Practice Set 2 — Wrap-Up Challenge¶
Instructions¶
This set simulates a real clinical competency exam.
- Problems are in random mixed order with no topic labels
- Numbers are harder than Set 1
- No hints are given
- Attempt every problem before revealing the answer
- Aim for 90% or higher (23 out of 25 correct)
Challenge Yourself
Do not reveal answers until you have committed to your solution in writing. The goal is to identify gaps before clinical practice — not after.
Problem 1
Order: atenolol 12.5 mg orally Stock: 25 mg per tablet How many tablets?
Answer
Walkthrough
The conversion factor comes from the stock strength: 25 mg = 1 tablet. Orient it with mg in the denominator so it cancels with the starting quantity:
Quick mental check: 12.5 mg is half of 25 mg, so the answer is half a tablet. ✓
Verify the tablet is scored before splitting.
Problem 2
Order: 750 mL 0.9% NaCl over 6 hours What is the flow rate in mL/hr?
Answer
Walkthrough
Flow rate is volume divided by time:
Quick mental check: 750 ÷ 6 = 125. ✓
Problem 3
Order: tobramycin 2.5 mg/kg IV Patient weight: 198 lb Stock: 40 mg/mL How many mL?
Answer
Convert weight: [\frac{198 \cancel{\text{ lb}}}{1} \times \frac{1 \text{ kg}}{2.2 \cancel{\text{ lb}}} = 90 \text{ kg}]
Full chain: [\frac{90 \cancel{\text{ kg}}}{1} \times \frac{2.5 \cancel{\text{ mg}}}{1 \cancel{\text{ kg}}} \times \frac{1 \text{ mL}}{40 \cancel{\text{ mg}}} = 5.625 \text{ mL}]
Walkthrough
First convert the patient's weight from lb to kg, then chain weight → dose (mg) → volume (mL):
Quick mental check: 198 lb ÷ 2.2 = 90 kg. 90 kg × 2.5 mg/kg = 225 mg, and 225 mg ÷ 40 mg/mL ≈ 5.6 mL. ✓
Round to: 5.6 mL
Problem 4
Convert 0.375 g to mcg.
Answer
Walkthrough
This is a two-step metric conversion: g → mg → mcg. Orient each factor so its denominator cancels the unit carried forward:
Quick mental check: g→mcg is six places to the right (×1,000,000). 0.375 × 1,000,000 = 375,000. ✓
Problem 5
Order: clarithromycin 0.5 g orally Stock: 250 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: 0.5 g = 500 mg, and 500 mg is double the 250 mg in 5 mL, so the answer is 10 mL. ✓
Problem 6
Order: 500 mL over 35 minutes What is the flow rate in mL/hr?
Answer
Convert time: [\frac{35 \cancel{\text{ min}}}{1} \times \frac{1 \text{ hr}}{60 \cancel{\text{ min}}} = 0.583 \text{ hr}]
Rate: [\frac{500 \text{ mL}}{0.583 \text{ hr}} = 857.6 \text{ mL/hr}]
Walkthrough
Convert minutes to hours first, then divide volume by time:
Quick mental check: 35 min ≈ 0.58 hr, and 500 ÷ 0.583 ≈ 858. ✓
Round to: 858 mL/hr
Verify This Rate
Rates above 500 mL/hr are unusual. Verify the order before programming the pump.
Problem 7
Order: amoxicillin 30 mg/kg/day orally divided every 8 hours Patient: child weighing 16 kg Stock: 200 mg/5 mL How many mL per dose?
Answer
Total daily dose: [\frac{16 \cancel{\text{ kg}}}{1} \times \frac{30 \text{ mg}}{1 \cancel{\text{ kg}}} = 480 \text{ mg/day}]
Single dose (every 8 hours = 3 doses/day): [\frac{480 \text{ mg/day}}{1} \times \frac{1 \text{ day}}{3 \text{ doses}} = 160 \text{ mg/dose}]
Volume: [\frac{160 \cancel{\text{ mg}}}{1} \times \frac{5 \text{ mL}}{200 \cancel{\text{ mg}}} = 4 \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: 16 kg × 30 mg/kg = 480 mg/day. Divided into 3 doses = 160 mg/dose, and 160 mg is 0.8 × 200 mg, so 0.8 × 5 mL = 4 mL. ✓
Problem 8
Order: heparin 1800 units/hr IV Stock: 25,000 units in 250 mL 0.9% NaCl What is the flow rate in mL/hr?
