One worked example for each of the 26 calculation types that come up in Part 1 of the registration assessment — the question as it would be asked, the method line by line, and the answer. Nothing is hidden behind a sign-up.
Every example here was produced by the same code that sets and marks questions in the app, so the working you read is the working the product does. Reading one through is worth less than sitting one, though — the practice engine is free and unlimited, and the numbers change every time.
01 · INFUSION & PUMP RATESWORKED EXAMPLE
Infusion & pump rates
mg/kg/hour to mL/hour from a bagged concentration.
A patient weighing 50 kg is prescribed an infusion containing 500 mg in 250 mL, to run at 0.5 mg/kg/hour. What infusion rate should the pump be set to, in mL/hour?
Check whether the quoted dose is per day or per dose, and how many divided doses are given.
03 · DILUTIONS & CONCENTRATIONSWORKED EXAMPLE
Dilutions & concentrations
C₁V₁ = C₂V₂ and % w/v strengths.
A specials manufacturing unit is preparing 1000 mL of a 2% w/v solution by diluting a 20% w/v concentrate. What volume of the concentrate is required, in mL?
METHOD
Step 1 — Use C₁V₁ = C₂V₂, so V₁ = (C₂ × V₂) ÷ C₁
Step 2 — V₁ = (2% × 1000 mL) ÷ 20% = 100 mL
Step 3 — Make the 100 mL of concentrate up to 1000 mL with the diluent.
ANSWER100 mL
The percentage units cancel in C₁V₁ = C₂V₂, leaving a volume. The stock volume is always less than the final volume.
04 · DISPLACEMENT VALUESWORKED EXAMPLE
Displacement values
Reconstituting powder injections to a target concentration.
A 250 mg vial of amoxicillin powder for injection is to be reconstituted to 50 mg/mL. Its product literature gives a displacement value of 0.08 mL per 100 mg. What volume of water for injections must be added, in mL?
METHOD
Step 1 — Final volume = 250 mg ÷ 50 mg/mL = 5 mL
Step 2 — Total displacement = 0.08 mL × (250 mg ÷ 100 mg) = 0.2 mL
Step 3 — Water to add = 5 mL − 0.2 mL = 4.8 mL
ANSWER4.8 mL
First scale the displacement value to the actual mass, then subtract it from the final volume.
05 · PERCENTAGE & RATIO STRENGTHSWORKED EXAMPLE
Percentage & ratio strengths
% w/v and 1:X ratio strengths to mg and mg/mL.
A solution has a ratio strength of 1:400 w/v. What is its strength as a percentage (% w/v)?
METHOD
Step 1 — 1:400 w/v means 1 g in 400 mL.
Step 2 — Per 100 mL: 1 g ÷ 400 mL × 100 mL = 0.25 g, so the strength is 0.25% w/v.
ANSWER0.25% w/v
A 1:N strength is 1 g in N mL, so the percentage (grams per 100 mL) is 100 ÷ N.
06 · IV DRIP RATES (DROPS/MIN)WORKED EXAMPLE
IV drip rates (drops/min)
Drops per minute from volume, time and a giving-set drop factor.
A 1000 mL bag of glucose 5% is running at 83 mL/hour through a standard giving set that delivers 20 drops/mL. How many drops per minute should the infusion be set to?
Use the weight you are given — the BNF advises ideal body weight where fat is likely to be the major contributor to body mass — and serum creatinine in µmol/L; the constant differs by sex (1.23 men, 1.04 women).
08 · MOLES & MILLIMOLESWORKED EXAMPLE
Moles & millimoles
mmol → mass → volume of a concentrate (electrolytes).
A 50% magnesium sulfate concentrate contains 5 g in 10 mL. (Molecular weight of magnesium sulfate heptahydrate = 246.47 g/mol.) How many millimoles of magnesium are in 9 mL of the concentrate?
METHOD
Step 1 — Mass in 9 mL = 5 g ÷ 10 mL × 9 mL = 4.5 g
Step 2 — Moles = 4.5 g ÷ 246.47 g/mol; × 1000 = 18.3 mmol (1 mmol of salt gives 1 mmol of magnesium)
ANSWER18.3 mmol
Mass ÷ molecular weight gives moles; ×1000 for millimoles. One mmol of these salts carries one mmol of the ion.
