Introduction
Pharmacy calculations represent one of the most critical and heavily tested competencies on the Pharmacy Technician Certification Exam (PTCE), encompassing essential mathematical skills that directly impact patient safety and medication accuracy. This topic area spans multiple domains of the PTCE, including the Medications domain (40% of exam weight) and Order Entry and Processing domain (21.25% of exam weight), making it a high-yield area for focused study preparation. Mastery of pharmacy calculations is fundamental to preventing dosing errors, ensuring proper medication concentrations, and maintaining the precision required in pharmaceutical compounding and dispensing. The mathematical concepts tested include dosage calculations, concentration and dilution problems, unit conversions, alligation methods, and intravenous flow rate determinations – all of which are encountered daily in pharmacy practice settings. Pharmacy technicians must demonstrate proficiency in these calculations to support pharmacists in delivering safe, effective patient care and to minimize the risk of medication errors that could lead to adverse patient outcomes. The PTCE emphasizes practical application of these mathematical principles through scenario-based questions that reflect real-world pharmacy situations, requiring candidates to apply formulas, perform dimensional analysis, and solve complex multi-step problems accurately. Understanding percentage strengths, ratio and proportion relationships, and business mathematics is also essential for inventory management, insurance calculations, and compounding procedures. Success in pharmacy calculations requires not only memorization of key formulas and conversion factors but also the ability to critically analyze problems, select appropriate calculation methods, and verify answers for reasonableness and accuracy. These practice questions are designed to reinforce fundamental calculation skills, build confidence in problem-solving approaches, and prepare candidates for the mathematical rigor expected on the PTCE examination.
Practice Questions
Question 1: A patient needs 250 mg of amoxicillin. The available strength is 125 mg/5 mL. How many milliliters should be dispensed?
A) 5 mL
B) 10 mL
C) 15 mL
D) 20 mL
Correct Answer: B
Explanation: Using the ratio and proportion method: 125 mg/5 mL = 250 mg/x mL. Cross multiply: 125x = 250 × 5 = 1250. Divide: x = 1250/125 = 10 mL. Alternatively, since 250 mg is exactly twice 125 mg, you need twice the volume: 2 × 5 mL = 10 mL.
Question 2: What is 0.5% expressed as a ratio strength?
A) 1:20
B) 1:50
C) 1:200
D) 1:500
Correct Answer: C
Explanation: To convert percentage to ratio strength, use the formula: 1:(100/percentage). For 0.5%: 1:(100/0.5) = 1:200. This means there is 1 part of active ingredient in every 200 parts of total solution.
Question 3: A prescription calls for 120 mL of a 15% solution. You have a 25% stock solution available. How many mL of the 25% solution do you need?
A) 48 mL
B) 72 mL
C) 96 mL
D) 108 mL
Correct Answer: B
Explanation: Using the dilution formula C1V1 = C2V2: (25%)(V1) = (15%)(120 mL). Solving: V1 = (15 × 120)/25 = 1800/25 = 72 mL of the 25% stock solution is needed.
Question 4: How many grams of active ingredient are in 500 mL of a 2.5% w/v solution?
A) 12.5 g
B) 25 g
C) 125 g
D) 200 g
Correct Answer: A
Explanation: For w/v percentage: % = (grams of solute/mL of solution) × 100. Rearranging: grams = (% × mL)/100 = (2.5 × 500)/100 = 1250/100 = 12.5 g of active ingredient.
Question 5: A pediatric patient weighs 35 kg and is prescribed a medication at 15 mg/kg/day divided into three doses. What is the amount per individual dose?
A) 150 mg
B) 175 mg
C) 200 mg
D) 225 mg
Correct Answer: B
Explanation: First calculate total daily dose: 35 kg × 15 mg/kg = 525 mg/day. Then divide by three doses: 525 mg ÷ 3 = 175 mg per individual dose.
Question 6: Convert 2.5 liters to milliliters.
A) 250 mL
B) 2,500 mL
C) 25,000 mL
D) 250,000 mL
Correct Answer: B
Explanation: To convert liters to milliliters, multiply by 1,000 (since 1 liter = 1,000 mL). Therefore: 2.5 L × 1,000 mL/L = 2,500 mL.
Question 7: Using the alligation method, how would you mix 20% and 5% alcohol solutions to make 500 mL of a 12% solution?