Answer
Concentration: [\frac{25{,}000 \text{ units}}{250 \text{ mL}} = 100 \text{ units/mL}]
Flow rate: [\frac{1800 \cancel{\text{ units/hr}}}{1} \times \frac{1 \text{ mL}}{100 \cancel{\text{ units}}} = 18 \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 ÷ 250 = 100 units/mL. 1800 ÷ 100 = 18 mL/hr. ✓
Problem 9
A 1000 mL bag starts at 2130 running at 80 mL/hr. What time will it complete?
Answer
Infusion time: [\frac{1000 \text{ mL}}{80 \text{ mL/hr}} = 12.5 \text{ hr}]
Convert decimal: [\frac{0.5 \text{ hr}}{1} \times \frac{60 \text{ min}}{1 \text{ hr}} = 30 \text{ min}]
Completion time: [2130 + 12 \text{ hr } 30 \text{ min} = 1000 \text{ next day}]
Walkthrough
First find the total infusion time (volume ÷ rate), convert the decimal-hour remainder to minutes, then add the total time to the start time:
Quick mental check: 1000 ÷ 80 = 12.5 hr = 12 hr 30 min. 2130 + 12 hr 30 min crosses midnight to 1000 the next morning. ✓
Completes at 1000 the following morning.
Problem 10
Order: digoxin 0.125 mg orally Stock: 62.5 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:
Quick mental check: 0.125 mg = 125 mcg, and 125 mcg is double the 62.5 mcg per tablet. ✓
Problem 11
Order: 1000 mL Lactated Ringer's over 12 hours Tubing: 15 gtt/mL What is the drip rate in gtt/min?
Answer
Convert time: [\frac{12 \cancel{\text{ hr}}}{1} \times \frac{60 \text{ min}}{1 \cancel{\text{ hr}}} = 720 \text{ min}]
Calculate: [\frac{1000 \text{ mL}}{720 \text{ min}} \times 15 \text{ gtt/mL} = 20.8 \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: 12 hr = 720 min. 1000 ÷ 720 ≈ 1.39 mL/min, and 1.39 × 15 ≈ 20.8 gtt/min. ✓
Round to: 21 gtt/min
Problem 12
Order: morphine 0.08 mg/kg IV PRN Patient weight: 187 lb Stock: 5 mg/mL How many mL? Round to nearest hundredth.
Answer
Convert weight: [\frac{187 \cancel{\text{ lb}}}{1} \times \frac{1 \text{ kg}}{2.2 \cancel{\text{ lb}}} = 85 \text{ kg}]
Full chain: [\frac{85 \cancel{\text{ kg}}}{1} \times \frac{0.08 \cancel{\text{ mg}}}{1 \cancel{\text{ kg}}} \times \frac{1 \text{ mL}}{5 \cancel{\text{ mg}}} = 1.36 \text{ mL}]
Walkthrough
First convert the patient's weight from lb to kg, then chain weight → dose (mg) → volume (mL):
Quick mental check: 187 lb ÷ 2.2 = 85 kg. 85 kg × 0.08 mg/kg = 6.8 mg, and 6.8 mg ÷ 5 mg/mL = 1.36 mL. ✓
Problem 13
Convert 4.5 L to mL.
Answer
Walkthrough
The conversion factor is 1 L = 1000 mL. Orient it with L in the denominator so it cancels:
$ \overfactor{\conv{4.5 \cn{\unit{L}}}{1}}{Starting Quantity} \times \factor{\conv{1000 \unit{mL}}{1 \cn{\unit{L}}}}{L to mL factor} = 4500 \unit{mL} $
Quick mental check: L→mL shifts the decimal three places to the right. 4.5 → 4500. ✓
Problem 14
Order: dopamine 8 mcg/kg/min IV Patient weight: 75 kg Stock: dopamine 800 mg in 500 mL D5W What is the flow rate in mL/hr?
