A-level Chemistry Tutor

Calculations and maths skills

At least 20% of the marks in A-level Chemistry are for mathematical skills. The specification lists them as M0.0 to M4.3; below is how each one is examined, and every past-paper question we have tagged to it (764 question parts, 270 of them straight calculations). Set out the working: OCR's mark schemes give the marks for each step and allow an error carried forward, and a bare wrong answer earns nothing.

All calculation questions with mark schemes What the Data Sheet gives you

The skills

SkillIn the specificationHow it is examinedQuestions
M0.0Recognise and make use of appropriate units in calculationsUnit conversions inside a calculation: cm³ to dm³ (divide by 1000), g to mg or tonnes, J to kJ, °C to K. Units for Kc, Kp and rate constants are worked out from the expression.126
M0.1Recognise and use expressions in decimal and ordinary formStandard form and decimal places: the Avogadro constant, Kw, Ka values. Keep the significant figures when converting between forms.38
M0.2Use ratios, fractions and percentagesMole ratios from balanced equations, percentage yield, atom economy, percentage by mass and percentage uncertainty.355
M0.3Estimate resultsEstimating or predicting how a value changes, for example how K changes with temperature.12
M0.4Use calculators to find and use power, exponential and logarithmic functionsCalculator work with powers and logs: pH = –log[H⁺], [H⁺] = 10^–pH, pKa, and the Arrhenius equation (A level).41
M1.1Use an appropriate number of significant figuresGiving the answer to the number of significant figures the question asks for, or that the data justify. Round only at the end.102
M1.2Find arithmetic meansMean titres from concordant results only; relative atomic mass as a weighted mean of isotopic masses.23
M1.3Identify uncertainties in measurements and use simple techniques to determine uncertainty when data are combinedPercentage uncertainty = (uncertainty × number of readings ÷ quantity measured) × 100. A burette titre uses two readings.17
M2.1Understand and use the symbols =, <, <<, >>, >, ∝, ~, ⇌Using the symbols correctly, including ⇌ for equilibria.1
M2.2Change the subject of an equationRearranging n = m/M, n = cV, pV = nRT, q = mcΔT, ΔG = ΔH – TΔS, Kc and Ka expressions, and rate equations for k.86
M2.3Substitute numerical values into algebraic equations using appropriate units for physical quantitiesSubstituting values with the right units: volumes in m³ and pressure in Pa for pV = nRT; ΔS in kJ when used with ΔH.248
M2.4Solve algebraic equationsMulti-step problems: Hess cycles, Born–Haber cycles, equilibrium tables, buffer calculations.54
M2.5Use logarithms in relation to quantities that range over several orders of magnitudeLogarithms for quantities that span many orders of magnitude: pH, pKa, ln k against 1/T (A level).37
M3.1Translate information between graphical, numerical and algebraic formsReading graphs, energy profiles, Boltzmann distributions, titration curves and spectra, and moving between a graph and an equation.133
M3.2Plot two variables from experimental or other dataPlotting points and drawing a line or curve of best fit with sensible scales.14
M3.3Determine the slope and intercept of a linear graphGradient and intercept of a straight-line graph: Ea from the gradient of ln k against 1/T, ln A from the intercept.13
M3.4Calculate rate of change from a graph showing a linear relationshipRate from the gradient of a straight section of a concentration–time graph.1
M3.5Draw and use the slope of a tangent to a curve as a measure of rate of changeDrawing a tangent to a curve and finding its gradient for the rate at that time (A level).13
M4.1Use angles and shapes in regular 2-D and 3-D structuresBond angles and shapes: 109.5°, 107°, 104.5°, 120°, 180°, 90°.40
M4.2Visualise and represent 2-D and 3-D forms including 2-D representations of 3-D objectsDrawing 3-D structures with wedge and dashed bonds: shapes of molecules, optical isomers, complex ions.84
M4.3Understand the symmetry of 2-D and 3-D shapesSymmetry in molecules: chiral centres, E/Z and cis–trans isomers, the number of NMR environments.39

Explanations written by the site from the specification (section 5e) and the mark schemes; being checked by our tutor. M0.4, M2.5 and M3.5 are examined at A level only.

