Formula sheets, the key method steps for every topic and 8 practice problems, with full solutions at the back.
A solution has a ratio strength of 1:10 000. You need 0.28 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
A vial holds 1000 mg of powder. You add 9.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 130 mg. Draw up the dose: what volume V do you give?
A patient weighs 12 kg. The prescribed dose is 30 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?
A child weighing 12 kg is prescribed 10 mg/kg per dose of an oral suspension that contains 125 mg in 5 mL. What volume V do you give?
A drip runs at 20 gtt/min through a set of 15 gtt/mL. How many millilitres V does the patient receive in 4 hours?
500 mg of a drug is diluted in 500 mL and given by gravity through a set of 15 gtt/mL. The order is 60 mg per hour. Find the drip rate R in drops per minute.
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 250 mL. The order is 20 units/kg/h for a patient who weighs 79 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 250 mg in 250 mL runs at 30 mL/h. The patient weighs 52 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
Answer: V = 2.8 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 = 1.3 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: D = 120 mg
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: V = 4.8 mL
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: V = 320 mL
Infusion rates: a pump is set in mL/h = volume/time in hours. A gravity drip is counted in drops per minute: gtt/min = volume (mL) × drop factor (gtt/mL)/time (min). The drop factor is printed on the tubing package: macrodrip sets deliver 10, 15 or 20 gtt/mL (blood sets often 10 gtt/mL in the US, 15 in the UK) and microdrip sets 60 gtt/mL. Always use the drop factor the question or package gives.
Answer: R = 15 gtt/min
Dose-based infusions: concentration = amount of drug in the bag/bag volume. Pump rate (mL/h) = dose per hour/concentration, and dose per hour = mL/h × concentration. Convert per-minute doses to per-hour (× 60) and keep the mass units the same (1 g = 1000 mg, 1 mg = 1000 mcg).
Answer: R = 15.8 mL/h
Heparin and insulin infusions: concentration = units in the bag/bag volume (units/mL). Pump rate (mL/h) = units per hour/concentration, and units per hour = mL/h × concentration. For a weight-based order, units/h = units/kg/h × weight first. A bolus volume = units needed/vial strength. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Answer: D = 9.6 mcg/kg/min
Titrated drips: first find the concentration in mcg/mL (mg × 1000/mL). For a weight-based order, mcg/min = mcg/kg/min × weight. Then mL/h = mcg/min × 60/concentration. Working backwards, mcg/kg/min = mL/h × concentration/(60 × weight). The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
This is independent practice material. ExamProblems is not affiliated with or endorsed by the organisation that runs this exam, and the exam name is used only to describe the content. The PTCE is run by the Pharmacy Technician Certification Board (PTCB), which is not affiliated with ExamProblems and does not endorse it.
ExamProblems · examproblems.com/courses/pharmacy-technician-math