A2 Physics Paper 5 Black Book
Cambridge A Level Physics 9702 Paper 5, Question 2
Data Analysis, Graphs &
Uncertainty
Edition 1
What This Guide Covers:
¥ Linearize equations and determine gradient/y-intercept expressions
¥ Complete data tables with properly calculated uncertainties
¥ Plot graphs with accurate error bars
¥ Determine gradients and y-intercepts with uncertainties
¥ Extract physical constants from graphical analysis
¥ 8 major topic areas with worked past paper examples
Argha Saha
,Paper 5, Question 2: Data Analysis 1
Abstract
This comprehensive guide provides systematic coverage of experimental data
analysis and graphical methods for Cambridge International AS & A Level Physics
(9702) Paper 5, question 2: Data Analysis and Evaluation. The document addresses
essential analytical skills including the linearization of physical equations to deter-
mine gradient and y-intercept expressions, completion of data tables with rigorous
uncertainty calculations, accurate graph plotting with error bars, determination of
gradients and y-intercepts with associated uncertainties, and extraction of physi-
cal constants through graphical analysis. Eight major topic areas spanning optics,
mechanics, thermodynamics, electromagnetism, and modern physics are illustrated
through detailed worked solutions from past examination papers, each fully aligned
with official mark schemes and examiner reports to ensure examination readiness
and technique mastery.
Author’s Note
Hello fellow physics enthusiast!
This guide is the result of countless hours spent analyzing past papers, marking schemes,
and examiner reports, combined with my own journey through teaching A-Level Physics
and studying astrophysics at university. I wanted to create something that I wish I had
when I was preparing for my exams: a comprehensive, no-nonsense guide that actually
helps you understand what examiners are looking for.
Modern AI tools like Claude Sonnet 4.5, Claude Opus 4.5, Gemini 2.5, Gemini 3.0, and
Nanobanana Pro have been invaluable collaborators in this project. They’ve helped me
organize information, cross-check facts against multiple sources, polish my explanations,
and create the diagrams you’ll see throughout (for question 1 that is, thanks especially
to Nanobanana Pro for those!). Think of them as tireless research assistants who never
get tired of double-checking details.
My goal? To give you what I believe is one of the most complete and practical guides to
Paper 5 out ther, something that genuinely prepares you to walk into that exam room
with confidence and aim for full marks.
Found something that doesn’t quite make sense? Spotted an error? Have suggestions
for how we can make this even better? I’d genuinely love to hear from you. Drop us an
email at:
•
•
Your feedback helps us improve this guide for everyone. We’re all in this together, and
I’m here to help you succeed.
Best of luck with your studies and HAVE FUN, you’ve got this!
Argha Saha
Sciencetadium
,Paper 5, Question 2: Data Analysis 2
Contents
Author’s Note 1
1 The Structure of Question 2: Complete Breakdown 5
1.1 Part (a): Determine Expressions for Gradient and Y-Intercept [1 mark1] 5
1.2 Part (b): Complete Results Table with Uncertainties [2 marks] . . . . . 6
1.3 Part (c): Graph with Error Bars, Best Fit, and Gradient [8 marks] . . . 6
1.3.1 Part (c)(i): Plot Points with Error Bars [2 marks] . . . . . . . . 6
1.3.2 Part (c)(ii): Draw Best Fit and Worst Acceptable Lines [2 marks] 7
1.3.3 Part (c)(iii): Determine Gradient with Uncertainty [2 marks] . . 7
1.3.4 Part (c)(iv): Determine Y-Intercept with Uncertainty [2 marks] . 7
1.4 Part (d): Determine Physical Constants [3 marks] . . . . . . . . . . . . 8
