25 Worked GPhC Calculation Examples

This version uses the uploaded PDF question set rather than a lighter illustrative list. The questions in that pack are numbered 16 to 40, but below they are presented as Worked Examples 1 to 25 for easier revision.

The goal is not to memorise the answers. The goal is to recognise the setup quickly, write the method cleanly, and reach the final answer without dropping marks on unit handling or arithmetic.

Worked example 1: loading dose plus first 24 hours of maintenance dosing

A 48-year-old patient is started on clarithromycin for a lower respiratory tract infection. The prescriber orders:

• a loading dose of 500 mg once, followed by
• 250 mg every 8 hours.

Only clarithromycin 250 mg tablets are available. Assume the first maintenance dose is given 8 hours after the loading dose, and include any dose due at 24 hours.

How many clarithromycin 250 mg tablets are required for the loading dose and the first 24 hours of treatment? Give your answer as a whole number.

The correct answer is 5 tablets

Step 1

Divide loading dose by tablet strength:

500 mg / 250 mg per tablet = 2 tablets

Step 2

Determine number of 8-hour intervals in 24 hours:

24 hours / 8 hours per dose = 3 doses

Each dose requires one 250 mg tablet:

3 doses x 1 tablet per dose = 3 tablets

Step 3

Add loading dose tablets and maintenance tablets:

2 tablets + 3 tablets = 5 tablets

Key Learning Point: When calculating medication for time periods, always include the dose at the endpoint if it aligns with the schedule.

Common Errors to Avoid: The loading dose requires two 250 mg tablets to reach 500 mg. Maintenance doses occur every 8 hours starting at 8 hours, resulting in three doses within 24 hours. Always verify that the final dose at exactly 24 hours is included in the count.

Worked example 2: insulin pen dose plus priming volume

A 32-year-old patient with type 1 diabetes is prescribed insulin aspart 40 units subcutaneously before breakfast. Insulin aspart is supplied as 150 units in 3 mL. The dose will be administered using an insulin pen which delivers insulin in 1-unit increments and must be primed with 2 units before each injection. The pen is used once daily for 28 days. Assume one prime is required for each daily injection.

How many mL of insulin aspart solution are required to provide 28 days of treatment? Give your answer to one decimal place.

The correct answer is 23.5 mL

Step 1

Add daily dose and priming units:

40 units + 2 units = 42 units per day

Step 2

Find mL per unit using concentration:

3 mL ÷ 150 units = 0.02 mL per unit

Multiply daily units by mL per unit:

42 units × 0.02 mL/unit = 0.84 mL per day

Step 3

Multiply daily volume by 28 days:

0.84 mL × 28 days = 23.52 mL

Round to one decimal place:

23.52 mL = 23.5 mL

Key Learning Point: Remember to include all pen priming requirements in total volume calculations to avoid underdosing.

Common Errors to Avoid: This calculation accounts for both the therapeutic dose and the priming requirement. A common mistake is forgetting to include the 2-unit prime in daily calculations. Always verify that unit-to-mL conversions match the concentration provided.

Worked example 3: one-third of a daily fluid requirement plus additive volume

A patient's total daily fluid requirement is 2500 mL. One third of this total is prescribed as an intravenous infusion of sodium chloride 0.9% to be administered evenly over 8 hours. The infusion will be prepared by adding 50 mL of an IV medicine to the bag (assume the final volume increases by 50 mL).

What rate, in mL/hour, should the infusion pump be set to deliver the prescribed volume over 8 hours? Give your answer to the nearest whole number.

The correct answer is 110 mL/hour

Step 1

Find one third of total daily fluid requirement:

2500 mL ÷ 3 = 833.33 mL

Add medication volume to IV bag:

833.33 mL + 50 mL = 883.33 mL total infusion volume

Step 2

Divide total volume by infusion duration:

883.33 mL ÷ 8 hours = 110.416 mL per hour

Round to nearest whole number:

110.416 mL per hour = 110 mL per hour

Key Learning Point: When adding medications to IV bags, always include the medication volume in your total infusion volume calculations to ensure accurate rate programming.

Common Errors to Avoid: This calculation accounts for both the baseline IV fluid requirement and the added medication volume. A common mistake would be to forget the 50 mL medication addition, which increases the total volume. Always verify that all components are included in the final volume calculation.

Worked example 4: using a stronger ointment to make a weaker one

A pharmacist is preparing a compounded dermatology ointment for a patient with eczema. The prescription requires an ointment containing 2% w/w of hydrocortisone. The final quantity to be prepared is 500 g. Hydrocortisone is supplied as a 10% w/w ointment, and the base available is hydrocortisone-free ointment base.

How many grams of the 10% w/w hydrocortisone ointment are required to prepare 500 g of a 2% w/w hydrocortisone ointment? Give your answer to the nearest whole number.

