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PEBC Calculations Practice Questions

Dilutions, infusion rates, mcg/kg/min doses and prescription quantities: ten PEBC-style calculations with every step worked out.

Updated November 13, 2026. Written by RxReady to the 2026 PEBC blueprint. These are practice questions, not real or recalled exam questions.

Calculations are some of the most winnable marks on the PEBC MCQ. They follow a small number of patterns, and once the set-up is right the arithmetic is simple. Most lost marks come from unit slips, reading a final volume as the amount to add, or skipping a conversion.

Every answer below shows the full working and names the exact trap behind each wrong option, so you can see which mistake you made, not just that you made one.

Use the same habits on exam day: write the units on every line, estimate the answer before you calculate, and check that the result makes clinical sense.

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Ten calculations questions

Question 1 · Prescription calculation

A patient takes vitamin D 1,000 IU daily. How many micrograms is this? (1 mcg vitamin D = 40 IU)

  1. A2.5 mcg
  2. B25 mcg
  3. C40 mcg
  4. D250 mcg
Show the answer

Answer: B) 25 mcg

1,000 IU / 40 IU per mcg = 25 mcg.

Why the other options are wrong

  • A) 2.5 mcg is a tenfold error.
  • C) 40 mcg confuses the conversion factor with the answer.
  • D) 250 mcg is a tenfold error in the other direction.

Key point: Vitamin D: 40 IU = 1 mcg, so 1,000 IU = 25 mcg.

Question 2 · Prescription calculation

How many millilitres of 70% isopropyl alcohol are needed to make 500 mL of 20% isopropyl alcohol?

  1. Aabout 71 mL
  2. Babout 143 mL
  3. Cabout 175 mL
  4. Dabout 350 mL
Show the answer

Answer: B) about 143 mL

C1V1 = C2V2: 70% x V1 = 20% x 500 mL, so V1 = 142.9 mL.

Why the other options are wrong

  • A) 71 mL would make about a 10% solution.
  • C) 175 mL would make about 24.5%.
  • D) 350 mL is 70% of 500 mL; it confuses the stock percentage with the volume.

Key point: C1V1 = C2V2 works for v/v dilutions too.

Question 3 · Half-life calculation

A drug has a volume of distribution of 40 L and a clearance of 4 L/h. Its elimination half-life is closest to

  1. A0.1 hours
  2. B6.9 hours
  3. C10 hours
  4. D69 hours
Show the answer

Answer: B) 6.9 hours

k = CL/Vd = 4/40 = 0.1 h⁻¹; t½ = 0.693/k = 0.693/0.1 = 6.9 h. 10 hours is Vd/CL (the mean residence time for a one-compartment model), not the half-life, and 0.1 is the elimination rate constant.

Why the other options are wrong

  • A) 0.1 is the elimination rate constant (h⁻¹), not the half-life.
  • C) 10 h is Vd ÷ CL (mean residence time), not the half-life.
  • D) 69 h misplaces the decimal.

Key point: t½ = 0.693 × Vd ÷ CL.

Question 4 · Continuous infusion

If the rate of a continuous IV infusion of a drug with linear kinetics is doubled, which of the following is correct?

  1. ACss doubles; time to steady state halves
  2. BCss is unchanged; time to steady state halves
  3. CCss doubles; time to steady state is unchanged
  4. DCss doubles; time to steady state doubles
Show the answer

Answer: C) Css doubles; time to steady state is unchanged

Css = infusion rate / CL, so doubling the rate doubles Css when clearance is constant. Time to steady state depends only on half-life (about 4-5 half-lives), which is unchanged by the infusion rate.

Why the other options are wrong

  • A) Time to steady state depends only on half-life, not rate.
  • B) Css changes with infusion rate.
  • D) Time to steady state doesn't depend on the infusion rate.

Key point: Css = rate ÷ CL. Time to steady state depends only on half-life.

Question 5 · Dilution (% w/v)

How many millilitres of sterile water must be added to 50 mL of povidone-iodine 10% w/v solution to produce a 2% w/v solution?

  1. A10 mL
  2. B200 mL
  3. C250 mL
  4. D500 mL
Show the answer

Answer: B) 200 mL

C1V1 = C2V2: 10% x 50 mL = 2% x V2, so V2 = 250 mL; water to add = 250 - 50 = 200 mL. 250 mL is the final volume rather than the amount of diluent, 10 mL inverts the ratio (50 x 2/10), and 500 mL multiplies 50 mL by the stock strength (10) without dividing by the target strength.

Why the other options are wrong

  • A) 10 mL inverts the ratio (50 x 2/10).
  • C) 250 mL is the final volume, not the volume of water to add.
  • D) 500 mL multiplies 50 mL by 10 (the stock strength) and never divides by the 2% target.

Key point: Water to add = final volume - stock volume.

Question 6 · IV infusion rates

Heparin 25,000 units in 500 mL D5W is ordered to run at 1,000 units per hour. Which of the following is the correct infusion rate?