1.5 Part (e): Percentage Uncertainty [1 mark1] (Sometimes asked) . . . . . 8
2 Linearization: Converting Non-Linear to Linear Relationships 9
2.1 Power Law: y = axn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Exponential Decay: y = Ae−bx . . . . . . . . . . . . . . . . . . . . . . . . 9
k
2.3 Inverse Square Law: y = x2
. . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Combined Linear Terms: y = mx + b . . . . . . . . . . . . . . . . . . . . 10
2.5 Summary Table of Linearization . . . . . . . . . . . . . . . . . . . . . . . 11
3 Eight Major Topic Areas with Worked Examples 12
3.1 Topic 1: Optics — Diffraction Gratings . . . . . . . . . . . . . . . . . . . 12
3.1.1 The Question (Verbatim from Question Paper) . . . . . . . . . . 12
3.1.2 Model Solution with Full Mark Scheme Alignment . . . . . . . . . 14
3.2 Topic 2: Circuits and Electricity — Parallel Resistors . . . . . . . . . . . 22
3.2.1 The Question (Verbatim from Question Paper) . . . . . . . . . . 22
3.2.2 Model Solution with Full Mark Scheme Alignment . . . . . . . . . 24
3.3 Topic 3: Mechanical Oscillations — Spring Constant . . . . . . . . . . . 34
3.3.1 The Question (Verbatim from Question Paper) . . . . . . . . . . 34
3.3.2 Model Solution with Full Mark Scheme Alignment . . . . . . . . . 36
3.4 Topic 4: Thermal Physics — Thermistor Resistance . . . . . . . . . . . . 48
Sciencetadium
, Paper 5, Question 2: Data Analysis 3
3.4.1 The Question (Verbatim from Question Paper) . . . . . . . . . . 48
3.4.2 Model Solution with Full Mark Scheme Alignment . . . . . . . . . 50
3.5 Topic 5: AC Circuits — Phase Difference in RC Circuit . . . . . . . . . . 55
3.5.1 The Question (Verbatim from Question Paper) . . . . . . . . . . 55
3.5.2 Model Solution with Full Mark Scheme Alignment . . . . . . . . . 57
3.6 Topic 6: Waves — Stationary Waves in Vertical Tube . . . . . . . . . . . 66
3.6.1 The Question (Verbatim from Question Paper) . . . . . . . . . . 66
3.6.2 Model Solution with Full Mark Scheme Alignment . . . . . . . . . 70
3.7 Topic 7: Astrophysics — Stellar Luminosity and Mass Relationship . . . 81
3.7.1 The Question (Verbatim from Question Paper) . . . . . . . . . . 81
3.7.2 Model Solution with Full Mark Scheme Alignment . . . . . . . . . 83
3.8 Topic 8: Optics — Young’s Double Slit Experiment . . . . . . . . . . . . 94
3.8.1 The Question (Verbatim from Question Paper) . . . . . . . . . . 94
3.8.2 Model Solution with Full Mark Scheme Alignment . . . . . . . . . 97
4 Comprehensive Uncertainty Analysis 109
4.1 Types of Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.1.1 Absolute Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.1.2 Relative (Fractional) Uncertainty . . . . . . . . . . . . . . . . . . 109
4.2 Propagation of Uncertainty in Calculations . . . . . . . . . . . . . . . . . 109
4.2.1 Sum or Difference: Q = A + B or Q = A − B . . . . . . . . . . . 109
4.2.2 Product or Quotient: Q = AB or Q = A/B . . . . . . . . . . . . 110
4.2.3 Powers: Q = An . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.3 Uncertainty in Calculated Transformed Quantities (Question 2, Part b) . 111
4.3.1 Uncertainty in 1/x . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.3.2 Uncertainty in 1/x2 . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.3.3 Uncertainty in Logarithms . . . . . . . . . . . . . . . . . . . . . . 112
4.4 Uncertainty in Gradient and Y-Intercept . . . . . . . . . . . . . . . . . . 112
4.4.1 Method: Line of Worst Fit . . . . . . . . . . . . . . . . . . . . . . 112
4.5 Percentage Uncertainty in Derived Constants . . . . . . . . . . . . . . . . 113
5 Common Mistakes in Question 2 and How to Avoid Them 114
5.1 Mistake 1: Incorrect Linearization . . . . . . . . . . . . . . . . . . . . . . 114