The correct answer is 100 g

Step 1

Find the amount of hydrocortisone needed in the final 2% w/w ointment:

2% of 500 g = (2 / 100) × 500 g = 10 g hydrocortisone

Step 2

Use C1V1 = C2V2 to find how much 10% ointment is needed:

C1V1 = C2V2

(2% × 500 g) / 10% = 100 g of 10% ointment

Key Learning Point: Always verify the total weights add to the final quantity (100 g + 400 g = 500 g) and re-check the final percentage (10 g in 500 g = 2%) to avoid errors.

Common Errors to Avoid: This works because 100 g of 10% ointment contains 10 g hydrocortisone. Mixed with 400 g of base (0%), the total hydrocortisone stays 10 g in 500 g overall, giving 2% w/w. A common mistake is mixing up different concentration bases, but here everything is w/w in grams.

Worked example 5: inhaler dose over multiple days

A 34-year-old patient with asthma is prescribed a salbutamol 100 micrograms/dose pressurised inhaler. The directions are 2 puffs every 4 hours when required for wheeze. Over the next 7 days the patient records using the inhaler 4 times each day. Each time they use the inhaler, they take 2 puffs.

How many micrograms of salbutamol will the patient inhale over 7 days? Give your answer as a whole number.

The correct answer is 5600 micrograms

Step 1

Multiply daily uses by puffs per use:

4 uses per day × 2 puffs/use = 8 puffs per day

Step 2

Multiply daily puffs by micrograms per puff:

8 puffs per day × 100 micrograms/puff = 800 micrograms per day

Step 3

Multiply daily dose by number of days:

800 micrograms per day × 7 days = 5600 micrograms

Key Learning Point: Always track units through each step: puffs → micrograms → total time period.

Common Errors to Avoid: This calculation works because we first determine the total puffs per day (4 uses × 2 puffs), then convert puffs to micrograms using the 100 microgram/puff ratio, and finally scale to 7 days. A common mistake is confusing 'uses' with 'puffs' — always verify that each use corresponds to the correct number of puffs.

Worked example 6: dilution from 30% w/v to 6% w/v

A hospital theatre suite requires 3 litres of hydrogen peroxide 6% w/v for immediate use in a surgical scrub area. A hydrogen peroxide 30% w/v stock solution is available. The final solution will be prepared by measuring the required volume of the 30% w/v stock solution and then adding sterile Water for Irrigation to make a final volume of 3 litres.

What volume, in mL, of hydrogen peroxide 30% w/v is required to prepare 3 litres of hydrogen peroxide 6% w/v? Give your answer as a whole number.

The correct answer is 600 mL

Step 1

Convert final volume to millilitres:

3 L × 1000 mL per L = 3000 mL

Set up dilution equation C1V1 = C2V2:

30% × V1 = 6% × 3000 mL

Solve for V1:

V1 = (6% × 3000 mL) / 30% = 600 mL

Key Learning Point: Always verify that the total volume after mixing equals the required final volume (600 mL stock + 2400 mL water = 3000 mL total).

Common Errors to Avoid: The amount of hydrogen peroxide (solute) remains constant during dilution. The 30% solution is 5 times stronger than the 6% solution, so we need 1/5 of the final volume (3000 mL ÷ 5 = 600 mL). Common mistake: forgetting to convert litres to millilitres before calculation.

Worked example 7: dopamine syringe pump rate

A 67-year-old man in intensive care weighs 83 kg and is prescribed dopamine 5 micrograms/kg/minute by continuous intravenous infusion. Dopamine is prepared by adding 200 mg to a syringe and making up to a final volume of 50 mL with glucose 5%.

What infusion rate, in mL/hour, should the syringe pump be set to deliver the prescribed dose? Give your answer to one decimal place.

The correct answer is 6.2 mL/hour

Step 1

Multiply prescribed dose by patient weight:

5 μg per kg/min × 83 kg = 415 μg/min

Step 2

Multiply per-minute dose by 60 minutes:

415 μg/min × 60 min = 24,900 μg per hour

Step 3

Convert 200 mg dopamine to micrograms:

200 mg × 1000 μg per mg = 200,000 μg

Calculate concentration in μg/mL:

200,000 μg ÷ 50 mL = 4,000 μg per mL

Step 4

Divide hourly dose by concentration:

24,900 μg per hour ÷ 4,000 μg per mL = 6.225 mL per hour

Round to one decimal place:

6.225 = 6.2 mL per hour

Key Learning Point: Always double-check unit conversions when working with micrograms and milligrams to prevent dangerous dosing errors.

