AS Physics₇₄₀₇

AS and A-level Physics Specification Specifications for first teaching in 2015

06 Jan 2017

PDF | 1.39 MB

6.0 Mathematical requirements and exemplifications

In order to be able to develop their skills, knowledge and understanding in physics, 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 40% of the marks in assessments for physics will require the use of mathematical skills. These skills will be applied in the context of Physics A-level 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 specification.

6.1 Arithmetic and numerical computation

	Mathematical skills	Exemplification of mathematical skill in the context of A-level Physics
MS 0.1	Recognise and make use of appropriate units in calculations	Students may be tested on their ability to: identify the correct units for physical properties such as ${m s}^{-1}$ , the unit for velocity convert between units with different prefixes eg ${cm}^{3}$ to $m^{3}$
MS 0.2	Recognise and use expressions in decimal and standard form	Students may be tested on their ability to: use physical constants expressed in standard form such as $c = {3.00 x 10}^{8}$ ${m s}^{-1}$
MS 0.3	Use ratios, fractions and percentages	Students may be tested on their ability to: calculate efficiency of devices calculate percentage uncertainties in measurements
MS 0.4	Estimate results	Students may be tested on their ability to: estimate the effect of changing experimental parameters on measurable values
MS 0.5	Use calculators to find and use power, exponential and logarithmic functions	Students may be tested on their ability to: solve for unknowns in decay problems such as $N = {N_{0} e}^{- λ t}$
MS 0.6	Use calculators to handle $s i n x$ , $c o s x$ , $t a n x$ when $x$ is expressed in degrees or radians	Students may be tested on their ability to: calculate the direction of resultant vectors

6.2 Handling data

	Mathematical skills	Exemplification of mathematical skill in the context of A-level Physics
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 a mean value for repeated experimental readings
MS 1.3	Understand simple probability	Students may be tested on their ability to: understand probability in the context of radioactive decay
MS 1.4	Make order of magnitude calculations	Students may be tested on their ability to: evaluate equations with variables expressed in different orders of magnitude
MS 1.5	Identify uncertainties in measurements and use simple techniques to determine uncertainty when data are combined by addition, subtraction, multiplication, division and raising to powers	Students may be tested on their ability to: determine the uncertainty where two readings for length need to be added together

6.3 Algebra

	Mathematical skills	Exemplification of mathematical skill in the context of A-level Physics
MS 2.1	Understand and use the symbols: =, <, <<, >>, >, $\propto$ , $\approx$ , $∆$	Students may be tested on their ability to: recognise the significance of the symbols in the expression $F \propto \frac{∆ p}{∆ t}$
MS 2.2	Change the subject of an equation, including non-linear equations	Students may be tested on their ability to: rearrange $E = {m c}^{2}$ to make $m$ the subject
MS 2.3	Substitute numerical values into algebraic equations using appropriate units for physical quantities	Students may be tested on their ability to: calculate the momentum $p$ of an object by substituting the values for mass $m$ and velocity $v$ into the equation $p = m v$
MS 2.4	Solve algebraic equations, including quadratic equations	Students may be tested on their ability to: solve kinematic equations for constant acceleration such as $v = u + a t$ and $s = u t + ½ a t^{2}$
MS 2.5	Use logarithms in relation to quantities that range over several orders of magnitude	Students may be tested on their ability to: recognise and interpret real world examples of logarithmic scales

6.4 Graphs

	Mathematical skills	Exemplification of mathematical skill in the context of A level Physics
MS 3.1	Translate information between graphical, numerical and algebraic forms	Students may be tested on their ability to: calculate Young modulus for materials using stress–strain graphs
MS 3.2	Plot two variables from experimental or other data	Students may be tested on their ability to: plot graphs of extension of a wire against force applied
MS 3.3	Understand that $y = m x + c$ represents a linear relationship	Students may be tested on their ability to: rearrange and compare $v = u + a t$ with $y = m x + c$ for velocity–time graph in constant acceleration problems
MS 3.4	Determine the slope and intercept of a linear graph	Students may be tested on their ability to: read off and interpret intercept point from a graph eg the initial velocity in a velocity–time graph
MS 3.5	Calculate rate of change from a graph showing a linear relationship	Students may be tested on their ability to: calculate acceleration from a linear velocity–time graph
MS 3.6	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: draw a tangent to the curve of a displacement–time graph and use the gradient to approximate the velocity at a specific time
MS 3.7	Distinguish between instantaneous rate of change and average rate of change	Students may be tested on their ability to: understand that the gradient of the tangent of a displacement–time graph gives the velocity at a point in time which is a different measure to the average velocity
MS 3.8	Understand the possible physical significance of the area between a curve and the x axis and be able to calculate it or estimate it by graphical methods as appropriate	Students may be tested on their ability to: recognise that for a capacitor the area under a voltage–charge graph is equivalent to the energy stored
MS 3.9	Apply the concepts underlying calculus (but without requiring the explicit use of derivatives or integrals) by solving equations involving rates of change, eg $\frac{Δ x}{Δ t} = - λ x$ using a graphical method or spreadsheet modelling	Students may be tested on their ability to: determine $g$ from distance-time plot for projectile motion
MS 3.10	Interpret logarithmic plots	Students may be tested on their ability to: obtain time constant for capacitor discharge by interpreting plot of log <math><mi mathvariant="italic">V</mi></math> against time
MS 3.11	Use logarithmic plots to test exponential and power law variations	Students may be tested on their ability to: use logarithmic plots with decay law of radioactivity / charging and discharging of a capacitor
MS 3.12	Sketch relationships which are modelled by $y = k / x$ , $y = {k x}^{2}$ , $y = k / x^{2}$ , $y = k x$ , $y = \sin x$ , $y = \cos x$ , $y = e^{\pm x}$ , and $y = \sin^{2} x$ , $y = \cos^{2} x$ as applied to physical relationships	Students may be tested on their ability to: sketch relationships between pressure and volume for an ideal gas

6.5 Geometry and trigonometry

	Mathematical skills	Exemplification of mathematical skill in the context of A-level Physics
MS 4.1	Use angles in regular 2D and 3D structures	Students may be tested on their ability to: interpret force diagrams to solve problems
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 force diagrams to solve mechanics problems
MS 4.3	Calculate areas of triangles, circumferences and areas of circles, surface areas and volumes of rectangular blocks, cylinders and spheres	Students may be tested on their ability to: calculate the area of the cross–section to work out the resistance of a conductor given its length and resistivity
MS 4.4	Use Pythagoras’ theorem, and the angle sum of a triangle	Students may be tested on their ability to: calculate the magnitude of a resultant vector, resolving forces into components to solve problems
MS 4.5	Use sin, cos and tan in physical problems	Students may be tested on their ability to: resolve forces into components
MS 4.6	Use of small angle approximations including $\sin θ \approx θ$ , $\tan θ \approx θ$ , $\cos θ \approx 1$ for small $θ$ where appropriate	Students may be tested on their ability to: calculate fringe separations in interference patterns
MS 4.7	Understand the relationship between degrees and radians and translate from one to the other	Students may be tested on their ability to: convert angle in degrees to angle in radians

5.0 General administration

7.0 Practical assessment

Mathematical skills

Exemplification of mathematical skill in the context of A-level Physics

MS 0.1

Recognise and make use of appropriate units in calculations