Pharmaceutical calculations are a cornerstone of pharmacy practice, demanding precision and accuracy to ensure patient safety and therapeutic efficacy. For PharmD students, mastering these skills is not just an academic requirement but a professional obligation. This area of study encompasses a wide range of mathematical applications, from basic dosage calculations based on weight or body surface area to more complex pharmacokinetic modeling. This quiz will test your knowledge on various calculation types encountered in both community and hospital pharmacy settings, including sterile compounding, dosage individualization, IV flow rates, dilutions, and concentrations. Honing these skills is critical for preparing and dispensing medications safely and effectively.
1. A physician orders 500 mL of a 20% dextrose solution. Your pharmacy only has 50% and 5% dextrose solutions in stock. How many mL of the 50% solution are needed?
- A. 150 mL
- B. 167 mL
- C. 250 mL
- D. 333 mL
Answer: B
2. You are asked to prepare a 1 L bag of 0.45% NaCl solution using sterile water for injection and a 23.4% NaCl solution. How much of the 23.4% NaCl solution is required?
- A. 19.2 mL
- B. 21.5 mL
- C. 23.4 mL
- D. 45.0 mL
Answer: A
3. A medication has a concentration of 250 mg/5 mL. A patient is prescribed a dose of 150 mg. How many mL should be administered?
- A. 2 mL
- B. 3 mL
- C. 4 mL
- D. 5 mL
Answer: B
4. An IV is running at 125 mL/hr. The IV bag contains 1 liter of fluid. How long will the bag last?
- A. 6 hours
- B. 8 hours
- C. 10 hours
- D. 12 hours
Answer: B
5. A patient weighs 150 lbs. What is their weight in kilograms? (1 kg = 2.2 lbs)
- A. 68.2 kg
- B. 75.0 kg
- C. 82.5 kg
- D. 330 kg
Answer: A
6. A drug is to be dosed at 5 mg/kg. The patient weighs 176 lbs. What is the correct dose in mg?
- A. 350 mg
- B. 400 mg
- C. 450 mg
- D. 880 mg
Answer: B
7. You need to prepare 60 g of a 2% hydrocortisone cream using a 5% hydrocortisone cream and a cream base (0%). How much of the 5% cream is needed?
- A. 12 g
- B. 24 g
- C. 30 g
- D. 48 g
Answer: B
8. An IV order is for 1000 mL of D5W to be infused over 10 hours. The administration set delivers 15 gtt/mL. What is the flow rate in gtt/min?
- A. 15 gtt/min
- B. 20 gtt/min
- C. 25 gtt/min
- D. 30 gtt/min
Answer: C
9. How many grams of sodium chloride are in 500 mL of 0.9% NaCl solution?
- A. 0.45 g
- B. 4.5 g
- C. 9 g
- D. 45 g
Answer: B
10. A child weighing 44 lbs is prescribed amoxicillin at a dose of 40 mg/kg/day, divided into two daily doses. What is the dose for a single administration?
- A. 200 mg
- B. 400 mg
- C. 800 mg
- D. 880 mg
Answer: B
11. A solution is available as 1:5000 w/v. What is its percentage strength?
- A. 0.002%
- B. 0.02%
- C. 0.2%
- D. 2%
Answer: B
12. A medication has a half-life of 6 hours. If a patient takes a 200 mg dose, how much of the drug will remain in the body after 24 hours?
- A. 6.25 mg
- B. 12.5 mg
- C. 25 mg
- D. 50 mg
Answer: B
13. You are to prepare 240 mL of a 1:250 solution from a stock solution of 4% strength. How many mL of the stock solution do you need?
- A. 6 mL
- B. 12 mL
- C. 24 mL
- D. 48 mL
Answer: C
14. An order for dopamine is written for 5 mcg/kg/min. The patient weighs 70 kg. The dopamine is supplied as 400 mg in 250 mL of D5W. What is the required infusion rate in mL/hr?
- A. 13.1 mL/hr
- B. 15.6 mL/hr
- C. 17.5 mL/hr
- D. 21.0 mL/hr
Answer: A
15. Calculate the Body Surface Area (BSA) for a patient who is 5’8″ tall and weighs 180 lbs using the Mosteller formula: BSA (m²) = √([Height(cm) x Weight(kg)] / 3600). (1 inch = 2.54 cm, 1 kg = 2.2 lbs)
- A. 1.89 m²
- B. 1.98 m²
- C. 2.05 m²
- D. 2.15 m²
Answer: B
16. How many milliequivalents (mEq) of KCl are in a 30 mL solution containing 10% w/v KCl? (MW of KCl = 74.5 g/mol)
- A. 20.1 mEq
- B. 30.0 mEq
- C. 40.3 mEq
- D. 74.5 mEq
Answer: C
17. You need to prepare 1 liter of a solution containing 40 mEq of potassium. You have vials of potassium chloride containing 2 mEq/mL. How many mL will you need?