Common Errors to Avoid: This calculation ensures the patient receives the exact prescribed dose by converting between weight-based dosing and solution concentration. Common errors include misplacing decimal points during unit conversions (mg to μg) or miscalculating time conversions (minutes to hours). Always verify that all units cancel appropriately to leave mL/hour.

Worked example 8: syringe driver rate in mm/hour

A patient is receiving a continuous infusion of midazolam via a syringe driver. The prescription is for 2.5 mg/hour over 24 hours. Midazolam is available as a 5 mg/mL solution. The syringe driver has a total barrel volume of 22 mL and a calibrated length of 55 mm.

Calculate the rate, in mm/hour, at which the syringe driver should be set to deliver the required dose. Round your answer to the nearest whole number.

The correct answer is 1 mm/hour

Step 1

Multiply hourly dose by duration:

2.5 mg per hour × 24 hours = 60 mg total dose

Step 2

Divide total dose by concentration:

60 mg ÷ 5 mg per mL = 12 mL total volume

Step 3

Calculate mm per mL using syringe calibration:

55 mm ÷ 22 mL = 2.5 mm per mL

Multiply volume by mm/mL conversion:

12 mL × 2.5 mm per mL = 30 mm total length

Step 4

Divide total length by infusion duration:

30 mm ÷ 24 hours = 1.25 mm per hour

Round to nearest whole number:

1.25 mm per hour = 1 mm per hour

Key Learning Point: Always verify that the calculated rate falls within the syringe driver's operational range (0–55 mm) to prevent mechanical errors.

Common Errors to Avoid: This calculation ensures the syringe driver delivers the exact dose by converting medication requirements through multiple unit conversions. The key is maintaining unit consistency at each step: mg → mL → mm. Common errors include misinterpreting the syringe calibration or skipping the final rounding step.

Worked example 9: tapered prednisolone course with 2.5 mg gastro-resistant tablets

Mrs D is prescribed prednisolone gastro-resistant tablets for an acute flare of ulcerative colitis. Prednisolone gastro-resistant tablets 2.5 mg are available. The prescribed tapering regimen is:

• 40 mg once daily for 5 days
• Then 30 mg once daily for 7 days
• Then 20 mg once daily for 7 days
• Then 10 mg once daily for 7 days
• Then 5 mg once daily for 4 days

How many 2.5 mg tablets are required to complete the full course?

The correct answer is 256 tablets

Step 1

Convert 40 mg daily dose to number of 2.5 mg tablets:

40 mg ÷ 2.5 mg/tablet = 16 tablets per day

Convert 30 mg daily dose to number of 2.5 mg tablets:

30 mg ÷ 2.5 mg/tablet = 12 tablets per day

Convert 20 mg daily dose to number of 2.5 mg tablets:

20 mg ÷ 2.5 mg/tablet = 8 tablets per day

Step 2

Multiply daily tablets by days for 40 mg phase:

16 tablets per day × 5 days = 80 tablets

Multiply daily tablets by days for 30 mg phase:

12 tablets per day × 7 days = 84 tablets

Multiply daily tablets by days for 20 mg phase:

8 tablets per day × 7 days = 56 tablets

Step 3

Add tablets from all phases:

80 + 84 + 56 + 28 + 8 = 256 total tablets

Key Learning Point: Always double-check tablet conversions when dealing with different strengths. For example, 5 mg is exactly two 2.5 mg tablets, not one.

Common Errors to Avoid: This calculation works by first determining how many 2.5 mg tablets are needed each day for each dose level, then multiplying by the number of days for that phase. Common mistakes include miscalculating the tablet conversions (e.g., using 5 mg tablets instead of 2.5 mg) or miscounting the days in each phase. Always verify that the total days add up to 5+7+7+7+4 = 30 days.

Worked example 10: full course volume from mg dose and liquid strength

A 7-year-old child weighing 26 kg is diagnosed with streptococcal pharyngitis. The prescriber selects phenoxymethylpenicillin oral solution at a dose of 250 mg four times daily for 10 days, in line with British National Formulary (BNF) recommendations.

The oral solution available contains 125 mg in 5 mL.

What total volume, in mL, of phenoxymethylpenicillin oral solution is required to complete the full 10-day course? Give your answer to the nearest whole number.

The correct answer is 400 mL

Step 1

Convert prescribed dose to volume using concentration:

250 mg × 5 mL / 125 mg = 10 mL per dose

Step 2

Multiply volume per dose by number of daily doses:

10 mL per dose x 4 doses per day = 40 mL per day

Step 3

Multiply daily volume by treatment duration:

40 mL × 10 days = 400 mL total

Key Learning Point: Always double-check concentration ratios in liquid medications to avoid under- or overdosing. For paediatric prescriptions, confirm weight-based dosing aligns with BNF guidelines.

