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Calculations: Practice is essential for the registration exam

With the registration exam confirmed for March 2021, now is the time to practice calculations so you can be prepared for the exam

The GPhC exam can be daunting if you are not prepared, with all trainee pharmacists expected to pass a two-hour 40-question calculations exam. As well as having a good understanding of the different types of questions that will be asked in the registration assessment framework, it is important to be familiar with the registration assessment specification for sittings in 2021 and the calculations answer sheet.

Due to COVID-19 restrictions, the 2021 registration assessment will be computer-based and delivered in Pearson VUE test centres within the UK. More information on the requirements for the March 2021 calculations exam, such as calculator requirements, can be found on the GPhC website.

Preparing for the exam involves regular practice of calculation questions so you are familiar with the types of questions that may be asked. Below are eight worked examples of calculations that we hope will meet some of your learning outcomes in relation to pharmaceutical calculations. Please feel free to use any calculation method that works well for you.

 

Question 1: A 28-year-old woman is administered potassium chloride as a slow infusion over 120 min at a rate of 0.1mmol potassium/kg per hour.

If 17mmol potassium is delivered during the infusion, what is the weight of the patient in pounds? [1kg = 2.2 pounds]

Click here for the comments, working out and answer

If 0.1mmol/kg per hour is rate used and 120min = 2 hours. Therefore, making the patient’s weight = x kg means that 0.1 × x × 2 = 17

Then 0.2x = 17 and x = 85kg, then 85kg x 2.2 pounds = 187 pounds

Answer: 187 pounds

 

Question 2: A 47-year-old man, weighing 74 kg, is prescribed dopamine at a dose of 2.5 microgram/kg/min. A 5mL vial of dopamine 40mg/mL concentrate for solution for infusion is diluted up to 250mL with 5% glucose and 0.45% sodium chloride solution

What is the final concentration of dopamine as a percentage w/v concentration? Give your answer to two decimal places.

Click here for the comments, working out and answer

Dopamine vial concentration = 40mg/mL. 40mg in 1mL therefore x in 5mL. X=200mg in a 5mL vial that is diluted to 250mL. The new concentration of this solution is: 200mg in 250mL. To calculate this as a percentage w/v we need to work this out in 100mL. 200mg in 250mL and X in 100mL

X = 80mg in 100mL but a percentage w/v is in grams per 100mL so need to convert mg to g, therefore 80mg = 0.08g. So, 0.08g/100mL

Answer = 0.08% w/v

 

Question 3: A 58-year-old man, weighing 85kg, with acute heart failure is prescribed a dobutamine infusion of 5 microgram/kg/min to be delivered via a syringe driver. Dobutamine is available at a strength of 250 mg/50mL.

What is the rate in mL/hr? Give your answer to one decimal place.

Click here for the comments, working out and answer

This figure needs to be converted to mg/hr. First, convert microgram to mg, by dividing by 1,000. 5 micrograms = 0.05mg. This is still per kg, so needs to be multiplied by 85 kg = 0.425 mg. This is still per minute, so needs to be multiplied by 60, since there are 60 minutes in one hour = 25.5 mg/hr. The nurse would then calculate how many mg per mL are in the constituted solution: 250 mg/50mL = 5mg in 1mL of solution. 25.5mg/5 = 5.1. Therefore, the syringe driver needs to be run at 5.1mL/hr

Answer: 5.1mL/hr

 

Question 4: A formula calls for 85g of a 2% hydrocortisone ointment to be diluted with 25g of Vaseline.

What would be the percentage concentration of hydrocortisone in the mixture? Give your answer to the nearest 0.05.

Click here for the comments, working out and answer

85g x 2% w/w ÷ 110g = 1.545 % w/w. Rounded to two decimals places = 1.55% w/w. 85g hydrocortisone plus 25g of Vaseline = 110g of new product. This still only contains the hydrocortisone from the original 85g of a 2% hydrocortisone. 2g in 100g, therefore X in 85g. X = 1.7g of hydrocortisone in original 85g and also in the new product of 110g

To calculate the new % w/w concentration: 1.7g in 110g. X in 100g and X = 1.54545454.% w/w. Therefore, to the nearest 0.05 = 1.55% w/w

Answer: 1.55% w/w

 

Question 5: You receive a request in your laboratory for a 3-ppm solution of sodium fluoride from an overseas company. There is 175mL of sodium fluoride stock solution available currently.

