Practice Set 1 — Review by Topic¶
Instructions¶
Work through each problem independently before revealing the answer. Write out every step using unit cancellation.
This set is organized by topic to help you identify specific areas that need review.
How to Use This Set
- Attempt every problem before checking the answer
- If you get a problem wrong, identify which factor was incorrect in your unit cancellation chain
- Note which topics give you the most trouble and review the relevant module before attempting Practice Set 2
Section 1 — Unit Conversions¶
Key conversions for this section
| Conversion |
|---|
| 1 kg = 1000 g |
| 1 g = 1000 mg |
| 1 mg = 1000 mcg |
Problem 1
Convert 0.045 kg to g.
Hint — Memorize important conversion factors
Recall that kilo- means thousand.
Answer
Walkthrough
The conversion factor is 1 kg = 1000 g or \(\dfrac{1 \text{\,kg}}{1,000 \text{\,g}}\). Place
kg in the denominator so it cancels with the starting quantity, leaving g:
Quick mental check: kilo means ×1000, so kg→g shifts the decimal three places to the right. 0.045 → 45. ✓
Problem 2
Convert 2.5 g to mg.
Answer
Walkthrough
The conversion factor is 1 g = 1000 mg. Orient it with g in the denominator so it cancels:
Quick mental check: g→mg shifts the decimal three places to the right. 2.5 → 2500. ✓
Problem 3
Convert 750 mcg to mg.
Hint — Direction check
mcg is a smaller unit than mg. Converting from a smaller unit to a larger unit always gives a smaller number. If your answer is larger than 750, the fraction is flipped.
Answer
Walkthrough
The conversion factor is 1 mg = 1000 mcg. Orient it with mcg in the denominator so it cancels:
Quick mental check: 1000 mcg = exactly 1 mg. 750 mcg is three-quarters of 1000, so the answer is 0.75 mg. ✓
Section 2 — Oral Tablets¶
Problem 4
Order: metoprolol 100 mg orally Stock: 50 mg per tablet How many tablets?
Answer
Walkthrough
The conversion factor comes from the stock strength: 50 mg = 1 tablet. Orient it with mg in the denominator so it cancels with the starting quantity:
Quick mental check: 100 mg is double the 50 mg per tablet, so the answer should be double 1 tablet. ✓
Problem 5
Order: warfarin 7.5 mg orally Stock: 5 mg per tablet How many tablets?
Answer
Walkthrough
The conversion factor comes from the stock strength: 5 mg = 1 tablet. Orient it with mg in the denominator so it cancels with the starting quantity:
Quick mental check: 7.5 mg is 1.5 times the 5 mg per tablet, so the answer is 1.5 tablets. ✓
Verify the tablet is scored before splitting.
High alert medication
Warfarin is a high alert medication. Verify the dose and stock concentration with an independent second check before administering.
Problem 6
Order: levothyroxine 0.15 mg orally Stock: 50 mcg per tablet How many tablets?
Answer
Walkthrough
The stock is in mcg, but the order is in mg — convert mg to mcg first, then apply the stock factor. Orient each factor so its denominator cancels the unit carried forward:
Quick mental check: 0.15 mg = 150 mcg, and 150 mcg is 3 times the 50 mcg per tablet. ✓
Section 3 — Oral Liquids¶
Problem 7
Order: amoxicillin 375 mg orally Stock: 250 mg/5 mL How many mL?
Answer
Walkthrough
The conversion factor comes from the stock concentration: 250 mg = 5 mL. Orient it with mg in the denominator so it cancels with the starting quantity:
Quick mental check: 375 mg is 1.5 times the 250 mg in 5 mL, so the answer is 1.5 × 5 = 7.5 mL. ✓
Problem 8
Order: ibuprofen 0.4 g orally Stock: 200 mg/5 mL How many mL?
Answer
Walkthrough
The stock is in mg, but the order is in g — convert g to mg first, then apply the stock factor:
Quick mental check: 0.4 g = 400 mg, and 400 mg is double the 200 mg in 5 mL, so the answer is 10 mL. ✓
Problem 9
Order: morphine 7.5 mg orally Stock: 10 mg/5 mL How many mL?
