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Measures

Revise Measures for Mathematics A 4MA1 (O Level) — revision notes, 290 practice questions and instant AI marking.

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  Pearson Edexcel International GCSE Mathematics A (4MA1)

Measures

The big idea: Compound measures are rates: speed is distance per unit of time, density is mass per unit of volume, pressure is force per unit of area. Get the units consistent first, and the formula does the rest.

Summary — What This Chapter Covers
  • Read scales by working out what one small division is worth.
  • Convert between the 12-hour clock (am/pm) and the 24-hour clock, and find time intervals.
  • Make sensible estimates of lengths, masses and capacities.
  • Three-figure bearings are measured clockwise from North; measure angles to the nearest degree.
  • Speed = distance ÷ time; density = mass ÷ volume; pressure = force ÷ area.
1. Scales and Estimates
Foundation & Higher

Reading instruments; sensible values

On any scale, first find the value of one small division: (difference between two labelled marks) ÷ (number of divisions between them). Then count divisions from the nearest labelled mark.

For estimates, compare with things you know: a door is about 2 m tall, a bag of sugar has a mass of about 1 kg, a can of drink holds about 330 ml, an adult is about 1.7 m tall.

Worked Example

A kitchen scale is labelled 2 kg and 3 kg, with 5 equal divisions between them. The pointer is on the third division after 2 kg. What is the reading?

2. Time and the 12- and 24-hour Clock
Foundation & Higher

am, pm and time intervals

24-hour times always use four digits: 7:05 am = 07:05, 7:05 pm = 19:05, midnight = 00:00, midday = 12:00. To find a time interval, count up to the next whole hour, then whole hours, then the remaining minutes. Never subtract times as if they were decimals.

Worked Example

A train leaves at 21:47 and arrives at 01:15 the next day. How long is the journey? Write both times using am and pm.

3. Angles and Bearings
Foundation & Higher

Three-figure bearings

A bearing is an angle measured clockwise from North, written with three figures: 045°, 160°, 300°. To measure, draw a North line at the point you are measuring from. Measure angles with a protractor to the nearest degree, using the scale that starts at 0 on one arm of the angle.

Back bearing bearing of A from B = bearing of B from A ± 180°
Worked Example

The bearing of B from A is 065°. Find the bearing of A from B.

Practice Question 1

The bearing of Q from P is 310°. Find the bearing of P from Q.

4. Speed, Distance and Time
Foundation & Higher

Average speed

Average speed = total distance ÷ total time. Times in hours and minutes must be changed to hours as a decimal or fraction: 15 minutes = 0.25 h, 40 minutes = 2/3 h.

Speed speed = distance ÷ time    distance = speed × time    time = distance ÷ speed
Worked Example

A car travels 150 km in 2 hours 15 minutes. Work out its average speed. Give your answer correct to 3 significant figures.

Practice Question 2

A cyclist rides at 48 km/h for 1 hour 40 minutes. How far does she travel?

5. Compound Measures
Foundation & Higher

Density and pressure

Memorise
Bearings
Speed

speed = distance ÷ time.

Density
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