A-Level Physics — 1) Quantities & Measurement (IP-Friendly Guide)

TL;DR
Mastering units, errors and vectors is not “intro fluff” — it is the quality-control layer that guards every mark in kinematics, fields and practical Paper 4. This guide turns the SEAB bullet-points into classroom-tested check-lists, mini-drills and WA timing hacks.

1 SI base quantities & units

The syllabus expects you to recall and use the seven base quantities — mass \((\pu{kg})\), length \((\pu{m})\), time \((\pu{s})\), electric current \((\pu{A})\), thermodynamic temperature \((\pu{K})\), amount of substance \((\pu{mol})\) and luminous intensity \((\pu{cd})\).

1.1 Why parents should care

A single wrong unit symbol turns a correct gradient into a 0 mark in Paper 4 ACE.

1.2 Mini-drill

Write the unit for gravitational field strength \(g\).
Answer: \(\ \pu{m.s-2}\) — two base units multiplied.

2 SI prefixes (p → T)

NIST refreshed this table in 2022 and added four larger prefixes up to \(10^{30}\).

Exam cue: never mix prefix symbols with powers of 2 (e.g. 1 kilobit = 1000 bit, not 1024 bit).

3 Derived units & dimensional homogeneity

Express derived quantities as products or quotients of the base units; e.g.
\[ 1 \space \pu{N} = 1\, \pu{kg.m.s-2}. \]

3.1 Homogeneity check

Verify \(s = ut + \tfrac12 at^2\):

• \([s]=\ \pu{m}\)
• \([ut]=\ \pu{\tfrac{m}{s}} \space \times \space \pu{s} = \pu{m}\)
• \([at^2] = \pu{\tfrac{m}{s^2}} \space \times \space \pu{s^2} = \pu{m}\)*

All terms reduce to metres ✔

4 Errors & uncertainties

4.1 Random vs systematic

Random errors scatter readings; systematic errors (e.g. zero error on a Vernier calliper) shift every value the same way.

4.2 Quoting a reading

Record the raw value and ± \(\frac12\) least-division:

Metre rule: \(42.0 \space \pu{cm} \pm 0.05 \space \pu{cm}\).

4.3 Propagation

For \(Q = \dfrac{A B^2}{C}\)
\[ \frac{\Delta Q}{Q} = \frac{\Delta A}{A} + 2\frac{\Delta B}{B} + \frac{\Delta C}{C}. \tag{1} \]

WA hack: add percent uncertainties when multiplying/dividing; add absolute uncertainties when adding/subtracting.

5 Scalars & vectors

Define a vector by magnitude + direction; represent it by an arrow.

5.1 Adding coplanar vectors

1. Tip-to-tail triangle
2. Resultant from start to finish

5.2 Component method

Resolve \(\vec{F}\) into \(F_x = F \cos \theta\) and \(F_y = F \sin \theta\). Blending with algebra simplifies WA calculations.

6 Order-of-magnitude estimation

The syllabus wants “reasonable estimates”. Learn touch-stones:

• Classroom length ≈ \(8 \space \pu{m}\)
• Human reaction time ≈ \(0.2 \space \pu{s}\)

Use 1-sig-fig values unless greater precision matters.

7 Three WA timing rules

1. 1 mark ≈ 1.5 min — same as SEAB design.
2. Start every data Q by copying units before numbers.
3. Show working to harvest method marks if arithmetic slips.

8 Bridge to Paper 4 practical

• Import readings into Sheets, plot XY scatter, insert trend-line.
• Use =LINEST(Y,X,TRUE,TRUE) to grab gradient ± SE.
• Quote final result to the same s.f. as the least precise raw input.

9 Further reading

• SEAB H2 Physics 9478 syllabus (2026)
• BIPM — SI Brochure, 9th Ed.
• NIST — SI Prefixes (2022 update)
• NPL — Uncertainty & Propagation
• Physics Classroom — Vectors & Motion

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Last updated 14 Jul 2025. Next review when SEAB issues the 2027 draft syllabus.