Answer
Walkthrough
The conversion factor comes from the stock concentration: 10 mg = 5 mL. Orient it with mg in the denominator so it cancels with the starting quantity:
Quick mental check: 7.5 mg is just under the 10 mg in 5 mL, so the answer should be just under 5 mL. ✓
Round to nearest tenth: 3.8 mL
Section 4 — Weight-Based Dosing (Adult)¶
Problem 10
Order: gentamicin 5 mg/kg IV Patient weight: 80 kg Stock: 40 mg/mL How many mL?
Answer
Walkthrough
This is a two-factor chain: weight → dose (mg) → volume (mL). Orient each factor so its denominator cancels the unit carried forward:
Quick mental check: 80 kg × 5 mg/kg = 400 mg, and 400 mg ÷ 40 mg/mL = 10 mL. ✓
Problem 11
Order: vancomycin 15 mg/kg IV Patient weight: 176 lb Stock: 500 mg/10 mL How many mL?
Answer
Convert weight: [\frac{176 \cancel{\text{ lb}}}{1} \times \frac{1 \text{ kg}}{2.2 \cancel{\text{ lb}}} = 80 \text{ kg}]
Full chain: [\frac{80 \cancel{\text{ kg}}}{1} \times \frac{15 \cancel{\text{ mg}}}{1 \cancel{\text{ kg}}} \times \frac{10 \text{ mL}}{500 \cancel{\text{ mg}}} = 24 \text{ mL}]
Walkthrough
First convert the patient's weight from lb to kg, then chain weight → dose (mg) → volume (mL):
Quick mental check: 176 lb ÷ 2.2 = 80 kg. 80 kg × 15 mg/kg = 1200 mg, and 1200 mg ÷ 500 mg × 10 mL = 24 mL. ✓
Problem 12
Order: ibuprofen 10 mg/kg orally, max 600 mg Patient weight: 85 kg Stock: 200 mg/5 mL How many mL?
Answer
Calculated dose: [\frac{85 \cancel{\text{ kg}}}{1} \times \frac{10 \text{ mg}}{1 \cancel{\text{ kg}}} = 850 \text{ mg}]
850 mg exceeds max of 600 mg — use 600 mg
Volume: [\frac{600 \cancel{\text{ mg}}}{1} \times \frac{5 \text{ mL}}{200 \cancel{\text{ mg}}} = 15 \text{ mL}]
Walkthrough
First find the calculated dose, compare it to the max, then convert the dose actually given to volume:
850 mg exceeds the 600 mg maximum — use 600 mg:
Quick mental check: 600 mg is 3 times the 200 mg in 5 mL, so the answer is 3 × 5 = 15 mL. ✓
Problem 13
Order: morphine 0.1 mg/kg IV PRN Patient weight: 154 lb Stock: 10 mg/mL How many mL?
Answer
Convert weight: [\frac{154 \cancel{\text{ lb}}}{1} \times \frac{1 \text{ kg}}{2.2 \cancel{\text{ lb}}} = 70 \text{ kg}]
Full chain: [\frac{70 \cancel{\text{ kg}}}{1} \times \frac{0.1 \cancel{\text{ mg}}}{1 \cancel{\text{ kg}}} \times \frac{1 \text{ mL}}{10 \cancel{\text{ mg}}} = 0.7 \text{ mL}]
Walkthrough
First convert the patient's weight from lb to kg, then chain weight → dose (mg) → volume (mL):
Quick mental check: 154 lb ÷ 2.2 = 70 kg. 70 kg × 0.1 mg/kg = 7 mg, and 7 mg ÷ 10 mg/mL = 0.7 mL. ✓
Section 5 — Weight-Based Dosing (Pediatric)¶
Problem 14
Order: amoxicillin 25 mg/kg orally Patient: child weighing 22 kg Stock: 250 mg/5 mL How many mL?
Answer
Walkthrough
This is a two-factor chain: weight → dose (mg) → volume (mL). Orient each factor so its denominator cancels the unit carried forward:
Quick mental check: 22 kg × 25 mg/kg = 550 mg, and 550 mg ÷ 250 mg × 5 mL = 11 mL. ✓
Problem 15
Order: paracetamol 15 mg/kg orally, max 500 mg Patient: child weighing 40 kg Stock: 250 mg/5 mL How many mL?