09 · PRESCRIBING COSTWORKED EXAMPLE
Prescribing cost
Cost savings from branded→generic switches, and the cost of a course.
A patient needs 30 mL of an oral liquid daily for 12 weeks. It is supplied in 150 mL bottles costing £12.20 each and must be dispensed in original (unopened) packs. What is the total cost? Give your answer in pounds to 2 decimal places.
METHOD
Step 1 — Course length = 12 weeks × 7 = 84 days; total volume = 30 mL × 84 = 2520 mL
Step 2 — Bottles = 2520 mL ÷ 150 mL = round up to 17 whole bottles
Step 3 — Cost = 17 × £12.20 = £207.40
ANSWER£207.40
Round the number of bottles UP — you cannot dispense part of an original pack.
10 · QUANTITIES TO SUPPLYWORKED EXAMPLE
Quantities to supply
Total tablets or liquid to dispense over a course, with device/pack rounding.
A child weighing 24 kg is prescribed 2.5 mg/kg three times a day of an oral liquid containing 100 mg in 5 mL. Each dose is measured to the nearest 0.1 mL. How many mL are needed for 2 weeks of treatment?
METHOD
Step 1 — Dose = 2.5 mg/kg × 24 kg = 60 mg
Step 2 — Volume per dose = 60 mg ÷ 20 mg/mL = 3 mL → measured as 3 mL
Step 3 — Course = 2 weeks × 7 = 14 days; total = 3 mL × 3 × 14 = 126 mL
ANSWER126 mL
Round each measured dose to the syringe graduation first, then multiply by doses per day and the number of days.
11 · BODY SURFACE AREA DOSINGWORKED EXAMPLE
Body surface area dosing
Total dose from a per-m² dose and a given BSA.
A patient with a body surface area of 1.7 m² is prescribed a drug at a dose of 750 mg/m². What is the total dose, in mg?
METHOD
Step 1 — Total dose = dose per m² × body surface area
Step 2 — 750 mg/m² × 1.7 m² = 1275 mg
ANSWER1275 mg
Multiply the per-m² dose by the body surface area.
12 · HALF-LIFE (FIRST-ORDER)WORKED EXAMPLE
Half-life (first-order)
Time for a concentration to fall to a fraction of its initial value.
A drug has a half-life of 12 hours and follows first-order kinetics. How many hours will it take for the blood concentration to fall to 12.5% of the initial concentration?
METHOD
Step 1 — Start at 100% and keep halving until you reach 12.5%: 100% → 50% → 25% → 12.5%.
Step 2 — That is 3 halvings, so it takes 3 half-lives.
Step 3 — Each half-life is 12 hours, so time = 3 × 12 = 36 hours.
ANSWER36 hours
Count how many times you halve 100% to reach the target percentage — that is the number of half-lives. Then multiply by the half-life.
13 · NUMBER NEEDED TO TREATWORKED EXAMPLE
Number needed to treat
NNT, ARR and RRR from event rates or trial counts.
In a placebo-controlled trial, the control event rate (CER) for a cardiovascular event was 0.31 and the experimental event rate (EER) was 0.114. Using the formulae provided, what is the minimum number of patients who must be treated to prevent one event?
Absolute risk reduction & number needed to treat
ARR =CER − EER
NNT =1ARR
METHOD
Step 1 — CER = 0.31; EER = 0.114
Step 2 — ARR = CER − EER = 0.31 − 0.114 = 0.196
Step 3 — NNT = 1 ÷ ARR = 5.1, rounded UP to 6 patients
ANSWER6 patients
NNT is always rounded UP — you cannot treat a fraction of a patient to prevent an event.
14 · ENTERAL FEED RATEWORKED EXAMPLE
Enteral feed rate
mL/hour from a daily calorie target and the feed energy density.
A patient requires 1200 kcal over 24 hours from an enteral feed containing 200 kcal per 100 mL, administered continuously over 24 hours. What rate, in mL/hour, should the feed run at? Give your answer to the nearest whole number.
