A-Level Physics: Measurements and Uncertainties

Every practical question and every calculated answer at A-Level Physics passes through the machinery of measurement: units, errors and uncertainty. Examiners test this machinery directly, and it underpins the required practicals — which makes this the right first quiz in the collection.

The units questions establish the foundations: which quantities are SI base units (kelvin and mole against the derived newton and joule), and how derived units decompose — a dedicated question resolves the joule into kg·m²·s⁻² and N·m, the fluency examiners expect when checking homogeneity of equations.

The error-theory questions target the distinction that costs the most marks: random versus systematic error. One question pins down that averaging repeated readings reduces random error while systematic errors shift every reading by the same amount and survive averaging; another asks you to pick genuine systematic errors (zero offsets, consistent calibration biases) from plausible decoys.

The calculation questions do real uncertainty propagation with concrete values: absolute uncertainty of a quotient (capacitance from charge and voltage), percentage uncertainty of a product (area from two lengths), the ½gt² experiment where the time's uncertainty counts twice, and a full density-of-a-cylinder problem combining mass, length and a squared radius into an 11% total — the multi-source propagation that practical-skills questions reward. An order-of-magnitude estimation question (atoms in a human body) completes the set.

Every question is self-contained with concrete values, and every explanation shows the propagation rule being applied. In line with the real exam's data booklet, nothing here asks you to recall a formula — only to use one correctly.

• Distinguish SI base units from derived units and decompose derived units
• Separate random from systematic errors and know which averaging reduces
• Propagate absolute uncertainties through sums and quotients
• Combine percentage uncertainties in products, counting squared quantities twice
• Estimate orders of magnitude with sensible physical assumptions

Topic scope follows the A-level physics content — as organised, for example, in section 3.1 (Measurements and their errors) of the AQA A-level Physics (7408) specification: SI units, limitations of measurement, uncertainty estimation and combination, and orders of magnitude.