All revision notes topics

Standard & Compound UnitsEdexcel IGCSE Maths: Revision notes

Section 1

How do you convert between metric units?

Metric units go up and down in powers of 10, so converting is just multiplying or dividing.

Length: 1 km=1000 m1\text{ km} = 1000\text{ m}, 1 m=100 cm1\text{ m} = 100\text{ cm}, 1 cm=10 mm1\text{ cm} = 10\text{ mm}

Mass: 1 tonne=1000 kg1\text{ tonne} = 1000\text{ kg}, 1 kg=1000 g1\text{ kg} = 1000\text{ g}

Capacity/Volume: 1 litre=1000 ml=1000 cm31\text{ litre} = 1000\text{ ml} = 1000\text{ cm}^3, 1 m3=1000 litres1\text{ m}^3 = 1000\text{ litres}

Rule: going from a larger unit to a smaller unit, you multiply. Going from smaller to larger, you divide.

Key termsconversion factormetric unit
Exam tip

Memorise the chant: 'big to small, multiply; small to big, divide'. It works for every metric conversion.

Example

Convert 3.2 m to cm: 3.2×100=320 cm3.2 \times 100 = 320\text{ cm} (larger to smaller unit, so multiply).

Section 2

Why is converting units2^2 and units3^3 different?

For area (units2^2), the conversion factor must be squared. For volume (units3^3), it must be cubed. This is because area and volume are two- and three-dimensional respectively.

Example: 1 m=100 cm1\text{ m} = 100\text{ cm}, so:

1 m2=1002 cm2=10,000 cm21\text{ m}^2 = 100^2\text{ cm}^2 = 10\\,000\text{ cm}^2

1 m3=1003 cm3=1,000,000 cm31\text{ m}^3 = 100^3\text{ cm}^3 = 1\\,000\\,000\text{ cm}^3

This is one of the most commonly tested traps in IGCSE Maths — students forget to square or cube the factor.

Key termsarea conversionvolume conversion
Common mistake

Do NOT just multiply by 100 when converting m2^2 to cm2^2 — you must multiply by 1002=10,000100^2 = 10\\,000.

Example

Convert 2 m22\text{ m}^2 to cm2^2: 2×10,000=20,000 cm22 \times 10\\,000 = 20\\,000\text{ cm}^2.

Section 3

What is density and how do you calculate it?

Density measures how much mass is packed into a given volume.

density=massvolume\text{density} = \dfrac{\text{mass}}{\text{volume}}

Units are typically g/cm3\text{g/cm}^3 or kg/m3\text{kg/m}^3.

Rearranged forms (use a formula triangle with mass on top, density and volume on the bottom):

mass=density×volume\text{mass} = \text{density} \times \text{volume} volume=massdensity\text{volume} = \dfrac{\text{mass}}{\text{density}}

Always check units match before substituting — mass in grams needs volume in cm3^3; mass in kg needs volume in m3^3.

Key termsdensitymassvolumeformula triangle
Think of it like this

Think of density like how tightly packed a crowd is in a room — same room (volume), more people (mass) means higher density.

Example

A block has mass 45 g and volume 15 cm3^3. Density =45÷15=3 g/cm3= 45 \div 15 = 3\text{ g/cm}^3.

Section 4

How do speed and pressure use the same idea?

Speed, density, and pressure are all compound units — units made of two other units divided by each other.

speed=distancetime(m/s or km/h)\text{speed} = \dfrac{\text{distance}}{\text{time}} \quad (\text{m/s or km/h})

pressure=forcearea(N/m2 or Pa)\text{pressure} = \dfrac{\text{force}}{\text{area}} \quad (\text{N/m}^2 \text{ or Pa})

To convert speed from km/h to m/s: multiply by 10001000 (km to m) then divide by 36003600 (hours to seconds), i.e. multiply by 10003600=518\dfrac{1000}{3600} = \dfrac{5}{18}.

To convert m/s to km/h: multiply by 185\dfrac{18}{5} (or ×3.6\times 3.6).

Key termscompound unitspeedpressure
Exam tip

To convert km/h to m/s multiply by 518\frac{5}{18}; to convert m/s to km/h multiply by 185\frac{18}{5} (or 3.6). Remember '5/18 down, 18/5 up'.

Example

A car travels at 72 km/h. In m/s: 72×518=20 m/s72 \times \frac{5}{18} = 20\text{ m/s}.

Must Know

  • Larger to smaller unit: multiply. Smaller to larger: divide.
  • Area conversions use the squared factor; volume conversions use the cubed factor.
  • density=massvolume\text{density} = \dfrac{\text{mass}}{\text{volume}}, units g/cm3^3 or kg/m3^3.
  • speed=distancetime\text{speed} = \dfrac{\text{distance}}{\text{time}}; pressure=forcearea\text{pressure} = \dfrac{\text{force}}{\text{area}}.
  • To convert km/h →\to m/s multiply by 518\frac{5}{18}; m/s →\to km/h multiply by 185\frac{18}{5}.
  • 1 litre=1000 cm31\text{ litre} = 1000\text{ cm}^3; 1 m3=1,000,000 cm31\text{ m}^3 = 1\\,000\\,000\text{ cm}^3.

That's the notes covered.

Carry on to the next subtopic.