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Sample Math Questions for the PTCB Exam!

Jun 25th, 2022
math questions for the ptcb exam

PTCB Math Made Simple

For many students, pharmacy math is one of the most challenging parts of the PTCB exam. There is a lot of ground to cover, and getting your ahead around the many types of questions can prove difficult. Here, we have put together some core math questions for the PTCB exam that you need to know.

As the adage goes, practice makes perfect. You need to practice as many sample math questions for the PTCB exam. The more questions you practice, the better. And it doesn’t matter if you get the questions wrong. Ultimately, you must start somewhere – and the great thing about detailed answer explanations is that you can plug any knowledge gaps you may have.

Practice questions give you the chance to audit your existing knowledge base – identifying both your strengths and weaknesses. That way, you can adjust your study plan going forward: investing more time on those weaknesses, and less time on your strengths – which you only need to occasionally revise to keep on top of things.

At first, math is difficult. With practice, it becomes effortless.

Here, we have put together a range of four PTCB math questions – some easy, some not so easy.

Attempt each question first before reading our prepared answers. That way, you can identify where you may have gone wrong. If you read the answer explanation first, it means you lose the opportunity to learn whether you were capable of answering it correctly to begin with.

Question 1

A patient must be administered an IV infusion of a medicine over the course of 7 hours. If the total volume of the infusion is 0.8L, what is the infusion rate in mL/min?

First, always identify units.

In this question, we have competing units. On the one hand, it details hours and liters, but the question asks us to deliver the answer in milliliters and minutes. This means that we need to convert between units.

In this case:

  • There are 60 minutes in 1 hour, or 420 minutes in 7 hours.
  • There are 1,000mL in 1 liter, meaning 0.8L contains 800mL.

Now that we have resolved the issue of units, we can continue to answer the question.

800mL is the total infusion, which is infused intravenously into the patient over a 420-minute period.

Therefore, 800mL / 420 minutes = 1.9 mL/min

You may ask, why isn’t it 420 minutes / 800mL?

Think about the order of units. The question asks us for mL/min. Therefore, the mL must be the numerator (top value in a fraction) and min must be the denominator (bottom value in a fraction).

Answer: 1.9mL per minute is infused into the patient over a 7-hour period.

At the end of the 7-hour period, all 800mL will have been administered.

Question 2

How much hydrocortisone powder is needed to compound 80 g of hydrocortisone cream at 1% concentration?

Concentrations are routinely asked on the PTCB test.

In this case, we are talking about solids and semisolids – powers/creams etc.

A 1% concentration = 1 gram of active ingredient in 100 grams of medicine.

In this case, we have 80 grams of cream. The question asks us to find out how much of that 80 grams is hydrocortisone powder. After all, creams are not just made from active ingredients (the drug). They are also formulated with non-active ingredients such as diluents, vehicles, and preservatives, to name a few. Non-active ingredients in a medicine are referred to as excipients.

Therefore, in this case, 1% of 80 grams = 0.8 grams

The other 99.2% are non-active ingredients.

Answer: 0.8 grams of hydrocortisone powder is needed to produce 80 grams of hydrocortisone cream at a concentration of 1%.

Question 3

How many mL of 60% alcohol should be mixed with 30% alcohol to prepare 50 mL of 50% alcohol?

At first, these kinds of question can seem difficult. It may be challenging to get your ahead around exactly what is going on.

Let’s try and break this one down into its component parts.

We have two solutions of differing concentrations:

  • An alcohol solution of 60 percent concentration.
  • A second alcohol solution of 30 percent concentration.

The question is asking us to mix these solutions together to produce 50mL of 50% concentration.

In other words, should we add 10mL of 60% solution with 40mL of 30% solution to produce 50mL of solution? Are these the correct quantities? That is the principle behind this question – to establish exactly how much of both solutions must be mixed together.

One of the simplest ways to answer this question is to use the alligation method. Alligation math questions for the PTCB exam have become more common in recent years.

To use the method, you must work through the problem in the following format:

  • Solution of Highest Concentration = 60 percent
  • Solution of Lowest Concentration = 30 percent
  • Solution of Desired Concentration = 50 percent

Now, we must:

  • Subtract lower concentration from desired concentration = 20
  • Subtract desired concentration from higher concentration = 10

The ratio is therefore 20 : 10.

20 : 10 is the same as 20 parts : 10 parts

Total number of parts = 30 parts

(20 / 30) x 50mL = 33.3mL of 60% solution needed

(10 / 30) x 50mL = 16.7mL of 30% solution needed

Conclusion – when we add together 33.3mL of 60% solution and 16.7mL of 30% solution, it gives us a solution of 50mL with a concentration of 50%.

Alligation questions are routinely asked on the PTCB exam. It is important that you commit this method to memory to ensure that you are fully prepared for this style of question.

Question 4

A pharmacy technician receives a prescription for carboplatin 50mg/m2 per dose. If the BSA of the patient is 1.4m2, how many milligrams of carboplatin are needed to satisfy the prescription?

Doses are not always determined based on whether the patient is an adult or a child. In some cases, the body surface area of the patient is needed to calculate the dose.

In this case, we are told that carboplatin – an anticancer drug – must be administered at a dose of 50 milligrams per every 1 meter squared of the body surface area (BSA) of the patient.

BSA of the patient = 1.4m2

Therefore: (1.4m2) x 50mg = 70 milligrams are needed

Intuitively, this makes sense. After all, if 50mg must be given for 1 meter squared, then clearly the dose of the medicine must be higher than 50mg for a patient who is 1.4 meters squared.

Answer: 70mg of carboplatin is needed for a patient whose BSA is 1.4m2

Final Thoughts

Studying pharmacy technician math doesn’t have to be difficult.

What matters is that you do not fall into the trap of memorizing methods for the sake of it.

You need to understand the method of resolving each problem. That way, you can identify how to solve a similar problem that is not the same as what you originally learned. If you find yourself memorizing methods for the sake of it, you will find it very difficult to adapt to new problems, even if they look similar to the questions you practiced up to this point.

Above, we broke each question down into its component parts – explaining the thought process behind each question and answer. This is the kind of preparation that you – the student – must apply to your own study.

Initially, this will take time, particularly if math is not your thing. But do remember – that accuracy is particularly important in pharmacy. By learning math, you are learning how to be accurate with patient’s lives.

Therefore, do not treat this subject lightly.

Consider it an important knowledge skill of your career, and one that helps to prevent medication errors from taking place.

For more in-depth feature lessons and full-length exams on math questions for the PTCB exam, become a registered member of PTCB Test Prep today. There, you can access our self-paced course that has helped thousands of students navigate their way through all modules of the 2022 PTCB examination.

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PTCB Test Prep Author


Elaine Walker

Elaine joined PTCB Test Prep in 2017, currently serving as the lead product development manager overseeing both course development and quality improvement. Mrs. Walker is a graduate of California State University and has worked as a pharmacy technician for over twenty years – with particular interests in pediatric pharmacy, extemporaneous compounding, and hospital pharmacy. Over the past 8-years, she has helped prepare thousands of students for the PTCB examination.