Answer
Calculated dose: [\frac{40 \cancel{\text{ kg}}}{1} \times \frac{15 \text{ mg}}{1 \cancel{\text{ kg}}} = 600 \text{ mg}]
600 mg exceeds max of 500 mg — use 500 mg
Volume: [\frac{500 \cancel{\text{ mg}}}{1} \times \frac{5 \text{ mL}}{250 \cancel{\text{ mg}}} = 10 \text{ mL}]
Walkthrough
First find the calculated dose, compare it to the max, then convert the dose actually given to volume:
600 mg exceeds the 500 mg maximum — use 500 mg:
Quick mental check: 500 mg is double the 250 mg in 5 mL, so the answer is 2 × 5 = 10 mL. ✓
Problem 16
Order: penicillin V 50 mg/kg/day orally divided every 6 hours Patient: child weighing 20 kg Stock: 125 mg/5 mL How many mL per dose?
Answer
Total daily dose: [\frac{20 \cancel{\text{ kg}}}{1} \times \frac{50 \text{ mg}}{1 \cancel{\text{ kg}}} = 1000 \text{ mg/day}]
Single dose (every 6 hours = 4 doses/day): [\frac{1000 \text{ mg/day}}{1} \times \frac{1 \text{ day}}{4 \text{ doses}} = 250 \text{ mg/dose}]
Volume: [\frac{250 \cancel{\text{ mg}}}{1} \times \frac{5 \text{ mL}}{125 \cancel{\text{ mg}}} = 10 \text{ mL}]
Walkthrough
This is a three-step chain: find the total daily dose, divide it into a single dose, then convert that dose to volume:
Quick mental check: 20 kg × 50 mg/kg = 1000 mg/day. Divided into 4 doses = 250 mg/dose, and 250 mg is double the 125 mg in 5 mL, so 10 mL. ✓
Section 6 — IV Flow Rates & Infusion Time¶
Problem 17
Order: 1000 mL 0.9% NaCl over 8 hours. What is the flow rate in mL/hr?
Answer
Walkthrough
Flow rate is simply volume divided by time:
Quick mental check: 1000 ÷ 8 = 125. ✓
Problem 18
Order: 250 mL over 45 minutes. What is the flow rate in mL/hr?
Answer
Convert time: [\frac{45 \cancel{\text{ min}}}{1} \times \frac{1 \text{ hr}}{60 \cancel{\text{ min}}} = 0.75 \text{ hr}]
Rate: [\frac{250 \text{ mL}}{0.75 \text{ hr}} = 333.3 \text{ mL/hr}]
Walkthrough
The order gives time in minutes, but rate is in mL/hr — convert minutes to hours first, then divide volume by time:
Quick mental check: 45 min is three-quarters of an hour, and 250 ÷ 0.75 ≈ 333. ✓
Round to: 333 mL/hr
Problem 19
A 1000 mL bag is running at 150 mL/hr. After 3 hours, how much fluid remains and how much longer will it run?
Answer
Volume infused: [\frac{150 \text{ mL/hr}}{1} \times \frac{3 \text{ hr}}{1} = 450 \text{ mL}]
Volume remaining: [1000 \text{ mL} - 450 \text{ mL} = 550 \text{ mL}]
Time remaining: [\frac{550 \text{ mL}}{150 \text{ mL/hr}} = 3.67 \text{ hr}]
Convert decimal to minutes: [\frac{0.67 \cancel{\text{ hr}}}{1} \times \frac{60 \text{ min}}{1 \cancel{\text{ hr}}} = 40 \text{ min}]
Walkthrough
This problem chains four steps: volume infused so far, volume remaining, time remaining, and converting the decimal-hour remainder to minutes:
Quick mental check: At 150 mL/hr, 3 hours uses 450 mL, leaving 550 mL. 550 ÷ 150 ≈ 3.67 hr, and 0.67 hr ≈ 40 min. ✓
550 mL remaining — 3 hours and 40 minutes.
Section 7 — Drip Rates¶
Problem 20
Order: 1000 mL over 8 hours Tubing: 20 gtt/mL What is the drip rate in gtt/min?
Answer
Convert time: [\frac{8 \cancel{\text{ hr}}}{1} \times \frac{60 \text{ min}}{1 \cancel{\text{ hr}}} = 480 \text{ min}]
Calculate: [\frac{1000 \text{ mL}}{480 \text{ min}} \times 20 \text{ gtt/mL} = 41.7 \text{ gtt/min}]
Walkthrough
Convert the infusion time to minutes, then combine the rate (volume ÷ time) with the tubing's drop factor:
Quick mental check: 8 hr = 480 min. 1000 ÷ 480 ≈ 2.08 mL/min, and 2.08 × 20 ≈ 41.7 gtt/min. ✓
Round to: 42 gtt/min
Problem 21
Rate: 60 mL/hr Tubing: 60 gtt/mL (microdrip) What is the drip rate?
