# Measures

> Edexcel International GCSE Mathematics A · 4MA1 2016 Spec
> Source: https://www.owlsprep.com/study/edexcel-igcse-math-a-s4-measures/

This guide covers all Edexcel IGCSE Math A (4MA1) section 4.4 measures content, including scale reading, time calculations, bearings, and compound measures with exam-aligned worked examples.

**Prerequisites:** [Basic whole number and decimal arithmetic](https://www.owlsprep.com/study/edexcel-igcse-math-a-s1-arithmetic/); [Basic unit conversion rules](https://www.owlsprep.com/study/edexcel-igcse-math-a-s4-unit-conversion/)

## Learning objectives

- Interpret scales on common measuring instruments and calculate 12/24-hour clock time intervals
- Make sensible real-world estimates of standard length, mass, time and volume measures
- Understand and apply three-figure bearing rules, measure angles to the nearest degree
- Calculate compound measures (speed, density, pressure) following unit consistency rules

## Scale Interpretation & Time Calculations

You will be expected to read scales on common instruments including rulers, measuring jugs, weighing scales and thermometers. Always check the increment value between marks first, do not assume each mark equals 1 unit.

For time calculations, you will work with both 12-hour (am/pm) and 24-hour clock formats. To find time intervals, count hours first then remaining minutes, or convert times to total minutes for easier subtraction.

**Worked example:** A bus departs at 09:45 and arrives at its destination at 13:10. Calculate the total journey time in hours and minutes.

1. Step 1: Count hours from 09:45 to 12:45 = 3 hours
2. Step 2: Count minutes from 12:45 to 13:10 = 25 minutes
3. Step 3: Total journey time = 3 hours 25 minutes

> **Exam tip**
>
> If a question asks for time in hours as a decimal, divide remaining minutes by 60, e.g. 3 hours 15 minutes = 3.25 hours.

*Calculator:* allowed

## Estimation & Angle Measurement

Sensible estimates use real-world reference points: a standard door is ~2m tall, an apple is ~100g, a can of drink is ~330ml, and a typical car journey speed is ~60km/h. You will not be penalised for reasonable estimates within a small range.

When measuring angles with a protractor, line the baseline up with one side of the angle, align the centre of the protractor with the vertex, and read the value to the nearest whole degree.

**Worked example:** Estimate the height of a standard two-storey house in metres.

1. Step 1: One storey of a house is roughly the height of 1.5 doors = ~3m
2. Step 2: Two storeys = 2 * 3m = 6m, so a reasonable estimate is between 5 and 7 metres

*Calculator:* allowed

## Three-Figure Bearings

**Three-figure bearing** — An angle measured **clockwise from North**, always written as three digits, with leading zeros added for angles less than 100°

*Example:* A direction 45° clockwise from North is written as 045°

Bearings are always measured clockwise, never anticlockwise. Common reference bearings are 000° (North), 090° (East), 180° (South), 270° (West).

**Worked example:** Write the three-figure bearing for a direction pointing South-West.

1. Step 1: South is 180°, West is 270°, South-West is halfway between the two
2. Step 2: Calculate halfway value: 180 + 45 = 225°
3. Step 3: The bearing is 225° (no leading zero needed as it is over 100°)

> **warning**
>
> You will lose marks if you write bearings as 2 digits, e.g. writing 45° instead of 045° is incorrect.

*Calculator:* allowed

## Compound Measures: Speed & Density (Recall Formulae)

You must memorise the formulae for speed and density, these will not be given in the exam. Always convert units to be consistent before substituting values into the formula.

$$speed = \frac{\text{distance}}{\text{time}}$$

$$density = \frac{\text{mass}}{\text{volume}}$$

**Worked example:** A cyclist travels 45km in 2 hours 15 minutes. Calculate their average speed in km/h.

1. Step 1: Convert 2 hours 15 minutes to a decimal: 15/60 = 0.25, so total time = 2.25 hours
2. Step 2: Substitute values into speed formula: speed = 45 / 2.25
3. $$45 / 2.25 = 20$$
4. Step 3: Average speed = 20 km/h

*Calculator:* allowed

## Pressure Calculations (Given Formula)

The pressure formula will always be given in the question when needed, so you do not need to memorise it. 1 Pascal (Pa) = 1 Newton per square metre (N/m²).

$$pressure = \frac{\text{force}}{\text{area}}$$

**Worked example:** A force of 200N is applied to a rectangular tabletop of length 2m and width 1m. Calculate the pressure on the table in Pa.

1. Step 1: Calculate area of the table: area = length * width = 2 * 1 = 2 m²
2. Step 2: Substitute values into given pressure formula: pressure = 200 / 2
3. $$200 / 2 = 100$$
4. Step 3: Pressure = 100 Pa

*Calculator:* allowed

## Common pitfalls

- **Wrong:** Writing bearings as 2 digits, e.g. 72° instead of 072°
  - Why it fails: Three-figure format is required by the specification, missing leading zeros lose marks
  - Correct: Add leading zeros to all bearings less than 100° to make 3 digits
- **Wrong:** Calculating speed using time in minutes without converting to hours for km/h units
  - Why it fails: Inconsistent units produce incorrect numerical results
  - Correct: Convert all input units to match the required output units before substituting into formulae
- **Wrong:** Measuring bearings anticlockwise from North
  - Why it fails: Bearings are defined as clockwise from North, anticlockwise measurement gives the wrong angle
  - Correct: Always measure angles clockwise starting from the North line
- **Wrong:** Using pressure = area/force instead of the given formula
  - Why it fails: Misapplying the given formula leads to incorrect results even if you know the relationship
  - Correct: Copy the pressure formula exactly as written in the question before substituting values
- **Wrong:** Rounding angle measurements to the nearest 10 degrees instead of nearest degree
  - Why it fails: The specification requires measurement to the nearest degree, coarse rounding loses marks
  - Correct: Read protractor markings carefully to identify the nearest whole degree value

## Cheatsheet

| Concept | Rule | Key Notes |
| --- | --- | --- |
| Scale Reading | Check increment value before counting marks | Do not assume each mark = 1 unit |
| Time Calculations | 12-hour uses am/pm, 24-hour uses 00:00 to 23:59 | Convert minutes to decimal hours for division |
| Three-figure Bearings | Clockwise from North, 3 digits with leading zeros | 0-99° get leading zero, e.g. 045° |
| Speed | speed = distance/time (recall) | Units: km/h, m/s, mph etc. |
| Density | density = mass/volume (recall) | Units: g/cm³, kg/m³ etc. |
| Pressure | pressure = force/area (given in exam) | 1 Pa = 1 N/m², use metres for area calculations |

## What's next

Now you have mastered the core measures content for Edexcel IGCSE Math A, you can build on this knowledge by practicing more complex unit conversion problems and moving to basic trigonometry content. Measures questions appear regularly in both foundation and higher tier papers, so make sure to work through past paper questions to familiarise yourself with common question formats and avoid the common pitfalls listed above. Once you are confident with basic bearings, you will later learn to solve trigonometric bearing problems as part of the advanced trigonometry section of the syllabus.

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