Common Registration Assessment, Part 1
Serial dilution factors
Follow two-stage dilutions, distinguish final volume from added diluent, and calculate the overall dilution factor.
Published 7 October 2026. Independent revision material, not GPhC questions, not for patient care.
A serial dilution takes an aliquot from one preparation and dilutes it again. The overall dilution factor is the product of the factors at each stage. It is not the sum.
For each stage, dilution factor = final volume ÷ aliquot volume. If 5 mL is made up to 50 mL, the factor is 10. If 5 mL is mixed with 50 mL water and volumes are additive, the final volume is 55 mL and the factor is 11. Label every container before working.
The method
- Draw the stock, intermediate and final containers.
- Write the aliquot and final volume for each stage.
- Calculate each factor as final volume ÷ aliquot.
- Multiply the factors for the overall factor.
- Divide stock concentration by that factor; work backwards by multiplying.
Three practice questions
Work each one on paper first, then open the answer. All drugs and patients are fictional.
Question 1
A 20 mg/mL stock is diluted by taking 5 mL and making up to 50 mL. Then 2 mL of the intermediate is made up to 40 mL. Find the final concentration.
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Answer: 0.1 mg/mL
Working: First factor = 50 ÷ 5 = 10. Second = 40 ÷ 2 = 20. Overall = 200. Final = 20 ÷ 200 = 0.1 mg/mL.
Question 2
Take 10 mL of a 12 mg/mL stock and add 20 mL water, assuming additive volumes. Then take 5 mL of the mixture and make up to 100 mL. Find the final concentration.
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Answer: 0.2 mg/mL
Working: First final volume = 30 mL; factor = 30 ÷ 10 = 3. Second factor = 100 ÷ 5 = 20. Overall = 60. Final = 12 ÷ 60 = 0.2 mg/mL.
Question 3
Two stages have dilution factors of 5 and 8. Final concentration is 0.25 mg/mL. What was the stock concentration?
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Answer: 10 mg/mL
Working: Overall factor = 5 × 8 = 40. Stock = 0.25 × 40 = 10 mg/mL.
Check each stage
Dilution with drug-free water cannot make a solution stronger in these exercises. If a stage increases concentration, check for an inverted factor or a confused final volume.
Where marks are lost
- Adding dilution factors.
- Using added water volume as final volume.
- Taking the second aliquot concentration from the original stock.
Frequently asked questions
Do all the stock contents pass to the final container?
No. Only the stated aliquot moves on. Its concentration is the concentration of the container it came from.
Must I calculate every intermediate amount?
Not always. The product of correctly identified factors can give the final concentration directly. Draw the stages first.
Sources
- The Pharmaceutical Journal, medication maths: dilutions
- 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
- Mixing solutions of different strengths
- Tablet quantities for reducing regimens
- Equivalent doses from provided conversion tables
- Thresholds and dose-banding algorithms
See also the formula sheet, the eight sample questions and the approved calculator page.