IPS module 3 practice math questions

Using a graduated cylinder, a pharmacist measured 30 mL of a liquid. On subsequent examination, using a narrow-gauge burette, it was determined that the pharmacist had actually measured 32 mL. What is the percentage of error in the original measurement?

% error= (error in measurement/ quantity desired)*100 Error in measurement is 32 mL-30 mL = 2 mL Percent error = 2 mL/30 mL = 6.67%

In compounding a prescription, a pharmacist weighed 0.05 gram of a substance on a balance insensitive to quantities smaller than 0.004 gram. What was the maximum potential error in terms of percentage.

(0.004/0.05)*100= 8%

If a 80-gram tube of an ointment contains 12 grams of active ingredient, what is the percent concentration of active ingredient in the ointment?

(12/80)*100= 15%

A Rx asks for an antibiotic suspension for a 10 year old with a dose of 12.5 mg/5 ml. You have a suspension with a concentration of 25 mg/5 ml (total volume 200 ml). The dose regime calls for a 100 ml final product. How much of the 25mg/5 ml suspension do you have to take to get a 12.5 mg/5 ml suspension?

(1ST quantity)(1st concentration) = (2nd quantity)(2nd concentration) (x)(25mg/5ml) = (100 ml)(12.5 mg/5ml) X = 50 ml Take 50 ml of the 25 mg/5 ml suspension, add 50 ml of appropriate solvent (i.e. dilute) to make a final product of 12.5 mg/5 ml suspension

A pharmacist attempts to weigh 0.375 gram of morphine sulfate on a balance of dubious accuracy. When checked on a highly accurate balance, the weight is found to be 0.400 gram. Calculate the percentage error in the first weighing.

(25/375)*100= 6.67%

A pharmacist weighed 475 milligrams of a substance on a balance of dubious accuracy. When checked on a balance with high accuracy, the weight was found to be 445 milligrams. Calculate the percentage or error in the first weighing.

(30/475)*100= 6.3%

During a clinical study, 48 out of a total of 2430 patients developed headache. Calculate the percent of patients who expressed this adverse effect.

(48/2430)*100= 2%

A patient is instructed to take one 50 μg tablet of pergolide mesylate (Permax) a day for the first two days of treatment; 150 μg/day on the third, fourth, and fifth days of treatment; 250 μg/day on sixth, seventh and eighth days; and 350 μg on the ninth day and return for further assessment. During this treatment period, how many milligrams of drugs were taken?

(50*2)+(150*3)+(250*3)+350 1,650 micrograms=1.65 mg

A clinical study for a new drug demonstrated that the drug met effectiveness criteria in 676 patients of the 940 patients enrolled in the study, express these results as a percent.

(676/940)*100= 72%

If 1500 g of a solution contains 75 g of a drug, what is the %w/w of the solution?

(75/1500)*100= 5% w/w

Calculate the volume in mL; of 100 g of each of the following? - Peanut oil (SG = 0.92) - Castor oil (SG = 0.96) - Polysorbate 80 (SG =1.08) - Phosphoric acid (SG = 1.70)

- Peanut oil 100/0.92= 108.7 - Castor oil 100/0.96= 104.17 - Polysorbate 100/1.08= 92.6 - Phosphoric acid 100/1.70=58.8

Express 1:4000 as a percentage strength

0.025% 1/4000=x/100

If an injectable solution contains 25 μg of a drug substance in each 0.5 mL, how many milliliters would be required to provide a patient with 0.25 mg of the drug substance?

0.025/0.25=0.5/x x=5 mL

In what proportion must glycerin with a specific gravity of 1.25 and water be mixed to prepare a liquid having a specific gravity of 1.10?

0.1 parts of glycerin + 0.15 parts of water

A liquid contains 0.25 mg of a substance per milliliter. How many grams of the substance will 3.5 L contain?

0.25/x=1/3500 875/1000=0.875g

A pharmacist had 5 grams of codeine sulfate. She used it in preparing the following: • 8 capsules each containing 0.0325 gram; • 12 capsules each containing 0.015 gram; • 18 capsules each containing 0.008 gram; How many grams of codeine sulfate were left after he had prepared the capsules?

0.26+ 0.18+0.144=0.584 5-0.584= 4.416 g

A pharmacist is to prepare 10 mL of amikacin sulfate in a concentration of 0.4 mg/0.1 mL for ophthalmic use. Available is an injection containing amikacin sulfate, 250 mg/mL. How many milliliters of this injection and of sterile normal saline solution as diluent should be used?

