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GPhC registration exam: 8 common errors and tips to avoid them in the calculations paper

Have you ever wondered why some candidates who believe that they have high calculations proficiency and competency still fail the exam? Here, we have compiled the most common errors, traps, and trips and how you can avoid them

1. Misreading the question


Misreading the question can lead you to answering the wrong question or make the question appear more difficult than it should be. As a minimum, read the question twice to make sure you understand it fully and its context. Highlight the key information in the question and any wording that is critical to answering the question.

 

2. Failure to apply rounding rules


You should be competent and up to date with applying all the rounding rules. When necessary, there will be instructions in the General Pharmaceutical Council (GPhC) exam about rounding for the final submitted answer. For example, instructions may include:

• rounding your answer up to the nearest pound
• giving your answer to one decimal place
• giving your answer to the nearest 0.05ml
• giving your answer to the nearest multiple of 5ml.

You would lose marks here unnecessarily by failing to follow the rounding instructions. If for instance, your final answer was 3.1234ml and you are required to round up to 0.05ml, you would lose marks by not submitting your final answer as 3.1ml (or 3.10ml).

You are expected to know at what stages in your calculation rounding should take place. Some questions require rounding to take place at the end of your calculation, whereas others require rounding earlier in the calculation. For example, when calculating the total amount of a medicine that should be supplied, rounding should occur for an individual dose before calculating a final amount as in the example below: 

 

Example question A

 

Rx: Trimethoprim 4mg/kg twice daily for a baby weighing 5.33kg. Supply enough quantity to last two weeks. A syringe graduated in 0.05ml would be supplied to measure the dose. How many millilitres (ml) of trimethoprim 50mg/5ml oral suspension sugar-free do you supply for two weeks? Give your answer to one decimal place.

Click here for the comments, working out and answer


Correct method: Rounding per dose earlier in calculation

Dose 4mg/kg x 5.33kg = 21.32mg
50mg = 5ml
21.32mg = X
X/21.32 = 5/50
X = 2.132ml rounded to 0.05ml = 2.15ml per dose (rounding needed because you have a syringe graduated in 0.05ml to measure your dose).
Quantity needed = 2.15 x 2 x 14 = 60.2ml

Correct answer: 60.2ml

Incorrect method: Rounding at the end of calculation

4mg/kg x 2/day x 5.33kg x 14 days = 596.96mg
50mg = 5ml
596.96mg = Xml
X/596.96 = 5/50
X = 59.696ml rounded to 59.7ml to one decimal place.

Are you comfortable with what the terms ‘round up’ and ‘round down’ mean? For example:

• round 215.8mg to the nearest 15mg = 210mg
• round down 215.8mg to the nearest 15mg = 210mg
• round up 215.8mg to the nearest 15mg = 225mg
It is also important to consider the dosage form when calculating doses and quantities to supply. For example, patients cannot take part of a capsule or suppository, and be mindful that ampoules are single use only.

 

3. Misunderstanding of wording and terminologies



Errors can result from misunderstanding the wording and terminology used in the question. This is especially true in dilutions and infusion questions, but it can also happen with any other question types. Table 1 below shows examples of dilution and infusion wording and terminology that you need to be familiar with, as it is used extensively in the British National Formulary (BNF), summary of product characteristics (SmPC) and other resources. This terminology can easily cause confusion.

Table 1: Common wording and terminology used in dilution calculations

 

Drug

Extract of terminology or wording used on ‘Directions for administration’

Correct interpretation

Incorrect interpretation

Vedolizumab (Entyvio®) Entyvio 300mg powder for concentrate for solution for infusion vials

Reconstitute with 4.8ml of water for injection… withdraw 5ml of reconstituted solution and add to 250ml of infusion fluid’.

Add 4.8ml to 300mg Entyvio powder and mix. Withdraw 5ml and add it to 250ml infusion fluid.

Add 4.8ml to 300mg Entyvio powder and mix. Withdraw 5ml and add it to 245ml infusion fluid.

Citramag effervescent powder sachets

(Citric acid anhydrous 17.79 gram;

Magnesium carbonate heavy 11.57 gram)

‘One sachet should be reconstituted with 200ml of hot water; the solution should be allowed to cool for approx. 30 minutes before drinking’.

