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What Math Gets Tested on the PTCB Exam?

Math is primarily tested as part of the Order Entry and Processing knowledge domain of the PTCB exam, though math may be tested across all four knowledge domains.

There are fourteen examinable topics on the PTCB exam:

Topic About
Dosing / quantities Determining the correct amount of drug a patient needs based on their prescription, weight, age, and condition to ensure safe, effective treatment.
Formulas Standardized mathematical expressions used to calculate drug doses, concentrations, compounding measurements, and other pharmacy-related values accurately and consistently.
Alligations A method for calculating the proportions of two solutions with different concentrations to create a desired final strength, often used in compounding.
Concentrations The measure of how much active ingredient is present in a solution, usually expressed as a percentage, ratio, or weight/volume.
Dilutions Reducing the strength of a solution by adding a diluent, calculated to achieve the desired concentration without affecting medication safety.
Conversions Changing units between systems (metric, household, apothecary) to ensure accurate dosing and prevent medication errors in pharmacy calculations.
Roman numerals Number system often used in prescriptions and compounding; pharmacy technicians must interpret them correctly to ensure accurate dosing and labeling.
Prescription interpretation Reading and understanding written prescriptions, including abbreviations, drug names, strengths, quantities, and directions, to ensure correct dispensing.
Compounding non-sterile medicines Preparing customized medications (creams, capsules, solutions) in a clean environment without the strict sterility required for injectable drugs.
IV flow rates and infusions Calculating how quickly intravenous fluids or drugs should be administered, often measured in mL/hour or drops/minute.
Body mass index (BMI) A calculation using height and weight to estimate body fat, sometimes used to determine safe dosing ranges for certain drugs.
Body surface area (BSA) A measurement based on height and weight used to calculate doses for chemotherapy and other body-size–dependent drugs.
Pediatric dosage calculations Determining safe doses for children, often based on weight (mg/kg) or body surface area, to avoid under- or overdosing.
Retail pharmacy Community pharmacy setting focused on dispensing drugs, counseling patients, handling insurance claims, and performing basic pharmacy math calculations.

Preparing for PTCB Math Questions.

Many pharmacy technicians understandably feel intimidated by PTCB math, but with the right approach, it becomes much more manageable.

The key is breaking concepts down into smaller, repeatable skills and practicing them until they become second nature. Focus on accuracy first — speed will come naturally as you build confidence.

Always work through problems step-by-step, double-check your units, and understand why formulas work, not just how to plug in numbers.

Review core topics daily

Review core topics daily.

Dosing, conversions, concentrations, and IV calculations are high-yield areas you’ll see on the exam.

Use a formula sheet

Use a formula sheet.

Keep key equations and conversion factors handy for quick reference during study sessions.

Practice without a calculator

Practice without a calculator.

While you may have one during the exam, working manually sharpens your skills and reduces careless errors.

Check your units

Check your units.

Mismatched units are one of the biggest causes of calculation mistakes in pharmacy math.

Simulate exam conditions

Simulate exam conditions.

Time yourself on practice questions to build speed and reduce test-day stress. Practicing under timed conditions tests your ability to work under pressure.

Work on weak areas first

Work on weak areas first.

Identify topics you struggle with and give them extra attention before moving on. We too often gravitate toward the topics we’re most comfortable with.

Consistent, focused practice will help you approach the PTCB math section with confidence

Consistent, focused practice will help you approach the PTCB math section with confidence — and avoid last-minute cramming that can lead to avoidable mistakes.

Sample PTCB Math Questions.

The best way to get comfortable with pharmacy math is through practice – and lots of it.

The sample PTCB math questions below reflect the style, format, and difficulty of math questions tested on the real exam. They’re designed to show you exactly what kind of math problems appear on the test — and how challenging they can be — so you can prepare your long-term study plan accordingly.

Try answering each question on your own before checking the answer explanation. This approach helps reveal — and plug — any potential gaps in your understanding.

Topic – Dilutions

Sample Question.

A pharmacy technician has 500 mL of a 15% saline solution. How much water should they add to dilute the solution to 5% strength?

  • 1000 mL
  • 750 mL
  • 1500 mL
  • 1250 mL

Answer Explanation:

Step 1

To answer this question, we can use the dilution formula:
C1 × V1 = C2 × V2

Where:

  • C1 = 15% (initial concentration)
  • V1 = 500 mL (initial volume)
  • C2 = 5% (final concentration)
  • V2 = ? (final volume after adding water)

We have three variables of the equation, meaning we can use the formula to calculate the fourth variable.