- A. 10 mL
- B. 20 mL
- C. 30 mL
- D. 40 mL
Answer: B
18. A Total Parenteral Nutrition (TPN) order calls for 250 mL of 70% Dextrose. How many grams of dextrose will this provide?
- A. 70 g
- B. 125 g
- C. 175 g
- D. 250 g
Answer: C
19. What is the ratio strength (w/v) of a solution made by dissolving five 325 mg tablets in enough water to make 200 mL?
- A. 1:123
- B. 1:150
- C. 1:200
- D. 1:325
Answer: A
20. A patient’s creatinine clearance is calculated to be 45 mL/min. The recommended dose for a drug is 500 mg for CrCl > 50 mL/min and 250 mg for CrCl 30-50 mL/min. What dose should be given?
- A. 125 mg
- B. 250 mg
- C. 375 mg
- D. 500 mg
Answer: B
21. A prescription calls for 30 capsules, each containing 1/8 grain of phenobarbital. How many milligrams of phenobarbital are needed in total? (1 grain = 64.8 mg)
- A. 200 mg
- B. 243 mg
- C. 260 mg
- D. 324 mg
Answer: B
22. An injectable drug has a concentration of 50,000 units/mL. A dose of 12,500 units is required. What volume should be drawn up?
- A. 0.20 mL
- B. 0.25 mL
- C. 0.40 mL
- D. 0.50 mL
Answer: B
23. If 50 mL of a 2.5% w/v solution is diluted to 1000 mL, what is the final percentage strength?
- A. 0.0625%
- B. 0.125%
- C. 0.25%
- D. 0.5%
Answer: B
24. A heparin drip is ordered to run at 18 units/kg/hr for a patient weighing 220 lbs. The pharmacy supplies a bag of heparin 25,000 units in 500 mL D5W. What is the flow rate in mL/hr?
- A. 18 mL/hr
- B. 25 mL/hr
- C. 36 mL/hr
- D. 50 mL/hr
Answer: C
25. How many grams of zinc oxide are needed to prepare 240g of a 10% zinc oxide paste?
- A. 10 g
- B. 12 g
- C. 20 g
- D. 24 g
Answer: D
26. If a pharmacist adds 15 mL of a 1:1000 (w/v) solution to 235 mL of sterile water, what is the final concentration (w/v) ratio strength?
- A. 1:12500
- B. 1:15000
- C. 1:16667
- D. 1:20000
Answer: C
27. A medication order calls for 1.5 million units of Penicillin G. The pharmacy has vials containing 5 million units per 10 mL. How many mL are needed for the dose?
- A. 1.5 mL
- B. 2.0 mL
- C. 3.0 mL
- D. 5.0 mL
Answer: C
28. Convert a concentration of 0.05% to parts per million (PPM).
- A. 5 PPM
- B. 50 PPM
- C. 500 PPM
- D. 5000 PPM
Answer: C
29. You need to make 500 mL of a 10% solution from a 25% stock solution. How much stock solution and how much diluent are required?
- A. 100 mL of stock, 400 mL of diluent
- B. 200 mL of stock, 300 mL of diluent
- C. 250 mL of stock, 250 mL of diluent
- D. 300 mL of stock, 200 mL of diluent
Answer: B
30. A drug has a volume of distribution (Vd) of 40 L and a clearance (Cl) of 5 L/hr. What is the elimination half-life (t½)? (t½ = 0.693 x Vd / Cl)
- A. 4.5 hours
- B. 5.5 hours
- C. 6.9 hours
- D. 8.0 hours
Answer: B
31. A prescription requires 25 mcg of levothyroxine. The available tablets are 0.05 mg. How many tablets are needed per dose?
- A. 0.25 tablets
- B. 0.5 tablets
- C. 1 tablet
- D. 2 tablets
Answer: B
32. An order is for vancomycin 1g in 250 mL of NS to be infused over 90 minutes. What is the rate of infusion in mL/hr?
- A. 125 mL/hr
- B. 150 mL/hr
- C. 167 mL/hr
- D. 250 mL/hr
Answer: C
33. You are compounding a cream and need 30 grams of a 1.5% strength ointment. You have 2.5% and 0.5% ointments available. How many grams of the 2.5% ointment do you need?