Answer
Dose per minute: [\frac{75 \cancel{\text{ kg}}}{1} \times \frac{8 \text{ mcg}}{1 \cancel{\text{ kg}} \cdot \text{min}} = 600 \text{ mcg/min}]
Convert to mg/hr: [\frac{600 \cancel{\text{ mcg/min}}}{1} \times \frac{1 \cancel{\text{ mg}}}{1000 \cancel{\text{ mcg}}} \times \frac{60 \text{ min}}{1 \text{ hr}} = 36 \text{ mg/hr}]
Concentration: [\frac{800 \text{ mg}}{500 \text{ mL}} = 1.6 \text{ mg/mL}]
Flow rate: [\frac{36 \cancel{\text{ mg/hr}}}{1} \times \frac{1 \text{ mL}}{1.6 \cancel{\text{ mg}}} = 22.5 \text{ mL/hr}]
Round to: 23 mL/hr
Walkthrough
This is a multi-step chain: first find the dose per minute, convert it to mg/hr, find the concentration of the stock, then divide to get the flow rate:
$ \overfactor{\conv{75 \cn{\unit{kg}}}{1}}{Starting Quantity} \times \factor{\conv{8 \unit{mcg}}{1 \cn{\unit{kg}} \cdot min}}{kg to mcg/min factor} = 600 \unit{mcg/min} $
$ \overfactor{\conv{600 \cn{\unit{mcg/min}}}{1}}{Starting Quantity} \times \factor{\conv{1 \unit{mg}}{1000 \cn{\unit{mcg}}}}{mcg to mg factor} \times \factor{\conv{60 \unit{min}}{1 \unit{hr}}}{min to hr factor} = 36 \unit{mg/hr} $
$ \overfactor{\conv{800 \unit{mg}}{500 \unit{mL}}}{Total \div Volume} = 1.6 \unit{mg/mL} $
$ \overfactor{\conv{36 \cn{\unit{mg/hr}}}{1}}{Starting Quantity} \times \factor{\conv{1 \unit{mL}}{1.6 \cn{\unit{mg}}}}{mg to mL factor} = 22.5 \unit{mL/hr} $
Quick mental check: 75 kg × 8 mcg/kg/min = 600 mcg/min. 600 mcg/min ÷ 1000 × 60 = 36 mg/hr. The stock is 1.6 mg/mL, so 36 ÷ 1.6 ≈ 22.5, rounded to 23 mL/hr. ✓
Problem 15
Order: ibuprofen 10 mg/kg orally, max 400 mg Patient: child weighing 48 kg Stock: 100 mg/5 mL How many mL?
Answer
Calculated dose: [\frac{48 \cancel{\text{ kg}}}{1} \times \frac{10 \text{ mg}}{1 \cancel{\text{ kg}}} = 480 \text{ mg}]
480 mg exceeds max of 400 mg — use 400 mg
Volume: [\frac{400 \cancel{\text{ mg}}}{1} \times \frac{5 \text{ mL}}{100 \cancel{\text{ mg}}} = 20 \text{ mL}]
Walkthrough
First find the calculated dose, then compare it against the maximum dose limit before converting to volume:
$ \overfactor{\conv{48 \cn{\unit{kg}}}{1}}{Starting Quantity} \times \factor{\conv{10 \unit{mg}}{1 \cn{\unit{kg}}}}{kg to mg factor (dose)} = 480 \unit{mg} $
480 mg exceeds the maximum of 400 mg, so use 400 mg:
$ \overfactor{\conv{400 \cn{\unit{mg}}}{1}}{Starting Quantity} \times \factor{\conv{5 \unit{mL}}{100 \cn{\unit{mg}}}}{mg to mL factor} = 20 \unit{mL} $
Quick mental check: 48 kg × 10 mg/kg = 480 mg, which is capped at 400 mg. 400 ÷ 100 × 5 = 20 mL. ✓
Problem 16
A 750 mL bag started at 0730 running at 125 mL/hr. It is now 1130. How much fluid remains and what time will the infusion complete?
Answer
Time elapsed: [1130 - 0730 = 4 \text{ hr}]
Volume infused: [\frac{125 \text{ mL/hr}}{1} \times \frac{4 \text{ hr}}{1} = 500 \text{ mL}]
Volume remaining: [750 - 500 = 250 \text{ mL}]
Time remaining: [\frac{250 \text{ mL}}{125 \text{ mL/hr}} = 2 \text{ hr}]
Completion time: [1130 + 2 \text{ hr} = 1330]
Completes at 1330 (1:30 PM).
