Free PTCB Practice Test · Topic Drill
Pharmacy Math Practice Test
30 PTCE-style questions, one at a time — just like exam day. Score and full explanations at the end. Free, no signup.
Pharmacy math is where candidates lose the easiest points — not because the math is hard, but because one skipped setup step flips the answer. These 30 questions cover the calculations you will actually be asked to do: days supply, dose conversions, percentage strengths, dilutions, alligation, and IV flow rates. Every explanation walks through the setup so you can see exactly where each wrong option comes from.
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Question 1 of 30.A prescription reads: amoxicillin 500 mg capsules, 1 capsule by mouth three times daily, dispense #30. What is the days supply?
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A prescription reads: amoxicillin 500 mg capsules, 1 capsule by mouth three times daily, dispense #30. What is the days supply?
- 7 days
- 10 days (correct answer)
- 15 days
- 30 days
The patient takes 3 capsules per day (three times daily), so 30 capsules divided by 3 capsules/day = 10 days supply. Answering 15 days would come from assuming twice-daily dosing, and 30 days assumes only one capsule per day; both misread the frequency, which must always be converted to total units per day before dividing.
A patient uses 40 units of U-100 insulin every day. How many days will one 10 mL vial last?
- 25 days (correct answer)
- 28 days
- 30 days
- 50 days
U-100 insulin contains 100 units/mL, so a 10 mL vial holds 100 x 10 = 1,000 units. Dividing 1,000 units by 40 units/day = 25 days supply. The tempting answers of 28 or 30 days are common billing cycle lengths, but the actual days supply must be calculated from the units in the vial, not assumed from the typical fill period.
A 5 mL bottle of ophthalmic solution is prescribed as 1 drop in each eye twice daily. Using a conversion of 20 drops per mL, what is the days supply?
- 12 days
- 20 days
- 25 days (correct answer)
- 50 days
The bottle contains 5 mL x 20 drops/mL = 100 drops. The patient uses 1 drop x 2 eyes x 2 times daily = 4 drops per day, so 100 / 4 = 25 days supply. Choosing 50 days is the classic error of forgetting that 'each eye' doubles the daily usage to 4 drops instead of 2.
A prescription is written for 120 mL of cough syrup with directions to take 5 mL every 6 hours as needed. What is the maximum days supply?
- 24 days
- 12 days
- 8 days
- 6 days (correct answer)
Every 6 hours allows a maximum of 4 doses in 24 hours, so the patient can use up to 4 x 5 mL = 20 mL per day. Then 120 mL / 20 mL/day = 6 days supply. The answer 24 is the total number of doses in the bottle, not days, and 8 days would result from incorrectly assuming only 3 doses per day.
A prednisone taper is written as: 40 mg daily for 3 days, then 30 mg daily for 3 days, then 20 mg daily for 3 days, then 10 mg daily for 3 days. Using 10 mg tablets, how many tablets should be dispensed?
- 10 tablets
- 12 tablets
- 30 tablets (correct answer)
- 40 tablets
Convert each step to tablets per day: 40 mg = 4 tabs, 30 mg = 3 tabs, 20 mg = 2 tabs, 10 mg = 1 tab. Each step lasts 3 days, so the total is (4 + 3 + 2 + 1) x 3 = 10 x 3 = 30 tablets. The answer 10 counts only one day at each strength and forgets to multiply by the 3-day duration of each step, 12 is the length of the taper in days rather than a tablet count, and 40 confuses the starting daily dose in milligrams with the number of tablets.
A prescription calls for amoxicillin 600 mg twice daily for 10 days using a 400 mg/5 mL suspension. What total volume should be dispensed?
- 75 mL
- 100 mL
- 120 mL
- 150 mL (correct answer)
Each dose is (600 mg / 400 mg) x 5 mL = 7.5 mL. Twice daily gives 7.5 x 2 = 15 mL per day, and 15 mL x 10 days = 150 mL to dispense. The answer 75 mL is the tempting result of forgetting the twice-daily frequency and calculating for only one dose per day.
A prescription reads: instill 2 drops into the left eye three times daily for 10 days. Using 20 drops per mL, what volume of solution will the patient use?
- 3 mL (correct answer)
- 5 mL
- 6 mL
- 12 mL
The patient uses 2 drops x 3 times daily = 6 drops per day, and 6 x 10 days = 60 drops total. Converting to volume: 60 drops / 20 drops per mL = 3 mL. The answer 6 mL is the common error of doubling for both eyes, but this prescription specifies the left eye only.
