# Several Math Practice Questions

by Kristin
(Louisiana)

1. How many grams of salicylic acid powder are needed to prepare 60 grams of a 25% w/w ointment if you have 100 grams of a 1% w/w ointment available to you?

2. How many grams of pure coal tar should be added to prepare a prescription for 5% coal tar in ointment base with a total weight of 60 grams?

3. How many ml of a commercially available phenobarbital 130mg/ml solution are needed to prepare 1L of a 10mg/ml pediatric solution?

4. How many grams of pure hydrocortisone powder are needed to prepare 45 grams of a 3% w/w ointment if you mix the powder with 0.5% hydrocortisone ointment? (Pure hydrocortisone powder is 100%)

5. Humalog Mix 75/25 contains 75% long acting insulin and 25% short acting insulin. How many units of long acting insulin are found in 63 units of Humalog Mix?

6. Humalog Mix 75/25 contains 75% long acting insulin and 25% short acting insulin. If the initial dose of Humalog Mix is 0.3units/kg/day, how many units of long acting insulin will a 42 year old female weighing 212lb receive per day?

7. Humalog Mix 75/25 contains 75% long acting insulin and 25% short acting insulin. The total daily dose is 21.6 units per day. If an insulin pen contains 3ml (100units/ml). How many days until the pen is empty?

8. Humalog Mix 75/25 contains 75% long acting insulin and 25% short acting insulin. How many units of short acting insulin are found in 63 units of Humalog Mix?

9. You are to prepare 2oz of Folic Acid 100mcg/ml using a stock of Folic Acid 5mg/ml. How many ml of diluent are needed? How much Folic Acid in ml do you need?

10. A loading dose of an anticonvulsant medication for children is 20mg/kg and infused at a rate of 0.5mg/kg per minute, over how many minutes would a dose be administered for a child weighing 50lb?

11. Calculate the amount of zinc sulfate in grams to fill the following prescription: Zinc sulfate 0.1% Boric acid 1:10 Distilled water qs ad 100ml.

12. Use the following concentrations to solve the problem. Gentamicin 80mg/ml

Magnesium sulfate 50% Atropine 1:200 10mg atropine =_ml

13. Use the following concentrations to solve the problem. Lidocaine 1% Heparin 10,000units/ml solution Folic acid 5mg/ml 300mg Lidocaine= _ml

14. An IV fluid containing NS is running at 125ml/h. how many 1L bags will be needed per day?

15. A drug order requires 50ml of a 2% neomycin solution. How much neomycin concentrate (1g/2ml) is needed to fill the order?

16. Humulin N 100units/ml 10ml vials are available. The patient has a prescription that reads “10units Q AM and 15units Q PM." How many days will the vial last?

17. Cleocin T 2% topical product used for acne. How many grams of clindamycin would be contained in a 2oz container?

18. A physician orders a 5% ophthalmic ointment. How much drug (in grams) would be needed to prepare a 3 gram tube of ointment?

19. A medication order is received for a child for dexamethasone 0.15mg/kg/day divided into two doses. The patient weighs 11kg. Dexamethasone solution injection is available as 4mg/ml concentration. You are asked to prepare 4ml of a pediatric dilution of dexamethasone (final concentration 100mcg/ml) from the commercially available solution.

a. How much of the dexamethasone solution is needed to prepare the pediatric dilution?
b. How much sterile water for injection is needed in ml to prepare the pediatric dilution?
c. How many ml of the dexamethasone pediatric dilution are needed to prepare one dose of the dexamethasone for this patient?

20. An order is received for piperacillin/tazabactom 3.375g IV every 6 hours in 100ml of NS infused over 1 hour. A bulk vial contains 40.5g of piperacillin/tazabactom.

a. How many ml/min will the patient receive during each infusion?
b. How many ml are needed to prepare one dose?
c. How many doses can be prepared from one bulk vial?

21. An order is received for amiodarone 150mg in 100ml of D5W infused over 10 minutes. A 3ml vial (50mg/ml) of amiodarone solution is available to prepare the infusion. If the administration set delivers 15 drops/ml.

a. How many drops per minute will this patient receive?
b. At what rate (ml/min) should the medication be infused?

### Comments for Several Math Practice Questions

 Several math practices questions by: Anonymous Where is the answer for all these questions?

