Appleton Pharmaceutical Calculations

Question 1

1. Micro, nano, atto, and mega are prefixes associated with which of the following measuring
   systems?

I. Avoirdupois
II. metric
III. Systeme International

(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II, and III

Answer 1

1. (D) The metric system is used exclusively in
   most nations in the world except the United
   States. The prefixes in the metric system are
   based on increasing or decreasing magnitudes
   of 10, 100, or 1000. Converting from
   one set of quantities to another simply requires
   the movement of decimal points. For
   example, converting 1 kg to g requires moving
   the decimal point three places to the
   right. The metric system has been expanded
   into the Systeme International (SI) measuring
   system that encompasses all types of measures.

Question 2

2. One hundred (100) micrograms equals (C)

I. 100,000 nanograms
II. 0.1 milligrams
III. 0.001 grams

(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II, and III

Answer 2

2. (C) In this example, consider one microgram
   as equaling 1000 nanograms; thus, 100 mcg =
   100,000 ng.
   Since 1 milligram equals 1000 mcg, 100
   mcg equals 0.1 mg. If 1 mg equals .001 gram,
   0.1 mg or 100 mcg equals 0.0001 g. It may be
   clearer if one solves this conversion using dimensional
   analysis.

Question 3

3. A patient’s serum cholesterol value is reported as 4 mM/L. This concentration expressed
   in terms of mg/dL will be (mol. wt. (E) 770mg
   cholesterol =386)

(A) 0.154 mg/dL
(B) 1.54 mg/dL
(C) 154 mg/dL
(D) 596 mg/dL
(E) 1540 mg/dL

Answer 3

3. (C) An increasing number of laboratory test
   values and drug doses are being reported in
   terms of millimoles (mM). Weight quantities
   expressed in molar amounts allow a more realistic
   evaluation of the actual number of
   drug molecules present, for example, when
   comparing salts of a drug. In this problem,
   the mM/L concentration is converted by recognizing
   that 1 mole of cholesterol weighs
   386 g and 4 mmoles equals 0.004 moles.
   386 x .004 moles = 1.544 g or 1540 mg/L
   1540 mg/L = 154 mg/dL

Question 4

4. What is the minimum amount of a potent
   drug that may be weighed on a prescription
   balance with a sensitivity requirement of 6
   mg if at least 98% accuracy is required?

(A) 6mg
(B) 120mg
(C) 180mg
(D) 200mg
(E) 300mg

Answer 4

4. (E) The minimum weight that can be measured
   on any balance can be determined if
   the balance’s sensitivity requirement (SR)
   and the acceptable percentage of error has
   been established. The equation is
   SR = (minimum weighable amount) x
   (acceptable error)
   In this problem, the SR was given as 6 mg
   and an accuracy of at least 98% or an error of
   not more than 2% is permissible.
   (23:35)
   100mL
   1dL = 4mg/dL
   6 mg = (x mg) (2%)
   6 mg = (x mg) (0.02)
   x=300mg

Question 5

5. The upper therapeutic drug concentration for
   (C) I and II only vancomycin is considered to be 40 microgram/ml
   Express this value in terms of mg/dL.

(A) 0.04mg/dL
(B) 0.44 mg/dL
(C) 4mg/dL
(D) 40 mg/dL
(E) 400 mg/dL

Answer 5

5. (C) Because 1000 )..I.g = 1 mg and 100 mL = 1
   dL, 40 )..I.g/mL = 0.04 mg/mL = 4 mg/dL
   Note that when dimensional analysis is
   used, all of the units cancel except those appropriate
   for the final answer.

Question 6

6. Calculate the dose of a drug to be adminis-
   (A) I only tered to a patient if the dosing regimen is
   (B) III only listed as 2 mg/kg/day. The patient weighs 175 lb.

(A) 78mg
(B) 160mg
(C) 140mg
(D) 350mg
(E) 770mg

Answer 6

6. (B) Because 1 kg = 2.2 lb
   ~
   175 lb x 2.2 lb x
   2mg
   kg
   160mg

Question 7

7. The adult dose of a drug is 250 mg. What
   would be the approximate dose for a 6-year old child weighing 60 lb? (Use Young’s Rule.)

(A) 60 mg
(B) 85 mg
(C) 100 mg
(D) 125 mg
(E) 180 mg

Question 8

8. A package insert lists a drug dose for a
   neonate as being 10 mcg/kg/day. The age
   range for a neonate is considered to be

(A) birth to 1 month
(B) 1 month to 6 months
(C) 1 month to 1 year
(D) birth to 1 week
(E) 1 year through 5 years

Question 9

9. The child’s dose of a drug is reported as 1.2
   mg/kg body weight. What is the appropriate
   dose for a child weighing 60 lb?