Answer
With microdrip tubing (60 gtt/mL), gtt/min always equals mL/hr:
60 gtt/min
Walkthrough
With a 60 gtt/mL set, the "hr to min" conversion factor (60 min/hr) and the drop factor (60 gtt/mL) are the same number — they cancel out, leaving gtt/min numerically equal to mL/hr. No calculation is needed:
Quick mental check: Any rate in mL/hr on microdrip tubing converts directly to gtt/min — no math required.
Section 8 — IV Medications¶
Problem 22
Order: vancomycin 1000 mg in 250 mL over 90 minutes What is the flow rate in mL/hr?
Answer
Convert time: [\frac{90 \cancel{\text{ min}}}{1} \times \frac{1 \text{ hr}}{60 \cancel{\text{ min}}} = 1.5 \text{ hr}]
Rate: [\frac{250 \text{ mL}}{1.5 \text{ hr}} = 166.7 \text{ mL/hr}]
Walkthrough
Convert minutes to hours first, then divide volume by time:
Quick mental check: 90 min = 1.5 hr, and 250 ÷ 1.5 ≈ 166.7. ✓
Round to: 167 mL/hr
Problem 23
Order: heparin 1000 units/hr IV Stock: 25,000 units in 500 mL 0.9% NaCl What is the flow rate in mL/hr?
Answer
Concentration: [\frac{25{,}000 \text{ units}}{500 \text{ mL}} = 50 \text{ units/mL}]
Flow rate: [\frac{1000 \cancel{\text{ units/hr}}}{1} \times \frac{1 \text{ mL}}{50 \cancel{\text{ units}}} = 20 \text{ mL/hr}]
Walkthrough
First find the stock's concentration (units per mL), then use it as the conversion factor for the ordered rate:
Quick mental check: 25,000 ÷ 500 = 50 units/mL. 1000 ÷ 50 = 20 mL/hr. ✓
Problem 24
Order: dopamine 5 mcg/kg/min IV Patient weight: 60 kg Stock: dopamine 400 mg in 250 mL D5W What is the flow rate in mL/hr?
Answer
Dose per minute: [\frac{60 \cancel{\text{ kg}}}{1} \times \frac{5 \text{ mcg}}{1 \cancel{\text{ kg}} \cdot \text{min}} = 300 \text{ mcg/min}]
Convert to mg/hr: [\frac{300 \cancel{\text{ mcg/min}}}{1} \times \frac{1 \cancel{\text{ mg}}}{1000 \cancel{\text{ mcg}}} \times \frac{60 \text{ min}}{1 \text{ hr}} = 18 \text{ mg/hr}]
Concentration: [\frac{400 \text{ mg}}{250 \text{ mL}} = 1.6 \text{ mg/mL}]
Flow rate: [\frac{18 \cancel{\text{ mg/hr}}}{1} \times \frac{1 \text{ mL}}{1.6 \cancel{\text{ mg}}} = 11.25 \text{ mL/hr}]
Walkthrough
This problem chains four steps: dose per minute, convert to mg/hr, find the stock's concentration, then convert the dose rate to a flow rate:
Quick mental check: 60 kg × 5 mcg/kg/min = 300 mcg/min = 18 mg/hr. The stock is 1.6 mg/mL, and 18 ÷ 1.6 ≈ 11.25 mL/hr. ✓
Round to: 11 mL/hr
Problem 25
An IV is running at 25 mL/hr.
Stock: morphine 50 mg in 500 mL 0.9% NaCl
What dose is the patient receiving per hour?
Answer
Concentration: \(\frac{50 \text{ mg}}{500 \text{ mL}} = 0.1 \text{ mg/mL}\)
Dose rate: [\frac{25 \text{ mL/hr}}{1} \times \frac{0.1 \text{ mg/mL}}{1} = 2.5 \text{ mg/hr}]
Walkthrough
First find the stock's concentration (mg per mL), then multiply the running rate by that concentration to get the dose rate:
Quick mental check: 50 mg in 500 mL is 0.1 mg/mL. 25 mL/hr × 0.1 mg/mL = 2.5 mg/hr. ✓