Walkthrough
First find how much time has elapsed and how much fluid has already infused, then work out what's left and when it will finish:
$ 1130 - 0730 = 4 \unit{hr} $
$ \overfactor{\conv{125 \unit{mL/hr}}{1}}{Starting Quantity} \times \factor{\conv{4 \unit{hr}}{1}}{Rate \times Time} = 500 \unit{mL} $
$ 750 - 500 = 250 \unit{mL} $
$ \overfactor{\conv{250 \unit{mL}}{125 \unit{mL/hr}}}{Volume \div Rate} = 2 \unit{hr} $
$ 1130 + 2 \unit{hr} = 1330 $
Quick mental check: 4 hours at 125 mL/hr = 500 mL infused, leaving 250 mL. At 125 mL/hr that's another 2 hours, so it finishes 2 hours after 1130, at 1330. ✓
Problem 17
Order: vancomycin 20 mg/kg IV over 90 minutes Patient weight: 220 lb Stock: 500 mg/10 mL What is the total dose in mg and the flow rate in mL/hr?
Answer
Convert weight: [\frac{220 \cancel{\text{ lb}}}{1} \times \frac{1 \text{ kg}}{2.2 \cancel{\text{ lb}}} = 100 \text{ kg}]
Total dose: [\frac{100 \cancel{\text{ kg}}}{1} \times \frac{20 \text{ mg}}{1 \cancel{\text{ kg}}} = 2000 \text{ mg}]
Volume to infuse: [\frac{2000 \cancel{\text{ mg}}}{1} \times \frac{10 \text{ mL}}{500 \cancel{\text{ mg}}} = 40 \text{ mL}]
Convert time: [\frac{90 \cancel{\text{ min}}}{1} \times \frac{1 \text{ hr}}{60 \cancel{\text{ min}}} = 1.5 \text{ hr}]
Flow rate: [\frac{40 \text{ mL}}{1.5 \text{ hr}} = 26.7 \text{ mL/hr}]
Round to: 27 mL/hr
Walkthrough
First convert the patient's weight to kg, then find the total dose and the volume to infuse, then convert the infusion time to hours to get the flow rate:
$ \overfactor{\conv{220 \cn{\unit{lb}}}{1}}{Starting Quantity} \times \factor{\conv{1 \unit{kg}}{2.2 \cn{\unit{lb}}}}{lb to kg factor} = 100 \unit{kg} $
$ \overfactor{\conv{100 \cn{\unit{kg}}}{1}}{Starting Quantity} \times \factor{\conv{20 \unit{mg}}{1 \cn{\unit{kg}}}}{kg to mg factor (dose)} = 2000 \unit{mg} $
$ \overfactor{\conv{2000 \cn{\unit{mg}}}{1}}{Starting Quantity} \times \factor{\conv{10 \unit{mL}}{500 \cn{\unit{mg}}}}{mg to mL factor} = 40 \unit{mL} $
$ \overfactor{\conv{90 \cn{\unit{min}}}{1}}{Starting Quantity} \times \factor{\conv{1 \unit{hr}}{60 \cn{\unit{min}}}}{min to hr factor} = 1.5 \unit{hr} $
$ \overfactor{\conv{40 \unit{mL}}{1.5 \unit{hr}}}{Volume \div Time} = 26.7 \unit{mL/hr} $
Quick mental check: 220 lb ÷ 2.2 = 100 kg. 100 kg × 20 mg/kg = 2000 mg, and 2000 mg ÷ 500 mg × 10 mL = 40 mL. 90 min = 1.5 hr, so 40 ÷ 1.5 ≈ 26.7, rounded to 27 mL/hr. ✓
Problem 18
Order: gentamicin 6 mg/kg/day IV divided every 8 hours Patient weight: 66 kg Stock: 10 mg/mL How many mL per dose?
