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Learning objectives
Core idea
Key formulae
Worked examples
Explore the graph
Common mistakes
Exam tip
Guided practice
Practice questions
Challenge
Summary
Quick quiz
Same topic, different board
Past paper questions

Learn4PH1Paper 2P · Paper 2 (all content)Practical skillsMeasurements, tables and graphs

Practical skills · Subtopic 1 of 1

Measurements, Tables and Graphs

Good practical work starts with a fair test: change one variable, measure another, and keep everything else the same. Record readings in tables with units in the headings and consistent precision. Plot graphs with sensible scales, draw a best-fit line, and use a large triangle to find the gradient. Repeat readings and avoid parallax and zero errors.

Cambridge 5054 Paper 3Cambridge 5054 Paper 4Cambridge 0625 Papers 5, 6Edexcel 4PH1 Paper 1PEdexcel 4PH1 Paper 2P≈ 30 minRevision 5 · updated 2026-10-27

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Section 1 of 14

Learning objectives

Identify independent, dependent and control variables.
Record results in tables with correct headings, units and precision.
Plot graphs, draw best-fit lines and calculate gradients.
Identify sources of error and suggest improvements.

Pause and think

Two students time a ball rolling down a ramp. One gets $1.2$ s, the other $1.8$ s. Who is right?

Section 2 of 14

Core idea

Start hereA fair test

Does a longer pendulum swing more slowly? If you change the length and the mass at the same time, you can't tell which caused the difference. Good experiments change one thing, measure another, and keep everything else fixed.

The big idea

Independent (change), dependent (measure), control (keep fixed). Repeat and average. Best-fit line; gradient from a large triangle.

1. Planning

Independent: what you change.
Dependent: what you measure.
Control: what you keep the same.
Repeat readings; spot anomalies.

2. Graphs

Drawing a line of best fit and finding the gradient

Draw a thin straight line with points evenly on either side (it need not pass through every point). Use a large triangle: gradient

=\dfrac{6}{300}=0.02

cm/g.

Worked exampleSpring constant from a graph

Force vs extension data.

Goal: $k$ .
Strategy: Best-fit line; large gradient triangle.

Force on $y$ , extension on $x$ ; scales filling most of the grid.
Straight best-fit line with points evenly either side.
$k=\frac{6.0-0}{0.24-0}=25\text{ N/m}$
Large triangle from the line, not data points.

Answer

25

N/m.

✓ CheckUnits: N ÷ m ✓.

Exam tipTables Headings with units (e.g. "length / cm"), consistent decimal places.

Common misconceptionDot-to-dot Draw one smooth best-fit line, not lines joining every point.

Pause and think

Why use a large gradient triangle?

Summary

Fair tests.
Best-fit lines; large triangles.

Anomaly: Result that does not fit the pattern.

HistoryGalileo times with water. With no stopwatch, Galileo timed rolling balls by collecting water flowing from a tank and weighing it: twice the water meant twice the time. Clever measurement methods have always been as important to physics as clever theories.

Fun factThe kilogram lost weight. For

130

years the kilogram was defined by a metal cylinder in a vault near Paris. Copies made at the same time drifted by up to

50

micrograms. In

2019

the kilogram was redefined using a fundamental constant, so it can never change again.

Section 3 of 14

Key formulae

Mean

\bar x=\frac{\text{sum of readings}}{\text{number of readings}}

Gradient

m=\frac{\Delta y}{\Delta x}

Table heading

\text{quantity / unit, e.g. } t\ /\ \text{s}

TrickThe big triangle. For a gradient, draw a triangle covering at least half the line. Read the corners carefully and show the values on your graph. Small triangles magnify reading errors.

Section 4 of 14

Worked examples

Example 1 · Mean of repeats0 / 2 steps

Three timings are

2.31

2.35

s and

2.33

s. Find the mean.

Example 2 · Gradient0 / 2 steps

A best-fit line passes through

(0.10, 0.80)

and

(0.60, 4.80)

, with load (N) on

y

and extension (m) on

x

. Find the gradient.

Section 5 of 14

Explore the graph

Best-fit line and gradient

Loading the interactive graph…

Try this

The points are a student's load (N) against extension (m) readings. Adjust $m$ and $c$ until the line is a good best fit.
A best-fit line should have roughly as many points above it as below.
Does your best line pass close to the origin? What does that tell you about the relationship?

