# Physical Quantities and Measurement Techniques

> Physics · CIE IGCSE 0625 2026-2028
> Source: https://www.owlsprep.com/study/cie-0625-u1-physical-quantities-and-measurement-techniques/

This guide covers core and extended content for physical quantities, SI units, and measurement techniques for CIE IGCSE Physics 0625, including instrument selection, error reduction, and extended precision tools.

**Prerequisites:** Basic arithmetic operations (addition, division, averages); Familiarity with standard school physics lab equipment

## Learning objectives

- Recall SI base units for core physical quantities
- Select appropriate measuring instruments for length, time, mass, and volume
- Distinguish between accuracy and precision, and reduce experimental errors
- Distinguish scalar and vector quantities, and find the resultant of two vectors at right angles (Extended only)

## Core: SI Units and Physical Quantities

**Physical Quantity** — A property of a material, object, or phenomenon that can be measured using a numerical value and a standard unit.

*Example:* Length, mass, time, temperature, electric current, volume

All physical quantities use SI (Système International) units to ensure consistency in measurements across the world. The five base SI units you need to recall for this syllabus are: metre ($m$) for length, kilogram ($kg$) for mass, second ($s$) for time, ampere ($A$) for electric current, and kelvin ($K$) for temperature. Derived units (e.g. $m/s$ for speed) are calculated by combining base units.

**Worked example:** State the correct SI base unit for each of the following physical quantities: a) Time b) Mass c) Electric current

1. Recall the standard SI base unit definitions from the syllabus
2. a) Time is measured in seconds, symbol $s$
3. b) Mass is measured in kilograms, symbol $kg$
4. c) Electric current is measured in amperes, symbol $A$

## Core: Basic Measurement Instruments

Selecting the correct measuring instrument depends on the quantity you are measuring and the level of precision you need. For core content: use rulers/measuring tapes for length (precision 1 mm), digital/analogue stopwatches for time (precision 0.01 s / 0.1 s), measuring cylinders for volume, and top-pan balances for mass.

**Parallax Error** — A common random error caused by reading a measurement scale from an angle, rather than directly perpendicular to the scale surface.

*Example:* Reading a water measuring cylinder from above gives a higher value than the true volume of the liquid.

**Worked example:** A student measures the height of a glass beaker using a ruler, and reads a value of 15.4 cm when their eye is 25 degrees above the scale line. Identify the error and state the correct measurement procedure.

1. Identify the error as parallax error, caused by reading the scale at an angle
2. The measured value of 15.4 cm is higher than the true height of the beaker
3. Correct procedure: Align your eye level directly perpendicular to the ruler scale at the top edge of the beaker before taking the reading

> **Exam tip**
>
> Always explicitly mention reading scales at eye level in exam answers for measurement procedure questions to earn full marks.

## Core: Accuracy, Precision and Error Reduction

**Accuracy** — A measure of how close a measured value is to the true, accepted value of the quantity being measured.

**Precision** — A measure of how close repeated measurements of the same quantity are to each other.

Random errors (e.g. human reaction time when using a stopwatch) can be reduced by taking at least 3 repeated measurements and calculating the average value. Systematic errors (e.g. zero error on a balance) cause all readings to be consistently high or low, and are eliminated by calibrating instruments before use or correcting readings for zero error.

**Worked example:** A student measures the time for 10 swings of a pendulum 3 times, getting values of 14.2 s, 14.4 s, and 14.3 s. Calculate the average period (time for 1 swing) of the pendulum, and explain why measuring 10 swings reduces error.

1. Calculate the average time for 10 swings: $\frac{14.2 + 14.4 + 14.3}{3} = 14.3$ s
2. Calculate the period for 1 swing: $\frac{14.3}{10} = 1.43$ s
3. Measuring 10 swings reduces the relative impact of human reaction time error when starting and stopping the stopwatch, leading to a more accurate period calculation

## Extended Only: Scalars and Vectors

Extended learners must distinguish between scalar and vector quantities. A scalar quantity has magnitude (size) only, whereas a vector quantity has both magnitude and direction.

