OCR A-Level Physics A Foundations of physics: units, vectors and uncertainty made exam-ready

What this module actually demands

Foundations of physics is the toolkit for the whole specification. It looks deceptively simple, but the techniques here, expressing units in base form, resolving vectors and propagating uncertainty, appear in almost every question in Modules 3 to 6 and across all three papers. OCR rewards candidates who handle them fluently and automatically.

This guide walks through the topics in order and sets out the exam patterns OCR repeats. Each topic has a matching dot-point page with practice; this overview ties them together.

Quantities, units and homogeneity

Physical quantities and units sets out the seven SI base units (kilogram, metre, second, ampere, kelvin, mole, candela) and how to express any derived unit in base form by following its defining equation, so the newton is $\text{kg m s}^{-2}$, the joule is $\text{kg m}^2\text{s}^{-2}$ and the volt is $\text{kg m}^2\text{s}^{-3}\text{A}^{-1}$. It covers prefixes from pico ($10^{-12}$) to giga ($10^{9}$), standard form, order-of-magnitude estimation, and checking the homogeneity of an equation by reducing every term to base units. A homogeneity check catches errors but cannot reveal a missing dimensionless constant.

Vectors and uncertainty

Scalars and vectors distinguishes magnitude-only quantities (mass, energy, speed) from magnitude-and-direction quantities (displacement, velocity, force), combines vectors tip-to-tail by scale drawing or by calculation using $R = \sqrt{A^2 + B^2}$ for perpendicular vectors, and resolves a vector of magnitude $F$ at angle $\theta$ into $F\cos\theta$ along an axis and $F\sin\theta$ perpendicular to it.

Measurements and uncertainties separates precision from accuracy and random from systematic error, expresses uncertainty in absolute, fractional and percentage form, and combines uncertainties: add absolute uncertainties for sums and differences, add percentage uncertainties for products and quotients, and multiply by the power when raising to a power.

How this module is examined

A typical OCR profile for Foundations of physics:

• Show-that and homogeneity. Reduce both sides of an equation to base units to prove consistency.
• Vector calculations. Resultant displacement or force by Pythagoras and trigonometry; resolving a force into components.
• Uncertainty arithmetic. Percentage uncertainty in a derived quantity, often with a squared or cubed term, and conversion back to an absolute uncertainty.
• Definitions. Precision versus accuracy, random versus systematic error.

Check your knowledge

A mix of recall and calculation questions covering the module. Attempt them under timed conditions, then check against the solutions.

1. Express the watt in SI base units. (1 mark)
2. Two perpendicular forces of $9.0\ \text{N}$ and $12\ \text{N}$ act on a point. Find the magnitude of the resultant. (2 marks)
3. A force of $30\ \text{N}$ acts at $25^{\circ}$ to the horizontal. Find its horizontal component. (2 marks)
4. State one difference between a random and a systematic error. (1 mark)
5. A quantity $Q = \frac{a}{b^2}$ has percentage uncertainties of $2\%$ in $a$ and $3\%$ in $b$. Find the percentage uncertainty in $Q$. (2 marks)
6. Write $0.000\,025\ \text{s}$ in standard form and in microseconds. (2 marks)