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 1:1000. You need 0.47 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
Practice exercise (made-up values, not clinical guidance). You must prepare 200 mL of 6% 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 13 kg is prescribed 2 mg/kg of a drug. The stock solution contains 10 mg/mL. Draw up the dose: what volume V do you give?
An infusion contains 40000 units of a drug in 1000 mL. The prescription is 2000 units per hour. At what rate R do you set the pump, in mL/h?
Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 150 mg of gentamicin. The level back-extrapolated to time zero is 6 mg/L and the half-life is 2 h. Find the clearance CL in L/h.
Practice exercise (made-up values, not clinical guidance). A 64 kg patient on regular tobramycin doses is at steady state. The target is a peak of 6 mg/L and a trough of 1 mg/L, and the volume of distribution is 0.3 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?
Answer: V = 0.47 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 = 160 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: 40 mL of 30% contains 12 g of drug, which is 6% of 200 mL.
Answer: V = 2.6 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: R = 50 mL/h
Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.
Answer: CL = 8.664 L/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: D = 96 mg
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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