Sciencetadium
Cambridge A Level Physics 9702 Paper 5, Question 2
Data Analysis, Graphs &
Uncertainty
Edition 1
What This Guide Covers:
¥ Linearize equations and determine gradient/y-intercept expressions
¥ Complete data tables with properly calculated uncertainties
¥ Plot graphs with accurate error bars
¥ Determine gradients and y-intercepts with uncertainties
¥ Extract physical constants from graphical analysis
¥ 8 major topic areas with worked past paper examples
Argha Saha
,Paper 5, Question 2: Data Analysis 1
Abstract
This comprehensive guide provides systematic coverage of experimental data
analysis and graphical methods for Cambridge International AS & A Level Physics
(9702) Paper 5, question 2: Data Analysis and Evaluation. The document addresses
essential analytical skills including the linearization of physical equations to deter-
mine gradient and y-intercept expressions, completion of data tables with rigorous
uncertainty calculations, accurate graph plotting with error bars, determination of
gradients and y-intercepts with associated uncertainties, and extraction of physi-
cal constants through graphical analysis. Eight major topic areas spanning optics,
mechanics, thermodynamics, electromagnetism, and modern physics are illustrated
through detailed worked solutions from past examination papers, each fully aligned
with official mark schemes and examiner reports to ensure examination readiness
and technique mastery.
Author’s Note
Hello fellow physics enthusiast!
This guide is the result of countless hours spent analyzing past papers, marking schemes,
and examiner reports, combined with my own journey through teaching A-Level Physics
and studying astrophysics at university. I wanted to create something that I wish I had
when I was preparing for my exams: a comprehensive, no-nonsense guide that actually
helps you understand what examiners are looking for.
Modern AI tools like Claude Sonnet 4.5, Claude Opus 4.5, Gemini 2.5, Gemini 3.0, and
Nanobanana Pro have been invaluable collaborators in this project. They’ve helped me
organize information, cross-check facts against multiple sources, polish my explanations,
and create the diagrams you’ll see throughout (for question 1 that is, thanks especially
to Nanobanana Pro for those!). Think of them as tireless research assistants who never
get tired of double-checking details.
My goal? To give you what I believe is one of the most complete and practical guides to
Paper 5 out ther, something that genuinely prepares you to walk into that exam room
with confidence and aim for full marks.
Found something that doesn’t quite make sense? Spotted an error? Have suggestions
for how we can make this even better? I’d genuinely love to hear from you. Drop us an
email at:
•
•
Your feedback helps us improve this guide for everyone. We’re all in this together, and
I’m here to help you succeed.
Best of luck with your studies and HAVE FUN, you’ve got this!
Argha Saha
Sciencetadium
,Paper 5, Question 2: Data Analysis 2
Contents
Author’s Note 1
1 The Structure of Question 2: Complete Breakdown 5
1.1 Part (a): Determine Expressions for Gradient and Y-Intercept [1 mark1] 5
1.2 Part (b): Complete Results Table with Uncertainties [2 marks] . . . . . 6
1.3 Part (c): Graph with Error Bars, Best Fit, and Gradient [8 marks] . . . 6
1.3.1 Part (c)(i): Plot Points with Error Bars [2 marks] . . . . . . . . 6
1.3.2 Part (c)(ii): Draw Best Fit and Worst Acceptable Lines [2 marks] 7
1.3.3 Part (c)(iii): Determine Gradient with Uncertainty [2 marks] . . 7
1.3.4 Part (c)(iv): Determine Y-Intercept with Uncertainty [2 marks] . 7
1.4 Part (d): Determine Physical Constants [3 marks] . . . . . . . . . . . . 8