How many grams of sodium chloride are contained in 500 mL of 0.9% sodium chloride (normal saline) solution?
- 0.45 g
- 0.9 g
- 4.5 g (correct answer)
- 9 g
A 0.9% w/v solution contains 0.9 g of drug per 100 mL. For 500 mL: 0.9 g x (500 / 100) = 0.9 x 5 = 4.5 g. The answer 0.9 g is only the amount in 100 mL, and 9 g would be the amount in a full liter, not 500 mL.
A pharmacy must prepare 500 g of a 40% ointment by mixing a 70% ointment with a 20% ointment. Using alligation, how many grams of the 70% ointment are needed?
- 100 g
- 200 g (correct answer)
- 250 g
- 300 g
By alligation, the 70% ointment contributes 40 - 20 = 20 parts and the 20% ointment contributes 70 - 40 = 30 parts, for 50 parts total. The 70% ointment is therefore (20 / 50) x 500 g = 200 g. Choosing 300 g reverses the alligation and gives the amount of the 20% ointment instead; the parts must be assigned diagonally, not straight across.
How many milliliters of a 25% stock solution are needed to prepare 1,000 mL of a 10% solution?
- 40 mL
- 250 mL
- 400 mL (correct answer)
- 500 mL
Using C1V1 = C2V2: 25% x V1 = 10% x 1,000 mL, so V1 = 10,000 / 25 = 400 mL of stock, then dilute to 1,000 mL. The answer 250 mL incorrectly multiplies 25% by 1,000 mL, confusing which concentration belongs with which volume in the equation.
A solution has a ratio strength of 1:400 w/v. What is its concentration in mg/mL?
- 0.25 mg/mL
- 0.4 mg/mL
- 1.25 mg/mL
- 2.5 mg/mL (correct answer)
A 1:400 w/v solution contains 1 g of drug in 400 mL. Converting to milligrams: 1,000 mg / 400 mL = 2.5 mg/mL. The answer 0.25 mg/mL is a decimal-place error from dividing 100 mg (instead of 1,000 mg) by 400 mL; ratio strengths are always defined in grams, so the gram must be converted to 1,000 mg first.
An injectable solution is labeled 50 mg/mL. What is its percentage strength (w/v)?
- 5% (correct answer)
- 10%
- 25%
- 50%
Percent w/v is grams per 100 mL. A 50 mg/mL solution contains 50 x 100 = 5,000 mg = 5 g per 100 mL, which equals 5%. The tempting answer 50% simply reuses the number from the mg/mL strength, but percent strength requires converting milligrams to grams per 100 mL.
A technician mixes 200 mL of a 10% solution with 300 mL of a 5% solution. What is the final concentration of the mixture?
- 6%
- 7% (correct answer)
- 7.5%
- 8%
Total drug: (200 x 0.10) + (300 x 0.05) = 20 g + 15 g = 35 g. Total volume: 200 + 300 = 500 mL, so the concentration is 35 / 500 = 0.07 = 7%. The answer 7.5% is the simple average of 10% and 5%, which is wrong because the volumes are unequal; the concentrations must be weighted by volume.
An IV order calls for 1,000 mL of normal saline to be infused over 8 hours. What is the flow rate in mL/hr?
- 80 mL/hr
- 100 mL/hr
- 125 mL/hr (correct answer)
- 150 mL/hr
Flow rate = total volume / total time = 1,000 mL / 8 hr = 125 mL/hr. The answer 100 mL/hr would only be correct for a 10-hour infusion; always divide by the actual infusion time stated in the order rather than a rounded time.
An IV of 1,000 mL is to run over 10 hours using tubing with a drop factor of 15 gtt/mL. What is the flow rate in drops per minute?
- 25 gtt/min (correct answer)
- 42 gtt/min
- 50 gtt/min
- 100 gtt/min
First find mL/hr: 1,000 / 10 = 100 mL/hr. Then convert to drops: 100 mL/hr x 15 gtt/mL = 1,500 gtt/hr, and 1,500 / 60 min = 25 gtt/min. The answer 100 is the rate in mL/hr, not gtt/min; the drop factor and the conversion to minutes must both be applied.
A 500 mL IV bag is infusing at 40 mL/hr. How long will the infusion last?
- 5 hours
- 8 hours
- 10 hours
- 12.5 hours (correct answer)
Infusion time = volume / rate = 500 mL / 40 mL/hr = 12.5 hours. Rounding down to 12 hours or estimating 10 hours understates the time; dividing 500 by 40 gives exactly 12.5, and partial hours are reported as decimals, not dropped.
