One fully worked problem for every question type on the site — 42 of them, across 19 topics.
A topic is not one question. “Dispensing quantity” is five different questions depending on whether you are counting bottles, vials, IV bags, inhalers, or tablets crushed for a batch, and each has its own setup. Every distinct question type this site can generate appears below, once, solved start to finish. If a type here looks unfamiliar, that is the one to go practise.
Express a 1:5,000 ratio strength as a percentage (w/v). Round your answer to two decimal places.
Answer 0.02 %
Anchors worth memorizing: 1:1,000 = 0.1% (epinephrine), 1:10,000 = 0.01%, 1:100,000 = 0.001%.
How many grams of active drug are in 300 mL of a 12.5% w/v solution? Round your answer to one decimal place.
Answer 37.5 g
How many mL of a 5% potassium permanganate stock solution are needed to prepare 490 mL of a 0.1% solution? Round your answer to two decimal places.
Answer 9.80 mL
The drug amount is unchanged by dilution; only concentration and volume change. Don't forget to QS to the final volume when the question asks for it.
You need 30 g of 1% hydrocortisone ointment, prepared from 2.5% and 0.5% stock. How many g of the 2.5% stock do you need? Round your answer to one decimal place.
Answer 7.5 g
Sanity check: 7.5×2.5% + 22.5×0.5% = 0.3 g = 30 g × 1% ✓
You mix 300 mL of 50% dextrose with 250 mL of 20% dextrose. What is the percentage strength of the final mixture? Round your answer to one decimal place.
Answer 36.4 %
Alligation MEDIAL = known quantities → find resulting strength. Alligation ALTERNATE = known strengths → find quantities.
How many milliequivalents are in 1 g of magnesium sulfate heptahydrate (MgSO₄·7H₂O)? (MW = 246.5, valence = 2) Round your answer to one decimal place.
Answer 8.1 mEq
Monovalent ions: mEq = mmol. Divalent (Ca²⁺, Mg²⁺): 2 mEq per mmol — forgetting valence is the classic error.
How many millimoles are in 13 g of sodium bicarbonate (NaHCO₃)? (MW = 84) Round your answer to one decimal place.
Answer 154.8 mmol
Calculate the osmolarity of a 10% dextrose monohydrate solution in mOsm/L. (MW = 198; does not dissociate (1 particle per molecule).) Round your answer to the nearest whole number.
Answer 505 mOsm/L
Landmarks: NS ≈ 308 mOsm/L, D5W ≈ 252 mOsm/L (dextrose monohydrate, MW 198) — both close enough to plasma (~285–295) to run peripherally. Particles: NaCl = 2, dextrose = 1 (nonelectrolyte).
Dopamine 400 mg in 250 mL D5W is ordered at 5 mcg/kg/min for a 89 kg patient. What rate in mL/hr should the pump be set at? Round your answer to one decimal place.
Answer 16.7 mL/hr
The three-step chain (concentration → mcg/min → mL/hr) never changes; only the numbers do. Weight only enters when the order is written per kg — norepinephrine and nitroglycerin are commonly ordered as a flat mcg/min.
An order calls for 1000 mL of NS over 3 hours with a set that delivers 20 drops/mL. What is the flow rate in drops per minute? Round your answer to the nearest whole number.
Answer 111 drops/min
Work in whole drops and whole minutes rather than a decimal mL/min — carrying a rounded mL/min into the next line is how a correct method produces a wrong number. Drops (gtt) are always whole; you can't give a partial drop.
A patient is 170 cm tall and weighs 83 kg. The order is etoposide 100 mg/m². Using the Mosteller formula, what dose in mg should be prepared? Round your answer to the nearest whole number.
Answer 198 mg
Keep BSA unrounded until the final multiplication — rounding BSA to 2 decimals early can shift the dose by several mg, which is why the steps above carry 5.
A TPN contains 500 mL dextrose 50%, 250 mL amino acids 10%, and 250 mL of 20% lipid emulsion. What are the NONPROTEIN kilocalories? (3.4 kcal/g dextrose, 4 kcal/g protein, 20% lipid = 2 kcal/mL) Round your answer to the nearest whole number.
Answer 1,350 kcal
Total vs NONPROTEIN kcal is decided by the question's wording — read the ask twice before adding.