  1. A10 mL/h
  2. B40 mL/h
  3. C25 mL/h
  4. D20 mL/h
Show the answer

Answer: D) 20 mL/h

Concentration = 25,000 units ÷ 500 mL = 50 units/mL; 1,000 units/h ÷ 50 units/mL = 20 mL/h. Why not the others: A: Delivers 500 units/h, half the ordered dose. B: Delivers 2,000 units/h, double the order. C: Delivers 1,250 units/h, an overdose of a high-alert drug. Key takeaway: Rate = dose per hour ÷ concentration. Double-check high-alert infusions.

Why the other options are wrong

  • A) 10 mL/h delivers only 500 units/h, half the ordered dose.
  • B) 40 mL/h delivers 2,000 units/h, double the order.
  • C) 25 mL/h delivers 1,250 units/h, an overdose of a high-alert drug.

Key point: Rate = dose per hour / concentration. Double-check high-alert infusions.

Question 7 · Alligation and dilution

An order calls for 500 mL of 10% dextrose. Only 50% dextrose and 5% dextrose are available. How many mL of 50% dextrose are needed?

  1. A100 mL
  2. B55.6 mL
  3. C444.4 mL
  4. D111.1 mL
Show the answer

Answer: B) 55.6 mL

Alligation: 50% contributes (10 − 5) = 5 parts; 5% contributes (50 − 10) = 40 parts; total 45 parts. 50% dextrose = 5/45 × 500 mL = 55.6 mL (plus 444.4 mL of 5%). Why not the others: A: Ignores that the 5% diluent also adds dextrose. C: That's the volume of 5% dextrose, not 50%. D: Uses 10 parts instead of 5 for the strong solution. Key takeaway: Alligation: parts = difference between the other strength and the target.

Why the other options are wrong

  • A) 100 mL ignores that the 5% diluent also adds dextrose (500 x 10% / 50%).
  • C) 444.4 mL is the volume of 5% dextrose needed, not the 50%.
  • D) 111.1 mL uses 10 parts instead of 5 for the strong solution (10/45 x 500).

Key point: Alligation: parts of each = difference between the other strength and the target.

Question 8 · Dose from infusion rate (mcg/kg/min)

A 70 kg patient is receiving dobutamine 250 mg in 250 mL D5W at 21 mL/h. Which of the following is the dose the patient is receiving?

  1. A0.005 mcg/kg/min
  2. B0.3 mcg/kg/min
  3. C0.5 mcg/kg/min
  4. D5 mcg/kg/min
Show the answer

Answer: D) 5 mcg/kg/min

Concentration = 1 mg/mL, so 21 mL/h = 21 mg/h = 21,000 mcg/h / 60 = 350 mcg/min; 350 / 70 kg = 5 mcg/kg/min. 0.005 is the dose in mg/kg/min mislabelled as mcg, 0.3 is the dose in mg/kg/h (21/70) mislabelled, and 0.5 mcg/kg/min is a tenfold error in the conversion.

Why the other options are wrong

  • A) 0.005 is the dose in mg/kg/min mislabelled as mcg/kg/min.
  • B) 0.3 is the dose in mg/kg/h (21/70) mislabelled as mcg/kg/min.
  • C) 0.5 mcg/kg/min is a tenfold error in the conversion.

Key point: To convert mL/h to mcg/kg/min: x concentration, x 1000, / 60, / weight.

Question 9 · Ratio strength dilution

How many millilitres of chlorhexidine gluconate 20% w/v concentrate are required to prepare 500 mL of a 1:5000 chlorhexidine gluconate solution?

  1. A0.05 mL
  2. B0.5 mL
  3. C2.5 mL
  4. D5 mL
Show the answer

Answer: B) 0.5 mL

1:5000 = 1 g in 5000 mL = 0.02% w/v. Amount needed = 500 mL x 0.0002 g/mL = 0.1 g; 0.1 g / 0.2 g/mL (20%) = 0.5 mL. 5 mL and 0.05 mL are tenfold errors, and 2.5 mL results from treating 1:5000 as 0.1%.

Why the other options are wrong

  • A) 0.05 mL is a tenfold underestimate.
  • C) 2.5 mL treats 1:5000 as 0.1% instead of 0.02%.
  • D) 5 mL is a tenfold overestimate.

Key point: Ratio strength 1:X means 1 g in X mL; convert to % before using C1V1 = C2V2.

Question 10 · Infusion rate calculation (mcg/kg/min)

A 90 kg patient in the intensive care unit is to receive propofol 10 mg/mL at 50 mcg/kg/min. Which of the following is the correct infusion rate?

  1. A2.7 mL/h
  2. B4.5 mL/h
  3. C27 mL/h
  4. D270 mL/h
Show the answer

Answer: C) 27 mL/h

50 mcg/kg/min x 90 kg = 4500 mcg/min = 4.5 mg/min x 60 = 270 mg/h; 270 mg/h / 10 mg/mL = 27 mL/h. 270 mL/h enters mg/h as mL/h, 4.5 mL/h uses mg/min as mL/h, and 2.7 mL/h is a tenfold error.

Why the other options are wrong

  • A) 2.7 mL/h is a tenfold error.
  • B) 4.5 mL/h uses the dose in mg/min as if it were mL/h.
  • D) 270 mL/h enters the dose in mg/h as if it were mL/h.

Key point: Convert mcg/kg/min to mg/h first, then divide by mg/mL.

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