Measure 200ml of hot water and add one sachet into it and mix.

Add one sachet, add sufficient hot water to produce 200ml of final mixture.

Plenvu® sachets

 

‘The contents of the single sachet for Dose 1 should be made up to 500ml with water and taken over 30 minutes’.

Add sufficient water to the contents of one sachet to make a final volume of 500ml.

Add 500ml of water to the contents of one sachet.

Vistaprep® oral powder

Dissolve the contents of each sachet in 1L water’.

Measure 1L of water, add contents of one sachet into the water.

Add sufficient water to the contents of one sachet and make up to 1L.

Movicol® liquid

Dilute 25ml of oral concentrate with 100ml of water’.

Add 100ml of water to 25ml of oral concentrate.

Add 75ml of water to 25ml of concentrate.

Ranitidine 50mg/2ml solution for injection ampoules

‘50mg every 8 hours, dose to be diluted to 20 ml.’

Add 2ml of ranitidine 50mg/2ml injection to 18ml of infusion fluid.

Add 2ml of ranitidine 50mg/2ml injection to 20ml of infusion fluid.

Omeprazole 40mg powder for solution for infusion vials

‘Reconstitute each 40mg vial with infusion fluid and dilute to 100ml with Glucose 5% or Sodium Chloride 0.9%’.

Add sufficient infusion fluid to reconstituted vial until final volume is 100ml.

Add 100ml of infusion fluid to reconstituted infusion vial contents.

Pantoprazole 40mg powder for solution for injection vials

‘Reconstitute 40mg with 10ml sodium chloride 0.9% and dilute with 100ml of infusion fluid’.

Add the contents of the reconstituted vial to 100ml of infusion fluid.

Add sufficient infusion fluid to the contents of the reconstituted vial to make up to 100ml.

Brinavess 500mg/25ml concentrate for solution for infusion vials

Dilute to a concentration of 4mg/ml with 100 ml’.

25ml of Brinavess 20mg/ml is added to 100ml of infusion fluid.

25ml of BRINAVESS 20mg/ml is made up to 100ml using infusion fluid.

Clarithromycin 500mg powder for concentrate for solution for infusion vials

‘Dissolve initially in water for injections (500mg in 10ml) then dilute to a concentration of 2mg/ml’.

Inject 10ml of water for injections into a vial containing 500mg, then add sufficient infusion liquid up to 250ml.

Note the manufacturer assumes negligible displacement volume here, otherwise the final concentration would NOT be 500mg/10ml!

Hydrogen Peroxide Solution 3% BP 10 Vols

‘As a mouthwash or gargle dilute one part of the peroxide to two parts of water’.

Add 1 part of peroxide to 2 parts of water so total is 3 parts eg 5ml peroxide + 10ml water, total volume is 15ml.

Add sufficient water to 1 part of peroxide to make a final volume of 2 parts.

Sodium bicarbonate 8.4% (1mmol/ml) solution for injection 10ml ampoules

‘For peripheral infusion, dilute 8.4% solution at least 1 in 10’.

For a 1 in 10 dilution, add 10ml of drug to 90ml of infusion fluid.

Add 10ml of drug to 100ml of infusion fluid.



So let us look at how a typical question with this confusing terminology would look.

Example question B

 

A 10ml ampoule of sodium bicarbonate solution is diluted 3 parts of drug to 27 parts of infusion fluid. The final concentration of the resulting infusion fluid is 0.84%. What is the initial concentration of sodium bicarbonate in the 10mlL ampoule as a percentage (%)? Give your answer to one decimal place.

 

Click here for the comments, working out and answer


Correct method:

3 parts of sodium bicarbonate + 27 parts of infusion fluid = 30 parts of mixture
Dilution factor is 30/3 or 10 times dilution
Initial concentration = 0.84% x 10 = 8.4% to one decimal place.

Correct answer: 8.4%

Incorrect method:

3 parts of sodium bicarbonate in 27 parts of infusion fluid
Dilution factor = 27/3 = 9 times dilution
Concentration = 0.84% x 9 = 7.56% rounded to 7.6%

Wrong answer: 7.6%

Unless you are aware of the correct interpretation, you would think you have nailed it when you have submitted a wrong answer.

