mathematical skills. These skills will be applied in the context of chemistry 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 the specifications.

## Arithmetic and numerical computation

Mathematical skills

Exemplification of mathematical skill in the context of Chemistry

MS 0.0

Recognise and make use of appropriate units in calculation

Students may be tested on their ability to:

• convert between units, eg cm3 to dm3 as part of volumetric calculations
• give units for an equilibrium constant or a rate constant
• understand that different units are used in similar topic areas, so that conversions may be necessary, eg entropy in J mol–1 K–1 and enthalpy changes in kJ mol–1.

MS 0.1

Recognise and use expressions in decimal and ordinary form

Students may be tested on their ability to:

• use an appropriate number of decimal places in calculations, eg for pH
• carry out calculations using numbers in standard and ordinary form, eg use of Avogadro’s number
• understand standard form when applied to areas such as (but not limited to) Kw
• 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 0.2

Use ratios, fractions and percentages

Students may be tested on their ability to:

• calculate percentage yields
• calculate the atom economy of a reaction
• construct and/or balance equations using ratios.

MS 0.3

Estimate results

Students may be tested on their ability to:

• evaluate the effect of changing experimental parameters on measurable values, eg how the value of Kc would change with temperature given different specified conditions.

MS 0.4

Use calculators to find and use power, exponential and logarithmic functions

Students may be tested on their ability to:

• carry out calculations using the Avogadro constant
• carry out pH and pKa calculations
• make appropriate mathematical approximations in buffer calculations.

## Handling data

Mathematical skills

Exemplification of mathematical skill in the context of Chemistry

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:

• calculate weighted means, eg calculation of an atomic mass based on supplied isotopic abundances
• select appropriate titration data (ie identification of outliers) in order to calculate mean titres.

MS 1.3

Identify uncertainties in measurements and use simple techniques to determine uncertainty when data are combined

Students may be tested on their ability to:

• determine uncertainty when two burette readings are used to calculate a titre value.

## Algebra

Mathematical skills

Exemplification of mathematical skill in the context of Chemistry

MS 2.1

Understand and use the symbols: =, <, <<, >>, >, , ~, equilibrium sign

No exemplification required.

MS 2.2

Change the subject of an equation

Students may be tested on their ability to:

• carry out structured and unstructured mole calculations, eg calculate a rate constant k from a rate equation.

MS 2.3

Substitute numerical values into algebraic equations using appropriate units for physical quantities

Students may be tested on their ability to:

• carry out structured and unstructured mole calculations
• calculate the value of an equilibrium constant Kc.
• carry out rate calculations

MS 2.4

Solve algebraic equations

Students may be tested on their ability to:

• carry out Hess’s law calculations
• calculate a rate constant k from a rate equation.

MS 2.5

Use logarithms in relation to quantities that range over several orders of magnitude

Students may be tested on their ability to:

• carry out pH and pKa calculations.

## Graphs

Mathematical skills

Exemplification of mathematical skill in the context of Chemistry

MS 3.1

Translate information between graphical, numerical and algebraic forms

Students may be tested on their ability to:

• interpret and analyse spectra
• determine the order of a reaction from a graph
• derive a rate expression from a graph.

MS 3.2

Plot two variables from experimental or other data

Students may be tested on their ability to:

• plot concentration–time graphs from collected or supplied data and draw an appropriate best-fit curve.

MS 3.3

Determine the slope and intercept of a linear graph

Students may be tested on their ability to:

• calculate the rate constant of a zero-order reaction by determination of the gradient of a concentration–time graph.

MS 3.4

Calculate rate of change from a graph showing a linear relationship

Students may be tested on their ability to:

• calculate the rate constant of a zero-order reaction by determination of the gradient of a concentration–time graph.

MS 3.5

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:

• determine the order of a reaction using the initial rates method.

## Geometry and trigonometry

Mathematical skills

Exemplification of mathematical skill in the context of Chemistry

MS 4.1

Use angles and shapes in regular 2D and 3D structures

Students may be tested on their ability to:

• predict/identify shapes of and bond angles in molecules with and without a lone pair(s), for example NH3, CH4, H2O etc.

MS 4.2

Visualise and represent 2D and 3D forms including two-dimensional representations of 3D objects

Students may be tested on their ability to:

• draw different forms of isomers
• identify chiral centres from a 2D or 3D representation.

MS 4.3

Understand the symmetry of 2D and 3D shapes

Students may be tested on their ability to:

• describe the types of stereoisomerism shown by molecules/complexes
• identify chiral centres from a 2D or 3D representation.