What are physical quantities in the context of Cambridge International A Levels Physics?

In Cambridge International A Levels Physics, physical quantities refer to properties or characteristics of phenomena that can be measured. They consist of a numerical magnitude and a unit. Examples include length, mass, time, and temperature. Understanding physical quantities is fundamental to studying physics as they form the basis for describing and analyzing physical phenomena.

How are physical quantities classified in Physics?

Physical quantities are classified into two main categories: scalar and vector quantities. Scalar quantities have only magnitude, such as mass and temperature, while vector quantities have both magnitude and direction, such as velocity and force. This classification helps in understanding how different quantities interact and are represented in physical equations.

Why is it important to use standard units for physical quantities in Physics?

Using standard units for physical quantities is crucial because it ensures consistency and accuracy in measurements and calculations. The International System of Units (SI) is the standard used globally, allowing scientists and students, including those studying Cambridge International A Levels, to communicate findings and compare results effectively. Standard units eliminate confusion and errors that could arise from using different measurement systems.

What is the difference between base and derived physical quantities?

Base physical quantities are fundamental quantities that are defined independently, such as length, mass, and time. Derived physical quantities, on the other hand, are formed by combining base quantities according to physical laws. For example, speed is a derived quantity calculated by dividing distance (a base quantity) by time (another base quantity). Understanding this distinction is essential for solving problems in physics.

How do you convert between different units of physical quantities?

Converting between different units of physical quantities involves using conversion factors, which are ratios that express how one unit relates to another. For example, to convert meters to centimeters, you multiply by 100, since 1 meter equals 100 centimeters. Mastery of unit conversion is important in Cambridge International A Levels Physics to ensure that calculations are accurate and results are expressed in the desired units.

Why is "Confusing physical quantity with its unit" a common mistake in Physical quantities?

Why it happens: Both have symbols. How to avoid it: Quantity (e.g. mass, m) has a UNIT (e.g. kg). Don't say 'kilogram is a quantity' — kilogram is a UNIT of the quantity 'mass'. Source: 9702 Examiner Reports 2022-2024

Why is "Treating homogeneity as proving an equation" a common mistake in Physical quantities?

Why it happens: If units match, formula seems valid. How to avoid it: Homogeneity is NECESSARY but NOT SUFFICIENT. E = mc^3 might be homogeneous (it isn't actually) but still wrong. Homogeneity catches mistakes; it doesn't prove correctness. Source: 9702 Examiner Reports 2022-2024

Physical Quantities and UnitsCambridge International A Levels Physics (9702)

Physical quantities

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Physical Quantities Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Base and derived quantities. The seven base SI quantities. Homogeneity of equations. Foundation for everything that follows.

What you’ll learn

Mapped to the Cambridge IGCSE 9702 syllabus (2025-2027).

1.1 — Distinguish base and derived quantities.
1.2 — Express derived quantities in base units.
1.3 — Use homogeneity to check equations.

Quantities and units

Number × unit.

Physical quantity. Anything measurable. Has NUMERICAL VALUE and UNIT.

Seven base quantities (SI):

Quantity	Symbol	Unit
Length	$l$	metre (m)
Mass	$m$	kilogram (kg)
Time	$t$	second (s)
Current	$I$	ampere (A)
Temperature	$T$	kelvin (K)
Amount of substance	$n$	mole (mol)
Luminous intensity	$I_v$	candela (cd)

Derived quantities built from these. Examples:

Speed = length/time → m/s.
Acceleration = velocity/time → m/s².
Force = mass × acceleration → kg·m/s² = N.
Energy = force × distance → kg·m²/s² = J.

Cambridge tip. Memorise the 7 base quantities + their units.

Seven base quantities.
Derived = combinations.
Always include unit.

See the full worked example for physical quantities →

Deriving base units

Express any unit in base.

Method. Replace named units with their definitions in base units.

Common derivations.

N = kg·m·s⁻².
J = N·m = kg·m²·s⁻².
W = J/s = kg·m²·s⁻³.
C = A·s.
V = J/C = kg·m²·A⁻¹·s⁻³.
Ω = V/A = kg·m²·A⁻²·s⁻³.
Pa = N/m² = kg·m⁻¹·s⁻².

Cambridge tip. Mark scheme rewards full derivation chain.

Replace named units with base.
Show derivation chain.
Common: N, J, W, C, V, Ω, Pa.

See the full worked example for physical quantities →

Homogeneity

Same units in every term.

Statement. An equation is homogeneous if every term has the same base units.

Use. Quick check on a derived formula. If terms have different units, equation is wrong. If same units, equation MIGHT be correct.

Method.

Write each term's units in base.
Compare.
Equation valid only if all match.

Example. Check $v^2 = u^2 + 2as$ .

$v^2$ : (m/s)² = m²/s².
$u^2$ : m²/s².
$2as$ : (m/s²)(m) = m²/s².
All match → homogeneous ✓.

Limit. Homogeneity catches dimension errors but NOT factor errors. $E = mc^3$ would actually be inhomogeneous (units kg·m³·s⁻³ vs energy kg·m²·s⁻²) but $E = 2mc^2$ would still pass homogeneity check despite being wrong.