 

4. Using a completely wrong method

 

Misunderstanding what is required to answer the question may result in a wrong method being used, thus yielding a wrong answer.

Example question C

 

You have been asked to aseptically prepare a 0.9% (w/v) sodium chloride infusion by adding 30% (w/v) of concentrated sodium chloride solution to a 250ml bag of sterile water for injection. How much in millilitres (ml) of 30% concentrated sodium chloride would you add to the bag to produce the desired strength? Give your answer to one decimal place.

 

Click here for the comments, working out and answer


Correct method:

You need to correctly interpret the dilution process to avoid errors. Note that the final volume after adding 30% (w/v) concentrated sodium chloride is not 250ml, it is (250ml + volume of sodium chloride added). This is where some candidates get it wrong. The correct calculation is set out below.

C1 = initial concentration of sodium chloride = 30%
C2 = final concentration of sodium chloride = 0.9%
V1 = initial volume of 30% sodium chloride = ?
V2 = final volume of sterile water and 30% sodium chloride or 250 + V1

Use modified C1V1 = C2V2
We know V2 = V1 + 250

30V1 = 0.9(250+V1)

30V1 = 225ml + 0.9V1

29.1V1 = 225ml

V1 = 225ml/29.1

V1 = 7.731958763ml rounded to 7.7ml

Correct answer: 7.7ml

Incorrect method:

C1V1 = C2V2
30xV1 = 0.9x250
V1 = 7.5ml
Note an incorrect final volume of 250ml has been used.

Incorrect answer: 7.5ml

The wording in the above question can be varied, eg 30% sodium chloride was added to 250ml as in the question above (final volume would be 250+V1) or sufficient sterile water was added to 30% sodium chloride to make up to 250ml (final volume would be 250ml).

 

5. Wasting time by using an unnecessarily long method



Some methods can save time and yield the correct answers quickly. Others can be unnecessarily long, making errors more likely, while wasting your valuable time. During your practice, you should have come across various methods for tackling the question, so the trick is to apply a method that is quick and accurate, as your time is precious.

 

Example question D

 

The directions for reconstitution of clarithromycin infusion are as follows: ‘Inject 10ml of water for injections into a vial containing 500mg powder for infusion, then add the contents of the reconstituted vial to 240ml of infusion fluid’. Assume negligible displacement volume for the powder. What is the final concentration of clarithromycin in the final mixture expressed in mg/ml? Give your answer to the nearest whole number.

 

Click here for the comments, working out and answer


Correct short method:

Negligible displacement volume from clarithromycin powder means that the final volume after mixing reconstituted vial and infusion fluid = 10ml + 240ml = 250ml
Concentration = 500mg/250ml = 2mg/ml to the nearest whole number.

Correct answer: 2mg/ml

Correct, but long method:

500mg reconstituted with 10ml
Concentration = 500mg/10ml = 50mg/ml
10ml + 240ml = 250ml
Dilution factor = 250ml/10ml = 25 times dilution
Required concentration = 50mg/ml /25 = 2mg/ml

Correct answer: 2mg/ml

 

 

6. Errors due to incorrect conversion of units



Errors can arise from the incorrect conversion of units. For example, conversion between nanogram (ng) to gram (g) or milligram (mg) can be problematic if you have not learnt conversions well enough.

The table below summarises the common conversion of units. Please note that this list is not exhaustive.

 

Common unit conversions

Concept of concentration

 

1kg = 1 000g

1g = 1 000mg

1mg = 1 000mcg

1mcg = 1 000ng

1 litre = 1 000ml

1dL = 100ml

1ml = 1 000microlitre

% (w/v) = g/100ml

% (w/w) = g/100g

1 in X = 1g in Xml

1ppm (w/w) = 1g/1million g

1ppm (w/v) = 1g/1million ml or

1mg/1 000ml

1ppm (v/v) = 1ml/1million ml

 

Example question E

 

A 60-year-old man has just received a prescription for metronidazole cream 3mcg/1g, to be applied twice daily. Express the concentration in parts per million (ppm)

 