A heparin infusion contains 25,000 units in 500 mL and is running at 20 mL/hr. How many units per hour is the patient receiving?
- 50 units/hr
- 500 units/hr
- 1,000 units/hr (correct answer)
- 1,250 units/hr
The concentration is 25,000 units / 500 mL = 50 units/mL. At 20 mL/hr, the patient receives 50 x 20 = 1,000 units/hr. The answer 1,250 units/hr comes from dividing 25,000 by 20, which incorrectly treats the pump rate as if it were the bag volume, and 50 reports the concentration in units/mL as if it were the hourly dose without ever applying the pump rate.
An IV admixture contains 2 g of drug in 250 mL and is infusing at 30 mL/hr. What dose is the patient receiving in mg/min?
- 2 mg/min
- 4 mg/min (correct answer)
- 8 mg/min
- 240 mg/min
The concentration is 2,000 mg / 250 mL = 8 mg/mL. At 30 mL/hr the patient receives 8 x 30 = 240 mg/hr, and 240 / 60 = 4 mg/min. The answer 240 is the correct hourly rate mislabeled as mg/min because the division by 60 minutes was skipped, 8 is the concentration in mg/mL rather than a dose rate, and 2 simply restates the grams in the bag.
A child weighing 44 lb is prescribed a drug at 15 mg/kg/day divided into two equal doses. How many milligrams are in each dose?
- 150 mg (correct answer)
- 300 mg
- 330 mg
- 660 mg
Convert weight: 44 lb / 2.2 = 20 kg. The daily dose is 15 mg x 20 kg = 300 mg, and dividing into two doses gives 300 / 2 = 150 mg per dose. The answer 300 mg is the total daily dose, and 330 mg results from multiplying by the weight in pounds instead of kilograms.
A pediatric patient weighing 25 kg is prescribed cefdinir at 14 mg/kg/day. What is the total daily dose?
- 175 mg
- 250 mg
- 300 mg
- 350 mg (correct answer)
Multiply the dose by the weight: 14 mg/kg x 25 kg = 350 mg per day. The answer 175 mg is half the daily dose and would only be correct if the question asked for one of two divided doses; since the weight is already given in kilograms, no pound conversion is needed.
A patient weighs 176 lb and is prescribed a drug dosed at 5 mg/kg. What is the correct dose?
- 200 mg
- 400 mg (correct answer)
- 500 mg
- 880 mg
Convert pounds to kilograms: 176 / 2.2 = 80 kg. Then 5 mg/kg x 80 kg = 400 mg. The answer 880 mg comes from multiplying 5 mg by the weight in pounds, the most common weight-based dosing error; always convert to kilograms first.
A 15 kg child is prescribed amoxicillin 40 mg/kg/day divided every 8 hours. The pharmacy stocks a 250 mg/5 mL suspension. How many milliliters should be given per dose?
- 2.5 mL
- 3 mL
- 4 mL (correct answer)
- 12 mL
The daily dose is 40 x 15 = 600 mg. Every 8 hours means 3 doses per day, so each dose is 600 / 3 = 200 mg. Converting to volume: (200 / 250) x 5 mL = 4 mL per dose. The answer 12 mL is the total daily volume, not the single-dose volume.
A prescription is written for gr iii (3 grains) of a drug. Using the standard conversion of 1 grain = 65 mg, how many milligrams is this?
- 130 mg
- 195 mg (correct answer)
- 300 mg
- 390 mg
Using 1 grain = 65 mg, 3 grains x 65 mg = 195 mg. The answer 130 mg misreads the Roman numeral iii as ii and converts only 2 grains, 390 mg doubles the result by misreading iii as vi (6 grains), and 300 mg incorrectly rounds a grain up to 100 mg instead of using the standard 65 mg conversion.
A prescription reads: take 1 tablespoonful by mouth three times daily for 10 days. What volume should be dispensed?
- 150 mL
- 225 mL
- 300 mL
- 450 mL (correct answer)
One tablespoonful = 15 mL, so the daily volume is 15 x 3 = 45 mL, and 45 x 10 days = 450 mL. The answer 150 mL comes from confusing a tablespoon (15 mL) with a teaspoon (5 mL), a threefold error that would cause significant underdispensing.
A levothyroxine tablet is labeled 0.125 mg. What is this strength in micrograms?