A TPN contains 250 mL of 8.5% amino acids. How many grams of nitrogen does it provide? (Protein is 16% nitrogen: N = protein ÷ 6.25) Round your answer to one decimal place.
Answer 3.4 g
Lower-yield for the exam, kept for completeness. Used for nitrogen-balance and calorie:nitrogen ratio questions.
A TPN contains 1000 mL dextrose 15%, 250 mL amino acids 8.5%, and 500 mL of 20% lipid emulsion. What are the total kilocalories? (3.4 kcal/g dextrose, 4 kcal/g protein, 20% lipid = 2 kcal/mL) Round your answer to the nearest whole number.
Answer 1,595 kcal
Total vs NONPROTEIN kcal is decided by the question's wording — read the ask twice before adding.
A TPN contains 250 mL of dextrose 20%. How many kilocalories does the dextrose provide? (IV dextrose = 3.4 kcal/g) Round your answer to the nearest whole number.
Answer 170 kcal
IV (TPN) energy densities: dextrose 3.4 kcal/g, protein 4 kcal/g, lipid 10% = 1.1 kcal/mL, 20% = 2 kcal/mL. ORAL/enteral nutrition uses 4 kcal/g carbohydrate, 4 protein, 9 fat — don't mix the two systems.
An oral nutrition supplement contains 30 g carbohydrate, 8 g protein, and 7 g fat per serving. How many kilocalories per serving? (Oral: 4 kcal/g carbohydrate, 4 kcal/g protein, 9 kcal/g fat) Round your answer to the nearest whole number.
Answer 215 kcal
The oral/enteral system (4/4/9) differs from IV: oral carbohydrate is 4 kcal/g, but IV dextrose monohydrate is 3.4 kcal/g. Route determines the numbers.
How many grams of NaCl must be added to make 30 mL of a 0.125% phenylephrine HCl solution isotonic? (E-value of phenylephrine HCl = 0.32) Round your answer to three decimal places.
Answer 0.258 g
E-value = grams of NaCl with the same osmotic effect as 1 g of drug. The exam gives you the E-value — the skill is the 4-step setup. The steps above carry 5 decimals on purpose: truncating an intermediate here is enough to move the final gram figure.
Calculate the creatinine clearance (Cockcroft-Gault) for a 71-year-old female, 5'6" tall, weighing 92 kg, with a serum creatinine of 2.2 mg/dL. Select the appropriate body weight: use actual body weight if it is below IBW, adjusted body weight if it exceeds 125% of IBW, and IBW otherwise. Round your answer to the nearest whole number.
Answer 27 mL/min
The weight-selection algorithm: always calculate IBW first. Underweight (actual < IBW) → use actual body weight. Obese (actual > 125% of IBW) → use AdjBW = IBW + 0.4(actual − IBW). Otherwise → use IBW.
A 500 mg IV bolus produces an initial plasma concentration (C₀) of 25 mg/L. What is the volume of distribution? Round your answer to one decimal place.
Answer 20.0 L
Vd is theoretical — a Vd far above total body water (~42 L) means extensive tissue binding (e.g., digoxin ~500 L).
A drug has an elimination rate constant of 0.2 hr⁻¹ and a Vd of 80 L. What is its total body clearance? Round your answer to one decimal place.
Answer 16.0 L/hr
Also rearranges to k = CL/Vd and t½ = 0.693·Vd/CL — same triangle, three disguises.
Two plasma levels are measured for a drug: 25 mg/L at hour 0 and 5 mg/L at hour 4. What is the elimination rate constant (k)? Round your answer to four decimal places.
Answer 0.4024 hr⁻¹
First-order elimination: plot ln(concentration) vs time and k is the negative slope. Half-life then follows from t½ = 0.693 ÷ k. Carry k to at least 4 decimals — it is small, so a truncated k throws every downstream figure off.
Target plasma concentration is 18 mg/L and the drug's Vd is 30 L. What IV loading dose is required? (Assume S = 1, F = 1.) Round your answer to the nearest whole number.
Answer 540 mg
Loading dose depends on Vd; maintenance dose depends on clearance. Exam questions love to make you mix these up.
A drug has an elimination rate constant of 0.087 hr⁻¹. What is its half-life? Round your answer to one decimal place.
Answer 8.0 hr
~94% of a drug is eliminated after 4 half-lives; steady state is reached after ~4–5 half-lives of dosing.