(A) 6 mg
(B) 9 mg
(C) 32 mg
(D) 72 mg
(E) 126 mg

Question 10

10. The infusion rate of theophylline established
    for a neonate is 0.08 mg/kg/hr. How many
    mg of drug are needed for a 12-hr infusion
    bottle if the body weight is 161b?
    (A) 0.58 mg
    (B) 14 mg
    (C) 30 mg
    (D) 150 mg
    (E) 7mg

Question 11

11. How many mg of codeine phosphate are being
    consumed daily by a patient taking the
    following prescription as directed?

Rx
Codeine Phosphate 200mg
Dimetapp Elix q.s 120ml
Sig: :5 i ti.d. p.c. & h.s.

(A) 6.25 mg
(B) 8.25 mg
(C) 19 mg
(D) 25 mg
(E) 33 mg

Question 12

12. How many mg of codeine base is in each
    dose of the cough product used in Question
    11? (Mol. wts: codeine = 299; codeine phosphate
    =406)

(A) 6 mg
(B) 8 mg
(C) 11 mg
(D) 16 mg
(E) 24 m

Answer 12

The relationship between codeine and
codeine phosphate is easily seen when
viewed as a chemical reaction

Question 13

13. The directions intended for the patient on a
    prescription read 1/1 tbsp ac and hs for 10
    days.1/ What is the minimum volume the
    pharmacist should dispense?

(A) 160 mL
(B) 200 mL
(C) 400 mL
(D) 600 mL
(E) 800 mL

Answer 13

13. (0) One tablespoonful (tbsp) delivers 15 mL
    of liquid. In this prescription, the patient is
    receiving four doses per day for 10 days.
    Therefore,
    15 mL x 4 doses x 10 days = 600 mL total

Question 14

The USP contains nomograms for estimating
body surface area (BSA) for both children
and adults. Which of the following measure-
ments must be known in order to use this
nomogram?
(A) age and height
(B) age and weight
(C) height and creatinine clearance
(D) height and weight
(E) weight and sex

Question 15

The adult dose of a drug is 200 mg. What is
an appropriate dose for an 8-year-old child
whose BSA is calculated to be .6 m2?
Rx
Codeine Phosphate
Dimetapp Elix
Sig: :5 i ti.d. p.c. & h.s.
(A) 6.25 mg
(B) 8.25 mg
200mg
q.s. 120 mLBlood pressure measurements were made for
1 week on five patients with the following
averages:
Patient 1 2 3 4 5
B.P. 140/70 160/84 180/88 190/90 150/70
What is the median systolic pressure?
(A) 80
(B) 83
(C) 84
(D) 160
(E) 164

Question 16

16. Blood pressure measurements were made for
    1 week on five patients with the following
    averages:
    Patient 1 2 3 4 5
    B.P. 140/70 160/84 180/88 190/90 150/70
    What is the median systolic pressure?
    (A) 80
    (B) 83
    (C) 84
    (D) 160
    (E) 164

Question 17

17. Using the above data, determine the approxi-
    mate average diastolic blood pressure value.
    (A) 80
    (B) 84
    (C) 100
    (D) 115
    (E) 160

Question 18

18. After 1 month of therapy, all of the patients
    listed in Question 16 had a systolic blood
    pressure reduction of 10 mm with a standard
    deviation (SD) of 5 mm. What percentage of
    patients had a reduction between 5 and 15
    mm?
    (A) 20%
    (B) 40%
    (C) 50%
    (D) 70%
    (E) 90%

Question 19

Lanoxin Pediatric Elixir contains 0.05 mg of
digoxin per mL. How many micrograms
(mcg) are there in 3 mL of the elixir?
(A) 0.0015
(B) 0.015
(C) 0.15
(D) 1.5
(E) 150

Question 20

A pharmacist adds 1 pint of Alcohol USP to 1
L of a mouthwash formula. What is the new
percentage of alcohol present if the origi-
nal mouthwash was labeled as 12% V /V
ethanol?
(A) 30%
(B) 38%
(C) 45%
(D) 57%
(E) 59%

Question 21

A prescription calls for the dispensing of a
4% Pilocar solution with the directions of “gtt
i au TID.” How many mg of pilocarpine hy-
drochloride is being used per day? Assume
that the dropper is calibrated to deliver 20
drops to the mL.
(A) 4mg
(B) 6 mg
(C) 12 mg
(D) 24 mg
(E) 60 mg