Cambridge tip. Use homogeneity as a SANITY CHECK — necessary but not sufficient.

All terms same base units.
Necessary, not sufficient.
Catches dimension errors only.

See the full worked example for physical quantities →

How it’s examined

Quantities and units underpin every problem. Most-tested: derive a unit in base SI (5-6 marks), homogeneity check (5 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/12 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

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Step-by-step worked examples — Physical quantities

Step-by-step solutions to past-paper-style questions on physical quantities, written exactly the way a tutor would explain them at the board.

1Base vs derived quantities (5 marks)
Extended• Adapted from 9702/12 May/Jun 2024• base quantities
Question
State the SEVEN base quantities and give one example of a derived quantity for each combination relevant to mechanics. (5 marks)
Step-by-step solution
1. Step 1
  Seven base quantities. Mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol), luminous intensity (cd).
2. Step 2
  Derived from length + time. Speed (m/s), acceleration (m/s²).
3. Step 3
  Derived from mass + length + time. Force (N = kg·m/s²), energy (J = kg·m²/s²).
4. Step 4
  Derived from current + time. Charge (C = A·s).
Answer
7 base: kg, m, s, A, K, mol, cd. Derived examples: m/s (speed), N (force), J (energy), C (charge).
2Derive base units (6 marks)
Extended• units
Question
Express the volt (V) in terms of base SI units. (6 marks)
Step-by-step solution
1. Step 1
  Volt definition. V = J/C (energy per unit charge).
2. Step 2
  Joule in base units. J = N·m = kg·m²/s².
3. Step 3
  Coulomb in base units. C = A·s.
4. Step 4
  Combine.
  $V = \dfrac{\text{kg} \cdot \text{m}^2 / \text{s}^2}{\text{A} \cdot \text{s}} = \text{kg} \cdot \text{m}^2 \cdot \text{A}^{-1} \cdot \text{s}^{-3}$
Answer
V = kg·m²·A⁻¹·s⁻³.
3Homogeneity check (5 marks)
Extended• homogeneity
Question
Check whether $v^2 = u^2 + 2as$ is homogeneous with respect to units. (5 marks)
Step-by-step solution
1. Step 1
  Units of $v^2$ and $u^2$ . Both have units (m/s)² = m²/s².
2. Step 2
  Units of $2as$ . $a$ in m/s², $s$ in m → m²/s².
3. Step 3
  All terms have same units (m²/s²) → equation is homogeneous.
Answer
All three terms have units m²/s². Equation is homogeneous.

Key Formulae — Physical quantities

The formulae you need to memorise for physical quantities on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Derived units from base
$[\text{velocity}] = \text{m s}^{-1}; \quad [\text{force}] = \text{kg m s}^{-2}; \quad [\text{energy}] = \text{kg m}^2 \text{ s}^{-2}$
When to use
Expressing derived units in terms of base SI units (m, kg, s, A).
Homogeneity
$\text{Equation is homogeneous} \iff \text{all terms have the same base units}$
When to use
Checking validity of equations. Quick sanity check on derived formulae.

Key Definitions and Keywords — Physical quantities

Definitions to memorise and the exact keywords mark schemes credit for physical quantities answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

Physical quantity
Examiner keyword
A measurable property of a physical phenomenon. Has both a NUMERICAL value and a UNIT.
Base quantity
Examiner keyword
One of seven quantities chosen as fundamental — length, mass, time, current, temperature, amount, luminous intensity.
Derived quantity
Examiner keyword
A quantity expressed as a combination of base quantities (e.g. velocity = length/time).
Homogeneity (of an equation)
Examiner keyword
All terms in the equation have the same SI base units.

Common Mistakes and Misconceptions — Physical quantities

The traps other students keep falling into on physical quantities questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Confusing physical quantity with its unit
9702 Examiner Reports 2022-2024
Why it happens
Both have symbols.
How to avoid it
Quantity (e.g. mass, $m$ ) has a UNIT (e.g. kg). Don't say 'kilogram is a quantity' — kilogram is a UNIT of the quantity 'mass'.
✕Treating homogeneity as proving an equation
9702 Examiner Reports 2022-2024
Why it happens
If units match, formula seems valid.
How to avoid it
Homogeneity is NECESSARY but NOT SUFFICIENT. $E = mc^3$ might be homogeneous (it isn't actually) but still wrong. Homogeneity catches mistakes; it doesn't prove correctness.

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

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Short walkthrough of the concepts students most often get stuck on.

Physical quantities — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Physical quantities

Short Study Notes in the form of Slides

Detailed Study Notes

What you’ll learn

How it’s examined

1Base vs derived quantities (5 marks)

2Derive base units (6 marks)

3Homogeneity check (5 marks)

Derived units from base

Homogeneity

Physical quantity

Base quantity

Derived quantity

Homogeneity (of an equation)

✕Confusing physical quantity with its unit

✕Treating homogeneity as proving an equation

Practice questions

Past paper style quiz

Assess your understanding

Video lesson

Physical quantities — frequently asked questions