The gradient of the best-fit line gives the spring constant.

In the real worldScientists repeat everything. Before a result is accepted, other labs must reproduce it. In

2011

an experiment seemed to show neutrinos travelling faster than light; other teams couldn't reproduce it, and the cause was found to be a loose fibre-optic cable.

Section 6 of 14

Common mistakes

IncorrectUnits in every cell of a table

CorrectUnits in the column heading

"length / cm" once at the top.

IncorrectJoining points dot to dot

CorrectDraw a best-fit line

Readings have random errors.

IncorrectGradient from two data points

CorrectUse points on the line

The line averages the data.

IncorrectInconsistent decimal places

CorrectSame precision throughout

Matches the instrument's resolution.

Expectation

Measure once, write it down, done

Reality

Repeat, average, check anomalies, write the unit

Section 7 of 14

Exam tip

Exam tipImprovements must be specific. "Be more careful" scores nothing. Say exactly what and why: "use a fiducial marker at the centre of the swing to reduce timing errors", or "repeat each reading three times and calculate a mean".

Section 8 of 14

Guided practice

SA-5054-PS1-0011 markL1 FoundationCalculatorMeasurements

A student investigates how the length of a pendulum affects its period. The independent variable is

Salam Academy Original Practice · Proposed mark scheme

Section 9 of 14

Practice questions

SA-5054-PS1-0021 markL1 FoundationCalculatorMeasurements

In the same pendulum experiment, which should be kept constant as a control variable?

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SA-5054-PS1-0031 markL1 FoundationCalculatorMeasurements

Three timings are

2.31

2.35

s and

2.33

s. Calculate the mean.

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SA-5054-PS1-0041 markL1 FoundationCalculatorMeasurements

Which is the correct heading for a column of time readings in seconds?

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SA-5054-PS1-0051 markL1 FoundationCalculatorMeasurements

To avoid parallax error when reading a measuring cylinder, you should

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SA-5054-PS1-0061 markL2 StandardCalculatorMeasurements

A newton meter reads

0.2

N with nothing attached. With a load it reads

3.7

N. Calculate the true weight of the load.

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SA-5054-PS1-0072 marksL2 StandardCalculatorGraphs

A best-fit line on a load (N) against extension (m) graph passes through

(0.10, 0.80)

and

(0.60, 4.80)

. Calculate the gradient.

Salam Academy Original Practice · Proposed mark scheme

SA-5054-PS1-0081 markL1 FoundationCalculatorGraphs

A graph of

y

against

x

is a straight line through the origin. This shows that

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SA-5054-PS1-0091 markL1 FoundationCalculatorGraphs

When drawing a line of best fit through scattered points, you should

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SA-5054-PS1-0101 markL2 StandardCalculatorMeasurements

A student times

20

oscillations of a pendulum as

31.2

s. Calculate the period, to

3

significant figures.

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More questions on every skill in this subtopic are in the question bank under Practise.

Section 10 of 14

Challenge

SA-5054-PS1-0113 marksL3 ExamCalculatorGraphs

A student plots p.d. (V) on the

y

-axis against current (A) on the

x

-axis for a resistor. The best-fit line passes through

(0.050, 0.60)

and

(0.250, 3.00)

. Calculate the resistance.

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Section 11 of 14

Summary

Independent: changed. Dependent: measured. Control: kept the same.
Table headings: quantity / unit; consistent precision.
Graph: labelled axes, best-fit line, big triangle for gradient.
Repeat, average, avoid parallax and zero errors.

Section 12 of 14

Quick quiz

Q1 · SA-5054-PS1-0121 markL1 FoundationCalculatorMeasurements

Repeating measurements and calculating a mean mainly helps to

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Section 13 of 14

Same topic, different board

Specification: International GCSE Physics 4PH1
Where: Practical skills (assessed within the written papers)
Expected: Core practicals assessed through questions on planning, results and evaluation.
Calculator: Calculator allowed in both papers.
Typical style: Structured questions with a list of equations to recall; Paper 2 adds extra content.
Open in: 4PH1 · Paper 1P 4PH1 · Paper 2P

Section 14 of 14

Past paper questions

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Salam Academy original content · Content status: reviewed and published. Syllabus mapping: Pearson Edexcel 4PH1, 2017 specification (official specification).