- A. 10 g
- B. 15 g
- C. 20 g
- D. 25 g
Answer: B
34. How many millimoles of magnesium sulfate are in 10 mL of a 50% magnesium sulfate solution? (MW of MgSO4 = 120.4 g/mol)
- A. 20.8 mmol
- B. 35.6 mmol
- C. 41.5 mmol
- D. 50.0 mmol
Answer: C
35. A patient needs to receive 375 mg of a drug orally. The drug is available as a 250 mg/5 mL suspension. How many mL should the patient take?
- A. 5 mL
- B. 7.5 mL
- C. 10 mL
- D. 12.5 mL
Answer: B
36. A TPN solution contains 500 mL of 10% amino acids. How many grams of protein does this provide?
- A. 25 g
- B. 50 g
- C. 75 g
- D. 100 g
Answer: B
37. If you dissolve 4 g of a substance in 50 mL of alcohol, what is the percentage strength (w/v) of the solution?
- A. 4%
- B. 5%
- C. 8%
- D. 12.5%
Answer: C
38. An infusion is to be administered at 30 mcg/min. The concentration of the drug is 50 mg in 250 mL. What is the rate in mL/hr?
- A. 9 mL/hr
- B. 12 mL/hr
- C. 15 mL/hr
- D. 18 mL/hr
Answer: A
39. A patient is to receive a drug at a dose of 2 mg/m². The patient’s BSA is 1.8 m². The drug is available in 2 mg vials. How many vials are needed?
- A. 1 vial
- B. 1.5 vials
- C. 2 vials
- D. 2.5 vials
Answer: C (You cannot dispense half a vial, so you must use 2)
40. To prepare 1 pint (473 mL) of a 1:500 solution, how many grams of drug are needed?
- A. 0.473 g
- B. 0.946 g
- C. 1.000 g
- D. 1.250 g
Answer: B
41. A pharmacist mixes 100g of 10% ichthammol ointment, 150g of 5% ichthammol ointment, and 250g of petrolatum (0%). What is the final percentage of ichthammol in the mixture?
- A. 3.5%
- B. 4.0%
- C. 4.5%
- D. 5.0%
Answer: A
42. How many calories are provided by 1 liter of a TPN solution containing 500 mL of 50% Dextrose and 500 mL of 10% Amino Acids? (Dextrose = 3.4 kcal/g, Amino Acids = 4 kcal/g)
- A. 850 kcal
- B. 1050 kcal
- C. 1250 kcal
- D. 1450 kcal
Answer: B
43. A dose of 250 mg is needed. The pharmacy stocks 125 mg tablets. How many tablets should be dispensed for a 10-day supply if the dose is taken twice daily?
- A. 20 tablets
- B. 30 tablets
- C. 40 tablets
- D. 50 tablets
Answer: C
44. A vial contains 1 g of powder. It is to be reconstituted to a final concentration of 100 mg/mL. How much diluent is needed if the powder volume is 0.8 mL?
- A. 9.0 mL
- B. 9.2 mL
- C. 10.0 mL
- D. 10.8 mL
Answer: B
45. What is the osmolarity (mOsmol/L) of a 0.9% NaCl solution? (MW of NaCl = 58.5 g/mol, i = 1.8)
- A. 154 mOsmol/L
- B. 278 mOsmol/L
- C. 308 mOsmol/L
- D. 315 mOsmol/L
Answer: B
46. A patient is receiving an infusion at 75 mL/hr. The bag contains 50 mg of a drug in 500 mL of NS. How many mg of the drug is the patient receiving per hour?
- A. 5 mg/hr
- B. 7.5 mg/hr
- C. 10 mg/hr
- D. 12.5 mg/hr
Answer: B
47. You need to prepare 120 mL of a suspension containing 40 mg/5 mL from tablets that are 20 mg each. How many tablets are needed?
- A. 24 tablets
- B. 36 tablets
- C. 48 tablets
- D. 60 tablets
Answer: C
48. An antibiotic is dosed at 15 mg/kg. The patient weighs 110 lbs. The drug is available as 250 mg capsules. How many capsules are needed for one dose?
- A. 1 capsule
- B. 2 capsules
- C. 3 capsules
- D. 4 capsules
Answer: C
49. An IV admixture contains 45 mEq of KCl in 1000 mL. The patient is to receive 5 mEq/hr. What is the infusion rate in mL/hr?
- A. 90 mL/hr
- B. 101 mL/hr
- C. 111 mL/hr
- D. 121 mL/hr
Answer: C
50. You have a stock solution of 1:750 w/v. How many mL of this solution would be needed to make 4 liters of a 1:2000 w/v solution?
- A. 1000 mL
- B. 1250 mL
- C. 1500 mL
- D. 1750 mL
Answer: C