METHOD
Step 1 — Daily volume = 1200 kcal ÷ 200 kcal/100 mL × 100 = 600 mL
Step 2 — Rate = 600 mL ÷ 24 hours = 25 mL/hour
ANSWER25 mL/hour
Find the total daily volume first, then divide by the number of hours the feed actually runs.
15 · ELECTROLYTE INTAKE VS DAILY MAXIMUMWORKED EXAMPLE
Electrolyte intake vs daily maximum
mmol → mass → percentage of the recommended daily maximum.
A patient takes 80 mL daily of a medicine containing 4 mmol of sodium per 10 mL. The relative atomic mass of sodium is 23, and adults are advised to have no more than 2.4 g of sodium a day. What percentage of this daily maximum does the dose provide? Give your answer to the nearest whole number.
METHOD
Step 1 — Daily sodium = 80 mL ÷ 10 mL × 4 mmol = 32 mmol
Step 2 — Mass = 32 mmol × 23 ÷ 1000 = 0.736 g
Step 3 — % of the daily maximum = 0.736 g ÷ 2.4 g × 100 = 31%
ANSWER31%
mmol → mass uses the relative atomic mass of sodium itself (÷1000 for grams); then compare with the daily maximum and ×100.
16 · SYRINGE PUMP RATEWORKED EXAMPLE
Syringe pump rate
Infusion rate as volume divided by time.
A syringe pump holds 17 mL of a medicine and is running at 1 mL/hour. How long, in hours, will the syringe last? Give your answer to one decimal place.
METHOD
Step 1 — Time = volume ÷ rate
Step 2 — 17 mL ÷ 1 mL/hour = 17 hours → 17 hours
ANSWER17 hours
The time a syringe lasts is its volume divided by the rate.
17 · RENAL DOSE ADJUSTMENTWORKED EXAMPLE
Renal dose adjustment
Cockcroft–Gault CrCl, then the dose-band % and the quantity to supply.
A 37-year-old man weighing 47 kg has a serum creatinine of 220 µmol/L. The recommended dose of a drug is 200 mg once daily, available as 100 mg capsules, for 28 days. Using the formula and dose adjustment provided, how many capsules are needed to complete the course?
Estimate CrCl, pick the dose % from the band, work out capsules per day, then multiply by the number of days.
18 · SALT & BASE CONVERSIONSWORKED EXAMPLE
Salt & base conversions
Hydrochloride ↔ base by the RMM ratio: % w/v or mg of base, mg of salt.
Assume the RMMs of morphine hydrochloride (C₁₇H₁₉NO₃·HCl) and hydrochloride (HCl) are 322 and 36 respectively. Calculate the percentage concentration (% w/v) of morphine base in morphine hydrochloride 0.2% w/v solution.
METHOD
Step 1 — Only the morphine part of the salt is base: RMM of base = 322 − 36 = 286.
Step 2 — Salt → base: multiply by RMM(base) ÷ RMM(salt).
Step 3 — 0.2% w/v × 286 ÷ 322 = 0.178% w/v of morphine base
ANSWER0.178% w/v
Salt → base: × RMM(base) ÷ RMM(salt). Base → salt: × RMM(salt) ÷ RMM(base). The salt figure is always the larger.
19 · OPIOID CONVERSIONWORKED EXAMPLE
Opioid conversion
Weak opioids to oral morphine, oral to subcutaneous over 24 hours, and breakthrough doses — BNF figures.
A patient receiving palliative care takes modified-release oral morphine sulfate 60 mg twice daily. They can no longer take oral medicines and are to be switched to a continuous subcutaneous infusion of diamorphine hydrochloride over 24 hours. Using the BNF equivalence provided, what dose of diamorphine hydrochloride, in mg, should be given over 24 hours?
Step 2 — Oral morphine 30 mg ≡ subcutaneous diamorphine 10 mg, a ratio of 3:1
Step 3 — 120 mg ÷ 3 = 40 mg over 24 hours
ANSWER40 mg
Always work from the 24-hour oral morphine total, then divide by the route’s ratio.
