Formula sheets, the key method steps for every topic and 10 practice problems, with full solutions at the back.
A child weighing 7 kg is prescribed 20 mg/kg of a drug. The stock solution contains 20 mg/mL. Draw up the dose: what volume V do you give?
The prescription is 0.92 mg. The ampoule contains 1000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
A drip runs at 35 gtt/min through a set of 20 gtt/mL. How many millilitres V does the patient receive in 8 hours?
1000 mL was ordered over 10 hours. After 5 hours you find that 560 mL is still in the bag, and the order must still finish on time. By what percentage Δ must the original pump rate be increased?
Practice exercise (made-up values, not clinical guidance). An infusion contains 250 units of regular insulin in 250 mL. The order is 0.1 units/kg/h for a patient who weighs 53 kg. Find the pump rate R in mL/h. Round to one decimal place.
Practice exercise (made-up values, not clinical guidance). A patient who weighs 76 kg has an order for norepinephrine at 6 mcg/min. The bag contains 8 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
Practice exercise (made-up values, not clinical guidance). The record shows a patient's intake and output for one 8-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the fluid balance B = intake − output in mL (a negative answer means a net loss). Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 06:30 and runs by pump at 100 mL/h. How many mL V are left in the bag at 09:00?
Practice exercise (made-up values, not clinical guidance). A drip-rate calculation gives 179.348 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?
Practice exercise (made-up values, not clinical guidance). A serum creatinine result is 1.1 mg/dL. Using 1 mg/dL = 88.4 µmol/L for creatinine, find c in µmol/L to the nearest whole number.
Answer: V = 7 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 = 0.92 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.
Answer: V = 840 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: Δ = 12 %
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: R = 5.3 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: R = 11.3 mL/h
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.
The order is per minute for the whole patient, so the weight is not needed.
Answer: B = −25 mL
Intake and output: intake counts everything that goes in (oral fluids, IV infusions, IV medications and flushes, tube feeds); ice chips count as half their volume. Output counts urine, drains, vomit and other losses. Balance = total intake − total output; a negative balance is a net loss. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Negative: the patient lost more fluid than went in.
Answer: V = 750 mL
Infusion time: time (h) = volume to infuse (mL)/rate (mL/h); use the volume still left in the bag, not the bag size. Volume infused = rate × time. Convert decimal hours to hours and minutes with the fraction × 60 (0.5 h = 30 min, not 50 min). The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Answer: x = 179 gtt/min
Rounding: look at the digit just after the place you round to: 5 or more rounds up, 4 or less leaves the digit as it is. Round only the final answer, never the steps. Typical exam rules: volumes of 1 mL or more to the nearest tenth, volumes below 1 mL to the nearest hundredth, drip rates to whole drops and weights to one decimal place; always follow the rule the question states.
Answer: c = 97 µmol/L
Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.
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