Formula sheets, the key method steps for every topic and 8 practice problems, with full solutions at the back.
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 18.2 mL of diluent. The prescribed dose is 2 400 000 units. What volume V do you draw up? Round to one decimal place.
Practice exercise (made-up values, not clinical guidance). You must prepare 1500 mL of 40% dextrose by mixing 70% and 10% dextrose. How many mL V of the 70% solution do you need? Round to the nearest whole mL.
A dose of 100 mg is needed from a 10% (w/v) solution. What volume V contains this dose?
An infusion contains 25000 units of a drug in 250 mL. The prescription is 1000 units per hour. At what rate R do you set the pump, in mL/h?
1000 mL was ordered over 6 hours. After 4 hours you find that 380 mL is still in the bag, and the order must still finish on time. To what rate R in mL/h must the pump be reset?
A bag contains 250 mg of a drug in 250 mL and runs at 5 mL/h. How many milligrams per hour D does the patient receive?
Practice exercise (made-up values, not clinical guidance). An infusion contains 100 units of regular insulin in 250 mL. The order is 0.1 units/kg/h for a patient who weighs 72 kg. Find the pump rate R in mL/h. Round to one decimal place.
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 6 mL/h. The patient weighs 82 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
Answer: V = 9.6 mL
Reconstitution: the powder takes up space, so the final volume is the diluent plus the powder volume. Concentration = drug in the vial/final volume, and the volume to give = dose/concentration. On a multi-strength label, use the concentration that belongs to the amount of diluent you actually added. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Answer: V = 750 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: 750 mL of 70% + 750 mL of 10% = 1500 mL.
Answer: V = 1 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: R = 10 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: R = 190 mL/h
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.
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
Answer: D = 5 mg/h
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 = 18 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 = 2 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