Common Errors to Avoid: This calculation works because we first determine how much solution contains the required 250 mg dose (10 mL), then scale up to daily and total needs. Common mistakes include miscalculating the concentration ratio (125 mg/5 mL) or miscounting the number of daily doses. Always verify that units cancel correctly during conversions.

Worked example 11: meropenem concentration target from grams and molarity

Mrs A is being treated in the infectious diseases' unit for hospital-acquired pneumonia. Due to an augmented renal clearance of greater than 120 mL/minute, the consultant prescribes meropenem 2 g to be administered as a continuous 24-hour infusion.

Local pharmacy protocol states:

The total 24-hour dose must be diluted to give a final concentration of 0.08 mol/L in order to minimise line occlusion.

Additional information:

• Molecular weight of meropenem = 383 g/mol
• Total prescribed dose over 24 hours = 2 g
• Meropenem is supplied in 1 g vials
• Standard 1-litre elastomeric pumps are used

What total volume, in mL, of infusion solution is required to achieve a concentration of 0.08 mol/L? Give your answer to the nearest whole number.

The correct answer is 65 mL

Step 1

Convert the prescribed mass of meropenem to moles:

Moles = Mass / RMM

Moles = 2 / 383 = 0.00522 mol

Step 2

Determine the required volume for the target concentration:

Volume (L) = Moles / Concentration

Volume = 0.00522 / 0.08 = 0.06525 L

Step 3

Convert to millilitres and round to the nearest whole number:

0.06525 L × 1000 = 65.25 mL

Final Result = 65 mL

Key Learning Point: Always convert mass to moles before using the molarity formula. Volume (L) is then found by dividing moles by the concentration (mol/L).

Common Errors to Avoid: The calculation naturally provides an answer in litres. Failing to multiply by 1000 to reach millilitres is a common oversight in clinical dosage calculations.

Worked example 12: monthly cost saving from changing vial strength

Your 45-bed orthopaedic ward administers cefuroxime surgical prophylaxis at a total dose of 3 g per day for 5 days for each patient. Cefuroxime is currently supplied as 750 mg vials costing £2.40 per vial. Whole vials must be used and cannot be shared. A manufacturer offers 1.5 g vials costing £3.95 per vial. Again, whole vials only. An audit shows that 120 orthopaedic patients commence prophylaxis each month.

Calculate the monthly saving, in pounds (£), if the ward switches to the 1.5 g vials. Give your answer to the nearest whole pound.

The correct answer is £1020

Step 1

Convert daily dose to total treatment dose:

3 g × 5 days = 15 g per patient

Calculate vials needed for 750 mg vials:

15 g ÷ 0.75 g per vial = 20 vials per patient

Calculate cost for 750 mg vials:

20 vials × £2.40 per vial = £48 per patient

Step 2

Calculate vials needed for 1.5 g vials:

15 g ÷ 1.5 g per vial = 10 vials per patient

Calculate cost for 1.5 g vials:

10 vials × £3.95 per vial = £39.50 per patient

Step 3

Find cost difference per patient:

£48 − £39.50 = £8.50 saving per patient

Calculate total monthly savings:

£8.50 × 120 patients = £1020 per month

Key Learning Point: Always verify that whole vials are used as required — rounding up is mandatory when calculating vial quantities, but in this case exact division was possible.

Common Errors to Avoid: This calculation works because we first determine the exact number of vials needed for each formulation based on the total treatment dose. The key insight is that while the 1.5 g vials cost more per vial, they require fewer vials per patient, leading to significant savings. Common mistakes include forgetting to convert grams to milligrams or miscalculating the number of vials needed.

Worked example 13: displacement volume after reconstitution

A patient receiving outpatient parenteral antimicrobial therapy requires a single 400 mg dose of teicoplanin for home administration.

Teicoplanin is supplied as 200 mg powder vials. Each vial has a displacement volume of 0.28 mL. For routine preparation, 3 mL of Water for Injections is added to each vial. For safety reasons, the complete contents of two reconstituted vials are withdrawn into a single syringe before any further dilution takes place.

Calculate the total volume, in mL, that will be drawn into the syringe from the two reconstituted vials. Give your answer to two decimal places.

The correct answer is 6.56 mL

Step 1

Calculate vials required for 400 mg dose:

400 mg ÷ 200 mg per vial = 2 vials

Step 2

Add diluent volume and displacement volume:

3 mL water + 0.28 mL displacement = 3.28 mL per vial

Step 3

Multiply single vial volume by 2:

3.28 mL per vial × 2 vials = 6.56 mL total volume

Key Learning Point: Always account for displacement volume when reconstituting powders — it's the hidden volume that affects final concentration.

Common Errors to Avoid: Displacement volume is the space the powder occupies when dissolved. When reconstituting, you add 3 mL water to each vial, but the powder itself adds an extra 0.28 mL to the final volume. This is why we add both volumes together. Common mistake: forgetting to include displacement volume in the total calculation.

