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Quizzes > Mathematics > Basic Math & Arithmetic

PTCB Calculations Quiz - Test Your Pharmacy Tech Math Skills

Take our free PTCB exam practice test and master pharmacy technician math practice!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration for PTCB practice quiz with pharmacy tech math problems on a coral background.

Use these PTCB practice questions to sharpen your pharmacy math, from dosage calculations to concentration conversions, and build speed and accuracy. After you finish, spot gaps before the exam, then try our full practice test and explore extra math practice to focus your study.

Convert 2500 milligrams to grams.
250 g
0.25 g
25 g
2.5 g
To convert milligrams to grams, divide by 1,000. Thus, 2,500 mg ÷ 1,000 = 2.5 g. This basic metric conversion is essential for accurate dosing in pharmacy practice.
How many milliliters are needed for a 150 mg dose if the solution strength is 50 mg per 5 mL?
20 mL
5 mL
15 mL
10 mL
Use the ratio method: (Desired Dose ÷ Concentration) × Volume = (150 mg ÷ 50 mg) × 5 mL = 15 mL. This ensures precise medication delivery. Always confirm calculations against reference materials.
What is the percentage strength (w/v) of a solution containing 10 grams of drug in 1 liter of solution?
10%
0.1%
1%
100%
Percentage strength (w/v) is grams per 100 mL. Here, 10 g per 1,000 mL is equivalent to 1 g per 100 mL, or 1%. This calculation aids in preparing accurate solutions.
A prescription calls for 2 teaspoons of liquid medication. How many milliliters should be dispensed?
15 mL
5 mL
4 mL
10 mL
One teaspoon is equivalent to 5 mL, so 2 teaspoons equal 10 mL. Proper household-to-metric conversion is critical for safe administration. Always verify standard conversion charts.
How many grams of sodium chloride are contained in 500 mL of a 0.9% (w/v) solution?
4.5 g
9 g
45 g
0.45 g
A 0.9% solution has 0.9 g per 100 mL; for 500 mL, multiply 0.9 g × 5 = 4.5 g. This is standard for normal saline. Accurate calculation ensures correct electrolyte therapy.
Convert 0.2 liters to milliliters.
200 mL
2,000 mL
20 mL
20,000 mL
To convert liters to milliliters, multiply by 1,000. Thus, 0.2 L × 1,000 = 200 mL. Metric conversions prevent dosing errors.
A patient weighing 70 kg is prescribed a drug at 10 mg/kg. What total dose should be prepared?
70 mg
70 g
700 mg
7 g
Multiply the patient's weight by the per-kilogram dose: 70 kg × 10 mg/kg = 700 mg. Weight-based dosing is common in PTCB calculations. Always verify with patient weight records.
If 30 tablets of 250 mg each are dispensed, what is the total amount of drug in grams?
7.5 g
0.75 g
75 g
750 g
Total drug = 30 tablets × 250 mg = 7,500 mg = 7.5 g. Summing individual tablet doses is essential for inventory checks.
An IV infusion is set at 120 mL/hr with a drop factor of 15 gtt/mL. What is the drop rate in gtt/min?
120 gtt/min
15 gtt/min
60 gtt/min
30 gtt/min
mL per minute = 120 mL/hr ÷ 60 = 2 mL/min. Multiply by the drop factor: 2 × 15 = 30 gtt/min. Accurate drip-rate calculations prevent infusion errors.
After reconstituting a 500 mg vial with 5 mL sterile water, what is the resulting concentration?
100 mg/mL
50 mg/mL
500 mg/mL
10 mg/mL
Concentration = total drug ÷ total volume: 500 mg ÷ 5 mL = 100 mg/mL. Accurate reconstitution is vital to maintain dosing precision.
If 2 g of medication are added to 250 mL D5W and ordered to infuse over 4 hours, what is the infusion rate in mL/hr?
62.5 mL/hr
100 mL/hr
50 mL/hr
75 mL/hr
Infusion rate = total volume ÷ time: 250 mL ÷ 4 hr = 62.5 mL/hr. This ensures the correct dose is delivered over the prescribed period.
Calculate the body surface area (BSA) for a patient weighing 60 kg and 160 cm tall using the Mosteller formula.
1.2 m²
2.0 m²
1.8 m²
1.63 m²
Mosteller formula: BSA = ?[(height cm × weight kg) ÷ 3600] = ?[(160×60) ÷ 3600] ? 1.63 m². BSA is important for many chemotherapy and pediatric doses.
An order requires 20 mEq of potassium chloride in 100 mL to infuse over 2 hours. What is the infusion rate in mEq/hr?