- 1.25 mcg
- 125 mcg (correct answer)
- 250 mcg
- 1,250 mcg
There are 1,000 mcg in 1 mg, so 0.125 mg x 1,000 = 125 mcg. The answer 1,250 mcg results from multiplying by 10,000 (a misplaced decimal), and 1.25 mcg from dividing instead of multiplying; both decimal errors are dangerous with a narrow-therapeutic-index drug like levothyroxine.
Convert a patient's temperature of 102.2 degrees Fahrenheit to Celsius.
- 39 degrees C (correct answer)
- 56.8 degrees C
- 70.2 degrees C
- 126.4 degrees C
Use the formula C = (F - 32) x 5/9. Substituting: 102.2 - 32 = 70.2, and 70.2 x 5/9 = 39 degrees C. The answer 70.2 stops after the subtraction without multiplying by 5/9, 56.8 skips the subtraction and multiplies 102.2 by 5/9 directly, and 126.4 multiplies 70.2 by 9/5 instead of 5/9; checking that the result is a plausible body temperature catches all three errors.
A pharmacy prices a drug at AWP plus 20% plus a $2.50 dispensing fee. If the AWP is $50.00, what is the retail price?
- $52.50
- $60.00
- $62.50 (correct answer)
- $72.50
Apply the markup first: $50.00 x 1.20 = $60.00, then add the dispensing fee: $60.00 + $2.50 = $62.50. The answer $60.00 forgets the dispensing fee, and $72.50 treats the 20% markup as a flat $20 added to the AWP.
A patient's insurance plan pays 80% of the cost of a prescription and the patient pays the remaining coinsurance. If the total cost is $120.00, how much does the patient pay?
- $20.00
- $24.00 (correct answer)
- $40.00
- $96.00
The patient owes 100% - 80% = 20% of the cost: $120.00 x 0.20 = $24.00. The answer $96.00 is the 80% portion the insurance pays, not the patient's share, and $20.00 mistakes the 20% coinsurance rate for a flat $20 copay.
A third-party plan reimburses the pharmacy at AWP minus 15% plus a $3.50 dispensing fee. If the AWP is $80.00, what is the total reimbursement?
- $64.50
- $68.00
- $68.50
- $71.50 (correct answer)
Calculate AWP minus 15%: $80.00 x 0.85 = $68.00, then add the dispensing fee: $68.00 + $3.50 = $71.50. The answer $68.00 omits the dispensing fee, and $68.50 incorrectly subtracts a flat $15.00 instead of 15% of the AWP.
A customer purchases an over-the-counter product priced at $84.00 with a 15% discount. What is the final price before tax?
- $71.40 (correct answer)
- $79.80
- $84.00
- $96.60
The discount is $84.00 x 0.15 = $12.60, so the final price is $84.00 - $12.60 = $71.40 (equivalently, $84.00 x 0.85). The answer $96.60 adds the 15% instead of subtracting it, which would be a markup rather than a discount.
FAQ: Pharmacy Math on the PTCE
How much math is on the PTCE?
Calculations are not a separate section — they appear inside Order Entry and Processing, which makes up 21.25% of the scored questions, and can surface in other domains too. Expect days supply, quantity to dispense, unit conversions, percentage strengths, and dilution problems. An on-screen calculator is built into the exam, and you can ask the test administrator for a handheld one if you prefer.
What conversions and formulas should I memorize for the PTCE?
The workhorses are: 1 kg = 2.2 lb, 1 tsp = 5 mL, 1 tbsp = 15 mL, 1 fl oz = about 30 mL, and percentage strength as grams per 100 mL (or per 100 g). Add ratio strengths (1:1000 means 1 g per 1,000 mL), the alligation grid for combining two strengths, and the days-supply setup: total quantity dispensed divided by total units taken per day. Every explanation in this drill shows the setup so you can rebuild it from scratch.
What should I do if I miss several pharmacy math questions?
Rework every missed problem on paper before reading the explanation, then compare your setup line by line. Most math mistakes on the PTCE are setup mistakes — a skipped unit conversion or a misread frequency — not arithmetic. Two or three cycles of retake-and-rework is usually enough to push a math score above 80%.
Are these questions taken from the real PTCE?
No. Real PTCE items are confidential and belong to PTCB — be wary of any site claiming to have them. Our questions are original, written to mirror the style, difficulty, and published content outline of the exam. Scoring well here is strong evidence you are ready, not a preview of the exact questions you will see.
Is this practice test really free?
Yes. Every question, explanation, and score report on PharmacyTechTest is free, with no signup, no credit card, and no trial that expires. Retake any test as many times as you want.
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