0.4/0.1=x/1 x= 4g/mL 4 parts= 0.16 mL 246 parts=9.84 mL 250 total parts=10 mL 0.16 mL of 250 mg/mL injection 9.84 mL of diluent

A formula calls for 0.2 mL of hydrochloric acid. Using a 10 mL graduate calibrated from 1 to 10 mL in 0.5 mL divisions, explain how you would obtain the desired quantity of hydrochloric acid by the aliquot method. (multiple of 5)

0.5 mL is the minimum (measuring at least 1 mL to be safe) 0.2 mLx 5= 1 0.8 mLx 5=4 mL 1 mLx 5= 5 mL Then can take a pipette and take 1 mL of this that would have 0.2 mL of HCl

A pediatric vitamin drug product contains the equivalent of 0.5 mg of fluoride ion in each milliliter. How many milligrams of fluoride ion would be provided by a dropper that delivers 0.6 mL?

0.5/x=1/0.6 0.3 mg

How many grams of an 8% w/w progesterone gel must be mixed with 1.45 g of a single-use 4% w/w progesterone gel to achieve a gel of 5.5% w/w strength?

0.54 g of 8% w/w progesterone gel will be mixed with 1.45 g of 4% w/w progesterone gel.

Convert 568g to kg Convert 568g to mg

0.568 kg 568,000 mg

An injection contains 3 mg of medication in each milliliter (mL). If a physician prescribes a dose of 0.5 mg to be administered to a hospital patient three times daily, how many milliliters of injection will be required over a 5-day period?

0.5x3=1.5x5= 7.5 3/7.5=1/x 3x=7.5 x=2.5 2.5 mL over a 5-day period

What is the percentage strength v/v of a solution of 800 g of a liquid with a SG of 0.8 in enough water to make 4000 mL?

0.8= 800/x x=1000 1,000:4,000 1:4 25% v/v

If an intravenous fluid is adjusted to deliver 15 mg of medication to a patient per hour, how many milligrams pf medication are delivered to a patient per half minute.

1 hr=60 min=120 half min 15/120=x/1 120x=15 x=0.125

If you have 200 mg of cocaine and need to prepare a 1% cocaine solution, what volume of solution in milliliters will you make?

1%= 1g/100mL 1g/100 mL= 0.2g/x x=20 mL

A low-strength aspirin tablet contains 81 mg of aspirin per tablet. How many tablets may be prepared from 1 kg aspirin?

1,000,000 mg/ 81 mg= 12,345 tablets

Review the following formula and answer the question: Drug B Formulation: Component I- 10 parts Component II-20 parts Component III-40 parts Calculate the volume of each component you will need to prepare a 100 mL formulation of drug B.

1. 70/10=100/x x=14.29 mL 2. 70/20=100/x x=28.57 mL 3. 70/40=100/x x=57.14 mL Total= 100 mL

Prescription for 60 g of a 0.75% w/w bexarotene gel. How many grams of each of a 1% w/w bexarotene gel and gel base must be used?

1.25 parts=60g 1.25/60=1/x x=48g (0.75%= 48g and 1%=12g)

How many grams of 2.5% hydrocortisone cream should be mixed with 360 g of 0.25% cream to make a 1 % hydrocortisone cream?

1.5x=360 x=240 0.75 parts=180g 180 g of 2.5% hydrocortisone cream should be mixed with 360 g of 0.25% cream

How many milliliters of a 1:250 w/v should be used to make 1 L of a 1: 1000 w/v solution? If the diluent is water, how much should be added?

1/250=0.004 x100= 0.04% 1/1000=0.001 = 0.01% 0.04x=0.01*1 0.01/0.04=0.25 0.25 L*1,000= 250mL 1:250 w/v of solvent If its water (1 mg=1 mL) 1000-250=750 mL

Express 1:420 as percentage strength

1/420=x/100 x=0.24%

How many mg of iodine should be used to compound this prescription Iodine 1:500 Hydrophilic ointment ad 8g

1/500=x/8 X=0.016g x1000 X=16 mg

How many milliliter of a 37% w/w HCl (specific gravity = 1.20) are required to make a 1 L 10% w/v solution?

10% w/v solution is 10 g in 100 mL As such 1L solution will contain 100 g 37% w/w = 37 g in 100 g; so 100 g will be present in 270 g of the formulation (37g/100g=100x x=270g) Convert SG to volume SG = weight/volume 1.20 = 270 g/ volume; volume = 225 mL (Answer) So take 225 mL of 37% w/w HCL and make the volume to 1L.

A cough syrup contains 10mg of dextromethorphan hydrobromide per 5mL. How many milligrams of the drug are contained in a 120 mL container of the syrup?

