Lesson 3 of 5 · Measurement, maths and practical skills

Graphs, linearisation and data analysis

8 min read · about 1 h 45 min with practice3 quick checks≈3% of the testCore

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Graph work is where practical-skills marks are won and lost. In AQA Paper 3 Section A, Edexcel Paper 3, OCR A Paper 3 and Cambridge Papers 3 and 5, most of the analysis marks follow from one straight-line graph: choosing what to plot, finding a gradient and an intercept, linking them to the physics, and putting an uncertainty on the result. The rules are strict but learnable, and examiners apply them the same way every series.

By the end you’ll be able to

Choose axes and scales, plot points to within half a small square and draw a best-fit line or smooth curve
Calculate gradients using a large triangle and read intercepts, stating units that follow from the axes
Draw error bars and a worst acceptable line to find the uncertainty in a gradient or intercept
Linearise y = kxⁿ using a log–log plot and y = Ae^(kx) using ln y against x, and extract n, k and A
Draw valid conclusions from data, identify anomalous points and suggest how to extend the range or improve reliability

What the exam asks

“Plot a graph of … against …” Marks go for the axes (quantity/unit), the scale, accurate points and a best-fit line.
“Determine the gradient / intercept.” You need a large triangle and correct units. An intercept may need $y = mx + c$ if the axis starts at a false origin.
“Show that the data support $y \propto x^n$ / ”, or

Check your understanding

3 questions on graphs, linearisation and data analysis. Every option is explained once you answer.

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Flashcards

The first 3 of 11 cards for this topic. Sign in and finish the lesson to review them with spaced repetition.

PromptCard 1 of 3

How should graph axes (and table headings) be labelled?

Relationship	Plot y	against x	Gradient	y-intercept
$T = 2\pi\sqrt{l/g}$	$T^2$	$l$	$4\pi^2/g$	0
$V = \varepsilon - Ir$	$V$	$I$	$-r$
$s = \tfrac{1}{2}gt^2$	$s$
$pV = nRT$ at constant $T$	$p$	$1/V$	$n R$
$y = kx^n$	$\lg y$	$\lg x$
$y = Ae^{kx}$	$\ln y$	$x$	$k$
$V = V_0e^{-t/RC}$	$\ln V$
$C = \dfrac{k}{(d+e)^2}$ (count rate, unknown offset $e$ )

T

nRT

n

n

-

1

C_0 = e^{6.50} = 665\ \text{min}^{-1}

Graphs, linearisation and data analysis

By the end you’ll be able to

What the exam asks

Check your understanding

Flashcards

Core ideas

Plotting to examiner standard

Gradient and intercept

Linearisation: make the physics a straight line

Logarithms in tables

Error bars and the worst acceptable line

Curves, tangents and areas

Conclusions and anomalies

Worked examples

Exam technique

Common mistakes

Quick recap

By the end you’ll be able to

What the exam asks

vii.Check your understanding

viii.Flashcards

Core ideas

Plotting to examiner standard

Gradient and intercept

Linearisation: make the physics a straight line

Logarithms in tables

Error bars and the worst acceptable line

Curves, tangents and areas

Conclusions and anomalies

Worked examples

Exam technique

Common mistakes

Quick recap

Check your understanding

Flashcards