Health care math

Health care math


Mr. T, a terminally ill prostate cancer patient has pain that is well controlled on Morphine Sustained Action, 90mg every 8 hours. He additionally uses 2 PRN doses of 30 mg Morphine IR each day. Mr. T is now unable to swallow and so the Morphine needs to be converted into a transdermal fentanyl patch. Calculate the hourly dose of the fentanyl patch and choose the closest match in available patches.



100 mcg/hr

200 mcg/hr

150 mcg/hr

125 mcg/hr



Mr. J is a 60-year-old lady with history of metastatic colon cancer. She is currently admitted to your unit for terminal care. She has moderate to severe pain which is well controlled on sustained release Morphine (MS Contin) 240 mg every 12 hours. For the past 12 hours Mrs. J has developed difficulty swallowing her medications. Adjusting for partial cross-tolerance (less 25%), the calculated equianalgesic hourly basal dose of a subcutaneous hydromorphone infusion is:


1 mg/hr

0.75 mg/hr

1.5 mg/hr

0.60 mg/hr



Mrs. S is a 55-year-old lady with history of metastatic breast cancer, s/p bilateral mastectomy and several rounds of chemotherapy. She is currently admitted for another round of palliative chemotherapy. The oncology team asks you to help with her pain management. She has moderate to severe unstable pain which you manage to control with morphine subcutaneous infusion at 10mg per hour. Mrs. S completes her chemotherapy and is now ready for discharge. Over the last 2 days her pain is well controlled, and you now want to switch her to oral morphine sulfate. Please calculate the equianalgesic dose of oral morphine. The equianalgesic dose of morphine sulfate sustained action (MS Contin) is _________ every 12 hours. ( Do Not adjust for Incomplete cross tolerance)


120 mg

240 mg

360 mg

480 mg

Mr. R is an 88 year old male with widely metastatic prostate cancer. He has opted for comfort care and is currently an in-patient at your hospice unit. His pain has been well controlled on sustained release oral Morphine (MS Contin) 150mg every 12 hours. You notice that for the last two days, Mr. R has had increasing difficulty swallowing and you want to switch him to a hydromorphone infusion. The correct equianalgesic dose of the basal hydromorphone infusion (not adjusting for cross-tolerance) for this patient is Hydromorphone _________ as a continuous infusion.


0.1 mg/hour

0.3 mg/hour

0.6 mg/hour

2 mg/hour



A 68 year old terminally ill cancer patient with bone mets is being converted to Methadone therapy. He is currently receiving 32 mg of Dilaudid every 8 hours. He can also receive 8 mg Dilaudid for breakthrough pain every 2 hours. He used all available PRN doses for the last 24 hours. First convert the PO Dilaudid to PO Morphine. What is the recommended Morphine to Methadone conversion?


1 mg Methadone: 5 mg Morphine

1 mg Methadone: 10 mg Morphine

1 mg Methadone: 20 mg Morphine

Number is too high to suggest conversion





  1. The PCA pump is running continuously at 2 mL/hr. The patient can get a 1.5 mL bolus every 10 minutes as needed. The remaining volume in the bag is 112 mL. How many hours until the bag will need to be changed if the patient is using 5 boluses each day? (Round to the nearest hour)


48 hours

40 hours

52 hours

36 hours



  1. Your patient can have 0.250 mg of Hyoscyamine for tracheal secretions every 4 hours as needed. On hand, the patient has elixir with a concentration of 0.125 mg/mL. What is the dose, in milliliters, the patient will take the sublingual route?


0.5 mL

2 mL

0.2 mL

1 mL

  1. Your chronic pain patient is taking 25 mg of Morphine every 4 hours for breakthrough pain in addition to her around the clock medication. How many mL will her dose be if the Morphine oral concentrate comes in 100mg/ 5mL?


1.25 mL

1.5 mL

5 mL

1 mL



  1. You have on hand, Tramadol suspension in a concentration of 10 mg/mL. The patient is ordered to take 35 mg every 12 hours for pain. How many milliliters will the patient take?


0.35 ml

35 ml

3.5 ml

30 ml



  1. Your patient needs to take Lorazepam, as ordered, for an episode of anxiety. The order reads 1 mg PO every 6 hours PRN for anxiety. On hand you have 2 mg /mL oral concentrate. How many mL will your patient need to take at each dose?


2 mL

0.25 mL

1 mL

0.5 mL



  1. Your patient is ordered 100 mg Trazodone, at bedtime, for insomnia. You have on hand, 50 mg tablets. How many tablets will your patient take?


0.5 tablet

1 tablets

2 tablets

1.5 tablets



  1. The PCA pump is running at 10 mL/hr and has a PRN bolus of 7.5 mL with a lockout period of 10 minutes. The patient reports using 2 boluses each day at bedtime. The bag has 212 mL remaining. How many hours until the bag will need to be changed? (Round to the nearest hour)


15 hours

20 hours

25 hours

10 hours



  1. Your patient is ordered liquid suspension of Dextromethorphan/Guaifenesin for cough as needed every 4 hours. The doctor wants him to have 400 mg of Guaifenesin at each dose. The suspension on hand contains 20 mg Dextromethorphan and 200 mg Guaifenesin in every 10 ml (20/200). How many ml will the caregiver administer at each dose?


4 ml

2 ml

15 ml

20 ml



  1. Your patient is ordered 375 mg of Ciprofloxacin for an ear infection. On hand, you have 750 mg tablets. What will you instruct your patient to administer?


2 tablets

1 tablet

1.5 tablets

0.5 tablets



  1. The PCA pump is set for 1.5 mL/hr and 0.5 mL bolus as needed every 10 minutes. The patient is using 6 boluses on average each day. How many hours until the pump will run out if the reservoir volume is at 79 mL? (Round to the nearest hour)


40 hours

39 hours

49 hours

30 hours



  1. Your patient is agitated and has a new order for Lorazepam 0.5 mg every 6 hours PRN agitation. Your Lorazepam arrived in 1 mg tablets. How many tablets are needed per dose?


2 tablets

1 tablet

1/2 tablet

3 tablets



  1. Your patient has an order for Prochlorperazine Maleate 20mg by mouth every 6 hours for nausea/vomiting. The medication has arrived in 10mg tablets. How many tablets would be given for each 20mg dose?


1 tablets

2 tablets

1/2 tablet

1 1/2 tablets



  1. Your patient is ordered 25 mg oral dose of Tramadol, to take every morning, for pain. They can increase the dose by 25 mg every 3 days to a max of 75 mg. On hand, you have 50 mg tablets. What will you instruct the patient on day one and day three?


1 tablet and 1.5 tablets

0.5 tablets and 2 tablets

1 tablet and 2 tablets

0.5 tablet and 1 tablet



  1. The PCA pump is continuously infusing Morphine at a rate of 7.5 mL/hr. The patient can also receive a 4 mL bolus every 15 minutes and the pump shows the patient is using approximately 12 boluses each day. The pump shows that 127 mL are left in the pump. How many hours until the PCA bag will need to be changed? (Round to the nearest hour)


10 hours

13 hours

23 hours

9 hours



  1. Your patient is getting Phenobarbital 60 mg by mouth Elixir, once daily at bedtime, for seizure control. The oral elixir comes in a 20mg/ 5mL concentration. How many mLs will the patient need to take at bedtime?


60 mL

30 mL

15 mL

5 mL


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