← Paper 5: Planning & Analysis guide
Drill the log-linearisation and straight-line graph marks that Q2 tests every series — 18 relationships, step-by-step feedback, and worked sketches.
Cambridge A Level Physics 9702 Paper 5 Question 2 (15 marks) requires candidates to linearise a given relationship and analyse a straight-line graph. A relationship — such as y = kxn, T = 2π√(m/k), or an exponential decay — must be rearranged so that plotting the correct quantities against each other yields a straight line. Marks are awarded for identifying what to plot, constructing the data table with correct headings and units, drawing the graph, finding the gradient and intercept, and deriving the unknown constants. Examiner reports show candidates most often lose marks by plotting the wrong quantities, choosing a gradient triangle covering less than half the line, or failing to carry units through to the final constants.
The trainer covers 18 relationships across mechanics, waves, electricity, and thermal physics, spanning linear, power-law, exponential, and inverse forms. Each card presents the raw relationship, prompts you to identify the correct graph form, then reveals the linearised equation, the expressions for gradient and intercept, and a worked sketch. All relationships reflect mark scheme conventions from May/June 2020 to May/June 2025.
Work through the deck once to identify any relationship where you hesitate on the linearised form or confuse gradient with intercept. Pair with the Paper 5 cheat sheet for the full mark-type breakdown across both questions, and the Paper 5 self-assessment checklist to audit your answers after each practice paper.
No spam, no daily nudges. Just a note when Paper 4, Paper 6, or the 9702 trainers are ready — plus the occasional examiner tip the week before an exam window.
Cambridge A Level Physics 9702 Paper 5 Question 2 gives you a relationship between two quantities and asks you to plot a straight line to find the unknown constants. Linearising means rearranging that relationship into the form y = mx + c, then choosing what to put on each axis so the gradient m and the intercept c carry the constants you actually need.
The period of a simple pendulum is T = 2π√(L/g). Squaring both sides gives T2 = (4π2/g) L, which matches y = mx + c with y = T2, x = L, gradient 4π2/g and intercept 0. Plot T2 in s2 against L in m, draw the best-fit line, measure the gradient over a triangle spanning at least half the line, then rearrange to g = 4π2 / gradient.
For a decay of the form A = A0 e-λt, take natural logs to get ln A = ln A0 - λt. Plot ln A against t. The line slopes downward with gradient -λ, so the decay constant λ is the magnitude of the gradient, and ln A0 is read from the intercept at t = 0.
Examiner reports flag the same errors every series: plotting the raw quantities instead of the linearised ones, mislabelling a logarithmic axis (a quantity like ln(I/A) is just a number, but the label must still show which unit I was divided by), using a gradient triangle shorter than half the drawn line, and forgetting to convert the gradient back into the physical constant at the end. Carry units through every step and quote the final constant with a unit and a sensible number of significant figures.
Should I use lg (base 10) or ln (base e)? For a power law y = a xn either works, because the base only changes the intercept; lg is conventional. For an exponential y = a ekx use ln, so the gradient comes out as k directly with no conversion factor.
What if the intercept is off the graph? Find the constant from the gradient where you can, or substitute a point that lies on the best-fit line back into y = mx + c. Do not read an intercept off an axis that does not start at zero without accounting for the offset.
How accurate does the line have to be? Cambridge expects points plotted to within half a small square, a best-fit line with the scatter balanced about it, and a gradient triangle covering more than half the drawn line. For the read-offs, choose two points that sit on grid lines — that is what keeps the coordinates easy to read accurately. Those are the marks Question 2 rewards.
Once the 18 relationships feel automatic, pair this with the Paper 5 cheat sheet for the full mark-type breakdown, the Paper 5 checklist to audit each practice answer, and the uncertainties trainer for the error-analysis marks that sit alongside Question 2. Full method walk-throughs are in the Paper 5 Planning and Analysis guide.