Paper 5 Planning, Analysis and Evaluation

Learning objectives

P5.1Planning variables, method and apparatusIdentify independent, dependent and controlled variables; describe how variables are varied, measured and kept constant; and present a workable labelled apparatus arrangement and procedure.P5.2Additional detail, safety and instrumentationAdd relevant practical detail, assess risks and precautions, and describe use of oscilloscopes, light gates, data loggers and sensors to measure quantities such as voltage, current, time, frequency, velocity and acceleration.P5.3Data analysis models and graph transformationsRearrange expressions into y = mx + c, y = ax^n and y = ae^(kx), use linear, logarithmic and exponential plots to find constants, and decide which derived quantities should be calculated for graphing.P5.4Tables, graphs and uncertainty treatmentComplete tables using Paper 3 conventions, calculate and record derived quantities, plot graphs with error bars, draw best-fit and worst acceptable lines, and calculate uncertainties in derived quantities, gradients and intercepts.P5.5Conclusions from constants, gradients and interceptsDetermine gradients and y-intercepts, derive expressions that link them to physical constants, state conclusions with units and appropriate significant figures, and express final values with uncertainty estimates.

State the independent variable and how it is varied over a safe useful range; state the dependent variable and exactly how it is measured/calculated; name each important control and how it is kept constant.

Draw a labelled arrangement showing geometry and connections that affect measurement: sensor positions, distances/angles, circuit topology, clamps and reference points. Include instrument ranges/resolutions where relevant.

Write an ordered method another student could reproduce: zero/calibrate, set IV, allow stabilization, measure DV, repeat, change IV and collect at least six well-spread values where feasible.

For every control, give a mechanism: same wire/length, regulate temperature, fixed alignment/distance, constant supply setting or randomized/repeated sequence when drift cannot be eliminated.

A variable list is not a plan. Check that every quantity in the later graph can be obtained from the described measurements and that no apparatus is present without a role.

For each instrument state what it senses, how it is connected/positioned, which display feature is read, its range/resolution or sampling condition, and how that reading becomes the required physical quantity.

Oscilloscope: connect across the signal; choose volts/div and time/div; amplitude=(vertical divisions)(volts/div), period=(horizontal divisions)(time/div), frequency=1/period.

Light gates: a card/flag of measured length ℓ interrupts the beam for time Δt, so speed v=ℓ/Δt; two gates can measure travel time or acceleration. Align gates and measure the same flag length used in the calculation.

Data logger/sensor: name the sensor, calibrate/zero it, select a sampling rate high enough for the event, log the required interval and export the actual voltage/time/force/temperature data used.

Risk statement = hazard + consequence + control: hot component→burn→allow cooling/tongs; high current→heating→series resistor/low supply/switch off; falling mass→impact→tray/clear area; laser→eye damage→never view beam.

Naming 'a sensor' or 'wear goggles' is incomplete. Measurement detail must produce the named variable; a precaution must interrupt the named hazard mechanism.

$model y=mx+c → plot y against x gradient=m; intercept=c$

$y=axⁿ → ln y=n ln x+ln a plot ln(y/unit) against ln(x/unit); gradient=n; intercept=ln a in the chosen unit system$

$y=ae^(kx) → ln y=kx+ln a plot ln(y/unit) against x; gradient=k; intercept=ln a$

If the question suggests transformed quantities, algebraically isolate them in Y=mX+c form, then write explicit expressions for gradient and intercept before calculating table columns.

If 1/f=1/fs−v/(kfs), plot Y=1/f against X=v: gradient=−1/(kfs), intercept=1/fs.

Do not choose axes by visual convenience. Axis choice must make the proposed model linear and leave constants recoverable from m and c; state reference units inside logarithms.

$for Q=A±B: ΔQ=ΔA+ΔB for Q=AB or A/B: %ΔQ≈%ΔA+%ΔB for Q=Aⁿ: %ΔQ≈|n|%ΔA$

Complete raw and derived columns with quantity/unit headings, consistent raw precision and justified calculated significant figures. Record each derived absolute uncertainty in the same unit/decimal place as its value.

Plot every required error bar symmetrically: from value−Δ to value+Δ, so total bar length is 2Δ. Plot points and bars within the stated graph precision.

Draw a best-fit line, then the steepest or shallowest worst acceptable line that remains consistent with all error bars. Do not simply join the topmost and bottommost raw points.

$Δm=|m_best−m_worst| (or Δm=(m_steep−m_shallow)/2 when both extremes are used) Apply the same method to intercept c.$

Error bars display absolute uncertainty even if calculated from percentages. Worst acceptable means compatible with all bars, not visually most different.

Calculate best-fit gradient/intercept with units. 2. Substitute them into the expressions derived before plotting. 3. Solve for each physical constant. 4. Propagate m/c uncertainty. 5. Report value±uncertainty.

$For 1/f against v: c=1/f_s ⇒ f_s=1/c m=−1/(k f_s) ⇒ k=−c/m$

$%Δf_s≈%Δc for k=−c/m: %Δk≈%Δc+%Δm$

Derive units algebraically from the m/c expression rather than guessing. In this example fs is Hz and k is m s⁻¹ when v is m s⁻¹ and 1/f is s.

Round uncertainty to one significant figure (sometimes two when the first digit is 1 or 2), then round the value to the same decimal place: Q=(value±ΔQ) unit. State whether the result supports the model within uncertainty.

Gradient/intercept are not automatically the requested constants. Use the derived mapping, include powers-of-ten from axis labels and keep sign information until the physical interpretation is made.

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—Cambridge International AS & A Level Physics (9702)Read

Paper 5 Planning, Analysis and Evaluation

Learning objectives

Turn a research question into measurable variables and a workable plan

Specify the full sensor-to-quantity chain and pair each risk with a control

Linearize the model before choosing calculated columns and graph axes

Carry uncertainty from the table through error bars to worst acceptable lines

Convert gradient and intercept into physical constants with units and uncertainty

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