A 100 mg IV dose gives an AUC of 50 mg·hr/L. A 200 mg oral dose gives an AUC of 90 mg·hr/L. What is the absolute bioavailability (%)? Round your answer to the nearest whole number.
Answer 90 %
Always dose-normalize both AUCs — comparing raw AUCs from different doses is the built-in trap.
A patient uses Novolin N (10 mL vial, 100 units/mL) at 40 units/day. Once in use, this product is stable for 42 days, after which any remaining insulin must be discarded. What is the day supply of one vial? Round down to the nearest whole number.
Answer 25 days
Insulin day supply = total units ÷ daily dose, then capped at the product's in-use stability. You can never dispense a partial day, so this always goes DOWN.
A patient takes Toujeo (glargine U-300) 40 units daily. Convert to Basaglar. What is the new daily dose? Round your answer to the nearest whole number.
Answer 32 units
Switches are 1:1 EXCEPT two cases at −20%: NPH (BID) → basal glargine, and Toujeo (U-300) → Lantus/Basaglar.
A patient is receiving 1.5 mg/day of hydromorphone (IV) and is being switched to codeine (PO). Using the equianalgesic table below, convert the dose and then reduce it by 50% for incomplete cross-tolerance. What is the starting daily dose of codeine (PO) in mg/day?
| Opioid | PO (mg) | IV (mg) |
|---|---|---|
| morphine | 30 | 10 |
| hydromorphone | 7.5 | 1.5 |
| oxycodone | 20 | — |
| hydrocodone | 30 | — |
| codeine | 200 | — |
| meperidine | 300 | 75 |
| fentanyl | — | 0.1 (= 100 mcg) |
Answer 100.0 mg/day
Two-step questions are the norm: convert on the table first, THEN reduce 25–50%. The reduction exists because tolerance to one opioid does not transfer completely to another — skipping it is how a conversion overdoses a patient. Reduce toward the larger end (50%) when the patient is elderly, frail, or the new opioid is methadone.
A patient's opioid regimen totals 205 mg/day of oral morphine equivalents. Using the conversion table below, which fentanyl patch strength (mcg/hr) is appropriate? This table comes from the product labeling and already builds in the conservative conversion factor, so no further cross-tolerance reduction is applied.
| Oral morphine (mg/day) | Fentanyl patch (mcg/hr) |
|---|---|
| 60–134 | 25 |
| 135–224 | 50 |
| 225–314 | 75 |
| 315–404 | 100 |
Answer 50 mcg/hr
Patch selection is a table LOOKUP, not a proportion — never interpolate between rows. The Duragesic table is deliberately conservative, so you do NOT subtract a further 25–50% on top of it. Patches are changed every 72 hours and are for opioid-tolerant patients only — both favorite exam distractors.
A patient takes codeine (PO) 60 mg, 2 times daily. Using the equianalgesic table below, what is the total daily dose in morphine milligram equivalents (MME/day)?
| Opioid | PO (mg) | IV (mg) |
|---|---|---|
| morphine | 30 | 10 |
| hydromorphone | 7.5 | 1.5 |
| oxycodone | 20 | — |
| hydrocodone | 30 | — |
| codeine | 200 | — |
| meperidine | 300 | 75 |
| fentanyl | — | 0.1 (= 100 mcg) |
Answer 18 MME/day
MME is just an equianalgesic conversion with 30 mg oral morphine as the anchor. 90 MME/day is the common review threshold in opioid safety guidance. MME factors are defined for ORAL opioids; a parenteral dose must first be converted to its oral equivalent, which is why the CDC table has no IV column.
An ipratropium/albuterol Respimat inhaler contains 60 actuations (puffs). The sig is 1 puff four times daily (QID). What is the days supply? Round down to the nearest whole number.
Answer 15 days
Inhaler days supply uses total actuations (not mL). Rescue/PRN inhalers are billed on maximum daily puffs.
A pediatric patient weighs 70.4 lb. The order is gentamicin 7.5 mg/kg/day divided three times daily (q8h). How many mg per dose? (Use 1 kg = 2.2 lb.) Round your answer to one decimal place.
Answer 80.0 mg/dose
Watch for mg/kg/DAY vs mg/kg/DOSE — the #1 trap in this family. Conversion factors also vary: 2.2 lb/kg is the exam convention, 2.2046 is the exact figure, so the question states which to use.