How many micrograms of sodium fluoride are needed to prepare the sodium fluoride stock solution such that a solution containing 3ppm of sodium fluoride results when 0.5mL is diluted to 150mL with water?

Click here for the comments, working out and answer

3g in 1,000,000mL = 3,000mg in 1,000,000mL = 3mg in 1,000mL = 0.3mg in 100mL = 0.0003g in 100mL (x 300) = 0.09g in 100mL = 90mg in 100mL

157,500 micrograms in 175mL. Original stock solution contains x micrograms of sodium fluoride. We take 0.5mL of this stock solution and dilute it to 150mL. We know that the concentration of this final solution is 3ppm and that the sodium fluoride in this final solution came from the 0.5mL of stock solution. 3ppm = 3 g in 1000000mL. X in 150mL. X = 0.00045g in 150mL. X = 0.45mg in 150mL (question is looking for micrograms so we may as well convert now). X = 450 micrograms in 150mL. We know that the only place the sodium fluoride has come from is the 0.5mL of stock solution. So, the original stock solution has a concentration of 450 micrograms in 0.5mL. If 450 micrograms are in 0.5mL, then x in 175mL. X = 157500 micrograms of sodium fluoride required to produce the original stock solution

Answer: 157,500 micrograms

 

Question 6: You are a community pharmacist locum and notice that the balance of methadone oral solution DTF in your controlled drugs cabinet is 1945mL, but the register says 1650mL. You have checked that sugar free methadone has not been dispensed instead. When investigating, you realise that the balance has not been checked for three weeks and in that time, you have dispensed eleven full bottles of 500mL. Your SOPs advise to divide the discrepancy by the total amount dispensed since the last correct balance check and then multiply by 100. If the result is an underage of less than 0.01 (1%), then you can go ahead and correct the balance in your CD register.

What is the % discrepancy for the methadone oral solution? Give your answer to one decimal place.

Click here for the comments, working out and answer

1945mL – 1650mL = 295mL overage. 11 bottles of 500mL = 5500mL. 295 mL ÷ 5500mL x 100 = 5.4%

Answer: 5.4%

 

Question 7: A 44-year-old woman, who is 1.74m tall and weighs 69kg and, is prescribed lapatinib ditosylate monohydrate for the treatment of adult patients with breast cancer, whose tumours overexpress HER2 (ErbB2) in combination with capecitabine for patients with advanced or metastatic disease with progression following prior therapy, which must have included anthracyclines and taxanes and therapy with trastuzumab in the metastatic setting. The recommended dose of capecitabine is 2000mg/m²/day taken in 2 divided doses, 12 hours apart on days 1-14 in a 21-day cycle.

How many tablets of capecitabine 300mg, would you dispense for this patient for three cycles?

Click here for the comments, working out and answer

Height of patient in cm = 174cm. Weight of patient in kg = 69kg

BSA = 69kg x 174/3600= 3.335

Square rooted = 1.8261982367. 1.8261982367 x 1000mg = 1826.198236774967

mg/300mg tablets = 6.0873 tablets per dose therefore 6 tablets per dose x 2 = 12 tablets per day

It is important to remember not to use the total daily dose or total timescale dose when calculating number of tablets or vials etc as this is the most common error in the GPhC assessment where an error occurs due to not considering that part of a tablet or part of a vial/syringe etc may be discarded at each dose. It would not make a difference in this calculation as the number of tablets remains the same, but worth remembering whenever tackling a question on quantity to supply

12 tablets daily x 14 days = 168 tablets for one cycle. 504 tablets for three cycles

Answer: 504 tablets

 

Question 8: A dermatologist has contacted you regarding one of his patients in the burns unit, who requires a gelatin infusion. He would like to make up a 200mL infusion containing a 1 in 4 gelatin 7% in dextrose 5% solution.

What volume, in mL, of dextrose 5% will be needed to prepare the required infusion?

Click here for the comments, working out and answer

1 in 4 = 4 parts consisting of:

  • 1 part of gelatin
  • 3 parts of dextrose

200mL ÷ the total of 4 parts = 50mL per part. 50mL x 1 part = 50mL gelatin 7% and 50mL x 3 parts = 150mL dextrose 5%

Answer: 150mL

 

The calculations presented here are for educational purposes only and the Summary of Product Characteristics (SmPC) should be strictly adhered to during your professional practice as a pharmacist. The views in this article do not represent the views of any organisations and may not completely reflect clinical practice.

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