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PLEASE SOLVE ALL PROBLEMS THAT ARE NOT SOLVED
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Pharmacology
Med Math Practice Questions
Instructor: Candace James-Marrast, PhD, RN
A. Dosage calculations Formula Factor Label Method (Dimensional Analysis)
( , , … )
1
ℎ ( , )
The provider orders Sodium Bicarbonate 500 mg. You’re supplied with 1 g tablets.
How many tablets should the nurse administer per dose? Tablets are scored.
= 0.5 tabs
B. Intake and Output
1. A nurse is caring for a client who had IV fluids initiated at 0630. The IV fluids are infusing
at 120 mL/hr. The nurse should record how many mL of IV fluids on the intake record at
0900?
0630 – 0730 = 60 minutes = 120 mL
0730 – 0830 = 120 minutes = 240 mL
0830 – 0900 = 60 minutes = 180 = 300 mL
Ans: 300
2. A nurse is calculating the intake of a client during the past 8 hr. The client’s intake
includes 500 mL fluid at breakfast 240 mL fluid for lunch; lactated Ringer’s IV at 125 mL/hr,
cefazolin 2 g IV intermittent bolus in 150 mL of 0.9% sodium chloride, two units of packed
RBCs of 200 mL and 300 mL; one IV bolus infusions of 250 mL of 0.9% sodium chloride,
famotidine 40 mg IV intermittent bolus in 100 mL of 0.9% sodium chloride. Urine output
750 mL. How many mL of intake should the nurse record?
500
240
125 x 8 = 1000
150
200
300
250
100
_______
2740 – 750 = 1990
_______
A nurse is calculating the intake of a client from the past 5 hr. The client’s intake
includes 0.9% NS at 125 mL/hr, three doses of Potassium rider 40 mEq in 100mL, three
doses of cefazolin in 250 mL and ceftriaxone in 500 mL every 12 hours, one bolus of
famotidine 4 mg IV in 100 mL of 0.9% sodium chloride. What should the nurse
document in the medical record?
125 x 5 = 625
100 x 3 = 300
250 x 3 = 750
500
100
_______
2275
_______
A nurse is caring for a client with a NG tube set to low intermittent suction. The nurse irrigates
the NG tube twice with 20 mL of normal saline solution during the shift. At the end of the shift,
the NG canister contains 500 mL. What amount of NG drainage should the nurse record?
Irrigation with 20 mL x 2 = 40. 500 at end of shift – 40 = 460 mL
C. IV Drip Rate – Calculations to determine drip rate
– Always express answer
– In gtt/min and to the nearest whole number
Formula #1 – Using drop factor or tubing size
= 1 = /
gtt fx = drop factor
gtt/min = drop per min
macrodrip tubing – drop factor = 10gtt/mL
microdrip tubing – drop factor = 60 gtt/mL
Examples:
1. Order: D5W 1000mL every 8 hours using a macrodrip tubing. What is the drip
rate?
1
1000
8 60
10
1
= . = /
2. Order: D5W 125mL every 1 hour using a macrodrip tubing. What is the drip
rate?
125
10
= . = /
60
1
3. Order: D5W 50mL every 2 hours using a microdrip tubing. What is the drip
rate?
50
60
= /
2 60
1
Formula #2 – Using volume, flow rate, and drop factor. Problem contains volume
included, but not needed for the calculation.
60 1
Example A
Order: 900mL at 30mL/hr at 15 drops/mL. What is the drip rate?
900mL at 30mL/hr at 15 drops/mL.
Volume
Not needed
flow rate
30
60
drop factor
15
1
= 7.5 = 8 gtt/min
Formula #3 – Using flow rate and drop factor. Problem contains no volume.
60 1
Example B
Order: 75mL/hr at 10 drops/mL. What is the drip rate?
60
1
=
75
60
10
1
= 12.5 = 13 gtt/min
D. IV Flow Rate – Calculations to determine Flow Rate
– Always express answer
– In mL/hour and to the nearest whole number
Formula #1 – Time more than 1 hour.