Question 22

The adult intravenous (IV) dose of zidovu-
dine is 2 mg/kg q 4 h six times daily. How
many mg will a 180-lb patient receive daily?
(A) 12 mg
(B) 164 mg
(C) 650 mg
(D) 980 mg
(E) 2160 mg

Question 23

A pharmacist dilutes 100 mL of Clorox with
sufficient water to make one quart of solu-
tion. Express the concentration of sodium
hypochlorite in the final dilution as a W/V
ratio. (Commercial Clorox contains 5.25%
W/V sodium hypochlorite.)
(A) 1/10
(B) 1/90
(C) 1/100
(D) 1/180
(E) 1/200

Question 24

Cocaine HCl
Tetracaine HCl 2%
Epinephrine HCl
Sodium Chloride injection
4%
O.5mL
1/2000
qs4mL

How many mg of cocaine HCl is in the final
solution?

(A) 400 mg
(B) 4 mg
(C) 20 mg
(D) 8 mg
(E) 160 mg

Question 25

How many mL of Adrenalin HCl Solution
(0.1%) may be used to prepare the solution?
(A) 0.002 mL
(B) 0.04 mL
(C) 1 mL
(D) 2mL
(E) 5 mL

Question 26

Parenteral Admixture Order
For: Alex Sanders Room: M 704
(A) .8
(B) 1.5
(C) 8
(D) 10
(E) 50
Cefazolin sodium 400 mg in 100 mL N IS
Infuse over 20 minutes q 6 hr ATC for 3 days
Available in the pharmacy are cefazolin
sodium I-gram vials with reconstitution di-
rections of 2.5 mL. SWFI will give 3.0 mL of
solution.

26. How many mL of the reconstituted solution
    are required for each day of therapy?
    (A) 1.2 mL
    (B) 4.8 mL
    (C) 3 mL
    (D) 6 mL
    (E) 12 mL

Question 27

What infusion rate in mL/min should the
nurse establish for each bottle?
(A) 0.15 mL/min
(B) 0.28 mL/min
(C) 1.1 mL/min
(D) 2 mL/min
(E) 5 mL/min

Question 28

An ICU medical order reads “KCl 40 mEq in
1 liter N/S. Infuse at 0.5 mEq/min.” How
many minutes will this bottle last on the pa-
tient?
(A) 20
(B) 80
(C) 500
(D) 1000
(E) 2000

Question 29

The attending physician changes the flow
rate of the above solution (KCl 40 mEq/1 L
N IS) to 2 mEq per hour. What will be the ap-
proximate flow rate in mL/minute?

(A) .8
(B) 1.5
(C) 8
(D) 10
(E) 50

Question 30

An administration set delivers 60 drops to
the mL. How many drops per minute are
needed to obtain 20 units of heparin per
minute if the IV admixture contains 15,000
units per 250 mL of normal saline?
(A) 20
(B) 40
(C) 60
(D) 80
(E) 120

Question 31

Dopamine (Intropin) 200 mg in 500 mL of
normal saline at 5 ).!g/kg/min is ordered for
a 155-lb patient. What is the final concentra-
tion of solution in ().!I mL?
(A) 0.4 ).!g/mL
(B) 2.5 ).!g/mL
(C) 40 ).!g/mL
(D) 400 ).!g/mL
(E) 25 ).!g/mL

Question 32

Referring to Question 31, at what rate
(mL/min) should the solution be infused to
deliver the desired dose of 5 ).!g/kg/min?
(A) 0.35 mL/min
(B) 0.40 mLImin
(C) 0.88 mL/min
(D) 2.0 mL/min
(E) 5.0 mL/min

Question 33

A 250-mL infusion bottle contains 5.86 g of
potassium chloride (KCl). How many mil-
liequivalents (mEq) of KCl are present? (Mol.
wt. KCl =74.6)
(A) 12.7mEq
(B) 20 mEq
(C) 78.5 mEq
(D) 150 mEq
(E) 157 mEq

Question 34

A solution contains 1.5 mEq of calcium per
100 mL. Express the solution’s strength of
calcium in terms of mg/L. (The atomic
weight of calcium is 40.)
(A) 30 mg/L
(B) 60 mg/L
(C) 150 mg/L
(D) 300 mg/L
(E) 600 mg/L

Question 35

Calcium chloride (CaCl2 • 2H20) has a for-
mula weight of 147. What weight of the
chemical is needed to obtain 40 mEq of cal-
cium? (Ca =40.1; Cl =35.5; H20 =18)
(A) 0.80 g
(B) 2.22 g
(C) 1.47 g
(D) 2.94 g
(E) 5.88 g

