Question 2 of Paper 5 is the same every session: a table to complete with logarithms and their absolute uncertainties, a graph with error bars, a line of best fit and a worst acceptable line, then the gradient and y-intercept with uncertainties and the constants that follow from them. Here the data is a draining cylinder, t = k hn, plotted as lg t against lg h. Plot every cross and draw every error bar yourself, drag both lines, read your own gradients and intercepts, and finish with n and k and their percentage uncertainties. Every attempt has different data. Allow about 35 minutes.
Checked: Cambridge 9702 Paper 5, 2023 to 2025. Only the papers in our collection are listed, so the real number may be higher. Question papers are available from Cambridge.
This workout needs JavaScript.
lg t = n lg h + lg k, so the gradient is n and the y-intercept is lg k.
lg (h / cm) and lg (t / s) to as many decimal places as the data has significant figures, and the uncertainty in lg t as lg (t + Δt) − lg t in every row.
Every cross within half a small square, every error bar symmetrical and the right length, a line of best fit with the points balanced about it, and a worst acceptable line that is the steepest or shallowest line through all the error bars.
Two points read from each of your own lines and far apart, gradient = Δy / Δx, the y-intercept by substitution into y = mx + c (never read off a false origin), and each uncertainty as the difference between the best-fit and worst-line values.
n = gradient and k = 10intercept to 2 or 3 significant figures and close to the true values, the percentage uncertainty in n from the gradient and in k from 10Δc, and a judgement of n against 0.50 that uses your own n ± Δn.
The marking follows the conventions in published Cambridge mark schemes. The experiments, readings and wording on this page are our own.