ℎ
Example: Order 250 mL of LR to infuse over 2 hours =
250
2
= 125 mL/hr
Formula #2 – Time less than 1 hour.
60
1
Example: Order 100 mL of LR to infuse over 30 mins. What is the flow rate?
100
60
= 200 /ℎ
30
1
Practice Time
Solve the problems below
1. The provider orders 1 liter of D5W to infuse at a rate of 75 mL/hr at 12 drops/mL.
The nurse started the infusion at 10:00 am.
a. What is drip rate?
b. How long will the D5W take to infuse?
c. What time will the infusion be completed?
2. Order: 1000 mL of D5 ½NS to infuse over 12 hours.
Available: Microdrip set
Calculate the IV flow rate in drops per minute. ______
3. Order: 3 L of IV solution to infuse over 24 hours: with 1 L of D5W and 2 L of D5 ½NS
a. One liter is equal to how many milliliters? ______
b. Each liter should infuse for how many hours? ______
c. The institution uses a set with a drop factor of 15 gtt/mL. How many drops per
minute should the patient receive per liter of fluid? ______
4. Order: 250 mL of D5W over 3 hours. Determine the flow rate. _____
5. Order: 1000 mL of D5 ½NS, 1 vial of multiple vitamin (MVI), and 10 mEq of potassium
chloride (KCl) to be infused over 10 hours. Available: 1000 mL of D5 1⁄2 NS; MVI: 1 vial
= 10 mL; KCl 20 mEq/20 mL vial Macrodrip set – 15 gtt/mL; microdrip set – 60 gtt/mL
a. What is the total volume of the solution?
b. How many drops per minute should the patient receive using the macrodrip set and
the microdrip set?
c. The IV pump is set at how many milliliters per hour?
Formula #3 – Using Order over Available, to calculate – ml/hr
Heparin drip to infuse at 400 units per hour.
The pharmacy sends a bag of Heparin 10,000 units in 125 ml NS. At what rate in ml/hour would
you set up the pump to run at?
400 units
1
125 mL
= 5 /ℎ
10,000 units
Order: Heparin sodium 750 units/h
Available: Heparin sodium 25000 units in 500 mL D5W
Calculate the milliliters per hour.
750 units
1
500 mL
25000 units = 15 mL
Formula #4 – Using Order; volume; and flow rate – to calculate – units/hr
Order in units Flow rate (mL/hr)
vol (in mL)
1 hr
Examples Ordered: heparin sodium 20,000 units in 1,000 mL D5W to infuse at 30 mL/h
Calculate the units per hour.
20,000 units
1000 mL
30 mL
1 hr = 600 units/hr
The health care provider prescribes heparin infusion 20,000 units in 500mL D5W at 1280
units/hr. 8000 hours PTT is 44 seconds. What rate should the nurse set the infusion. The
parameters for continued infusion are:
1. PTT 40-49 sec. increase rate by 100 units/hr.
2. PTT 50-75 sec. keep the same rate.
3. PTT 76-85 sec. decrease rate by 100 units/hr.
4. PTT 86-100 sec. decrease rate by 200 units/hr.
5. PTT 100 sec. call the provider.
Rate is 44 sec. so increase by 100 = 1280 + 100 = 1380
Then solve for ml/hr
Rate to infuse in units
vol
1
Amount of infuse in units
1380 units
1
500 mL
20,000 units = 34.5 mL
Note: In practice – Never give heparin 9 mL/hr
Practice Time
Heparin sodium 80 units/kg IV bolus is ordered followed by heparin sodium infusion at
15 units/kg/h for a patient who weighs 175 lb.
Available: 20,000 units/500 mL (40 units/I mL).
a. Calculate the amount of bolus in units and milliliters to administer.
b. Calculate flow rate in units per hour.
c. Calculate flow rate in milliliters per hour.
Answers:
a. Calculate the amount of bolus (flow rate) in units and milliliters.