Click here for the comments, working out and answer


This is a simple question requiring knowledge of the concept of concentration and conversion of units. First, you should be able to define parts per million that is 1g in 1 000 000g or 1mg in 1 000 000mg or 1mcg/1 000 000mcg. Second, you need to convert 3mcg/1g to have common units in the denominator and numerator. You can either choose a common unit of g, mg or mcg, it does not matter what you choose. Let us work with mcg, then 3mcg/(1g x 1 000mg/1g x 1 000mcg/1mg) = 3mcg/1 000 000mcg = 3ppm

Correct answer: 3ppm

 

 

7. Errors due to incorrect use of the artefact or SmPC



Common problems in using the SmPC include using wrong sections of the SmPC. This may be caused by reading under a section relating to an incorrect dose or indication, relative to what is asked in the question. Some drugs may have multiple indications and it is important to read your information in the correct section of the SmPC.

Some drugs may require dosage adjustment due to renal and hepatic impairment, so it is important to carefully check your scenario and. if appropriate. apply the dosage adjustment.

Occasionally, you are required to estimate renal function using provided formula and select the appropriate dose for the patient. Let us look at an example below where this applies.

Example question F

 

A 60-year-old woman is due to commence treatment with gabapentin. She weighs 60kg, her height is 168cm and her serum creatinine level is 300 micromol/l. What MAXIMUM daily dose of gabapentin would you recommend? Give your answer to the nearest whole number.

 

Click here for the comments, working out and answer


Formula:
CrCl (ml/minute) = [140 – age (years)] x weight (kg) x 1.23 (male) OR x 1.04 (female)/ [(serum creatinine (micromol/l)]


Resource: Gabapentin SmPC available at: emc Gabapentin SmPC

Comments, explanations, and answer

You first need to calculate the CrCl (ml/min) using the provided formula. Then look up for the maximum recommended dose that is appropriate for that CrCl. The workings are now set out below.

CrCl (ml/minute) = [140 – age (years)] x weight (kg) x 1.23 (male) OR x 1.04 (female)]/[(serum creatinine (micromol/l)];

CrCl (ml/min) = (140-60) x 60 x 1.04/300micromol/l = 16.64ml/min;

Look under dose with impaired renal function,

4.2 Posology and method of administration Table 2.

The recommended dose is 150-600mg/day, so maximum is 600mg/day.

Correct answer: 600mg/day

 

 

8. Practising topics outside the framework



You should be guided by topics in the framework below and avoid wasting time practising questions that are not in the framework.

 

Calculation topics in the framework sitting summer 2022

 

  • doses and dose regimens
  • dosage and unit conversions
  • estimations of kidney function
  • displacement volumes and values
  • concentrations (eg expressed as w/v, % or 1 in x)
  • dilutions
  • molecular weight
  • using provided formulae
  • infusion rates
  • pharmacokinetics
  • health economics
  • quantities to supply

 

Conclusion

 

To sum up, read the questions carefully, understand the rounding rules and common wording, especially for dilutions, and use a short method that yields the correct answer. Be competent with conversion of units and understand fully the various definitions of concentration. Familiarise yourself with the SmPC so that you can look up information in the correct section. Last but not least, practise regularly guided by topics in the GPhC framework.

Good luck in your upcoming exams!



Authors:
Luso Kumwenda: MSc Community Pharmacy (Cardiff), B Pharm Hons (Zimbabwe), Independent Prescriber, MRPharmS, Mentor at UKBPA & RPS, Founder of Focus Pre-Reg

Emmanuel Chisadza: MBA (London), Practice Certificate In Pharmacy Management (Kent/Greenwich), B Comm. (UNISA), B. Pharm Hons (Zimbabwe), MRPharmS.
Disclaimer: The views in this article are our own and do not represent the views of any organisations we are associated with.

Acknowledgements: The questions were kindly provided by: Focus Pre-Reg Revision

Disclaimer: The questions and explanations presented here are for educational purposes only and do not replace your training, knowledge and application of professional judgement as a pharmacist or trainee pharmacist. The concentrations calculations depicted here cannot be viewed to reflect the calculations in real practice. Please consult the relevant smpc and clinical guidelines to inform your concentrations calculations in practice. The views in this article are our own and do not represent the views of any organisations we are associated with.



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