Answer
Total daily dose: [\frac{66 \cancel{\text{ kg}}}{1} \times \frac{6 \text{ mg}}{1 \cancel{\text{ kg}}} = 396 \text{ mg/day}]
Single dose (every 8 hours = 3 doses/day): [\frac{396 \text{ mg/day}}{1} \times \frac{1 \text{ day}}{3 \text{ doses}} = 132 \text{ mg/dose}]
Volume: [\frac{132 \cancel{\text{ mg}}}{1} \times \frac{1 \text{ mL}}{10 \cancel{\text{ mg}}} = 13.2 \text{ mL}]
Walkthrough
First find the total daily dose, then divide by the number of doses per day, then convert the single dose to volume:
$ \overfactor{\conv{66 \cn{\unit{kg}}}{1}}{Starting Quantity} \times \factor{\conv{6 \unit{mg}}{1 \cn{\unit{kg}}}}{kg to mg factor (dose)} = 396 \unit{mg/day} $
$ \overfactor{\conv{396 \unit{mg/day}}{1}}{Starting Quantity} \times \factor{\conv{1 \unit{day}}{3 \unit{doses}}}{day to doses factor} = 132 \unit{mg/dose} $
$ \overfactor{\conv{132 \cn{\unit{mg}}}{1}}{Starting Quantity} \times \factor{\conv{1 \unit{mL}}{10 \cn{\unit{mg}}}}{mg to mL factor} = 13.2 \unit{mL} $
Quick mental check: 66 kg × 6 mg/kg = 396 mg/day. 396 ÷ 3 doses = 132 mg/dose, and 132 mg ÷ 10 mg/mL = 13.2 mL. ✓
Problem 19
Order: 500 mL over 4 hours Tubing: 10 gtt/mL What is the drip rate in gtt/min?
Answer
Convert time: [\frac{4 \cancel{\text{ hr}}}{1} \times \frac{60 \text{ min}}{1 \cancel{\text{ hr}}} = 240 \text{ min}]
Calculate: [\frac{500 \text{ mL}}{240 \text{ min}} \times 10 \text{ gtt/mL} = 20.8 \text{ gtt/min}]
Round to: 21 gtt/min
Walkthrough
First convert the infusion time to minutes, then divide the volume by time and multiply by the drop factor:
$ \overfactor{\conv{4 \cn{\unit{hr}}}{1}}{Starting Quantity} \times \factor{\conv{60 \unit{min}}{1 \cn{\unit{hr}}}}{hr to min factor} = 240 \unit{min} $
$ \overfactor{\conv{500 \unit{mL}}{240 \unit{min}}}{Volume \div Time} \times \factor{\conv{10 \unit{gtt}}{1 \unit{mL}}}{drop factor (tubing)} = 20.8 \unit{gtt/min} $
Quick mental check: 4 hr = 240 min. 500 mL ÷ 240 min ≈ 2.08 mL/min, × 10 gtt/mL ≈ 20.8, rounded to 21 gtt/min. ✓
Problem 20
An IV is running at 40 mL/hr. Stock: heparin 25,000 units in 500 mL What dose is the patient receiving per hour?
Answer
Concentration: [\frac{25{,}000 \text{ units}}{500 \text{ mL}} = 50 \text{ units/mL}]
Dose rate: [\frac{40 \text{ mL/hr}}{1} \times \frac{50 \text{ units/mL}}{1} = 2000 \text{ units/hr}]
Walkthrough
First find the concentration of the stock, then multiply the running rate by the concentration to get the dose being delivered per hour:
$ \overfactor{\conv{25000 \unit{units}}{500 \unit{mL}}}{Total \div Volume} = 50 \unit{units/mL} $
$ \overfactor{\conv{40 \unit{mL/hr}}{1}}{Starting Quantity} \times \factor{\conv{50 \unit{units/mL}}{1}}{concentration factor} = 2000 \unit{units/hr} $
Quick mental check: 25,000 units in 500 mL is 50 units/mL. At 40 mL/hr, that's 40 × 50 = 2000 units/hr. ✓
Problem 21
Order: prednisolone 2 mg/kg/day orally divided every 12 hours Patient: child weighing 14 kg Stock: 5 mg/5 mL solution How many mL per dose?