A vial contains 1 g of powdered drug. Adding 9.7 mL of diluent yields a final concentration of 100 mg/mL. What is the powder (displacement) volume? Round your answer to two decimal places.
Answer 0.30 mL
The dry powder occupies space (displacement). Powder volume = final reconstituted volume − volume of diluent added.
A solution has a specific gravity of 1.15. What volume in mL contains 225 g? Round your answer to one decimal place.
Answer 195.7 mL
Rearranged from weight = volume × specific gravity. A liquid denser than water (SG > 1) occupies less volume per gram.
A patient has Na⁺ 132, Cl⁻ 102, and HCO₃⁻ 18 (all mEq/L). What is the anion gap? Round your answer to the nearest whole number.
Answer 12 mEq/L
Normal anion gap ≈ 8–12 mEq/L (potassium omitted). Elevated gap points to MUDPILES causes (lactic acidosis, DKA, salicylates, etc.).
A patient has a measured serum calcium of 8.5 mg/dL and an albumin of 2.8 g/dL. What is the corrected calcium? Round your answer to one decimal place.
Answer 9.5 mg/dL
Only correct when albumin is low. Each 1 g/dL of albumin below 4.0 masks ~0.8 mg/dL of calcium.
A patient has a WBC of 12,000 cells/mm³ with 20% segs and 2% bands. What is the absolute neutrophil count (ANC)? Round your answer to the nearest whole number.
Answer 2,640 cells/mm³
Neutrophils only — segs plus bands. Neutropenia: ANC < 1500 mild, < 1000 moderate, < 500 severe (high infection risk).
A patient's measured total phenytoin level is 12 mcg/mL with an albumin of 3 g/dL and normal renal function. What is the corrected phenytoin level? (Sheiner-Tozer) Round your answer to one decimal place.
Answer 17.1 mcg/mL
Sheiner-Tozer adjusts total phenytoin for hypoalbuminemia. For CrCl < 10 mL/min, the 0.2 factor becomes 0.1.
A maintenance 0.9% sodium chloride infusion is running at 100 mL/hr. Pharmacy supplies it in 1000 mL bags. How many bags must be sent to cover the next 72 hours without the line running dry? Round up to the next whole number.
Answer 8 bags
A partly used bag cannot cover the gap at the end of the window, so the last bag has to be a whole one. This counts bags needed to cover the time — the final bag will still have volume in it when the window ends, and IV admixtures also carry their own hang-time limits that can force a bag change before it empties.
A patient weighing 80 kg is prescribed liposomal amphotericin B 5 mg/kg IV for one dose. The drug is stocked as 50 mg single-dose vials. How many vials must be opened to prepare this dose? Round up to the next whole number.
Answer 8 vials
A single-dose vial that is entered is a single-dose vial that is spent, so any fraction costs a whole extra vial and the remainder is discarded. This is also the number to quote for cost and for waste — not the calculated dose.
A prescription is written for prednisolone 15 mg/5 mL oral solution, 7.5 mL twice daily (BID) for 10 days. The product is supplied in 120 mL bottles. How many bottles must be dispensed to complete the course? Round up to the next whole number.
Answer 2 bottles
Suspensions are dispensed in whole manufacturer bottles, so a course that needs 2.25 bottles is dispensed as 3. Sending home 2 guarantees the patient runs out before the antibiotic course is finished — the single most common version of this error.
A prescription for budesonide/formoterol inhaler reads: 2 puffs twice daily. Each inhaler is labelled 120 actuations. How many inhalers must be dispensed for a 60-day supply? Round up to the next whole number.
Answer 2 inhalers
Inhalers are dispensed whole, so a 90-day supply needing 2.7 inhalers is billed as 3. Watch the actuation count on the label rather than assuming: rescue HFAs are commonly 200 actuations while most maintenance HFAs are 120, and the same sig gives a different quantity for each.
A compounding order calls for 45 capsules, each containing 2.5 mg of spironolactone. The powder will be prepared by crushing commercial 25 mg spironolactone tablets. How many tablets are needed to compound this prescription? Round up to the next whole number.
Answer 5 tablets
Whole tablets go into the mortar, so the count is a ceiling and the surplus powder is waste. Note this is the minimum — a real compounder adds an overage on top for loss during trituration and filling, which is why the batch is often prepared from one or two more tablets than the calculation alone demands.