1. Pharmaceutical Calculations
Dr Kathy Burnett
Senior Lecturer in Pharmacy Practice
University of Ulster

2. Learning Outcomes
After attending today’s workshop you should be able to:
Understand the main types of calculations covered in the pre-registration exam
Competently perform examples of pharmacy related calculations
Appreciate the format of the calculations section of registration exam

3. Why calculations?
At least 1.5 million Americans are injured annually as a result of medication errors
10-fold dosing errors are common
Peppermint Water PJ 1 Feb 2003 Vol 270 Pg 172
“If you have no confidence in maths, or are just no good at it, you can kill a patient”
[Dr C Hall, Nursing Standard, 2004]

4. Pre-registration examination
Calculations must be passed
OPEN BOOK paper
20 questions
Currently 80% pass mark
Potentially 100%
No room for errors – patients can be killed!
Reference sources are the CURRENT BNF edition 70 (September 2015 – March 2016) and BNFC

5. Question format False / true answer
Determine which variable you are going to prove or disprove

6. Exercise 1

7. Question 1
1.25 g of potassium permanganate is required to produce 1 L of a solution such that 10 mls of this solution diluted to 250 mls gives a 0.01% solution suitable for wound cleansing.
 0.01% = 0.01 g in 100mls = g in 250 mls
0.025 g in 250 mls comes from 10 mls so there is g in the 10 mls
A x x = 1000 x = 2.5 g
vol
FALSE

8. Question 2
If 300 mls of a 15% solution is added to 200 mls of a 45% solution the resulting mixture is a 27% solution.
Solution 1
A x x = 45 g
Vol
Solution 2
A y y = 90 g Final amount A = = 135 g
Vol Final volume = = 500 mls
Product
A z z = 27%
Vol
TRUE

9. Question 3 The formula for Ammonia and Ipecacuanha Mixture BP is:
Ammonium bicarbonate mg
Liquorice liquid extract ml
Ipecacuanha tincture ml
Concentrated camphor water ml
Concentrated anise water ml
Double-strength chloroform water ml
Water to ml
You have been asked to prepare 12 bottles each containing 60 mls of the mixture. You only have concentrated chloroform water to use. It is appropriate to use 18 mls concentrated chloroform water to fulfil the order.

10. Question 3 To make 12 bottles x 60 mls = 720 mls
Need 5 mls DS chloroform water in 10 mls, so will need 360 mls DS chloroform water for 720 mls
SS 1:40
DS 1:20
Conc 1:1
Concentrated chloroform water is therefore 20 x stronger than DS, so need to divide amount by 20
360 mls / 20 = 18 mls concentrated chloroform water required.
TRUE
Give out chloroform water handout if required

11. Question 4 A prescription reads:
Prednisolone tablets, 30 mg daily for 7 days, then reduce by 5 mg every three days to a maintenance dose of 5 mg daily. To be reviewed at outpatient clinic on 5th April.
The prescription is dispensed on 12th March It would be appropriate to dispense 91 x 5 mg prednisolone tablets to last from the first dose on dispensing day to the last dose on the day of the clinic appointment.

12. Question 4 30 mg = 6 x 5 mg tablets, etc. 6 x 7 days = 42 tablets
6 x 7 days = 42 tablets
5 x 3 days = 15 tablets
4 x 3 days = 12 tablets
3 x 3 days = 9 tablets
2 x 3 days = 6 tablets
= 19 days treatment
12 March – 5 April = 20 days in March and 5 days in April = 25 days in total
1 x 6 days = 6 tablets
Total = = 90 tablets
FALSE

13. Question 5
30 g of Diprosalic® ointment contains 0.9 g salicylic acid and 0.15 g betamethasone diproprionate.
Diprosalic® ointment contains 3% salicylic acid and 0.05% betamethasone (BNF pg 1025)
3% = 3 g in 100 g = 0.9 g in 30 g
0.05% = 0.05 g in 100 g = g in 30 g
FALSE

14. Question 6
A 3 month baby weighing 5.2kg has been prescribed 0.78 mls of Augmentin-Duo® twice daily. It is appropriate for you to contact the prescriber as this is an underdose.
 BNF for children
Augmentin-Duo® 0.15 ml / kg twice daily
= 0.15 x 5.2 = 0.78 mls twice daily
 FALSE

15. Question 7
A patient has an Atrovent® inhaler and his directions are mcg three to four times a day. He is going on holiday for six weeks and it is appropriate for you to advise the patient that he should take two inhalers on holiday with him.
 Atrovent® inhaler 20 mcg has 200 doses (BNF pg 218)
If patient needs maximum dose = 2 puffs four times a day = 8 puffs a day
8 x 42 days = 336 doses
Two inhalers required
 TRUE

