Formula sheets, the key method steps for every topic and 6 practice problems, with full solutions at the back.
A solution has a ratio strength of 1:10 000. You need 0.78 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
Practice exercise (made-up values, not clinical guidance). You must prepare 300 mL of 3% hydrogen peroxide from a 30% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
A child weighing 14 kg is prescribed 20 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?
The prescription is 410 units of a drug that comes as 1000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
Practice exercise (made-up values, not clinical guidance). After an IV dose of gentamicin, the level is 8 mg/L at 1 h and 2.5 mg/L at 6 h. Assume first-order elimination. Find the half-life t½.
Practice exercise (made-up values, not clinical guidance). A 60 kg patient has a digoxin level of 0.6 mcg/L; the target is 1 mcg/L. The volume of distribution is 7 L/kg and the tablets have F = 0.7. What extra loading dose LD raises the level to the target?
Answer: V = 7.8 mL
Strength to volume: turn the strength into mg per mL first. A w/v percentage is grams per 100 mL, so x% = 10x mg/mL. A ratio strength 1:n is 1 g in n mL. After reconstitution the concentration is the powder's dose over the final volume (diluent + powder volume). Then volume = dose/concentration.
Answer: V = 270 mL
Alligation: to mix a higher strength H and a lower strength L into a target strength T, take (T − L) parts of H and (H − T) parts of L. The parts are crossed: each stock gets the distance from the target to the other stock. Water or a plain base counts as 0%. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Check: 30 mL of 30% contains 9 g of drug, which is 3% of 300 mL.
Answer: V = 5.6 mL
Drawing up a dose: volume = (prescribed dose/stock strength) × stock volume. Convert to the same units first, then check that the volume fits the syringe and lands on one of its graduations.
On this 10 mL syringe every small line is 0.2 mL.
Answer: V = 0.41 mL
Drawing up a dose: volume = (prescribed dose/stock strength) × stock volume. Convert to the same units first, then check that the volume fits the syringe and lands on one of its graduations.
On this 1 mL syringe every small line is 0.01 mL.
Answer: t½ = 2.98 h
Clearance and volume: at steady state the dosing rate equals the elimination rate, so the maintenance rate = CL × Css. A loading dose is LD = Vd × C/(S × F), with S the salt factor (fraction of active drug in the salt) and F the bioavailability (1 for IV). From two levels, k = ln(C₁/C₂)/Δt; for an IV bolus Vd = dose/C₀ and CL = k × Vd. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Answer: LD = 240 mcg
Designing a regimen: with rapid IV doses the level falls from peak to trough during the interval, so τ = ln(Cpeak/Ctrough)/k and the dose that restores the peak is Vd × (Cpeak − Ctrough). The average steady-state level is Css,avg = S·F·dose/(CL·τ). An infusion rises as C = (R/CL)(1 − e−kt). For a drug cleared by the kidneys, the dose is scaled with the creatinine clearance. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
In practice the dose is rounded to a convenient amount.
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