Bolus in units
80 units
Bolus in mL
6364 units
1kg
1kg
2.2 lbs
175 lbs
= 6363.63 = 6364 unit bolus
1 mL
40 = 159 = 159 mL bolus
b. Calculate flow rate in units per hour
15 units
1 kg
175 lbs
= 1193.18 = 1193 /ℎ
1 kg
2.2
c. Calculate flow rate in milliliters per hour
1 mL
40 units
15 units
1 kg
1 kg
2.2
175 lbs
= 29.8 = 30 /ℎ
Practice Time
Ordered: Heparin sodium 800 units/h.
Available: Heparin sodium 40 units/mL.
Calculate the flow rate. _________
Order: 25000 units heparin sodium in 250 mL 0.9% sodium
chloride (NS) to infuse at 35 mL/h.
Calculate units per hour. _________
E. Infusion Time and Completion Time
Infusion Time – How long will administration of this drug take to infuse?
Completion Time – At what time will the infusion end?
Infusion time – To determine how long it will take to infuse an ordered IV solution
Use the equation cited below to determine when an infusion may be completed
If your time is in a decimal form, you need to determine how many minutes the infusion
will take by multiplying the decimal by 60. Example: 11.35 would be .35(60) = 21
11 hours and 21 minutes
Formula
Time (in hours) = Volume to be infused in mLs
mL/ hr [flow rate]
Example 1: The provider orders 1 liter of NS to infuse at a rate of 90 mL/hr. The nurse
started the infusion at 8:00 am (0800 hours).
Infusion Time – How long will the drug take to infused?
=
1000
90
= 11.11 hours
Time = 11.11 hours
11 hours .11(60 minutes)
11 hours 6.6 minutes = 7 minutes
Ans: Time to infuse = 11 hours 7 minutes
Completion Time (end time) – What time will the infusion be completed?
Formula: Start time of infusion + Infusion time
Step 1) First calculate the infusion time
Using the example above – the infusion time is 11 hours and 7 minutes
Step 2) Add the start time to the hours the medication took to infuse
Start time = (8am = 0800 hours) + infusion time (11 hours 7 minutes = 1107)
0800
1107
1907
Ans: Infusion will be completed at 1907 hours
Example 2: Order: 900mL at 30mL/hr at 15 drops/mL.
How long will administration of this drug take to infuse?
Time (in hours) =
/ℎ [ ]
900
= 30 /ℎ = Ans: 30 hours
Example 3: The provider orders 500 mL of LR to infuse over 4 hours using a macrodrip
tubing. The nurse started the infusion at 7:20 am.
a. What is the flow rate?
500
4 ℎ
ℎ
= 125mL/hr
b. What is drip rate?
500
4 60 =240
1
10
1 = . = /
c. What time will the infusion be completed? Start time + Infusion time
Infusion time = 4 ℎ ( ℎ )
Completion time = Start Time + 4 hours = 7:20am + 4 hours = 11:20am
F. Reading Labels
Practice Time
Order: Heparin 6000 units subcutaneous NOW and 2500 units subcutaneous daily.
a. How many milliliters should the nurse administer for the NOW dose? ______________
b. How many milliliters should the nurse administer for the daily dose? _____________
c. How many vial(s) of heparin are needed? ________________
More Practice – Reading Labels
Order: Cefaclor oral suspension 20 mg per kg per day in three divided doses for a
pediatric patient who weighs 66 lb.
How many milliliters will the nurse administer per dose? _____________
a. What is the generic name? __________________________
b. What is the trade name? ______________________________
c. Is this drug a controlled substance? ____________
d. What is the amount of the drug and the form? _________________
e. How many tablets are in the package? ____________
f. How should this drug be stored? ____________________
a. What is the generic name? __________________________
b. What is the trade name? ______________________________
c. Is this drug a controlled substance? ____________
d. What is the amount of the drug and the form? _________________
e. How many tablets are in the package? ____________
f. How should this drug be stored? ____________________
G. Reconstitution Problems
Reconstitution and Injectable Medications
Instructions:
Reconstitution is needed when medications are stored as powders because
they are unstable as liquids. The label will indicate what solution and the
amount to mix with the powder. Usually it is either sterile water or sterile
0.9% saline. The liquid that is mixed with the powder is referred to as the
diluent.