20 · CORTICOSTEROID EQUIVALENCEWORKED EXAMPLE
Corticosteroid equivalence
Equivalent anti-inflammatory doses from the BNF table.
A patient takes dexamethasone 4 mg daily and is to be switched to prednisolone at an equivalent anti-inflammatory dose. Using the table provided, what daily dose of prednisolone, in mg, is equivalent?
Scale through the table: how many “prednisolone 5 mg units” is the current dose, then multiply by the new drug’s row.
21 · INSULIN DOSES & SUPPLYWORKED EXAMPLE
Insulin doses & supply
How long a cartridge lasts and cartridges for a course, safety tests included.
A patient uses Humulin I (isophane insulin) cartridges: each 3 mL cartridge holds 300 units (100 units/mL). Their dose is 20 units in the morning and 18 units in the evening. Before each injection they do a 2-unit safety test (air shot), as the pen instructions require. For how many whole days will one cartridge last?
METHOD
Step 1 — Units a day = (20 + 2) + (18 + 2) = 42 units
Step 2 — 300 units ÷ 42 units a day = 7.14 → 7 whole days
ANSWER7 days
Count every unit that leaves the pen — safety tests included — and round down to whole days.
22 · IDEAL BODY WEIGHTWORKED EXAMPLE
Ideal body weight
IBW from height, and doses calculated on it for obese patients.
A woman who is 5 feet 9 inches tall and weighs 123 kg is prescribed intravenous aciclovir 10 mg/kg every 8 hours. For obese patients the BNF advises calculating the dose on ideal body weight for height. Using the formula provided, what dose, in mg, should be given every 8 hours?
Ideal body weight (IBW)
IBW, men (kg) =50 + 2.3 × (height in inches − 60)
IBW, women (kg) =45.5 + 2.3 × (height in inches − 60)
Step 2 — Dose = 10 mg/kg × 66.2 kg = 662 mg → 662 mg every 8 hours
ANSWER662 mg
Use the patient’s height, not their weight, to find the ideal body weight — then dose on that.
23 · ALLIGATIONWORKED EXAMPLE
Alligation
Mixing two strengths to make a third — ointments and glucose infusions.
An aseptic unit must prepare 250 mL of glucose 15% for a neonatal unit, by mixing glucose 50% with glucose 5%. What volume, in mL, of glucose 50% is required?
METHOD
Step 1 — Parts of glucose 50% = 15 − 5 = 10; parts of glucose 5% = 50 − 15 = 35; total 45 parts
Step 2 — glucose 50% = 10 ÷ 45 × 250 mL = 55.6 mL
ANSWER55.6 mL
Alligation: the stronger takes (target − weaker) parts and the weaker (stronger − target); scale the parts to the total.
24 · PARTS PER MILLIONWORKED EXAMPLE
Parts per million
% ↔ ppm, mg per litre, and fluoride content.
A mouthwash contains sodium fluoride 0.05% w/v. According to the BNF, sodium fluoride provides approximately 1 part of fluoride ion for every 2.2 parts of the salt, by mass. What is the fluoride ion content, in parts per million (ppm)?
1% is 10 000 ppm. Then take the fluoride share of the salt.
25 · OSMOLARITYWORKED EXAMPLE
Osmolarity
mOsmol/L from strength, molecular weight and dissociation — single and mixed infusions.
An infusion of potassium chloride 0.15% in sodium chloride 0.9% is to be given. It contains potassium chloride (molecular weight 74.5; dissociates completely into potassium and chloride ions), and sodium chloride (molecular weight 58.5; dissociates completely into sodium and chloride ions). What is its osmolarity, in milliosmoles per litre (mOsmol/L)? Give your answer to the nearest whole number.
Grams per litre ÷ molecular weight, × the particles it dissociates into, × 1000 — and add the solutes together.
26 · VIALS & WASTEWORKED EXAMPLE
Vials & waste
Whole single-use vials per dose, vials for a course, and what is discarded.
A patient is prescribed an intravenous antibacterial 750 mg four times a day for 5 days. It is supplied only as single-use 500 mg vials, and any unused portion of an opened vial must be discarded. How many vials are needed for the full course?