Worked example 14: IU to micrograms to mL

A late-preterm neonate weighing 3.4 kg is diagnosed with severe vitamin D deficiency. The consultant prescribes colecalciferol 1,000 international units (IU) per kg, to be administered intramuscularly once weekly for 6 weeks. The only preparation available is colecalciferol injection 300 micrograms per mL.

The following conversion applies:

1 microgram colecalciferol = 40 IU

Before the first dose is dispensed, the exact volume must be documented on the medication chart.

Calculate the volume of colecalciferol solution, in mL, required for one weekly dose. Give your answer to two decimal places.

The correct answer is 0.28 mL

Step 1

Multiply weight by prescribed dose:

1,000 IU per kg × 3.4 kg = 3,400 IU per dose

Step 2

Divide total IU by conversion factor:

3,400 IU ÷ 40 IU/microgram = 85 micrograms

Step 3

Divide micrograms by solution concentration:

85 micrograms ÷ 300 micrograms per mL = 0.2833... mL

Round to two decimal places:

0.2833 rounded to two decimals = 0.28 mL

Key Learning Point: Always verify unit conversions when dealing with medication dosing. For neonates, precise rounding is critical — in this case, rounding to two decimal places as specified.

Common Errors to Avoid: This calculation works because we first determine the total therapeutic requirement in standard units (IU), then convert to the physical form available (micrograms), and finally calculate the physical volume needed. Common errors include misapplying the conversion factor or rounding too early in the calculation chain.

Worked example 15: osmolarity contribution from electrolytes

A bespoke 1-litre parenteral nutrition (PN) bag is being reformulated to include two additional electrolytes.

The modified admixture will contain:

• Calcium 20 mmol, supplied as calcium gluconate. For osmolarity calculations, each millimole of calcium gluconate is considered to contribute one osmotically active particle.
• Phosphate 30 mmol, supplied as sodium phosphate. Sodium phosphate dissociates so that each millimole produces two osmotically active particles.

No other components of the PN formulation are altered and the baseline osmolarity remains unchanged.

Calculate the additional osmolarity contributed by these electrolytes alone. Express your answer in mOsm/L, rounded to the nearest whole number.

The correct answer is 80 mOsm/L

Step 1

Multiply mmol by osmotic particles per mmol:

20 mmol × 1 mOsm/mmol = 20 mOsm

Step 2

Multiply mmol by osmotic particles per mmol:

30 mmol × 2 mOsm/mmol = 60 mOsm

Step 3

Add contributions from both electrolytes:

20 mOsm + 60 mOsm = 80 mOsm

Convert to osmolarity per litre:

80 mOsm ÷ 1 L = 80 mOsm per L

Key Learning Point: Multiply each electrolyte's mmol by its dissociation factor to get mOsm. Sum all contributions for total osmolarity.

Common Errors to Avoid: Osmolarity depends on how many particles each electrolyte produces in solution. Calcium gluconate remains as single particles while sodium phosphate splits into two ions. Always verify dissociation factors from the question text — this determines the multiplier for each electrolyte.

Worked example 16: long taper course with 5 mg soluble tablets

A 62-year-old man weighing 85 kg is being discharged from the respiratory ward following an exacerbation of his COPD. He has been counselled on a reducing course of oral prednisolone. The hospital pharmacist has recommended a specific tapering regimen to his GP. The patient will only be supplied with prednisolone 5 mg soluble tablets.

How many prednisolone 5 mg soluble tablets should be supplied to complete the entire course? Give your answer as a whole number.

The correct answer is 180 tablets

Step 1

40 mg daily for 5 days:

40 mg ÷ 5 mg/tablet × 5 days = 40 tablets

35 mg daily for 5 days:

35 mg ÷ 5 mg/tablet × 5 days = 35 tablets

30 mg daily for 5 days:

30 mg ÷ 5 mg/tablet × 5 days = 30 tablets

Step 2

25 mg daily for 5 days:

25 mg ÷ 5 mg/tablet × 5 days = 25 tablets

20 mg daily for 5 days:

20 mg ÷ 5 mg/tablet × 5 days = 20 tablets

15 mg daily for 5 days:

15 mg ÷ 5 mg/tablet × 5 days = 15 tablets

Step 3

10 mg daily for 5 days:

10 mg ÷ 5 mg/tablet × 5 days = 10 tablets

5 mg daily for 5 days:

5 mg ÷ 5 mg/tablet × 5 days = 5 tablets

Step 4

Add all calculated tablets:

40 + 35 + 30 + 25 + 20 + 15 + 10 + 5 = 180 tablets

Key Learning Point: Calculating the total quantity of tablets required for a tapering dose regimen.

