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Assessed mathematical skills and measurement conventions

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5 topics · 29 learning objectives

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  1. A.0 Arithmetic and numerical computation

    1. A.0.1—Units in calculations

      Recognise and use appropriate units in calculations, including converting units such as mm³ to cm³ in volumetric calculations and determining units for rates such as breathing rate.

    2. A.0.2—Decimal and standard form

      Recognise and use decimal and standard form; choose appropriate decimal places; calculate with ordinary and standard form; apply standard form to organelle sizes; convert between forms while retaining significant figures, for example 0.0050 mol dm⁻³ = 5.0 × 10⁻³ mol dm⁻³.

    3. A.0.3—Ratios, fractions and percentages

      Use ratios, fractions and percentages, including percentage yields, surface-area-to-volume ratios, measurement scales and phenotypic ratios in monohybrid and dihybrid crosses.

    4. A.0.4—Estimating results

      Estimate results to sense-check whether calculated values are appropriate.

    5. A.0.5—Powers, exponentials and logarithms

      Use calculators to find and use power, exponential and logarithmic functions, including estimating bacterial population growth over time.

    6. A.0.P—SI unit prefixes

      Know and convert between the SI prefixes kilo, centi, milli, micro and nano, as clarified by Pearson for International A Level Biology candidates.

  2. A.1 Handling data

    1. A.1.1—Significant figures

      Use an appropriate number of significant figures; report calculated results consistently with the precision of the raw data and the least accurate measurement.

    2. A.1.2—Arithmetic means

      Calculate arithmetic means from biological data, such as mean stomatal counts.

    3. A.1.3—Tables, diagrams, bar charts and histograms

      Construct and interpret frequency tables and diagrams, bar charts and histograms; use clear headings, units and consistent decimal places; select suitable formats and interpret biological tables and graphs such as enzyme-activity graphs and ECG traces.

    4. A.1.4—Simple probability

      Understand simple probability and use probability and chance appropriately, including in genetic inheritance.

    5. A.1.5—Sampling scientific data

      Understand sampling principles for scientific data, including analysing randomly collected data and calculating an index of diversity to compare habitats.

    6. A.1.6—Mean, median and mode

      Understand and calculate or compare the mean, median and mode of biological datasets.

    7. A.1.7—Scatter diagrams and correlation

      Use scatter diagrams to identify correlations between variables, for example between lifestyle factors and health.

    8. A.1.8—Order-of-magnitude calculations

      Make order-of-magnitude calculations, including manipulating magnification = image size ÷ real-object size.

    9. A.1.9—Statistical tests

      Select and use statistical tests, including chi-squared tests for observed versus expected results, Student's t-tests and correlation coefficients.

    10. A.1.10—Dispersion, standard deviation and range

      Understand measures of dispersion, including range and standard deviation; calculate standard deviation and judge when it is more useful, including when data contain an outlier.

    11. A.1.11—Measurement uncertainty

      Identify measurement uncertainties and use simple techniques to determine uncertainty when data are combined, including calculating percentage error.

  3. A.2 Algebra

    1. A.2.1—Mathematical symbols

      Understand and use the symbols =, <, ≪, ≫, >, ∝ and ~.

    2. A.2.2—Changing the subject of an equation

      Change the subject of an equation and manipulate equations in biological contexts such as magnification.

    3. A.2.3—Substitution into algebraic equations

      Substitute numerical values into algebraic equations using appropriate physical units, including using a supplied formula to calculate an index of diversity.

    4. A.2.4—Solving algebraic equations

      Solve algebraic equations in biological contexts, for example cardiac output = stroke volume × heart rate.

    5. A.2.5—Logarithmic quantities

      Use logarithms for quantities spanning several orders of magnitude, including logarithmic scales for microorganism growth.

  4. A.3 Graphs

    1. A.3.1—Translating between data forms

      Translate information between graphical, numerical and algebraic forms, including using data represented by dissociation curves.

    2. A.3.2—Plotting two variables

      Plot two variables from experimental or other data and select appropriate formats such as bar charts, histograms, graphs and scattergrams.

    3. A.3.3—Linear relationships

      Understand that y = mx + c represents a linear relationship and predict or sketch linear graphs in biological contexts.

    4. A.3.4—Graph intercepts

      Determine a graph intercept, including reading an intercept such as the compensation point in plants.

    5. A.3.5—Rates from linear graphs

      Calculate rate of change from a graph showing a linear relationship, for example transpiration rate.

    6. A.3.6—Tangents and instantaneous rates

      Draw and use the slope of a tangent to a curve as a measure of rate of change, such as product formation at a point on an enzyme-reaction curve.

  5. A.4 Geometry and trigonometry

    1. A.4.1—Circumference, area and volume

      Calculate circumferences, surface areas and volumes of regular shapes, including circles, rectangular and cylindrical prisms and spheres, and apply these calculations to cells.