Question 36

A floor nurse requests a 50-mL minibottle to
contain heparin injection 100 units/mL. The
number of mL of heparin injection 10,000
units/mL needed for this order will be
(A) 0.1 mL
(B) 0.5 mL
(C) 1 mL
(D) 2.5 mL
(E) 5 mL

Question 37

The estimated creatinine clearance rate for a
120-lb male patient is 40 mLImin. What
maintenance dose should be administered if
the normal dose was calculated to be 80 mg?
(Assume only renal elimination.)
(A) 60 mg
(B) 20 mg
(C) 120 mg
(D) 160 mg
(E) 240 mg

Question 38

A nursing floor requests one pint of 50% Iso-
propyl alcohol as a rubbing compound. How
many mL of Isopropyl Rubbing Alcohol (70%
VIV) will be needed for compounding this
order?
(A) 170
(B) 342
(C) 480
(D) 672
(E) 684

Question 39

A physician requests 1 lb of bacitracin oint-
ment containing 200 U of bacitracin per
gram. How many grams of bacitracin oint-
ment (500 UI g) must be used to make this
ointment?
(A) 182 g
(B) 200 g
(C) 227 g
(D) 362 g
(E) 400 g

Question 40

Coal tar solution
Salicylic acid
Urea
Triamcinolone acetonide
Alcohol USP
Propylene glycol
5mL
aa5%
0.25 g
20mL
qs 120 mL

Answer 40

What weight of salicylic acid is needed to
prepare 1 pt of the formula listed?
(A) 11.8 g
(B) 12 g
(C) 23.7 g
(D) 24 g
(E) 25 g

Question 41

What percent V IV concentration of alcohol
would be listed on the label?
(A) 8%
(B) 15.8%
(C) 16.7%
(D) 19%
(E) 20%

Question 42

How many mL of triamcinolone acetonide
aqueous injection (40 mg/mL) could be used
to prepare 240 mL of the formula?
(A) 6.3 mL
(B) 12.5 mL
(C) 1.2 mL
(D) 10 mL
(E) 15 mL

Question 43

Propylene glycol was purchased at a cost of
$24.00 per pound. What is the cost of 100 mL
of the liquid? (Specific gravity =1.04)
(A) $2.60
(B) $2.64
(C) $2.75
(D) $5.50
(E) $13.00

Question 44

A pharmacist adds 2 mL of tobramycin injec-
tion (40 mg/mL) to 4 mL of tobramycin oph-
thalmic solution 0.3%. The concentration of
tobramycin in the final mixture will be
___ g/mL.
(A) 0.012
(B) 0.015
(C) 0.03
(D) 0.052
(E) 0.092

Question 45

A hospital clinic requests 2 lb of 2% hydro-
cortisone ointment. How many grams of 5%
hydrocortisone ointment could be diluted
with white petrolatum to prepare this order?
(A) 18.2 g
(B) 27.5 g
(C) 45.4 g
(D) 363 g
(E) 545 g

Question 46

How many mL of glycerin would be needed
to prepare 1 lb of an ointment containing 5%
WIW glycerin? (The density of glycerin is
1.25 g/mL.)
(A) 1.2 mL
(B) 18.2 mL
(C) 22.7mL
(D) 24 mL
(E) 28.4 mL

Question 47

A total parenteral nutrition (TPN) order re-
quires 500 mL of D30W. How many mL of
DsoW should be used if the D30W is not avail-
able?
(A) 125 mL
(B) 300 mL
(C) 375 mL
(D) 400 mL
(E) 200 m

Question 48

How many grams of 1% hydrocortisone
cream must be mixed with 0.5% hydrocorti-
sone cream if one wishes to prepare 60 grams
of an 0.8% W/W preparation?

(A) 6 g
(B) 12 g
(C) 24 g
(D) 36 g
(E) 48 g

Question 49

How many grams of pure hydrocortisone
powder must be mixed with 60 g of 0.5% hy-
drocortisone cream if one wishes to prepare a
2.0% W/W preparation?

(A) 0.90 g
(B) 0.92 g
(C) 0.30 g
(D) 1.2 g
(E) 1.53 g

Question 50

How much sodium chloride is needed to ad-
just the following prescription to isotonicity?
(The E value for sodium thiosulfate is 0.31.)