Common Errors to Avoid: This calculation works by determining how many 5 mg tablets are needed each day for each dose level, then multiplying by the number of days. Common errors include miscalculating tablets per dose (e.g., using 5 mg tablets for 35 mg dose as 7 tablets instead of 35/5=7) or miscounting the 5-day periods. The tapering schedule ensures gradual dose reduction while maintaining therapeutic effect.

Worked example 17: paediatric single-dose liquid volume

A 4-year-old child presents to the GP with otitis media. The child weighs 16 kg and is not allergic to penicillin. The GP decides to prescribe amoxicillin oral suspension. The available formulation is Amoxicillin 250 mg/5 mL sugar-free oral suspension. The recommended dose for this indication in children aged 1–4 years is 30 mg/kg three times a day for 5–7 days.

What is the volume, in mL, of amoxicillin 250 mg/5 mL oral suspension required for a single dose? Give your answer to one decimal place.

The correct answer is 9.6 mL

Step 1

Multiply weight by prescribed dose:

30 mg per kg × 16 kg = 480 mg per dose

Step 2

Set up proportion:

250 mg → 5 mL

480 mg → ? mL

480 mg × 5 mL / 250 mg

Calculate volume:

480 × 5 ÷ 250 = 9.6 mL

Key Learning Point: Always verify that units cancel correctly during conversions. For example, mg in the numerator and denominator should cancel out to leave mL as the final unit.

Common Errors to Avoid: The concentration tells us how much medication is in each mL. By dividing the required dose by the concentration, we find how many mL contain that amount. Common mistakes include forgetting to convert mg to mL or misreading the concentration ratio.

Worked example 18: aminophylline loading infusion rate

A 68-year-old man weighing 75 kg is admitted to the acute medical unit with a severe asthma attack. He is not currently taking any theophylline preparations. The doctor prescribes an intravenous loading dose of aminophylline 5 mg/kg to be infused over 30 minutes. The hospital pharmacy supplies a pre-prepared infusion bag of aminophylline 500 mg in 500 mL of sodium chloride 0.9%.

What is the infusion rate, in mL/hour, required to administer the loading dose correctly? Give your answer to the nearest whole number.

The correct answer is 750 mL/hour

Step 1

Multiply weight by prescribed dose:

5 mg per kg × 75 kg = 375 mg loading dose

Step 2

Calculate concentration of solution:

500 mg ÷ 500 mL = 1 mg per mL concentration

Convert dose to volume:

375 mg × 1 mL per mg = 375 mL required

Step 3

Convert infusion time to hours:

30 minutes ÷ 60 minutes per hour = 0.5 hours

Divide volume by time:

375 mL ÷ 0.5 hours = 750 mL per hour

Key Learning Point: Always double-check time conversions when calculating infusion rates. For aminophylline, rapid infusion can cause cardiac arrhythmias, so ensure the calculated rate is both mathematically correct and clinically appropriate.

Common Errors to Avoid: This calculation works because the concentration simplifies the math (1 mg/mL). Common errors include miscalculating time conversion (30 minutes = 0.5 hours) or confusing mg/mL with mg/kg. Always verify that the infusion rate is physiologically reasonable for the medication.

Worked example 19: opioid conversion to alfentanil

A 54-year-old palliative care patient with metastatic breast cancer is currently taking MST Continus (morphine sulfate) 60 mg tablets, two tablets every 12 hours. Over the last week, she has also required four doses of Oramorph 10 mg/5 mL solution (10 mg per dose) daily for breakthrough pain. Because of swallowing difficulties, the team decides to switch her analgesia to a continuous subcutaneous infusion of alfentanil over 24 hours via a syringe driver.

Calculate the total quantity of alfentanil, in mg, required for the 24-hour syringe driver. Give your answer to one decimal place.

The correct answer is 9.3 mg

Step 1

Multiply tablets per dose by mg per tablet:

2 tablets × 60 mg/tablet = 120 mg per dose

Calculate daily dose:

120 mg per dose × 2 doses per day = 240 mg regular dose per day

Step 2

Multiply doses per day by mg per dose:

4 doses per day × 10 mg per dose = 40 mg breakthrough dose per day

Step 3

Add regular and breakthrough doses:

240 mg + 40 mg = 280 mg total morphine per day

Step 4

Apply conversion ratio:

280 mg morphine × 1 mg alfentanil / 30 mg morphine = 9.333... mg alfentanil

Round to one decimal place:

9.333 rounded to 1 decimal = 9.3 mg

Key Learning Point: Always calculate total daily dose (TDD) including all components before conversion.

Common Errors to Avoid: This calculation uses a standard opioid conversion ratio (30 mg oral morphine = 1 mg SC alfentanil). Common errors include forgetting to account for both regular and breakthrough doses, or misapplying the conversion ratio. Always verify the conversion factor from the provided table.