10/x=5/120 240 mg of the drug will be in 120 mL container.

If an insulin injection contains 100 units of insulin in each milliliter, how many milliliters should be injected to receive 40 units of insulin?

100/40= 1/x 0.4 mL

What is the ratio strength of 90 tablets of levothyroxine (each tablet is 125 μg) that is dissolved in enough water to make 500 mL?

11,250 ug= 0.01125g 0.01125g/1g= 500ml/ x x= 44,444 1:44,444

If 12 tablets contain 4000 milligrams of aspirin, how many milligrams should 5 tablets contain?

12/5=4,000/x 12x=20,000 x=1,667

What is the percentage strength (w/v) of a solution of urea if 80 mL contains 12 g?

12/80=x/100 x=15%

What is the specific gravity of a solution having a volume of 1.5 L and weighing 1200 grams?

1200/1500=0.8

A formula for 1250 tablets contains 6.25 grams of diazepam. How many grams of diazepam should be used in preparing 350 tablets?

1250/350=6.25/x 1.75 grams of diazepam will be needed to prepare 350 tablets

The Rx asks for 150 ml 10% calcium-gluconate solution. You have a 20% and 5% solution on hand. How much of each do you mix to get a 10% solution?

15 parts= 150 mL 15/100=5/x x=50 mL of 20% 15/100=10/x x=100 mL of 5%

How much drug should be used to prepare a 50 ml solution, where 5 ml of this solution diluted to 500 ml will yield a 1:1000 solution?

1:1000 is 1 gram in 1000 ml 1/1000=x/500 X = 0.5 g (0.5 g) (500 mL) = (x g)( 50 mL) X = 5 g. Therefore 50 ml will contain 5 grams. 500 ml will contain 0.5 g

Express 0.02% as a ratio strength

1:5000 0.02/100=1/x X=5,000

What is the ratio strength (w/v) of a solution made by dissolving five tablets , each containing 2.25 g of sodium chloride, in enough water to make 1800 mL

2.25x5=11.25 11.25/ 1800= 1/x x=160 1:160

20 mg of atorvastatin but he weighed 19.5 what is the error

2.5% error

How many kilograms of hydrocortisone should be used to compound the following prescription? Hydrocortisone 2.5% Hydrophilic ointment ad 100 g

2.5/1000= 0.0025 kg

In what proportion should 20% benzocaine ointment be mixed with an ointment base to produce a 2.5% benzocaine ointment?

2.5/17.5=1/x 1:7

A certain injectable contains 2 mg of a drug per milliliter of solution. What is the ratio strength (w/v) of the solution?

2/1000=0.002 1:500

How many milliliters of each of a 20% w/v solution and a 70% w/v solution should be used in preparing 1 gallon of a 3.5% solution? 1 gallon is 3785 mL

20 g/mL 70g/mL 3032.6 mL of 20% w/v solution and 752.4 mL of 70% w/v solution will be mixed together.

A prescription calls for 20 μL of clove oil. Using 5-mL graduate calibrated in units of 0.5 mL, how would to obtain the required amount of clove oil using aliquot method and alcohol as diluent? (multiple of 50)

20 microliters= 0.02 mL 0.02 x 50= 1mL 0.98x50= 49 mL 1mL x50= 50 mL 1 mL would contain 0.02 mL of the drug

If 20 tablets contain 4000 milligrams of aspirin, how many tablets should 800 milligrams?

20/x=4,000/800 4,000x=16,000 x=4 tablets

Acyclovir suspension contains 200 mg of acyclovir in each 5 mL. How many milligrams of acyclovir are contained in 472 mL of suspension?

200/x=5/10,000 18,880 mg of acyclovir are contained in 472 mL of suspension

How many ml of a 2 M MgSO4 solution should be used to make a 100 ml of a 50 mM solution?

2000x=50*100 X=2.5 ml

As part of a clinical study, a pharmacist is asked to prepare modifications of standard 22 g, 2% w/w mupirocin ointments by adding non-medicated ointment base. Required for the clinical study is 1.75% w/w mupirocin ointment. Calculate the amount of non-medicated ointment base you need to add to the standard ointment to obtain the required formulation.

22x2=Cx1.75 44/1.75=25.142g 25.142-22= 3.14g X= 25.14 g of the required ointment will be prepared. The amount of non-medicated ointment base will be 25.14 g- 22.0 g = 3.14 g Have to subtract because you are seeing how much to add

How many ml of liquefied phenol should be used to make a 2.5% solution with a total of 240 mL?