1.5 Part (e): Percentage Uncertainty [1 mark1] (Sometimes asked) . . . . . 8
2 Linearization: Converting Non-Linear to Linear Relationships 9
2.1 Power Law: y = axn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Exponential Decay: y = Ae−bx . . . . . . . . . . . . . . . . . . . . . . . . 9
k
2.3 Inverse Square Law: y = x2
. . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Combined Linear Terms: y = mx + b . . . . . . . . . . . . . . . . . . . . 10
2.5 Summary Table of Linearization . . . . . . . . . . . . . . . . . . . . . . . 11
3 Eight Major Topic Areas with Worked Examples 12
3.1 Topic 1: Optics — Diffraction Gratings . . . . . . . . . . . . . . . . . . . 12
3.1.1 The Question (Verbatim from Question Paper) . . . . . . . . . . 12
3.1.2 Model Solution with Full Mark Scheme Alignment . . . . . . . . . 14
3.2 Topic 2: Circuits and Electricity — Parallel Resistors . . . . . . . . . . . 22
3.2.1 The Question (Verbatim from Question Paper) . . . . . . . . . . 22
3.2.2 Model Solution with Full Mark Scheme Alignment . . . . . . . . . 24
3.3 Topic 3: Mechanical Oscillations — Spring Constant . . . . . . . . . . . 34
3.3.1 The Question (Verbatim from Question Paper) . . . . . . . . . . 34
3.3.2 Model Solution with Full Mark Scheme Alignment . . . . . . . . . 36
3.4 Topic 4: Thermal Physics — Thermistor Resistance . . . . . . . . . . . . 48
Sciencetadium
, Paper 5, Question 2: Data Analysis 3
3.4.1 The Question (Verbatim from Question Paper) . . . . . . . . . . 48
3.4.2 Model Solution with Full Mark Scheme Alignment . . . . . . . . . 50
3.5 Topic 5: AC Circuits — Phase Difference in RC Circuit . . . . . . . . . . 55
3.5.1 The Question (Verbatim from Question Paper) . . . . . . . . . . 55
3.5.2 Model Solution with Full Mark Scheme Alignment . . . . . . . . . 57
3.6 Topic 6: Waves — Stationary Waves in Vertical Tube . . . . . . . . . . . 66
3.6.1 The Question (Verbatim from Question Paper) . . . . . . . . . . 66
3.6.2 Model Solution with Full Mark Scheme Alignment . . . . . . . . . 70
3.7 Topic 7: Astrophysics — Stellar Luminosity and Mass Relationship . . . 81
3.7.1 The Question (Verbatim from Question Paper) . . . . . . . . . . 81
3.7.2 Model Solution with Full Mark Scheme Alignment . . . . . . . . . 83
3.8 Topic 8: Optics — Young’s Double Slit Experiment . . . . . . . . . . . . 94
3.8.1 The Question (Verbatim from Question Paper) . . . . . . . . . . 94
3.8.2 Model Solution with Full Mark Scheme Alignment . . . . . . . . . 97
4 Comprehensive Uncertainty Analysis 109
4.1 Types of Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.1.1 Absolute Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.1.2 Relative (Fractional) Uncertainty . . . . . . . . . . . . . . . . . . 109
4.2 Propagation of Uncertainty in Calculations . . . . . . . . . . . . . . . . . 109
4.2.1 Sum or Difference: Q = A + B or Q = A − B . . . . . . . . . . . 109
4.2.2 Product or Quotient: Q = AB or Q = A/B . . . . . . . . . . . . 110
4.2.3 Powers: Q = An . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.3 Uncertainty in Calculated Transformed Quantities (Question 2, Part b) . 111
4.3.1 Uncertainty in 1/x . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.3.2 Uncertainty in 1/x2 . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.3.3 Uncertainty in Logarithms . . . . . . . . . . . . . . . . . . . . . . 112
4.4 Uncertainty in Gradient and Y-Intercept . . . . . . . . . . . . . . . . . . 112
4.4.1 Method: Line of Worst Fit . . . . . . . . . . . . . . . . . . . . . . 112
4.5 Percentage Uncertainty in Derived Constants . . . . . . . . . . . . . . . . 113
5 Common Mistakes in Question 2 and How to Avoid Them 114
5.1 Mistake 1: Incorrect Linearization . . . . . . . . . . . . . . . . . . . . . . 114
Sciencetadium