Worked example 20: minimum concentration and maximum final volume

A 62-year-old female weighing 58 kg is being treated for ventricular arrhythmia in the High Dependency Unit. She has already received a loading dose of IV amiodarone. The cardiologist prescribes a maintenance infusion of 900 mg to be administered over the next 24 hours. The hospital policy for amiodarone infusions requires the drug to be diluted with Glucose 5% to a final concentration of not less than 600 micrograms/mL. Amiodarone is supplied as 150 mg/3 mL ampoules.

What is the rate, in mL/hour, to administer this infusion using the maximum final volume required to achieve the minimum specified concentration? Give your answer to one decimal place.

The correct answer is 62.5 mL/hour

Step 1

Convert micrograms to milligrams:

600 micrograms per mL ÷ 1000 = 0.6 mg per mL

Step 2

Apply concentration-volume formula:

900 mg ÷ 0.6 mg per mL = 1500 mL

Step 3

Divide total volume by duration:

1500 mL ÷ 24 hours = 62.5 mL per hour

Key Learning Point: Always convert micrograms to milligrams when working with concentrations. Remember: minimum concentration corresponds to maximum volume. Verification: 1500 mL × 0.6 mg/mL = 900 mg ✓

Common Errors to Avoid: This calculation relies on the inverse relationship between concentration and volume. When using the minimum required concentration (0.6 mg/mL), the volume becomes maximized. Common errors include misinterpreting 'minimum concentration' as requiring minimum volume, or failing to convert between mg and micrograms. Always verify that units are consistent before performing calculations.

Worked example 21: percentage w/v from grams and final volume

A hospital pharmacy technician prepares a stock solution of chlorhexidine gluconate for use in a minor procedures room. The preparation is made by dissolving 5 g of chlorhexidine gluconate powder and making up to a final volume of 50 mL with purified water.

The solution is labelled before release for clinical use.

What percentage w/v concentration should be stated on the label? Give your answer as a whole number.

The correct answer is 10% w/v

Step 1

Write formula for w/v percentage:

Percentage (w/v) = (Weight of solute / Volume of solution) × 100

Substitute given values:

(5 g / 50 mL) × 100 = 10%

Key Learning Point: Always ensure units match the percentage definition: grams per 100 mL for w/v. Verify the final volume includes both solute and solvent.

Common Errors to Avoid: Percentage w/v (weight/volume) expresses grams of solute per 100 mL solution. This calculation shows 5 g in 50 mL equals 10 g in 100 mL, hence 10% w/v. Common errors include confusing w/v with v/v or forgetting to multiply by 100.

Worked example 22: dilution from 1 in 10 to 1 in 50

A hospital pharmacy holds a 1 in 10 stock solution of chlorhexidine concentrate. A diluted solution of 1 in 50 is required for use in a clinical procedure room. The final volume required is 200 mL.

Assume the dilution is prepared by measuring the required volume of the 1 in 10 stock solution and adding purified water to make a final volume of 200 mL.

What volume, in mL, of the 1 in 10 stock solution is required to prepare 200 mL of a 1 in 50 solution? Give your answer as a whole number.

The correct answer is 40 mL

Step 1

Set up proportion for 1 in 50 solution:

1 g → 50 mL

? g → 200 mL

Calculate required solute:

(200 mL × 1 g) / 50 mL = 4 g

Step 2

Set up proportion for 1 in 10 stock:

1 g → 10 mL

4 g → ? mL

Calculate required volume:

(4 g × 10 mL) / 1 g = 40 mL

Key Learning Point: Always verify dilution calculations using the formula C1V1 = C2V2. For this problem: (1/10)V1 = (1/50)(200) → V1 = 40 mL.

Common Errors to Avoid: Common errors include confusing '1 in X' ratios as parts solute vs parts solvent instead of total solution.

Worked example 23: Cockcroft-Gault and dose table application

An 82-year-old woman is being considered for anticoagulation for stroke prevention in non-valvular atrial fibrillation. She weighs 58 kg and has a stable serum creatinine of 145 micromol/L. Her medical history includes hypertension and osteoarthritis. You are asked to recommend an appropriate starting dose of dabigatran etexilate.

Use the Cockcroft-Gault formula:

CrCl (mL/min) = (140 – Age) × Weight (kg) × Constant ÷ Serum creatinine (micromol/L)

Constant = 1.23 for males; 1.04 for females.

What is the most appropriate total daily dose of dabigatran etexilate in mg for this patient? Give your answer as a whole number.