5 mEq/hr
40 mEq/hr
10 mEq/hr
20 mEq/hr
Rate in mEq/hr = total mEq ÷ time: 20 mEq ÷ 2 hr = 10 mEq/hr. This calculation ensures safe electrolyte replacement.
A pediatric order calls for amoxicillin 5 mg/kg for a 15 kg child. What dose should be administered?
50 mg
75 mg
15 mg
100 mg
Multiply weight by dose: 15 kg × 5 mg/kg = 75 mg. Pediatric dosage calculations require precision to ensure safety.
How many grams of dextrose are needed to prepare 500 mL of a 10% (w/v) solution?
5 g
50 g
100 g
10 g
A 10% solution has 10 g per 100 mL. For 500 mL: 10 g × 5 = 50 g. This is essential for accurate parenteral nutrition compounding.
To dilute insulin from 2 mg/mL to 1 mg/mL, how many milliliters of diluent are needed for 10 mL of stock solution?
20 mL
10 mL
15 mL
5 mL
Desired volume = (Concentration stock × Volume stock) ÷ Desired concentration = (2 mg/mL × 10 mL) ÷ 1 mg/mL = 20 mL. You have 10 mL stock, so add 10 mL diluent.
Using alligation, how many milliliters of 25% solution are needed to prepare 100 mL of a 20% solution by mixing with a 10% solution?
40 mL
50 mL
66.7 mL
33.3 mL
Alligation: (Desired - Low)/(High - Low) × Total = (20 - 10)/(25 - 10) × 100 = (10/15) × 100 = 66.7 mL of the 25% solution. The rest is the 10% solution. Alligation is key for compounding varying concentrations.
A medication is ordered at 4 mcg/kg/min for a 70 kg patient. The stock concentration is 400 mcg/mL. What is the infusion rate in mL/hr?
42 mL/hr
18 mL/hr
56 mL/hr
28 mL/hr
Dose in mcg/min = 4 × 70 = 280 mcg/min. Convert to hourly: 280 × 60 = 16,800 mcg/hr. At 400 mcg/mL, 16,800 ÷ 400 = 42 mL/hr.
An IV bag contains 20 mEq KCl in 250 mL. If the order is 20 mEq/hr, what rate in mL/hr should be set?
125 mL/hr
50 mL/hr
100 mL/hr
250 mL/hr
20 mEq in 250 mL means each mEq = 12.5 mL. For 20 mEq/hr: 20 × 12.5 = 250 mL/hr. Correct drip rates prevent hyperkalemia or hypokalemia.
Ceftriaxone 2 g is to be infused over 30 minutes. The reconstituted concentration is 200 mg/mL. What infusion rate in mL/hr is required?
10 mL/hr
40 mL/hr
20 mL/hr
30 mL/hr
Total volume = 2000 mg ÷ 200 mg/mL = 10 mL. To infuse in 0.5 hr, rate = 10 mL ÷ 0.5 hr = 20 mL/hr. Ensures correct antibiotic exposure time.
To prepare 1 L of 3:1 TPN using dextrose 70% and amino acids 10%, how many milliliters of each component are required?
600 mL dextrose, 400 mL amino acids
500 mL dextrose, 500 mL amino acids
800 mL dextrose, 200 mL amino acids
750 mL dextrose, 250 mL amino acids
Ratio 3:1 means 3 parts dextrose, 1 part amino acids for a total of 4 parts. 1 L ÷ 4 = 250 mL per part; dextrose = 3×250 = 750 mL, amino acids = 250 mL. Proper compounding is critical for TPN safety.
What is the osmolarity (mOsm/L) of a 5% dextrose solution in 500 mL? (MW dextrose = 180.16 g/mol)
333 mOsm/L
277 mOsm/L
250 mOsm/L
500 mOsm/L
5% = 5 g/100 mL = 50 g/L. Moles = 50 g ÷ 180.16 g/mol = 0.277 mol/L. Dextrose is non-electrolyte, so Osm = 277 mOsm/L.
According to USP, what is the beyond-use date for a non-sterile aqueous formulation stored at room temperature?
7 days
30 days
90 days
14 days
USP guidelines specify a maximum 14-day beyond-use date for non-sterile aqueous formulations at room temperature. This helps ensure product stability and safety. Always follow USP chapters for compounding.
Calculate the osmolarity of a solution containing 150 mEq of Na? and 150 mEq of Cl? in 1 L of solution.
225 mOsm/L
600 mOsm/L
150 mOsm/L
300 mOsm/L
Monovalent ions: mEq ? mmol. Total osmoles = 150 mmol Na? + 150 mmol Cl? = 300 mOsm/L. Calculating osmolarity is key for IV fluid selection.
A lyophilized powder is reconstituted to 50 mg/mL. If the half-life of degradation is 12 hours, how much drug remains per mL after 8 hours?
20 mg/mL
45 mg/mL
38 mg/mL
31 mg/mL
First-order decay: remaining = 50 mg × (1/2)^(8/12) ? 50 × 0.613 = 30.7 mg/mL ? 31 mg/mL. This calculation guides stability and use-up timelines.
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Study Outcomes

