Equations and Calculations

Equations and Calculations for IGCSE Biology Edexcel

Finding Area

• To find the area of a two-dimensional shape, multiply its length by its width:

  $Area = Length \times Width$

Finding Surface Area (of a Cube)

• To find the surface area of a cube, multiply the area of one surface by the number of surfaces (6 for a cube):

  $Surface\ Area = Area\ of\ 1\ Surface \times No.\ of\ Surfaces$

• Example: A cube with 2.5 cm sides has a surface area of:

  $2.5 \times 2.5 \times 6 = 37.5 cm^2$

Finding Volume

• To find the volume of a rectangular prism (including a cube), multiply its length, width, and height:

  $Volume = Length \times Width \times Height$

Finding the Mean/Average

• The mean (average) is calculated by summing all the items in a set and dividing by the number of items:

  $Mean = \frac{Sum\ of\ all\ items}{Number\ of\ items}$

• Note: Exclude anomalous results (outliers) when calculating the mean.

Finding the Mode

• The mode is the number that appears most frequently in a set of numbers.

Finding the Median

• The median is the middle number in a data set when the numbers are arranged in numerical order.

Finding the Percentage Change

• The percentage change is calculated as follows:

  $Percentage\ Change = \frac{Final\ Value - Starting\ Value}{Starting\ Value} \times 100$

• Note:

  • If asked for a percentage decrease, quote it as a positive number.

  • If asked for a percentage change and the value has decreased, quote it as a negative number.

Finding What Percentage One Number Is of Another

• To find what percentage A is of B:

  $Percentage = \frac{A}{B} \times 100$

Finding Speed

• Speed is calculated by dividing the distance traveled by the time taken:

  $Speed = \frac{Distance}{Time}$

Converting Units

• Conversion table:

  • nm (nanometer) $\xrightarrow{\times 1000}$ μm (micrometer) $\xrightarrow{\times 1000}$ mm (millimeter) $\xrightarrow{\times 1000}$ m (meter) $\xrightarrow{\times 1000}$ km (kilometer)

  • km (kilometer) $\xrightarrow{\div 1000}$ m (meter) $\xrightarrow{\div 1000}$ mm (millimeter) $\xrightarrow{\div 1000}$ μm (micrometer) $\xrightarrow{\div 1000}$ nm (nanometer)

• Examples:

  • 6,000,000 nm = 6000 μm = 6 mm = 0.006 m = 0.000006 km

  • 6 x $10^6$ nm = 6 x $10^3$ μm = 6 x $10^{-3}$ m = 6 x $10^{-6}$ km

Converting to Standard Form

• Standard form is expressed as:

  $a \times 10^b$

  Where 1 \le a < 10, and b is an integer.

Using Ratios to Find an Unknown Value

• If a : b = c : d, then:

  $\frac{a}{b} = \frac{c}{d}$

• Therefore:

  $a = \frac{bc}{d}$

Calculating Magnification

• Magnification is calculated as:

  $Magnification = \frac{Image\ Size}{Actual\ Size}$

• Therefore:

  • $Image\ Size = Actual\ Size \times Magnification$

  • $Actual\ Size = \frac{Image Size}{Magnification}$

• Important: The image size and actual size MUST have the same units.

• Note: If given a diagram without the image size, use a ruler to calculate the image size.

Units, Abbreviations and More

• Units of Length & Abbreviations:

  • nanometre (nm)

  • micrometre (μm)

  • millimetre (mm)

  • centimetre (cm)

  • metre (m)

  • kilometre (km)

• Units of Mass/Weight & Abbreviations:

  • milligram (mg)

  • gram (g)

  • kilogram (kg)

• Amount of a substance:

  • mole (mol)

• Units of Time & Abbreviations:

  • millisecond (ms)

  • second (s)

  • minute (min)

  • hour (h)

• Temperature:

  • degrees Celsius (°C)

• Units of Area & Abbreviations:

  • millimetre squared (mm²)

  • centimetre squared (cm²)

  • metre squared (m²)

  • kilometre squared (km²)

  • hectare (ha)

• Units of Volume:

  • millimetre cubed (mm³)

  • centimetre cubed (cm³)

  • decimetre cubed (dm³)

  • metre cubed (m³)

• Capacity:

  • litre (l)

  • millilitre (ml)

  • centilitre (cl)

• Concentration of a solution:

  • moles per decimetre cubed (mol dm⁻³)

• Energy:

  • joule (J)

  • kilojoule (kJ)

  • megajoule (mJ)

• Luminous intensity:

  • lux (lx)

• Note that 1 cm³ = 1 ml, and 1 dm³ = 1 l