About this test
Pharmacy calculations are woven throughout the PTCE: the 2026 content outline flags calculation-based knowledge in every domain, from days supply and dilutions in Order Entry to dose checks in Medications. Math questions are also where prepared candidates gain the most ground, because unlike recall questions, they're 100% learnable.
Every question in this practice test includes a complete worked solution, and each distractor is a real calculation mistake (inverted ratio, decimal shift, wrong conversion factor), so reviewing your errors teaches you exactly which step went wrong.
New to the material? Work through our 2026 PTCB study guide first.
Then reinforce it one topic at a time with how to calculate days supply, how to calculate alligation, pharmacy math conversions, IV flow rate and drip rate calculations, and concentrations and dilutions.
What's in the question bank
| Topic | Questions in bank |
|---|---|
| Unit Conversions | 4 |
| Ratio Proportion | 4 |
| Percentage Strength | 4 |
| Dilutions Alligation | 4 |
| Days Supply | 3 |
| Dosage By Weight | 3 |
| Iv Drip Rates | 3 |
| Business Math | 3 |
Sample questions with answers
These 8 questions come straight from the 30-question bank the timed test above draws from. Work each one before you open the answer: recalling it cold is what moves it into long-term memory.
1. How many milliliters of isopropyl alcohol are needed to compound 480 mL of a 70% (v/v) isopropyl alcohol solution?
- A.144 mL
- B.33.6 mL
- C.686 mL
- D.336 mL
Show answer and explanation
Correct answer: D. 336 mL
Step 1: A 70% v/v solution contains 70 mL of alcohol per 100 mL of final solution. Step 2: Multiply: 0.70 x 480 mL = 336 mL of isopropyl alcohol. Note: 144 mL is the volume of the diluent (the other 30%), not the alcohol; 686 mL comes from dividing 480 by 0.70 instead of multiplying.
2. How many milliliters of a 10% stock solution are required to prepare 250 mL of a 2% solution?
- A.25 mL
- B.50 mL
- C.125 mL
- D.5 mL
Show answer and explanation
Correct answer: B. 50 mL
Step 1: Use the dilution equation C1V1 = C2V2. Step 2: Plug in: 10% x V1 = 2% x 250 mL. Step 3: Solve: V1 = (2 x 250) / 10 = 500 / 10 = 50 mL of stock, then q.s. with diluent to 250 mL. Inverting the concentrations (10 x 250 / 2) would give 1,250 mL, and 25 mL comes from halving instead of solving the equation.
3. A compounding order calls for 120 g of a 5% ointment. The pharmacy stocks a 10% ointment and a 2% ointment. Using alligation, how many grams of the 10% ointment are required?
- A.75 g
- B.60 g
- C.45 g
- D.36 g
Show answer and explanation
Correct answer: C. 45 g
Step 1: Set up the alligation grid with 10% (high), 2% (low), and 5% (desired). Step 2: Parts of 10% = 5 - 2 = 3 parts; parts of 2% = 10 - 5 = 5 parts; total = 8 parts. Step 3: Grams of 10% ointment = 120 g x (3/8) = 45 g. Choosing 75 g mixes up the parts (that is the amount of the 2% ointment).
4. A technician dilutes 50 mL of 50% dextrose injection to a final volume of 250 mL with sterile water for injection. What is the percentage strength of the final solution?
- A.10%
- B.25%
- C.5%
- D.20%
Show answer and explanation
Correct answer: A. 10%
Step 1: Use C1V1 = C2V2. Step 2: Plug in: 50% x 50 mL = C2 x 250 mL. Step 3: Solve: C2 = 2,500 / 250 = 10%. A quick check: the volume increased 5-fold (50 mL to 250 mL), so the strength drops 5-fold (50% to 10%). The 25% answer comes from halving instead of using the 5-fold dilution factor.
5. How many milliliters of sterile water must be ADDED to 120 mL of a 25% solution to reduce it to a 10% solution?
- A.300 mL
- B.120 mL
- C.48 mL
- D.180 mL
Show answer and explanation
Correct answer: D. 180 mL
Step 1: Find the final volume with C1V1 = C2V2: 25% x 120 mL = 10% x V2, so V2 = 3,000 / 10 = 300 mL. Step 2: The question asks for the water ADDED, so subtract the starting volume: 300 mL - 120 mL = 180 mL. Answering 300 mL is the classic trap of reporting the final volume instead of the added diluent.
6. A prescription reads: metoprolol 50 mg, take 1 tablet by mouth twice daily, quantity dispensed #60. What is the days' supply?
- A.15 days
- B.30 days
- C.60 days
- D.45 days
Show answer and explanation
Correct answer: B. 30 days
Step 1: Calculate the daily usage: 1 tablet x 2 doses per day = 2 tablets/day. Step 2: Divide the quantity dispensed by the daily usage: 60 tablets / 2 tablets per day = 30 days. Answering 60 days ignores the twice-daily dosing; 15 days doubles the daily use by mistake.
7. A pharmacy dispenses 150 mL of an antibiotic suspension with the directions: give 5 mL by mouth three times daily. What is the days' supply?
- A.5 days
- B.15 days
- C.10 days
- D.30 days
Show answer and explanation
Correct answer: C. 10 days
Step 1: Calculate the daily volume: 5 mL x 3 doses per day = 15 mL/day. Step 2: Divide the total volume by the daily volume: 150 mL / 15 mL per day = 10 days. Answering 30 days uses only one 5 mL dose per day; 5 days doubles the daily volume by mistake.
8. A patient injects insulin glargine U-100, 35 units subcutaneously twice daily, using a 10 mL vial. How many full days will one vial last?
- A.14 days
- B.28 days
- C.15 days
- D.10 days
Show answer and explanation
Correct answer: A. 14 days
Step 1: U-100 insulin contains 100 units/mL, so a 10 mL vial holds 100 x 10 = 1,000 units. Step 2: Calculate daily use: 35 units x 2 = 70 units/day. Step 3: Divide: 1,000 / 70 = 14.28..., which is 14 full days (round DOWN for days' supply; the partial 15th day cannot be completed from the vial). Answering 28 days forgets that the dose is given twice daily.
Ready for the full timed run? Scroll back up and start the Pharmacy Math Practice, or browse every free PTCB quiz by exam domain.
Key concepts to know
The conversions you must own
1 kg = 2.2 lb, 1 tsp = 5 mL, 1 tbsp = 15 mL, 1 fl oz = 30 mL (household convention), 1 gr = 65 mg (pharmacy convention), 1 L = 1,000 mL. Most exam math errors are conversion errors, not arithmetic errors.
Ratio & proportion solves most problems
Set the known relationship on one side, the unknown on the other, cross-multiply, and sanity-check the units. If your answer's units don't match the question, you inverted something.
Alligation for mixing strengths
When mixing a higher and lower strength to hit a target concentration, alligation gives the parts of each: differences on the diagonal become the ratio. It turns an intimidating problem into subtraction.
Pharmacy Math Practice: FAQ
How much math is on the PTCB exam?
PTCB doesn't publish an exact count, but the 2026 content outline marks calculation-based knowledge areas in all four domains, with the heaviest concentration in Order Entry & Processing (22.5% of the exam). Expect roughly 10-15 questions with a calculation component.
Can I use a calculator on the PTCE?
Yes, an on-screen calculator is provided in the Pearson VUE testing software. You can't bring your own.
Official sources checked
This quiz's content and explanations are built from and cross-checked against primary sources. Verify current exam facts directly with PTCB.