M0.0: Recognise and make use of appropriate units in calculations

Unit conversions inside a calculation: cm³ to dm³ (divide by 1000), g to mg or tonnes, J to kJ, °C to K. Units for Kc, Kp and rate constants are worked out from the expression.

126 questions

M0.1: Recognise and use expressions in decimal and ordinary form

Standard form and decimal places: the Avogadro constant, Kw, Ka values. Keep the significant figures when converting between forms.

38 questions

M0.2: Use ratios, fractions and percentages

Mole ratios from balanced equations, percentage yield, atom economy, percentage by mass and percentage uncertainty.

355 questions

M0.3: Estimate results

Estimating or predicting how a value changes, for example how K changes with temperature.

12 questions

M0.4: Use calculators to find and use power, exponential and logarithmic functions

Calculator work with powers and logs: pH = –log[H⁺], [H⁺] = 10^–pH, pKa, and the Arrhenius equation (A level).

41 questions

M1.1: Use an appropriate number of significant figures

Giving the answer to the number of significant figures the question asks for, or that the data justify. Round only at the end.

102 questions

M1.2: Find arithmetic means

Mean titres from concordant results only; relative atomic mass as a weighted mean of isotopic masses.

23 questions

M1.3: Identify uncertainties in measurements and use simple techniques to determine uncertainty when data are combined

Percentage uncertainty = (uncertainty × number of readings ÷ quantity measured) × 100. A burette titre uses two readings.

17 questions

M2.1: Understand and use the symbols =, <, <<, >>, >, ∝, ~, ⇌

Using the symbols correctly, including ⇌ for equilibria.

1 questions

M2.2: Change the subject of an equation

Rearranging n = m/M, n = cV, pV = nRT, q = mcΔT, ΔG = ΔH – TΔS, Kc and Ka expressions, and rate equations for k.

86 questions

M2.3: Substitute numerical values into algebraic equations using appropriate units for physical quantities

Substituting values with the right units: volumes in m³ and pressure in Pa for pV = nRT; ΔS in kJ when used with ΔH.

248 questions

M2.4: Solve algebraic equations

Multi-step problems: Hess cycles, Born–Haber cycles, equilibrium tables, buffer calculations.

54 questions

M2.5: Use logarithms in relation to quantities that range over several orders of magnitude

Logarithms for quantities that span many orders of magnitude: pH, pKa, ln k against 1/T (A level).

37 questions

M3.1: Translate information between graphical, numerical and algebraic forms

Reading graphs, energy profiles, Boltzmann distributions, titration curves and spectra, and moving between a graph and an equation.

133 questions

M3.2: Plot two variables from experimental or other data

Plotting points and drawing a line or curve of best fit with sensible scales.

14 questions

M3.3: Determine the slope and intercept of a linear graph

Gradient and intercept of a straight-line graph: Ea from the gradient of ln k against 1/T, ln A from the intercept.

13 questions

M3.4: Calculate rate of change from a graph showing a linear relationship

Rate from the gradient of a straight section of a concentration–time graph.

1 questions

M3.5: Draw and use the slope of a tangent to a curve as a measure of rate of change

Drawing a tangent to a curve and finding its gradient for the rate at that time (A level).

13 questions

M4.1: Use angles and shapes in regular 2-D and 3-D structures

Bond angles and shapes: 109.5°, 107°, 104.5°, 120°, 180°, 90°.

40 questions

M4.2: Visualise and represent 2-D and 3-D forms including 2-D representations of 3-D objects

Drawing 3-D structures with wedge and dashed bonds: shapes of molecules, optical isomers, complex ions.

84 questions

M4.3: Understand the symmetry of 2-D and 3-D shapes

Symmetry in molecules: chiral centres, E/Z and cis–trans isomers, the number of NMR environments.

39 questions

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