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Assessed mathematical skills and measurement conventions

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  1. C.0 Arithmetic and numerical computation

    1. C.0.1—Units in calculations

      Recognise and use appropriate units in calculations, including identifying derived units and converting between units with different prefixes.

    2. C.0.2—Decimal and standard form

      Recognise and use decimal and standard form, including physical constants such as c = 3.00 × 10^8 m s−1.

    3. C.0.3—Ratios, fractions and percentages

      Use ratios, fractions and percentages, including efficiency and percentage uncertainty calculations.

    4. C.0.4—Estimating results

      Estimate results, including the effect of changing experimental parameters on measurable values.

    5. C.0.5—Powers, exponentials and logarithms

      Use calculators for power functions. Exponential and logarithmic functions, including radioactive-decay calculations such as N = N0e^(−λt), are A2-only applications.

    6. C.0.6—Trigonometric calculator functions

      Use calculators for sin, cos and tan when angles are expressed in degrees or radians, including calculating the direction of resultant vectors.

    7. C.0.P—SI unit prefixes

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

  2. C.1 Handling data

    1. C.1.1—Significant figures

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

    2. C.1.2—Arithmetic means

      Calculate arithmetic means, including a mean value from repeated experimental readings.

    3. C.1.3—Simple probability

      Understand simple probability, including probability in radioactive decay as an A2 application.

    4. C.1.4—Order-of-magnitude calculations

      Make order-of-magnitude calculations, including evaluating equations whose variables have different orders of magnitude.

    5. C.1.5—Combined measurement uncertainty

      Identify measurement uncertainties and determine uncertainty when data are combined by addition, subtraction, multiplication, division or powers.

  3. C.2 Algebra

    1. C.2.1—Mathematical symbols

      Understand and use =, <, ≪, ≫, >, ∝, ≈ and Δ in physical relationships.

    2. C.2.2—Changing the subject of equations

      Change the subject of equations, including non-linear equations such as rearranging E = mc².

    3. C.2.3—Substitution into equations

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

    4. C.2.4—Solving algebraic equations

      Solve algebraic equations, including quadratic equations and kinematic equations for constant acceleration.

    5. C.2.5—Logarithmic quantities

      Use logarithms for quantities spanning several orders of magnitude and interpret real-world logarithmic scales.

  4. C.3 Graphs

    1. C.3.1—Translating between data forms

      Translate information between graphical, numerical and algebraic forms, including using stress–strain graphs to calculate Young modulus.

    2. C.3.2—Plotting two variables

      Plot two variables from experimental or other data, including extension against applied force.

    3. C.3.3—Linear relationships

      Understand that y = mx + c represents a linear relationship and compare physical equations with that form.

    4. C.3.4—Slope and intercept

      Determine the slope and intercept of a linear graph and interpret their physical significance.

    5. C.3.5—Rate from a linear graph

      Calculate rate of change from a graph showing a linear relationship, such as acceleration from a velocity–time graph.

    6. C.3.6—Tangents and instantaneous rates

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

    7. C.3.7—Instantaneous and average rates

      Distinguish between instantaneous and average rates of change and interpret them physically.

    8. C.3.8—Area under a graph

      Interpret and calculate or estimate the physical significance of the area between a curve and the x-axis. A2 applications include energy stored under a capacitor voltage–charge graph.

    9. C.3.9—Graphical calculus concepts

      Apply concepts underlying calculus without explicit differentiation or integration by solving rate-of-change equations graphically or with spreadsheet modelling.

    10. C.3.10—Interpreting logarithmic plots

      Interpret logarithmic plots, including obtaining a capacitor-discharge time constant from log voltage against time.

    11. C.3.11—Testing laws with logarithmic plots

      Use logarithmic plots to test exponential and power-law variations, including radioactive decay and capacitor charging or discharging.

    12. C.3.12—Sketching modelled relationships

      Sketch relationships modelled by reciprocal, inverse-square, square, linear, trigonometric and exponential functions. Exponential and squared-trigonometric forms are A2-only applications.

  5. C.4 Geometry and trigonometry

    1. C.4.1—Angles in regular structures

      Use angles in regular two- and three-dimensional structures, including interpreting force diagrams.

    2. C.4.2—Representing two- and three-dimensional forms

      Visualise and represent two- and three-dimensional forms, including two-dimensional representations and force diagrams.

    3. C.4.3—Areas and volumes

      Calculate triangle and circle areas, circumferences, and surface areas and volumes of blocks, cylinders and spheres.

    4. C.4.4—Pythagoras and triangle angles

      Use Pythagoras' theorem and the angle sum of a triangle, including resultant-vector calculations.

    5. C.4.5—Trigonometry in physical problems

      Use sin, cos and tan in physical problems, including resolving forces into components.

    6. C.4.6—Small-angle approximations

      Use small-angle approximations sin θ ≈ θ, tan θ ≈ θ and cos θ ≈ 1 where appropriate, including interference-fringe calculations.

    7. C.4.7—Degrees and radians

      Understand the relationship between degrees and radians and convert between them.