A) 233 mL of 20% and 267 mL of 5%
B) 300 mL of 20% and 200 mL of 5%
C) 267 mL of 20% and 233 mL of 5%
D) 200 mL of 20% and 300 mL of 5%
Correct Answer: A
Explanation: Using alligation: The difference between desired (12%) and lower strength (5%) is 7 parts. The difference between higher strength (20%) and desired (12%) is 8 parts. Ratio is 7:8. For 500 mL total: 20% solution = (7/15) × 500 = 233 mL; 5% solution = (8/15) × 500 = 267 mL.
Question 8: An IV solution is to be administered at 125 mL/hr using tubing with a drop factor of 15 drops/mL. What is the drip rate in drops per minute?
A) 25 drops/min
B) 31 drops/min
C) 42 drops/min
D) 56 drops/min
Correct Answer: B
Explanation: Formula: Drip rate = (Volume per hour × Drop factor) ÷ 60 minutes. Calculation: (125 mL/hr × 15 drops/mL) ÷ 60 min/hr = 1875 ÷ 60 = 31.25 drops/min, rounded to 31 drops/min.
Question 9: A patient’s insurance covers 80% of the medication cost. If the total cost is $240, how much does the patient pay?
A) $32
B) $48
C) $56
D) $64
Correct Answer: B
Explanation: If insurance covers 80%, the patient pays 20%. Calculate 20% of $240: 0.20 × $240 = $48. Alternatively, calculate insurance payment ($240 × 0.80 = $192) and subtract from total ($240 – $192 = $48).
Question 10: How many capsules are needed for a 30-day supply if the patient takes 2 capsules three times daily?
A) 120 capsules
B) 150 capsules
C) 180 capsules
D) 240 capsules
Correct Answer: C
Explanation: Daily dose = 2 capsules × 3 times = 6 capsules per day. For 30 days: 6 capsules/day × 30 days = 180 capsules total.
Question 11: Express 3/8 as a decimal and percentage.
A) 0.375 and 37.5%
B) 0.625 and 62.5%
C) 0.333 and 33.3%
D) 0.750 and 75%
Correct Answer: A
Explanation: To convert fraction to decimal: 3 ÷ 8 = 0.375. To convert to percentage: 0.375 × 100 = 37.5%. This is a fundamental conversion skill needed for concentration calculations.
Question 12: A stock solution contains 250 mg of drug in 10 mL. How would you prepare 50 mL of a solution containing 15 mg/mL?
A) Take 3 mL of stock and dilute to 50 mL
B) Take 5 mL of stock and dilute to 50 mL
C) Take 30 mL of stock and dilute to 50 mL
D) Take 15 mL of stock and dilute to 50 mL
Correct Answer: C
Explanation: Stock concentration = 250 mg/10 mL = 25 mg/mL. Desired solution = 15 mg/mL × 50 mL = 750 mg total needed. Volume of stock needed = 750 mg ÷ 25 mg/mL = 30 mL. Take 30 mL of stock and dilute to 50 mL total volume.
Question 13: What is the business formula for calculating markup percentage?
A) (Selling price – Cost) ÷ Cost × 100
B) (Cost – Selling price) ÷ Selling price × 100
C) (Selling price ÷ Cost) × 100
D) (Cost ÷ Selling price) × 100
Correct Answer: A
Explanation: Markup percentage = [(Selling price – Cost) ÷ Cost] × 100. This formula calculates the percentage increase from cost to selling price. For example, if an item costs $20 and sells for $25, markup = [(25-20) ÷ 20] × 100 = 25%.
Question 14: A prescription reads “Take 1 tablet BID for 14 days.” How many tablets should be dispensed?
A) 14 tablets
B) 28 tablets
C) 42 tablets
D) 56 tablets
Correct Answer: B
Explanation: BID means twice daily (bis in die). Daily tablets = 1 tablet × 2 times = 2 tablets per day. For 14 days: 2 tablets/day × 14 days = 28 tablets total.
Question 15: What is the ratio of ingredients needed to compound 240 g of an ointment containing 2.5% hydrocortisone?
A) 6 g hydrocortisone, 234 g base
B) 24 g hydrocortisone, 216 g base
C) 60 g hydrocortisone, 180 g base
D) 12 g hydrocortisone, 228 g base
Correct Answer: A
Explanation: For 2.5% w/w ointment: Hydrocortisone needed = 2.5% × 240 g = 0.025 × 240 = 6 g. Base needed = 240 g – 6 g = 234 g. The ratio is 6 g active ingredient to 234 g ointment base.