Common Registration Assessment, Part 1
Area under the curve calculations
Three original questions on area under the curve, with the working shown and the usual traps pointed out.
Published 4 October 2026. Independent revision material, not GPhC questions, not for patient care.
Area under the curve measures total drug exposure. In the assessment it appears in two forms: adding up trapezoids under measured levels, or using a provided relationship such as AUC = dose / clearance.
The questions here are fictional and practise only the arithmetic. Draw the level-time picture in your head before you calculate, and keep the units as mg.h/L throughout.
The method
- List the levels against their sampling times.
- For each pair of neighbours, average the two levels and multiply by the time gap.
- Add the trapezoid areas together.
- For a formula question, write the provided relationship and substitute.
- Check the units: concentration times time, for example mg.h/L.
Three practice questions
Work each one on paper first, then open the answer. All drugs and patients are fictional.
Question 1
After a fictional IV bolus, the starting level is 25 mg/L and the elimination rate constant is 0.2 per hour. Using AUC = C0 / k, what is the AUC?
Show the answer
Answer: 125 mg.h/L
Working: AUC = 25 / 0.2 = 125 mg.h/L.
Question 2
Levels of a fictional drug are 10, 8, 6, 4 and 2 mg/L at 0, 1, 2, 3 and 4 hours. Estimate the AUC using the trapezoidal method.
Show the answer
Answer: 24 mg.h/L
Working: Trapezoids: (10+8)/2 = 9, (8+6)/2 = 7, (6+4)/2 = 5, (4+2)/2 = 3, each over 1 hour. 9 + 7 + 5 + 3 = 24 mg.h/L.
Question 3
A fictional 250 mg dose is given to a patient with a clearance of 5 L/hour. Using AUC = dose / clearance, what is the AUC?
Show the answer
Answer: 50 mg.h/L
Working: AUC = 250 / 5 = 50 mg.h/L.
Pairs and gaps
Trapezoid questions come down to averaging pairs and minding the time gap. Formula questions come down to substituting exactly what the stem gives.
Where marks are lost
- Adding the levels instead of averaging each neighbouring pair.
- Forgetting the time gap when the samples are not hourly.
- Mixing up which formula applies: trapezoids for measured levels, formulas only when the stem provides them.
Frequently asked questions
Why average the pairs?
Each trapezoid approximates the curve as a straight line between two samples, so its height is the average of the two levels.
Is the trapezoidal answer exact?
It is an estimate, and it is the estimate the assessment expects when levels are given at intervals.
Sources
- The Pharmaceutical Journal, back to basics: pharmacokinetics
- GPhC, 2026 assessment specification and permitted items
The questions above are original and use fictional drugs. PreRegExamPrep is not affiliated with or endorsed by the General Pharmaceutical Council.
Practise until the method is automatic
Try 15 free questions with worked answers. No sign-up required.
More calculation topics
- Dose by weight calculations for the GPhC assessment
- Volume to give: liquid medicine calculations
- Percentage strength calculations: w/v, w/w and ratios
- Dilution calculations with C1V1 = C2V2
- Infusion rate calculations in mL per hour
- Drip rate calculations: drops per minute
- Body surface area calculations
- Creatinine clearance (Cockcroft-Gault) calculations
- Moles and millimoles calculations
- Displacement volume calculations for reconstitution
- Quantity to supply calculations
- Using a provided formula in calculations
- Dose information from packaging and labels
- Diluting a stock to a lower strength
- Medicine cost and switch calculations
- Rounding rules in calculations
- Enteral feed rate calculations
- Electrolyte content over time
- Infusion dose per kg per hour
- Rounding doses to measurable volumes
- Relative risk and relative risk reduction
- Absolute risk reduction and number needed to treat
- Odds ratio and confidence intervals
- Relative versus absolute risk reduction
- Loading dose and volume of distribution
- Top-up doses from measured drug levels
- Salt correction factors
- Mass and molar drug concentrations
- Half-life and falling drug levels
- Steady-state concentration and infusion rate
- Bioavailability and equivalent oral doses
- Oral maintenance dose and dosing interval
- Elimination rate constant and half-life
- Accumulation towards steady state
- Ratio strengths and one in X
- Serial dilution factors
- Mixing solutions of different strengths
- Tablet quantities for reducing regimens
- Equivalent doses from provided conversion tables
- Thresholds and dose-banding algorithms
- Unit conversions for mass and volume
- Units and units per mL
- Reconstituting powders and final concentration
- Millimoles and milliequivalents
- Infusion time and volume remaining
- Days supply from pack sizes
- Percentage w/v and w/w conversions
- Ideal and adjusted body weight from formulae
- Diluting creams and ointments by weight
- Scaling a formula to a batch size
- Age-band doses from a provided table
- Tablet fractions and split doses
- Stones, pounds, inches and metric conversions
- Micrograms per minute from mg per hour
- Percentage change and mark-up
- Molar solutions and mass per volume
- Osmolarity from component concentrations
- Direct proportion and cross-multiplication
- Scientific notation and very small quantities
- Stock use and reorder quantities
- Parts per million and very dilute solutions
- Sodium chloride equivalents and isotonic solutions
- Density and specific gravity conversions
- Doses per day and hours between doses
- Finding the volume of diluent to add
- Capping a dose at a stated maximum
- Whole vials and ampoules to draw up
- Reading values from a provided graph
- Micrograms per kg per minute infusions
- Percentage composition of a compound preparation
- Suppository displacement values
- Isotonicity by freezing point depression
- Energy content of parenteral nutrition
- Syringe driver rate calculations
- Renal dose adjustments using provided bands
- Insulin units and infusion calculations
- Working backwards from a stated dose
- Doses and days from multi-dose devices
- Combined additives in one infusion
See also the formula sheet, the eight sample questions and the approved calculator page.