Physics 9702 · syllabus 1
Cambridge A Level Physics 9702 — Physical quantities and units topical past papers
How physical quantities are stated and checked: SI base units and prefixes, homogeneity, uncertainties in measurement, and adding and resolving vectors.
- Questions
- 606
- Years
- 2009–2026
- With mark scheme
- 100%
- Questions 2022–2026
- 134
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What Physical quantities and units covers
Every physical quantity is a number with a unit, and this topic sets the rules for both. You work from the SI base quantities used at AS — mass, length, time, current and temperature — and express every derived unit, from the newton to the ohm, in terms of kg, m, s, A and K. That lets you test whether an equation is homogeneous: if the base units on the two sides differ, the equation is wrong, although matching units do not prove it right.
Measurement comes next. Random errors scatter readings either side of the true value and are reduced by repeating and averaging; systematic errors, including zero errors, shift every reading the same way and are not reduced by repetition. Precision describes how close repeated readings are to each other, accuracy how close they are to the true value. You combine uncertainties by adding absolute uncertainties for sums and differences, and percentage uncertainties for products, quotients and powers.
The topic ends with scalars and vectors: adding and subtracting coplanar vectors by scale drawing or calculation, and resolving a vector into two perpendicular components. These tools are used in almost every later topic, and the uncertainty work returns in the practical papers. The content itself is AS material, examined on Papers 1 and 2.
In the syllabus
The headings this topic has in the Cambridge International 2025–2027 syllabus, as the board prints them.
- 1 Physical quantities and units
- 1.1 Physical quantities
- 1.2 SI units
- 1.3 Errors and uncertainties
- 1.4 Scalars and vectors
What you should be able to do
- Express derived units such as the joule, the pascal and the volt in SI base units
- Check the homogeneity of an equation using base units
- Convert between prefixes from pico to tera, including squared and cubed units such as mm² and cm³
- Make sensible order-of-magnitude estimates of everyday physical quantities
- Combine absolute and percentage uncertainties to find the uncertainty in a derived quantity
- Resolve a vector into perpendicular components and find a resultant by drawing or calculation
Key ideas
- SI base units used at AS: kg, m, s, A and K; for example 1 N = 1 kg m s⁻² and 1 J = 1 kg m² s⁻²
- Sums and differences: absolute uncertainties add, so Δ(a − b) = Δa + Δb
- Products and quotients: percentage uncertainties add; for a power, multiply by the power, so for y = x³ the percentage uncertainty is 3 × that of x
- Components of a vector F at angle θ to the horizontal: F cos θ horizontally and F sin θ vertically
- Accuracy is closeness to the true value; precision is the closeness of repeated readings to each other
How Physical quantities and units has been examined
From 2022 to 2026, Physical quantities and units was on Paper 2 · AS Level Structured Questions in 11 of 11 exam series, worth about 13% of that paper’s marks.
| Paper | Questions | Share of marks | Series |
|---|---|---|---|
| Paper 1 · Multiple Choice | 103 | 8% | 11 of 11 |
| Paper 2 · AS Level Structured Questions | 29 | 13% | 11 of 11 |
| Paper 4 · A Level Structured Questions | 2 | 1% | 2 of 11 |
Momentum’s own count, over the questions in its bank for these years: a series is one exam session, every zone included, and a question filed under two chapters counts in both. Median marks per question: 1.
Filed in Momentum under: Physical Quantities & Units, Measurement Techniques.
A worked example
A metal cube has a mass of 48.0 ± 0.5 g and a side length of 2.00 ± 0.02 cm. Calculate its density in kg m⁻³, with its absolute uncertainty.
- Convert to SI: m = 0.0480 kg and l = 0.0200 m, so V = l³ = 8.00 × 10⁻⁶ m³
- Density: ρ = m/V = 0.0480 / 8.00 × 10⁻⁶ = 6000 kg m⁻³
- Percentage uncertainty in m: 0.5 / 48.0 × 100 = 1.0%
- Percentage uncertainty in l: 0.02 / 2.00 × 100 = 1.0%; l is cubed, so V carries 3 × 1.0% = 3.0%
- Total: 1.0% + 3.0% = 4.0%, and 4.0% of 6000 kg m⁻³ is 240 kg m⁻³, which rounds to 200 kg m⁻³ at one significant figure
Answer: ρ = (6.0 ± 0.2) × 10³ kg m⁻³
Written by Momentum for this page, with its own numbers; it is not taken from a past paper.
Mistakes that cost marks
- Converting mm² to m² by multiplying by 10⁻³ instead of 10⁻⁶ — the prefix is squared along with the unit, so 0.20 mm² is 2.0 × 10⁻⁷ m², not 2.0 × 10⁻⁴ m²
- Subtracting uncertainties when two readings are subtracted — uncertainties always add, which is why a small difference between two large readings carries a large percentage uncertainty
- Forgetting to multiply by the power — when a length is cubed to give a volume, its percentage uncertainty counts three times
- Calling readings accurate because they are precise — a set of readings can agree closely with each other and all be wrong by the same zero error
- Writing the newton as kg m s⁻¹ in a homogeneity check — that is the unit of momentum; force is kg m s⁻², and the slip makes a correct equation look inhomogeneous
Exam technique
- In a homogeneity question, reduce each side to base units line by line and finish with a sentence saying the units match; a pure number such as ½ has no unit and drops out
- Give a final uncertainty to one or two significant figures and the value to the same decimal place, for example (6.0 ± 0.2) × 10³ kg m⁻³
- For vectors, a sketch with the angle marked earns credit and prevents sin and cos mix-ups; for a scale drawing, state the scale you used
- In estimate questions, write down the values you assumed and give the answer to one significant figure
Practising in Momentum
- Every question in a chapter as one list, from every paper and year in the bank, newest first or shuffled.
- Each question turns over to its own part of the mark scheme, where the board published one.
- Narrow by paper, year, session, zone and marks, and star the questions worth keeping.
- Pick chapters, a number of questions and a time, and the exam builder draws a mock to sit and mark.
Past-paper questions and mark schemes are the copyright of Cambridge International. Momentum shows them to signed-in learners for revision and does not publish them on these pages.