Question 2 of 9702 Paper 5 gives you data that only becomes a straight line after taking logs. You calculate the log values and their uncertainties, plot them with error bars, draw best and worst lines, and find the constants with their uncertainties. Practise the calculations first, then plot a full log graph below.
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Fresh data each time, already converted to logs, with the uncertainty of each point. Work through all six steps: the last one is the worst acceptable line.
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A power law y = a xⁿ needs lg y against lg x. An exponential y = a eᵏˣ needs ln y against x.
Each log value has as many decimal places as the raw value has significant figures (or one more), and the column heading shows what was divided by its unit, such as lg (T / s).
The uncertainty in a log value is half the difference between the log of the largest and smallest values. Every point gets its own bar.
The worst acceptable line is the steepest or shallowest line through all the error bars. The uncertainty in the gradient is the difference between the two gradients.
Read the constants from the gradient and intercept, give their uncertainties, and compare them with any value the question predicts.
The marking follows the conventions in published Cambridge mark schemes. The experiments, readings and wording on this page are our own.