Answer
Total daily dose: [\frac{14 \cancel{\text{ kg}}}{1} \times \frac{2 \text{ mg}}{1 \cancel{\text{ kg}}} = 28 \text{ mg/day}]
Single dose (every 12 hours = 2 doses/day): [\frac{28 \text{ mg/day}}{1} \times \frac{1 \text{ day}}{2 \text{ doses}} = 14 \text{ mg/dose}]
Volume: [\frac{14 \cancel{\text{ mg}}}{1} \times \frac{5 \text{ mL}}{5 \cancel{\text{ mg}}} = 14 \text{ mL}]
Walkthrough
First find the total daily dose, then divide by the number of doses per day, then convert the single dose to volume:
$ \overfactor{\conv{14 \cn{\unit{kg}}}{1}}{Starting Quantity} \times \factor{\conv{2 \unit{mg}}{1 \cn{\unit{kg}}}}{kg to mg factor (dose)} = 28 \unit{mg/day} $
$ \overfactor{\conv{28 \unit{mg/day}}{1}}{Starting Quantity} \times \factor{\conv{1 \unit{day}}{2 \unit{doses}}}{day to doses factor} = 14 \unit{mg/dose} $
$ \overfactor{\conv{14 \cn{\unit{mg}}}{1}}{Starting Quantity} \times \factor{\conv{5 \unit{mL}}{5 \cn{\unit{mg}}}}{mg to mL factor} = 14 \unit{mL} $
Quick mental check: 14 kg × 2 mg/kg = 28 mg/day. 28 ÷ 2 doses = 14 mg/dose, and since the stock is a 1:1 ratio (5 mg per 5 mL), 14 mg = 14 mL. ✓
Problem 22
Order: morphine 4 mg/hr IV continuous Stock: morphine 100 mg in 500 mL 0.9% NaCl What is the flow rate in mL/hr?
Answer
Concentration: [\frac{100 \text{ mg}}{500 \text{ mL}} = 0.2 \text{ mg/mL}]
Flow rate: [\frac{4 \cancel{\text{ mg/hr}}}{1} \times \frac{1 \text{ mL}}{0.2 \cancel{\text{ mg}}} = 20 \text{ mL/hr}]
Walkthrough
First find the concentration of the stock, then divide the ordered dose rate by the concentration to get the flow rate:
$ \overfactor{\conv{100 \unit{mg}}{500 \unit{mL}}}{Total \div Volume} = 0.2 \unit{mg/mL} $
$ \overfactor{\conv{4 \cn{\unit{mg/hr}}}{1}}{Starting Quantity} \times \factor{\conv{1 \unit{mL}}{0.2 \cn{\unit{mg}}}}{mg to mL factor} = 20 \unit{mL/hr} $
Quick mental check: 100 mg in 500 mL is 0.2 mg/mL. 4 mg/hr ÷ 0.2 mg/mL = 20 mL/hr. ✓
Problem 23
Order: 1000 mL over 10 hours. After 6 hours only 500 mL has infused. 500 mL remains with 4 hours left on the order. What rate is needed to complete on time? Is this within the 25% adjustment guideline?
Answer
Required rate: [\frac{500 \text{ mL}}{4 \text{ hr}} = 125 \text{ mL/hr}]
Original rate: [\frac{1000 \text{ mL}}{10 \text{ hr}} = 100 \text{ mL/hr}]
Percentage increase: [\frac{125 - 100}{100} \times 100 = 25\%]
Exactly 25% — at the limit of the guideline. Consult the prescriber before adjusting.
25% adjustment guideline
Many facilities use a policy that IV rates should not be increased by more than 25% without prescriber notification. This is a clinical practice standard, not a universal rule — always follow your facility's specific policy.
Walkthrough
First find the rate needed to finish on time, then compare it to the original ordered rate to find the percentage change:
$ \overfactor{\conv{500 \unit{mL}}{4 \unit{hr}}}{Volume \div Time} = 125 \unit{mL/hr} $
$ \overfactor{\conv{1000 \unit{mL}}{10 \unit{hr}}}{Volume \div Time} = 100 \unit{mL/hr} $
$ \frac{125 - 100}{100} \times 100 = 25\% $
Quick mental check: The new rate (125 mL/hr) is 25 mL/hr more than the original (100 mL/hr), and 25 is 25% of 100 — exactly at the guideline limit, so the prescriber should be consulted. ✓
Problem 24
Convert 2 tbsp to mL then to L.