Some labels will specify the total amount in the vial after reconstitution is
completed.
ERROR ALERT! The amount of diluent is not used in the calculations. The
label will indicate (the concentration), which is expressed in different units (g,
mg, mcg) contained in how many mL in order to solve for the dose to
administer to the patient.
Key Points to Remember:
The amount of the diluent NEVER goes into your calculation
The concentration is the same as the Available or Have
Reconstitution – Practice Time
6. Order: Nebcin (tobramycin) 88 mg IM STAT
A. How much diluent is added to reconstitute the vial?
__________________
B. What is the concentration of the medication after the reconstitution? ____________
C. How many mLs should the nurse administer for one dose?
__________________
D. Mark the syringe below with the appropriate dose.
7. Read the medication label below and answer the following questions
A.
How much diluent is added to reconstitute the vial?
____________________
B.
What is the concentration of the medication after the reconstitution? ________________
8. Order: Ceftriaxone 25g IV every 12 hours
a. How much diluent is added to reconstitute the vial for IM administration? _____________
b. How much diluent is added to reconstitute the vial for IV administration? _____________
c. What is the concentration of the medication for IM administration? ________________
d. What is the concentration of the medication for IV administration? ________________
e. How many mLs should the nurse administer to deliver the IM dose? ________________
f. How many mLs should the nurse administer to deliver the IV dose? ________________
g. How should this drug be stored? ____________________
Reconstitution Examples without labels
Ceftriaxone 1g (gm) before surgery
Try these additional questions
1.
The physician orders 500 mg of a medication. The reconstitution directions say to
add 6.2 mL of sterile water to yield a concentration of 450 mg/mL. What should the
nurse administer to the patient?
____________________mL
2.
The physician orders 400 mg of a medication. The reconstitution directions say to
add 7.2 mL of sterile water to yield a concentration of vial read 650 mg/mL.
How many mL should the nurse administer to the patient?
_____________mL
H. Weight Based and Pediatric Safe Dose Range
Weight Based and Pediatric Safe Dose Range
Instructions:
1. Always round your answer at the end of the calculation, not at every step of your
calculation. This means if you have a 3-part or 4-part calculation, calculate the entire
problem – then round your answer at the end.
2. Always round your answers to the NEAREST Tenth (except for any volume less
than 1mL OR unless otherwise instructed).
3. Use the “Label Factor Method” to ensure you are performing the calculations accurately
and put labels in the calculation.
4. When working with decimals, remember to use a preceding zero as appropriate (.345 =
0. 345) and avoid using a trailing zero at the end of a decimal number (3.40 = 3.4)
Example #1 – mg to administer
A nurse is caring for a client with a new prescription for enoxaparin 3 mg/kg/day subcutaneous daily in
2 equally divided doses x 7 days. The client weighs 130 lbs. How many mg should the nurse administer
per dose? (Round the answer to the nearest whole number. Use a leading zero if it applies. Do not use a
trailing zero.)
Formula
ℎ
1
130
1
1
1
2.2
3
1
OR
ℎ
1
1
2.2
1
= 177.27 = 177.3 daily. In 2 divided doses = 88.6 mg
Example #2 – Dose Range
Problem #1
Doctor’s Order: Kanamycin sulfate injection 150mg/kg/24 hours IM in three divided
doses to an adult weighing 132 lbs. The safe dose range (dose reference) of this drug is 2 to 3
mg/kg/day.
Available: Kanamycin sulfate injection 500 mg/2mL.
a.
Dose Range – What is the safe dose range for this patient?
Using the Factor Label Method
Begin with the weigh in lbs, then X by the
conversion, then X by the low and high range Parameter) separately. If the weigh is
in kg, weight in kg X by low and high range (parameter) separately.