Rx
Sodium thiosulfate
1.2%
Sodium chloride
qs
Purified water qs 100ml

(A) 0.37 g
(B) 0.45 g
(C) 0.53 g
(D) 0.31 g
(E) 0.90 g

Question 51

How much additional sodium chloride
should be added to the following prescrip-
tion to maintain isotonicity? (Zincfrin is an
isotonic solution)

(A) 0.135 g
(B) 0.4 g
(C) 0.54 g
(D) 0.9 g
(E) None (because Sterile Water for Injection
is already isotonic)

Question 52

How many mg of sodium chloride are
needed to adjust 30 mL of a 4% cocaine HCl
solution to isotonicity. The freezing point de-
pression of a 1% solution of cocaine Hel is
.09 degrees.
(A) 62
(B) 83
(C) 108
(D) 120
(E) 270

Question 53

Estimate the milliosmolarity (mOsm/L) for
normal saline. (Na =23; Cl =35.5)
(A) 150 mOsm/L
(B) 300 mOsm/L
(C) 350 mOsm/L
(D) 400 mOsm/L
(E) 600 mOsm/L

Question 54

How many milliosmoles are present in a so-
lution prepared by dissolving 1000 mg of
sodium chloride in 100 mL DsW? (Na =23; Cl
=35.5; hydrous dextrose =198)
(A) 30
(B) 60
(C) 150
(D) 300
(E) 600

Question 55

How many grams of glacial acetic acid
(99.9% W/W) must be added to 1 gallon of
purified water to prepare an irrigation solu-
tion containing 0.25% W/V acetic acid?

(A) 1.2 g
(B) 9.5 g
(C) 12 g
(D) 20 g
(E) 95 g

Question 56

How much elemental iron is present in every
300 mg of ferrous sulfate (FeS04 • 7HzO)?
[Atomic weights: iron = 55.9; S = 32; 0 = 16;
H =1. Iron has valences of +2 and +3.]

(A) 30 mg
(B) 60 mg
(C) 110 mg
(D) 120 mg
(E) 164 mg

Question 57

The USP states that 1 g of a chemical is solu-
ble in 10 mL of alcohol. What is the percent-
age strength of a saturated solution of this
chemical if alcohol has a sp. gr. of 0.80?
(A) 10.0% W/V
(B) 10.0% W/W
(C) 11.1% W/V
(D) 11.1% W/W
(E) 12.5% W/V

Question 58

What is the decay constant (k) of the ra-
dioisotope 3Zp if its half-life is 14.3 days? (As-
sume that radiopharmaceuticals follow first-
order kinetics.)

(A) 0.048/ day
(B) 0.07/ day
(C) 0.097/ day
(D) O.l/day
(E) 0.15/ day

Question 59

A radiopharmacist prepares a solution of
99mTc (40 mCi/mL) at 6:00 AM. If the solution
is intended for administration at 12:00 noon
at a dose of 20 mCi, how many mL of the
original solution are needed? (The half-life of
the radioisotope is 6 hours.)

(A) 0.5 mL
(B) 1.0 mL
(C) 1.5 mL
(D) 2.0 mL
(E) 5.0 mL

Question 60

60. What concentration of the original 99mTc solu-
    tion described in Question 59 will remain 24
    hours after its original preparation?
    (A) 15 mCi
    (B) 10 mCi
    (C) 7.5 mCi
    (D) 5.0 mCi
    (E) 2.5 mCi

Question 61

Rx
Magnesium carbonate
15g
Citric acid (anhydrous)
27.4g
Syrup
60ml
Purified water qs to 350ml

How many grams of magnesium is present in
every 350 mL dose? (Mg = 24.3; Carbonate =
60)
(A) 2.5
(B) 4.32
(C) 6.08
(D) 6.7
(E) 8.6

Question 62

What percent W/V of hydrated citric acid
could be listed in a formula if the anhydrous
citric acid is not available? The hydrated
form of citric acid contains 10% water. (Mole-
cular weight citric acid, anhydrous = 192
g/mole; water =18 g/mole)
(A) 7.0
(B) 7.8
(C) 8.7
(D) 24.7
(E) 30.4

Question 63

A nursing home patient is experiencing diar-
rhea from his enteral nutritional solution,
which has an osmolarity of 520 mOsm/L.
How many mL of purified water are needed
to reduce 500 mL of this solution to an osmo-
larity of 300 mOsm/L?
(A) 290 mL
(B) 310 mL
(C) 360 mL
(D) 500 mL
(E) 870 mL

Question 64

The level of iron impurities in a water sample
is 2 mg per liter. Express this concentration in
terms of ppm.
(A) 0.2 ppm
(B) 2ppm
(C) 20 ppm
(D) 200 ppm
(E) 2000 ppm

Question 65

The concentration of mercury in a water sam-
ple is reported as 5 ppm. Express this concen-
tration as a percentage.
(A) 0.00005%
(B) 0.0005%
(C) 0.005%
(D) 0.05%
(E) 0.5%