 Problems 1,2,3 by: Brad Wojcik, Pharm D Problem 1) This is an alligation problem. Draw a box and put 25 in the middle, 1 in the lower left corner and 100 in the upper left corner. Take the difference diagonally and you get 24 in upper right and 75 in lower right. You have a total of 99 parts. 24/99 parts are the 100% salicylic acid and 75/99 parts are the 1% oint. (24/99)(60 g) = 14.5 g of sal acid (75/99)(60 g) = 45.5 g 1% oint. Problem 2) 5% ( 60 g) = 0.05 (60 g) = 3 gProblem 3) It is easiest to use V1C1=V2C2 1000 mL (10 mg/ml) = V2 (130 mg/mL) V2 = 1000 mL (10 mg/mL)(1 mL/130 mg) = 76.9 mL

 Problems 4,5,6 by: Brad Wojcik, Pharm D Problem 4) This is an alligation problem. Draw a box and put 3 in the middle, 0.5 in the lower left corner and 100 in the upper left corner. Take the difference diagonally and you get 2.5 in upper right and 97 in lower right. You have a total of 99.5 parts. 2.5/99.5 parts are the 100% HC and 97/99.5 parts are the 0.5% oint. (2.5/99.5)(45 g) = 1.13 g of HC powder (97/99.5)(45 g) = 43.87 g 0.5% oint.Problem 5) 63 units (0.75) = 47.25 unitsProblem 6) 212 lb (1 kg/2.2 lb) (0.3 units/kg day)(0.75) = 21.7 units/day

 problems 7,8,9 by: Brad Wojcik, Pharm D Problem 7) 3 mL(100 units/mL)(1 day/21.6 units) = 13 days Problem 8) 63 units (0.25) = 15.75 unitsProblem 9) Calculate number of mg of folic acid needed in the 2 oz. 2 oz (30 mL/oz)(100 mcg/mL)(1 mg/1000 mcg) = 6 mgNow calculate how many mL of the stock solution you need to get the 6 mg. 6 mg (1 mL/5 mg) = 1.2 mL

 Problems 10,11,12 by: Brad Wojcik, Pharm D Problem 10)1) First change lb to kg for the patient.50 lb (1 kg/2.2 lb) = 22.7 kg2) Calculate total mg to be infused.22.7 kg (20 mg/kg) = 454 mg3) Calculate mg/min for this patient.22.7 kg (0.5 mg/kg min)= 11.35 mg/ min4) Calculate number of minutes needed to infuse 454 mg at the rate of 11.35 mg/min.454 mg (1 min/11.35 mg) = 40 minProblem 11) 100 mL (0.1 g/100 mL) = 0.1 gProblem 12) 1:200 means 1 g/200 mL ( or 1000 mg/200 mL)10 mg (200 mL/1000 mg) = 2 mL

 Problems 13,14,15 by: Brad Wojcik, Pharm D Problem 13) 1% solution is 1 g/100 mL or 1000 mg/1000 mL. 300 mg(100 mL/1000 mg) = 30 mLProblem 14) 24 h( 125 mL/h)(1 bag/1000 mL) = 3 bagsProblem 15) Using V1C1=V2C2 50 mL(2 g/100 mL)= V2 (1 g/2 mL)V2= 50 mL(2 g/100 mL)(2 mL/1 g) = 2 mL

 Problems 16,17,18 by: Brad Wojcik, Pharm D Problem 16) Pt will receive 25 units/day. 1 vial (10 mL/vial)(100 units/mL)(1 day/25 units) = 40 daysProblem 17) 2 oz (30 mL/oz)(2 g/100 mL) = 1.2 g Problem 18) 3 g oint (5 g active ing/100 g oint) = 0.15 g AI

 Problems 19,20,21 by: Brad Wojcik, Pharm D Problem 19 ) a) Calculate mg needed to make the ped dilution. 4 mL (100 mcg/mL)(1 mg/1000 mcg) = 0.4 mg . Now calculate amount of concentrate needed for 0.4 mg. 0.4 mg (1 mL/4 mg) = 0.1 mLb) The total volume is 4 mL and the concentrate is 0.1 mL so the diluent would be 3.9 mL.c) 11 kg (0.15 mg/kg day)(1 day/2 dose)(1 mL/ 100 mcg)(1000 mcg/1 mg) = 8.25 mL/doseProblem 20) a) 100 mL/60 min = 1.7 mL/minb) can’t do this because only the weight of the drug is given, not the volume.c) 40.5 g (1 dose/3.375 g) = 12 dosesProblem 21) a) 100 mL/10 min (15 gtt/ml) = 150 gtt/minb) 100 mL/10 min = 10 mL/min