**Scalar quantity** — A quantity with magnitude (size) only. The scalars named in the 0625 syllabus are: distance, speed, time, mass, energy and temperature.

**Vector quantity** — A quantity with both magnitude and direction. The vectors named in the 0625 syllabus are: force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength.

You must also determine the resultant of two vectors that act at right angles (limited to forces or velocities only). Because the two vectors are perpendicular, the magnitude of the resultant is found with Pythagoras' theorem, and its direction with the tangent ratio (or by drawing a scale diagram).

$$R = \sqrt{a^2 + b^2}$$

**Worked example:** Two forces act on a point at right angles to each other: 3.0 N acting east and 4.0 N acting north. Determine the magnitude and direction of the resultant force.

1. Step 1: The forces are perpendicular, so use Pythagoras for the magnitude:

   $$R = \sqrt{(3.0)^2 + (4.0)^2} = \sqrt{9 + 16} = \sqrt{25} = 5.0 \text{ N}$$
2. Step 2: Find the direction using the tangent ratio (angle north of east):

   $$\tan\theta = \frac{4.0}{3.0} \implies \theta = \tan^{-1}(1.33) = 53^\circ$$
3. Step 3: State the resultant fully: 5.0 N at 53° north of east (a vector needs both magnitude and direction).

## Common pitfalls

- **Wrong:** Mixing up accuracy and precision definitions in exam answers
  - Why it fails: The two terms have distinct, assessable definitions and examiners penalize incorrect usage
  - Correct: Use the mnemonic: Accuracy = Close to True value, Precision = Close to each other
- **Wrong:** Reading a measuring cylinder from the top of the liquid meniscus
  - Why it fails: The standard convention for water-based liquids is to take readings from the bottom of the concave meniscus
  - Correct: Align eye level with the bottom of the meniscus when reading measuring cylinders or graduated scales
- **Wrong:** Adding two vectors that act at right angles by simple arithmetic (e.g. 3 N + 4 N = 7 N)
  - Why it fails: Perpendicular vectors do not add directly; their combined effect is the diagonal of the rectangle they form
  - Correct: Use Pythagoras for the magnitude: resultant = √(3² + 4²) = 5 N, then state its direction
- **Wrong:** Measuring the time for a single pendulum swing to calculate period
  - Why it fails: Human reaction time (≈0.2 s) creates a large relative error for short time periods of less than 2 s
  - Correct: Measure the time for 10 or 20 swings, then divide by the number of swings to get the average period
- **Wrong:** Treating distance and displacement, or speed and velocity, as the same thing
  - Why it fails: Distance and speed are scalars (magnitude only); displacement and velocity are vectors that also carry a direction
  - Correct: State a direction whenever the quantity is a vector, and quote magnitude only for a scalar

## Cheatsheet

| Quantity / Concept | Instrument or Rule | Precision / Note | Tier |
| --- | --- | --- | --- |
| Length | Ruler / measuring tape | 1 mm; read at eye level | Core |
| Time | Digital stopwatch / clock | 0.01 s; time many swings, then ÷ number | Core |
| Volume (liquid) | Measuring cylinder | read at the bottom of the meniscus | Core |
| Volume (irregular solid) | Displacement in a measuring cylinder | V = final − initial water level | Core |
| Mass | Top-pan balance | 0.1 g | Core |
| Scalar vs vector | Scalar = magnitude only; vector = magnitude + direction | scalars: distance, speed, time, mass, energy, temperature | Extended |
| Resultant of two ⟂ vectors | R = √(a² + b²), forces or velocities only | direction by tan⁻¹ or scale drawing | Extended |

## What's next

Now that you have mastered physical quantities and measurement techniques, you are ready to move on to kinematics, where you will use measured values of length and time to calculate speed, velocity, and acceleration. These measurement skills form the foundation of all practical physics questions in both core and extended CIE IGCSE Physics 0625 papers, so make sure to review the error reduction rules and the scalar/vector distinction regularly before attempting practical or theory exam questions. You will also use these techniques in all required practical assessments for the syllabus.

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