Weight X Conversion (if needed) X Low Range/High Range
132
1
132
1
1
2
= / [Low Dose]
2.2
1
3
= / [High Dose]
2.2
Safe dose range = Low dose-high dose (space) mg/day = 120-180 mg/day
Example #3 – mL to Administer
ℎ
1
1
( , , )
( ,
OR
ℎ
1
( , , )
1
2.2
1
( , )
b. mL to administer – How much should the nurse administer per dose?
Using example above
ℎ
1
( , , )
1
2.2
1
( , )
132
1
1
150
2
500 = 36 per day 36/3 =12 = per dose
2.2
1
/ , in 3 divided doses = 12mL/dose
b. Determining whether the dose is therapeutic, subtherapeutic or toxic
Is this dose subtherapeutic, therapeutic, or toxic for this patient?
(Chose one and explain. Yes or no will not be accepted.)
150 mg (the order prescribed by the provider is within the dose range
= Dose is therapeutic
c. Convert to ounces
How many oz should the nurse administer?
1oz = 30mL
Use the Factor Label Method
12
1
1
30
= 0.4 oz.
Problem #2
Doctor’s Order: Kanamycin sulfate injection 150mg/kg/24 hours IM in three divided
doses to an adult weighing 132 lbs. The safe dose range of this drug is 1 to 2 mg/kg/day.
a. What is the safe dose range for this patient?
Using the Factor Label Method
Begin with the weigh in lbs, then X by the
conversion, then X by the low and high range Parameter) separately. If the weigh is
in kg, weight in kg X by low and high range (parameter) separately.
Weight X Conversion (if needed) X Low Range/High Range
132
1
132
1
1
1
= / [Low Dose]
2.2
1
2
= / [High Dose]
2.2
b. Is this dose subtherapeutic, therapeutic, or toxic for this patient?
(Chose one and explain. Yes or no will not be accepted.)
______Toxic______
Problem #3
Doctor’s Order: Kanamycin sulfate injection 150mg/kg/24 hours IM in three divided
doses to an adult weighing 132 lbs. The safe dose range of this drug is 3 to 5 mg/kg/day.
a. What is the safe dose range for this patient?
Using the Factor Label Method
Begin with the weigh in lbs, then X by the
conversion, then X by the low and high range Parameter) separately. If the weigh is
in kg, weight in kg X by low and high range (parameter) separately.
Weight X Conversion (if needed) X Low Range/High Range
132
1
132
1
1
3
= / [Low Dose]
2.2
1
5
= / [High Dose]
2.2
a. Is this dose subtherapeutic, therapeutic, or toxic for this patient?
(Chose one and explain. Yes or no will not be accepted.)
______Subtherapeutic______
Problem #4
A child who weighs 10 kg will begin taking oral trimethoprim–sulfamethoxazole
(TMP–SMX). The liquid preparation contains 40 mg of TMP and 200 mg of SMX
per 5 mL. The nurse determines the child’s dose should be 8 mg of TMP and 40
mg of SMX/kg/day divided into two doses. How much medication per dose should
the nurse administer for this child is correct?
Note: The nurse determines the child’s dose should be 8 mg of TMP and 40
mg of SMX/kg/day [is the same as the provider’s order].
10
1
10
1
8
1
40
1
5
40 = 10 mL/day in two doses – 10/2 = 5mL/dose
5
200 = 10 mL/day in two doses – 10/2 = 5mL/dose
Practice Time
Solve the problems (1 – 10) on the following pages
1. The prescriber orders Trexall (methotrexate) 150 mg IV once every 14 days to treat a
cancer. The patient weighs 164 lbs.
The safe dose for this drug is 2.5 mg/kg IV every 14 days.
What would be the safe dose for this patient?
_________________mg
Is the dose ordered for this patient safe? (yes/no)
_______________
2. The prescriber orders gentamycin sulfate 3 mg/kg/day IVPB in 3 divided doses q8h for a
client weighing 161 pounds.
How many kg does the patient weigh?