Answer
tbsp to mL: [\frac{2 \cancel{\text{ tbsp}}}{1} \times \frac{15 \text{ mL}}{1 \cancel{\text{ tbsp}}} = 30 \text{ mL}]
mL to L: [\frac{30 \cancel{\text{ mL}}}{1} \times \frac{1 \text{ L}}{1000 \cancel{\text{ mL}}} = 0.03 \text{ L}]
Walkthrough
This is a two-step conversion: first tbsp to mL, then mL to L:
$ \overfactor{\conv{2 \cn{\unit{tbsp}}}{1}}{Starting Quantity} \times \factor{\conv{15 \unit{mL}}{1 \cn{\unit{tbsp}}}}{tbsp to mL factor} = 30 \unit{mL} $
$ \overfactor{\conv{30 \cn{\unit{mL}}}{1}}{Starting Quantity} \times \factor{\conv{1 \unit{L}}{1000 \cn{\unit{mL}}}}{mL to L factor} = 0.03 \unit{L} $
Quick mental check: 1 tbsp = 15 mL, so 2 tbsp = 30 mL. mL→L shifts the decimal three places left: 30 → 0.03. ✓
Problem 25
Safe dose range: 15–30 mg/kg/day Order: amoxicillin 20 mg/kg/day divided every 8 hours Patient: child weighing 27 kg Stock: 250 mg/5 mL Is the dose safe? If yes, how many mL per dose?
Answer
Minimum safe dose: [\frac{27 \cancel{\text{ kg}}}{1} \times \frac{15 \text{ mg}}{1 \cancel{\text{ kg}}} = 405 \text{ mg/day}]
Maximum safe dose: [\frac{27 \cancel{\text{ kg}}}{1} \times \frac{30 \text{ mg}}{1 \cancel{\text{ kg}}} = 810 \text{ mg/day}]
Ordered dose: [\frac{27 \cancel{\text{ kg}}}{1} \times \frac{20 \text{ mg}}{1 \cancel{\text{ kg}}} = 540 \text{ mg/day}]
540 mg/day falls between 405 and 810 mg/day ✓ Dose is safe.
Single dose (every 8 hours = 3 doses/day): [\frac{540 \text{ mg/day}}{1} \times \frac{1 \text{ day}}{3 \text{ doses}} = 180 \text{ mg/dose}]
Volume: [\frac{180 \cancel{\text{ mg}}}{1} \times \frac{5 \text{ mL}}{250 \cancel{\text{ mg}}} = 3.6 \text{ mL}]
Walkthrough
First check the ordered dose against the safe range by calculating the minimum, maximum, and ordered daily doses, then divide the ordered dose into individual doses and convert to volume:
$ \overfactor{\conv{27 \cn{\unit{kg}}}{1}}{Starting Quantity} \times \factor{\conv{15 \unit{mg}}{1 \cn{\unit{kg}}}}{kg to mg factor (dose)} = 405 \unit{mg/day} $
$ \overfactor{\conv{27 \cn{\unit{kg}}}{1}}{Starting Quantity} \times \factor{\conv{30 \unit{mg}}{1 \cn{\unit{kg}}}}{kg to mg factor (dose)} = 810 \unit{mg/day} $
$ \overfactor{\conv{27 \cn{\unit{kg}}}{1}}{Starting Quantity} \times \factor{\conv{20 \unit{mg}}{1 \cn{\unit{kg}}}}{kg to mg factor (dose)} = 540 \unit{mg/day} $
540 mg/day falls between 405 and 810 mg/day, so the dose is safe:
$ \overfactor{\conv{540 \unit{mg/day}}{1}}{Starting Quantity} \times \factor{\conv{1 \unit{day}}{3 \unit{doses}}}{day to doses factor} = 180 \unit{mg/dose} $
$ \overfactor{\conv{180 \cn{\unit{mg}}}{1}}{Starting Quantity} \times \factor{\conv{5 \unit{mL}}{250 \cn{\unit{mg}}}}{mg to mL factor} = 3.6 \unit{mL} $
Quick mental check: 27 kg × 15–30 mg/kg gives a safe range of 405–810 mg/day. The ordered 27 × 20 = 540 mg/day fits inside that range. 540 ÷ 3 doses = 180 mg/dose, and 180 ÷ 250 × 5 = 3.6 mL. ✓
How Did You Do?
- 23–25 correct — excellent, you are ready for clinical practice
- 20–22 correct — good, review the topics you missed and retry
- Below 20 — return to the relevant modules for review
Remember
Clinical competency requires 90% or higher — 23 out of 25 correct. If you are not there yet, that is what review is for. Keep practicing.