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 0.67 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
Practice exercise (made-up values, not clinical guidance). You have 60 g of 2.5% hydrocortisone ointment. How many grams m of 0.5% hydrocortisone ointment must you add to make a 1% ointment? Round to the nearest whole gram.
A child weighing 16 kg is prescribed 4 mg/kg of a drug. The stock solution contains 10 mg/mL. Draw up the dose: what volume V do you give?
You must prepare 250 mL of a 0.5% (w/v) solution from a 20% (w/v) stock solution. How much water W must be added to the stock?
Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 110 mg of gentamicin. The level back-extrapolated to time zero is 6 mg/L and the half-life is 3 h. Find the clearance CL in L/h.
Practice exercise (made-up values, not clinical guidance). A 92 kg patient takes oral theophylline (F = 1) every 8 h. The clearance is 0.035 L/kg/h. Each dose is 300 mg of theophylline. Find the average steady-state level Css,avg.
Answer: V = 0.67 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: m = 180 g
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: 60 g + 180 g = 240 g of 1% ointment.
Answer: V = 6.4 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: W = 243.8 mL
Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.
Answer: CL = 4.236 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: Css,avg = 11.65 mg/L
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.
ExamProblems · examproblems.com/courses/pharmacy-calculations