________________kg
How much medication should the patient receive per day?
______________mg
How much medication should the patient receive per dose?
_____________mg
ERROR ALERT! Wording is a source of confusion. Questions that ask for mg/kg/day are
calculating the total dose in a day. If it says to administer the medication in divided doses, the
nurse needs to divide the total for the day by the number of doses requested. If the order is given
in individual doses, like Question #2, the nurse must multiply the amount per dose by the number
of doses to determine the total per day.
3. The prescriber orders gentamycin sulfate 240 mg IVPB q12h for a patient who weighs 172 lb.
The safe dose range for gentamycin is 1 mg/ kg up to 5 mg/kg per day.
How many kg dose the patient weigh?
___________kg
What is the lowest effective dose per day for this patient?
____________mg
What is the highest effective dose per day for this patient?
____________mg
What is the total dose per day ordered for
390.9 mg/day
q dose space mg/day = 78.1-
____________mg
Based on the calculations above, is the dose ordered for this patient within the safe
dose range?
___________________
Would the dose be considered subtherapeutic, therapeutic, or toxic?
_____________________
4.
The prescriber orders morphine sulfate 0.3 mg IM stat for a child who weighs 68
pounds. The recommended dose is 0.01 mg per kg.
How many kg does the child weigh?
_____________kg
What would be the recommended dose for a child of this weight?
____________mg
Is this a safe dose for this child?
______________
The morphine sulfate on hand comes in a concentration of 0.5 mg per mL.
How many mL should the nurse administer to the child if the dose is determined
to be safe?
____________mL
I. Desired Over Have
Practice Time
The prescriber orders Amoxil oral suspension 0.25 g by mouth every 12 hours for a pediatric
patient at home. The label on the bottle reads:
125 mg/5 mL
NDC 0029-6008-23
AMOXIL
AMOXICILLIN
FOR ORAL SUSPENSION
a. Mark an “X” next to the measure on the medication cup to indicate how much liquid
medication to administer to the child with each dose: Show your working.
150 mL
(when reconstituted)
25 mL_____
20 mL _____
15 mL_____
10 mL_____
5 mL_____
3 mL_____
b. The patient’s mother does not have a medicine cup. She only has teaspoons. How
many teaspoons of medicine should she administer to the child for each dose?
The prescriber orders morphine sulfate 0.175 mg IVP now for a patient. The label below show
how the medication is available
a. How much morphine sulphate should the nurse administer to the patient to deliver this dose?
b. Circle the best syringe below and draw an arrow on the syringe to indicate where the nurse
should pull back on the plunger to administer this dose. Choose only ONE syringe.
J. Insulin Problems
The prescriber orders 18 units of NPH insulin and 5 units of Regular insulin in one injection
subcutaneously every morning. Fill in the blank spaces below to describe how the nurse should
accurately mix the two types of insulin in the same syringe. In your answer, use a capital R for
the regular Insulin.
a.
_______ of ___________ insulin should be added to the syringe first.
b.
_______ of _______ insulin should be added to the syringe second.
c.
The total amount of insulin in the syringe after the two types of insulin have been
mixed equals _________.
J. B. has a diagnosis of Diabetes Mellitus Type 2 and is on daily Insulin injections. The
prescriber orders NPH insulin 35 units and Regular insulin 9 units subcutaneously daily before
breakfast in one injection.
The required amount of air is already in the syringe.
Fill in the spaces below with the appropriate information and draw a line from the information to
the syringe on the right to indicate how far back the nurse should position the plunger to draw up
the amount required to add each type of insulin. In your answer, use a capital R for the
regular Insulin.
a. _______ units of ______ insulin should be added to the
syringe FIRST by drawing the plunger back to _______.
Draw an arrow to indicate how far back the
nurse needs to position the plunger to add the first
amount of insulin.
b. ______ units of ________ insulin should be added to
the syringe SECOND by drawing the plunger back to
______. Draw an arrow to indicate how far back the
nurse needs to position the plunger to add the second
amount of insulin.
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