  1. Apply Dosage Math Strategies -

    Use targeted techniques to accurately calculate medication dosages and concentration strengths for diverse prescription scenarios.

  2. Perform Unit Conversions -

    Convert between metric, apothecary, and household systems with confidence to tackle pharmacy technician math practice challenges.

  3. Solve Pharmacy Tech Math Problems -

    Work through realistic free PTCB practice questions to strengthen your approach to common dosage calculation exercises.

  4. Assess Strengths and Weaknesses -

    Analyze your performance on PTCB 90-question practice test items to identify areas for targeted review.

  5. Improve Speed and Accuracy -

    Develop time-management skills and precision techniques to boost your performance on a free PTCB exam practice test.

  6. Build Exam-Day Confidence -

    Gain familiarity with pharmacy technician math practice formats to approach the PTCB exam with reduced anxiety and increased certainty.

Cheat Sheet

  1. Ratio & Proportion Calculations -

    Understanding ratio and proportion is essential for solving core pharmacy tech math questions, especially when you dive into free PTCB practice questions. Set up relationships like dosage on hand/quantity on hand = dosage desired/quantity desired, then cross-multiply and divide to find the unknown. As ASHP emphasizes, repeated practice on university-mandated problems builds instinctive calculation skills.

  2. Dimensional Analysis (Factor Label Method) -

    Dimensional analysis, or the factor label method, ensures you track and cancel units systematically - this method is endorsed by University of Florida's College of Pharmacy. For instance, to convert 250 mg to grams, multiply 250 mg × (1 g/1000 mg) = 0.25 g, and watch the mg units cancel out.

  3. Weight-Based Dosage Calculations -

    Weight-based dosing, a staple in pediatric pharmacy, uses the formula Dose (mg) = mg/kg × patient weight (kg); for example, a 20 kg child receiving 5 mg/kg needs 100 mg of medication. Reliable sources like the FDA's dosing guidelines stress the importance of accurate weight measurement to avoid under- or overdosing.

  4. Concentration & Dilution Formulas (C1V1 = C2V2) -

    Knowing how to use C1V1 = C2V2 is vital for preparing dilutions; this formula directly links initial concentration and volume to final concentration and volume. For example, to prepare 500 mL of a 2% solution from a 5% stock, set 5% × V1 = 2% × 500 mL, giving V1 = 200 mL of stock plus 300 mL diluent. According to USP chapter 771, mastering this relationship minimizes compounding errors.

  5. IV Flow Rate & Drop Factor Computations -

    Calculating IV flow rates often uses the formula (Total Volume × Drop Factor) / Time (minutes) = drops per minute, or simply mL/hour on infusion pumps. Pharmacy tech math practice from the University of Michigan highlights that understanding both manual drips and pump programming ensures safe, accurate patient care.

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