240 x 0.025= 6mL

How many milliliters of water must be added to 250 mL of a 25% w/v stock solution of sodium chloride to prepare 0.9% w/v sodium chloride?

25%* 250=0.9%* x x=6944-250= 6694.4mL

An elixir contains 25 mg of drug in each 5 mL. How many milligrams of the drug would be used in preparing 4000 mL of the elixir?

25/x=5/4,000 5x=100,000 x=20,000 mg

How many grams of digoxin (Lanoxin) would be required to make 25,000 tablets each containing 250 mcg digoxin?

250/1000=.25 mg/1000= 0.00025*25,000= 6.25 g

If 400 mL of a 20% w/v solution were diluted to 2 liters, what would be the percentage strength?

2L=2,000 mL 20%*400= 2,000x x=4% 4% w/v

How many colchicine tablets, each containing 600 mcg, may be prepared from 30 g colchicine?

30/0.0006=50,000 tablets

If a pharmacist added 12 g of azelaic acid to 50 g of an ointment containing 15% azelaic acid, what would be the final concentration of azelaic acid in the ointment?

31.5% w/w

What is the weight, in grams, of 3620 mL of alcohol with a SG of 0.82?

3620 mLx0.82=2968.4 g

Acetaminophen, in amounts greater than 4 g per day, has been associated with liver toxicity. What is the maximum number of 500-mg tablets of acetaminophen that a person may take daily and not reach the toxic level?

4,000/500= 8 tablets

In preparing 250 ml of a lotion, you use 4 ml liquefied phenol. What is the percentage (v/v) of the liquefied phenol in the lotion?

4/x=250/100 x=1.6% v/v

You want to make 120 mL of a solution that is 60% v/v isopropyl alcohol (IPA) in water, and you want to use a 70% IPA solution and a 30% IPA solution. How many milliliters of each will you need?

40 parts= 120ml 40/120=30/x x=90 mL of 70% IPA 40/120=10/x x=30 mL of 30% IPA

A penicillin V potassium preparation provides 400,000 units of activity in each 250 mg tablet. How many total units of activity would a patient receive from taking four tablets a day for 10 days?

400,000/x=250/10,000 16,000,000 units

What is the volume, in mL, of 400 g of nitric acid, SG of 1.40.

400/1.4=285.71 mL

Calculate the total weight of the following formula for a pediatric chewable gummy gel base for medication? Gelatin: 43.4 g Glycerin: 155 mL (SG=1.25) Purified water: 21.6 mL

43.4g+ 21.6g=61.5g 1 mL H2O=1 g H2O SG= g/ml SG*mL=g 1.25x 155=193.75+61.5=258.75 g

If 30 milliliters (mL) represent 1/6 of the volume of the prescription, how many milliliters will represent 1⁄4 of the volume?

45 mL

How many mL of a nonmedicated base must be added to 1 pint of ranitidine syrup, 15 mg/mL to change its concentration to 5 mg/ml? (1 pint= 473 mL)

473x15=5x 473x15=7,095 7095/5=1419 1419-473=946 mL

How many milliliters of liquefied phenol should be used in compounding the following: Liquefied phenol 5% Calamine lotion 500 mL

5%= V/V 5mL in 100mL 500x.05=25 mL

How much water should be mixed with 5 L of a 85% v/v alcohol to make 50% v/v alcohol.

5*85=425 425/50=8.5-5L= 3.5L So, add 3.5 L of water + 5L of alcohol to make the final product.

An injection contains 5 mg of drug in each 10 mL vial. If the dose of the drug for a patient is determined to be 150 μg, how many milliliters should be administered?

5/0.15=10/x x=0.3 mL

How many grams of dextrose are required to make 4000 mL of a 5% solution?

5/100=x/4000 100x= 20,000 X=200 g Or 4,000x.05=200.0 g

If 500 ml of a 15% solution is diluted to 1250 ml, what will be the % strength (v/v)?

500x15=1250x 500x15=7,500/1250= 6%

A prescription calls for 0.06 g of one ingredient, 2.5 mg of another, and enough of a third to make 0.5 g. How many milligrams of the third ingredient should be used?

60 mg+2.5 mg+x= 500mg x=437.5 mg

A capsule contains the following amounts of substances: 0.075 g, 20 mg, 0.0005 g, 4 mg, and 500 μg. What is the total weight of the substances in the capsule?

75 mg+20 mg+ 0.5 mg+ 4 mg+0.5 mg= 100 mg

How many grams of zinc oxide should be added to 3200 g of 5% zinc oxide ointment to prepare an ointment containing 20% of zinc oxide?