Step 2

We need to calculate V2:

V2 =
C1 × V1
C2
 =
15 × 500
5
 = 1500 mL

Since the final volume is 1500 mL and the starting volume is 500 mL, the volume of water to add is:

1500 mL - 500 mL = 1000 mL

Note:

Many math problems can be solved in multiple ways. If formulas aren’t your strong suit, consider solving the math problem using basic logic.

For example:
since you want to dilute a 15% solution to 5%, the new concentration is one-third of the original (5% is one-third of 15%). This means the total volume must triple to reduce the strength by that amount.

You currently have 500 mL, so tripling it gives 1500 mL as the final volume. To reach 1500 mL, you need to add enough water to make up the difference:
1500 mL (final volume) – 500 mL (original volume) = 1000 mL of water.

So, the pharmacy technician should add 1000 mL of water.

Topic – IV Flow Rates and Infusions

Sample Question.

A pharmacy technician is preparing an IV infusion of 1500 mL to run over 6 hours. The IV tubing delivers 20 drops (gtt) per mL. What should be the flow rate in drops per minute (gtt/min)?

  • 50 gtt/min
  • 83 gtt/min
  • 100 gtt/min
  • 125 gtt/min

Answer Explanation:

Step 1

An IV infusion of 1500 mL is administered over 6-hours.
Therefore, 250mL of medicine is administered per hour (1500 mL / 6 hours).

Step 2

There are 60-minutes in an hour, so 4.17mL is administered per minute (250 mL / 60 minutes).

The question tells us that the IV tubing delivers 20 drops per mL.

Therefore:

4.17mL x 20 drops = 83.4 drops per minute

When rounded down, the answer is 83 drops / minute.
For questions like this, always work in a step-by-step manner.

Topic – Retail Pharmacy

Sample Question.

A pharmacy purchases a medicine for $15.00 and applies a 40% markup. At what price does the pharmacy need to sell the medicine?

  • $18.50
  • $19.50
  • $21.00
  • $22.50

Answer Explanation:

Step 1

Markup is the amount added to the cost price of a product to determine its selling price. In other words, it represents the retailer’s profit margin expressed as a percentage of the purchase cost.

To calculate markup amount, we use the following formula:
Markup amount = Purchase price × Markup percentage

Step 2

Let’s plug in the values from the question:

Markup amount = $15.00 x 40%
Markup amount = $6.00

With the markup amount known, we add this value to the cost price of the product:
$15.00 + $6.00 = $21.00

The cost price of the product for the pharmacy is $15.00 and when a 40% markup is applied, the pharmacy sells the produce to the public for $21.00.

Topic – Prescription Interpretation

Sample Question.

A prescription reads: "Take 1 tablet PO q6h x 7 days."
If the tablets come in bottles of 30, how many tablets should the pharmacy technician dispense?

  • 28 tablets
  • 30 tablets
  • 35 tablets
  • 42 tablets

Answer Explanation:

Step 1

First, let’s interpret the prescription and establish what it asks.

  • Prescription: Take 1 tablet PO q6h x 7 days
  • PO means by mouth
  • q6h means every 6 hours (4 times per day)
  • x 7 days means for 7 days

Step 2

4 tablets must be taken per day, or 28 tablets over the course of 7-days. This means the pharmacy technician should dispense 28 tablets to cover the full 7-day treatment (meaning only 1 bottle will need to be dispensed).

Topic – Concentrations

Sample Question.

A pharmacy technician prepares 250 mL of a solution containing 750 mg of a drug. The solution is further diluted with 500 mL of saline. What is the final concentration of the drug in mg/mL after dilution?

  • 0.5 mg/mL
  • 1 mg/mL
  • 2 mg/mL
  • 3 mg/mL

Answer Explanation:

Step 1

First, calculate the total volume after dilution.

  • Original solution volume = 250 mL
  • Diluent added = 500 mL

New total volume = 250 mL + 500 mL = 750 mL

Step 2

Identify the total amount of drug.

  • Total drug amount = 750 mg (unchanged by dilution volume added)

Step 3

Calculate the final concentration.

Concentration =
Total drug (mg)
Total volume (mL)
 =
750 mg
750 mL
 = 1 mg/mL
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