16. Question 8
You have been asked to prepare 300 mls of Magnesium Trisilicate Mixture BP. You will be required to use 12 g of light magnesium carbonate.
BNF Magnesium Trisilicate Mixture BP contains 5% light magnesium carbonate (BNF pg 61)
5% = 5 g in 100 mls = 15 g in 300 mls
 FALSE

17. Question 9
A patient is receiving Nutriflex Lipid plus® 2500 ml infusion. The prescriber wishes to increase the potassium content of the bag to 80 mmol. It would be appropriate for you to suggest that 10 mls of Potassium Chloride Concentrate is added to the bag.
 Nutriflex Lipid plus® 2500 ml contains 28 mmol K+ per litre = 70 mmol K+ (BNF pg 875)
Need to add 10 mmol K+
Potassium chloride concentrate contains 20 mmol K+ per 10 ml
(BNF pg 863) Add 5 mls Potassium chloride concentrate
 FALSE

18. Question 10
A pharmacist adds 59 mls water to an antibiotic powder to produce 100 ml of a 125 mg / 5 ml solution. The displacement volume of the antibiotic powder is 9 mls per 125 mg antibiotic.
 A x x = 100 x 125 = 2500 mg
Vol
Amount water displaced = 100 – 59 = 41 mls
DV y y = 125 x 41 = 2.05 mls per 125 mg antibiotic A
FALSE

19. Question 11
9.17g base is required to produce 10 x 1 g suppositories each containing 125 mg paracetamol given that the displacement value of paracetamol is 1.5.
 10 suppositories will need 10 x 125 mg = 1250 mg or 1.25 g paracetamol
10 x 1 g base = 10 g base
 Displacement value = weight of drug that displaces 1 g base
Displacement amount:
Paracetamol x=1 x 1.25 = g base
Base x
 Therefore amount of base required = (10 x 1) – = 9.17 g base
 TRUE

20. Question 12
Lithium carbonate (RMM 74 g) is a prescription-only medicine, but if it is in preparations intended for internal use with a maximum dose of 5 mg (calculated as base) and a maximum daily dose of 15 mg (calculated as base) the preparation is a P medicine. A tablet containing 20 mg of lithium carbonate to be taken three times a day can be sold over the counter. Lithium base has a RMM of 14 g.
Base x x = 20 x 14 = 3.78 mg – less than 5 mg
Salt so single tablet okay
One tablet 3 times a day = 3 x 3.78 mg = mg so daily dose okay
TRUE

21. Question 13
A syringe driver contain 5 mls of injection Y and has a length of 60 mm. Injection Y is a strength of 5 mg/ml. If a patient needs to receive 3 mg of drug Y per hour, the syringe driver should be set at a rate of 7.2 mm / hr.
Injection Y is 5 mg / ml = 25 mg within 5 mls syringe driver
 Inj x = 3 x 5 = 0.6 mls
Vol x
 Mm y y = 60 x = 7.2 mm / hr Ml
TRUE

22. Question 14
A patient is given an intravenous dose of gentamicin and his one-hour peak serum concentration is found to be 13.5 mg/litre. Given that 10 hours later his serum concentration is mcg/mL the elimination half-life of gentamicin in this patient is 2.5 hours. (You can assume that the distribution is complete and the elimination is described by a 1st order process)
Peak = 13.5 mg/L = mcg/L = 13.5 mcg/mL
mcg/mL
t t t t t hrs
FALSE

23. Question 15
A consultant wishes to prescribe rifabutin for an immunocompromised patient for the prophylaxis of Mycobacterium avium infection. The patient is 37 years old, weighs 56 kg and is 1.68 m tall. On his medical notes you notice that the serum creatinine is 0.13 micromol / ml. It is appropriate for you to recommend 300 mg once daily for prophylactic treatment.
Body surface area (m2) = √ [ {wt (kg) x ht (cm)} / 3600]
Creatinine clearance mL/min = constant x (140-age) x ideal wt (kg)
serum creatinine (micromole/L)

24. Question 15 Constant = 1.04 (for women); 1.23 (men)
creatinine = 0.13 micromole/mL = 130 micromole/L
wt = 56 kg
 creatine clearance = 1.23 x (140-37) x =54.57 mL/min
130
 Body SA = √ [ {wt (kg) x ht (cm)} / 3600]
 = √ [ {56 x 168} / 3600]
= 1.62 m2
Creatinine clearance = mL/min for 1.62 m2
= mL/min/1.73 m2
 BNF (pg 507)
If creatinine clearance is less than 30 mL/min/1.73 should half normal dose so this dose is fine for this patient
TRUE

25. Exercise 2

26. Exercise 2 Answers 1 6 11 2 7 12 3 8 13 4 9 14 5 10 15