The correct answer is 150 mg

Step 1

Subtract age from 140:

140 − 82 = 58

Multiply by weight and gender constant:

58 × 58 kg × 1.04 = 3498.56

Divide by serum creatinine:

3498.56 ÷ 145 micromol per L = 24.13 mL/min

Step 2

Compare CrCl to dosing guidelines:

24.13 mL/min falls in 15–30 mL/min range = 75 mg twice daily

Step 3

Multiply dose per administration by frequency:

75 mg × 2 = 150 mg

Key Learning Point: Use the female constant (1.04) in Cockcroft-Gault calculations for women. Round CrCl to one decimal place for accurate dosing category placement.

Common Errors to Avoid: The Cockcroft-Gault formula adjusts for age, weight, and gender to estimate kidney function. Common errors include using the wrong gender constant or misinterpreting the creatinine clearance range. Always verify the patient's creatinine units (micromol/L vs. mg/dL) before calculation.

Worked example 24: reconstitution with displacement then dose volume

A 5-year-old child weighing 18 kg is prescribed ceftazidime for a cystic fibrosis exacerbation. The dose required is 50 mg/kg to be administered every 8 hours intravenously. The ward stock consists of 2 g vials of ceftazidime powder. The displacement volume for the 2 g vial is specified as 1.5 mL. The nurse intends to reconstitute the vial with 10 mL of Water for Injections aimed at producing a solution for injection.

What volume, in mL, of the reconstituted solution must be drawn up to administer a single dose? Give your answer to two decimal places.

The correct answer is 5.18 mL

Step 1

Multiply weight by prescribed dose:

50 mg per kg × 18 kg = 900 mg per dose

Step 2

Convert vial strength to mg:

2 g → 2000 mg = 2000 mg per vial

Calculate total reconstituted volume:

10 mL diluent + 1.5 mL displacement volume = 11.5 mL total volume

Calculate concentration:

2000 mg ÷ 11.5 mL = 173.91 mg per mL concentration

Step 3

Set up proportion:

2000 mg → 11.5 mL

900 mg → ? mL

Solve for unknown volume:

900 mg × 11.5 mL ÷ 2000 mg = 5.175 mL

Round to two decimal places:

5.175 rounded to two decimals = 5.18 mL

Key Learning Point: Always include displacement volume when calculating reconstituted concentrations.

Common Errors to Avoid: This calculation accounts for the displacement volume when reconstituting the powder. A common mistake is to forget that the displacement volume adds to the diluent volume, which affects the final concentration. Always verify that the total reconstituted volume includes both the diluent and displacement volume.

Worked example 25: intermediate dilution step before final mouthwash preparation

A pharmacist needs to prepare a 500 mL bottle of 0.02% w/v chlorhexidine gluconate solution for a patient to use as a mouthwash during a period of neutropenia. The dispensary stocks chlorhexidine gluconate 5% w/v concentrate. To improve accuracy, the pharmacist decides to first create an intermediate stock solution by diluting 10 mL of the 5% concentrate to 100 mL with water.

How many mL of the intermediate stock solution are required to prepare the final requested 500 mL bottle? Give your answer to the nearest whole number.

The correct answer is 20 mL

Step 1

Determine grams in 10 mL of 5% concentrate:

5 g / 100 mL × 10 mL = 0.5 g

Calculate concentration after diluting to 100 mL:

0.5 g / 100 mL = 0.5% w/v

Step 2

Set up C1V1 = C2V2 equation:

0.5% × V1 = 0.02% × 500 mL

Solve for V1:

10 / 0.5 = 20 mL

Key Learning Point: Always double-check unit conversions and ensure concentrations are expressed in the same format (e.g., both as percentages or both as grams per litre) before applying the dilution formula.

Common Errors to Avoid: This problem uses the dilution principle where concentration multiplied by volume remains constant before and after dilution. The intermediate step ensures accurate measurement by creating a more manageable concentration. Always verify that units cancel correctly during calculations to avoid errors.

How to use these examples properly

1. Do the question first without looking at the worked answer.
2. Write out the full setup, even if you think the answer is obvious.
3. Mark whether the error was conceptual, unit-based, or arithmetic.
4. Repeat missed questions after a gap rather than immediately.
5. Use these examples to build method speed, then move to fresh timed practice.

Quick FAQs

• Are these questions closer to the real exam standard? Yes. These examples are based on the uploaded PDF set and are closer in tone and structure to higher-quality exam-style calculations than the lighter draft version.
• Should I memorise the numbers in these examples? No. Memorise the setup patterns, not the final numbers. You want to recognise which method to use when the values change.
• Why are some examples longer than others? Because the real calculation paper mixes straightforward arithmetic with multi-step questions that test unit handling, dilution logic, dose conversion, and clinical interpretation in the same item.
• Do I still need more practice after these 25? Yes. These 25 examples are a strong worked foundation, but real improvement comes from repeating the method across a larger set of timed questions.