Medication (HSC SSCE Mathematics Standard): Revision Notes

Medication

Understanding medication concentration

When doctors prescribe medicines, they need to calculate the correct amount for each dose. Medications are often in liquid form, and their strength is shown as a concentration. A concentration tells us how much of the active medicine ingredient is dissolved in a certain volume of liquid.

Concentrations are expressed as mass per volume, such as $5 \text{ g}/10 \text{ mL}$ or $100 \text{ mg}/50 \text{ mL}$. This means we measure the mass of the medicine (in grams or milligrams) in a specific volume of liquid (in millilitres).

Converting concentration

Sometimes we need to convert a concentration from one unit to another. For example, we might need to change milligrams per millilitre (mg/mL) to grams per millilitre (g/mL).

Calculating volume required

When medication is available in liquid form, we often need to calculate how much liquid to give a patient. This depends on three key factors:

• The strength required (how much medicine the patient needs)
• The stock strength (the concentration of medicine available)
• The volume of stock (the volume of liquid that contains the stock strength)

The formula to calculate the volume required is:

$\text{Volume required (mL)} = \frac{\text{Strength required (mg)}}{\text{Stock strength (mg)}} \times \text{Volume of stock (mL)}$

Formulae for children and infants

Children and infants require different medication dosages than adults because their bodies process medicines differently. Their smaller body size and developing organs mean they need carefully calculated smaller doses to avoid harm.

There are three main formulae used to calculate safe medication dosages for children and infants. Each formula is used in different situations depending on the child's age or weight.

The three formulae are:

1. Fried's rule (for children aged 1–2 years)

$\text{Dosage} = \frac{\text{Age of infant (months)} \times \text{Adult dose}}{150}$

This rule uses the infant's age in months and divides by $150$ to find the appropriate child's dose.

2. Young's rule (for children aged 1–12 years)

$\text{Dosage} = \frac{\text{Age of child (years)} \times \text{Adult dose}}{\text{Age of child (years)} + 12}$

This is the most commonly used formula for school-aged children. Notice that we add $12$ to the child's age in the denominator.

3. Clark's rule (general formula based on weight)

$\text{Dosage} = \frac{\text{Weight (kg)} \times \text{Adult dose}}{70}$

This rule is based on the child's weight in kilograms and uses $70$ kg as the standard adult reference weight.