SI units, estimation and the maths toolkit

By the end you’ll be able to

Express any derived unit in SI base units and use base units to check the homogeneity of an equation

Convert fluently between prefixes (p to T) and give answers in standard form to an appropriate number of significant figures

Make order-of-magnitude estimates of physical quantities (e.g. the energy of a sprinter, the number of atoms in a coin) with stated assumptions

Rearrange and combine equations, use sine/cosine/tangent and small-angle approximations, and handle powers, exponentials and natural logarithms

Interpret gradients as rates of change and areas under graphs as physical quantities (distance, impulse, work, charge)

What the exam asks

Base units. “Which of these is the SI base unit expression for the volt / pascal / Planck constant?” This is a fixture of the MCQ sections: AQA Papers 1 and 2 (25 MCQs each), OCR A Section A (15) and Cambridge Paper 1 (40).
Homogeneity. “Show that the equation is homogeneous” or “Determine the base units of the constant $k$ .”
Prefixes and standard form. These are hidden in almost every calculation: data given in mm, μF, kΩ, MeV or nm.
Estimation. “Estimate…” or “What is the order of magnitude of…?” You must choose sensible values, state them and give 1–2 significant figures.
Maths skills. Rearranging, trigonometry, small-angle approximations, logarithms and exponentials, and interpreting gradients and areas. These are examined inside physics contexts, never as abstract maths.

Core ideas

The SI base units

AQA and OCR list six base units. Cambridge 9702 lists the first five, but you still use the mole in thermal physics. The seventh SI base unit, the candela, is not examined on any board.

Quantity	Base unit	Symbol
mass	kilogram	kg
length	metre	m
time	second	s
electric current	ampere	A
temperature	kelvin	K
amount of substance	mole	mol

Charge is not a base quantity: .

Unit	From	Base units
newton, N	$F = ma$	$\text{kg m s}^{-2}$
joule, J	$W = Fs$	$\text{kg m}^2\text{ s}^{-2}$
watt, W	$P = W/t$	$\text{kg m}^2\text{ s}^{-3}$
pascal, Pa	$p = F/A$	$\text{kg m}^{-1}\text{ s}^{-2}$
volt, V	$V = P/I$	$\text{kg m}^2\text{ s}^{-3}\text{ A}^{-1}$
ohm, Ω	$R = V/I$	$\text{kg m}^2\text{ s}^{-3}\text{ A}^{-2}$
farad, F	$C = Q/V$	$\text{kg}^{-1}\text{ m}^{-2}\text{ s}^4\text{ A}^2$
tesla, T	$B = F/(Il)$	$\text{kg s}^{-2}\text{ A}^{-1}$

Quantity	Typical value
adult mass / height	70 kg / 1.7 m
walking / sprinting speed	1.5 m s⁻¹ / 10 m s⁻¹
car mass / motorway speed	1500 kg / 30 m s⁻¹
height of one storey	3 m
atom / nucleus diameter	$10^{-10}$ m / $10^{-15}$ m
density of water / air	1000 kg m⁻³ / 1.2 kg m⁻³
visible wavelengths	400–700 nm
room temperature / atmospheric pressure	290 K / $1.0\times10^5$ Pa

Graph (y against x)	Gradient means	Area under means
displacement–time	velocity	—
velocity–time	acceleration	displacement
momentum–time	resultant force	—
force–time	—	impulse (change of momentum)
force–extension	stiffness $k$ (linear region)	work done / elastic energy
current–time	—	charge
charge–time	current	—
power–time	—	energy transferred

By the end you’ll be able to

What the exam asks

Core ideas

The SI base units

Check your understanding

Flashcards

Derived units in base units

Homogeneity

Prefixes, powers and awkward units

Significant figures and standard form

Estimation

The maths toolkit

Worked examples

Exam technique

Common mistakes

Quick recap

By the end you’ll be able to

What the exam asks

Core ideas

The SI base units

vii.Check your understanding

viii.Flashcards

Derived units in base units

Homogeneity

Prefixes, powers and awkward units

Significant figures and standard form

Estimation

The maths toolkit

Worked examples

Exam technique

Common mistakes

Quick recap

Check your understanding

Flashcards