80 parts=3200 g x=40 40x15=600 g 600 g of zinc oxide + 3200 g of 5% zinc oxide ointment.

You want to make a 5% Drug XYZ ointment for a patient. You have in your pharmacy a 10% XYZ ointment and 1% XYZ ointment base. What would you do? How much of each component you would need to make the formulation?

9 parts= 100g 9/100=4/x x=44.4g of 10% 9/100=5/x x=55.56g of 1%

In a clinical study of niacin, as a lipid lowering drug, 60% of the 90 patients in the study group developed flushing. Calculate the number of patients having this reaction.

90*0.6 54 patients

The Class III prescription balance has a sensitivity of 6 mg. A. What % error would result in weighing 5 mg of a drug substance on the balance? B. How about the % error of weighing 200 mg?

A. 6/5x100=120% B. 6/200 x100= 3% equation: % error= (sensitivity/ quantity desired)x 100

If 10ml of sulfuric acid weighs 18g, what is its density?

Density=mass/volume Density = 18 (g)/ 10 (mL) Density = 1.8 g/mL

In a clinical study of divalproex sodium in patients prone to migraine headaches, nausea occurred in 40 of 202 patients whereas the use of a placebo resulted in nausea in 6 of 81 patients. Compare these data in terms of percent of subjects reporting nausea in each study group.

Drug group: 19.8% of subjects developed the S/E. Placebo: 7.4% of placebo subjects developed the S/E.

Assume that you have a prescription balance with sensitivity requirement of 5 mg. Present how you would weigh 5 mg of atropine sulfate with an accuracy ± 5%, using lactose as the diluent. (multiple of 20)

LWQ= (5/5)x100=100 mg 5x20=100 95x20=1,900 100x20=2,000

A prescription balance has a sensitivity requirement of 6.5 mg. Present how you would weigh 15 mg of atropine sulfate with an accuracy ± 5%, using lactose as the diluent. (multiple of 10)

LWQ= (6.5/5)*100= 130 total weight= 130 130=15+x x=115 15*10=150 115*10=1150 130x10= 1300 (final aliquot weight)

Assume that you need to weigh 5 mg of a prescription using a balance with sensitivity requirement of 6 mg and must maintain a percent error of not more than 5%. (multiple used 25)

LWQ= 120 mg total weight=120 mg 120=5+x x=115 5 mg x 25 = 125 mg 115 mg x25= 2875 mg 120x25=3,000mg (final aliquot weight)

What is the least weighable quantity that will result in an error of 5% or less on a Class III prescription?

LWQ= 6mg/5% X 100% = 120 mg LWQ= (sensitivity/%error toterated)*100

Express 5 ppm of iron in water as a ratio strength and percent strength

Ratio strength= 1:200,000 Percent strength= 0.0005%

How many milliliters of 50%w/v dextrose solution and how many milliliters of 5% w/v dextrose solution are required to prepare 4500 mL of a 10% w/v solution?

The total product is 45 parts corresponding to 4500 mL 50% w/v dextrose correspond to 5 parts 5% w/v dextrose corresponds to 40 parts 500 mL of 50% w/v dextrose solution will be mixed with 4000 mL of 5% dextrose

Review the following formula and answer the question: Drug A Formulation: Component I- 10 mL Component II- 40 mL Component III- 150 mL What is the total volume of the formulation? What is the percentage of component II in the formulation?

Total volume= 200 mL 40/200=0.2 x100= 20%

If 54.96ml of an oil weighs 52.78g, what is the SG of the oil?

Volume substance= volume of water 54.96 mL= 54.96 mL SG=0.9603

If a pint of a certain liquid weighs 500 g, what is the SG of the liquid? Note that I pint (16 fl.oz) = 473 mL

Weight of 473 mL of water= 473 g SG=500g/473 g= 1.06 (unitless)

A 500-mL pycnometer is found to weigh 120 g when empty, 171 g when filled with water, and 160 g when filled with an unknown liquid. Calculate the SG of the unknown liquid.

Weight of water = 171-120 g = 51 g Weight of unknown liquid: 160 -120 g = 40 g SG = 40 g/51 g SG = 0.78

The literature for a pharmaceutical product states that 26 patients of the 3103 enrolled in a clinical study reported headache after taking the product. (a) Calculate the decimal fraction and (b) the percentage of patients reporting this adverse effect.

a= 0.0084 b=0.84%

Calculate the weight in grams of 0.1 liter of suspension having a density of 7.22 g/mL

d=m/v x/100ml=7.22 x=722g

How many grams of potassium permanganate should be used in preparing 500 mL of a 1: 2500 solution?

x/500=1/2500= 0.2g