Read the pH: below 7.35 is acidosis, above 7.45 alkalosis.
Find the value that explains it: PaCO₂ moving opposite to the pH is respiratory, HCO₃⁻ moving with the pH is metabolic.
Look at the other value: normal means uncompensated, abnormal in the compensating direction means partial compensation, and a normal pH with both abnormal means full compensation.
In a metabolic acidosis, compare PaCO₂ with Winter’s formula, 1.5·HCO₃⁻ + 8 ± 2, and calculate the anion gap Na⁺ − (Cl⁻ + HCO₃⁻).
Check a high anion gap with the delta ratio and, when albumin is low, with the corrected gap.
Nursing math & unit conversions
Metric steps
1 kg = 1000 g, 1 g = 1000 mg, 1 mg = 1000 mcg, 1 L = 1000 mL
Weight and length
1 kg = 2.2 lb, 1 lb = 16 oz, 1 in = 2.54 cm, 1 ft = 12 in
Household measures
1 tsp = 5 mL, 1 tbsp = 15 mL, 1 fl oz = 30 mL, 1 cup = 8 fl oz = 240 mL
Write the given quantity with its unit and the unit you want.
Pick the equivalent: 1000 between kg, g, mg and mcg or L and mL; 1 kg = 2.2 lb; 1 tsp = 5 mL, 1 tbsp = 15 mL, 1 fl oz = 30 mL, 1 cup = 240 mL.
Write it as a fraction so that the unwanted unit cancels; for a rate, use one fraction per unit that changes.
Check the direction: a smaller unit gives a bigger number.
Round only the final answer, to the precision the question names.
2Practice problems
1.Clinical assessment scoresMedium
Practice exercise (made-up values, not clinical guidance). A patient has a pulse of 133/min and a blood pressure of 119/65 mmHg. Find the shock index SI = HR/SBP. Round to two decimal places.
HR 133/minBP 119/65 mmHg
SI =
2.Clinical assessment scoresHard
Practice exercise (made-up values, not clinical guidance). An adult weighs 112 kg and is 150 cm tall. Calculate the BMI and click the WHO weight category.
112 kg150 cm
1underweight
2healthy weight
3overweight
4obesity class I
5obesity class II
6obesity class III
3.Arterial blood gas interpretationMedium
Practice values: Na⁺ 129 mmol/L, glucose 30.3 mmol/L and urea 7.8 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.
Na⁺ 129 mmol/Lglucose 30.3 mmol/Lurea 7.8 mmol/L
Osm = mOsm/kg
4.Arterial blood gas interpretationHard
At sea level, a practice gas taken on 30% oxygen shows PaO₂ 58 mmHg (7.7 kPa) and PaCO₂ 40 mmHg (5.3 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.
What does the Malnutrition Universal Screening Tool (MUST) assess?
ASwallowing ability
BThe level of pain
CThe risk of malnutrition
DThe risk of falling
6.Nursing fundamentalsHard
A patient with a valid DNACPR (DNR) decision, whose death was expected, stops breathing. What should the nurse do?
AStart CPR but stop after five minutes
BNot start CPR, note the time, inform the team and support the family
CStart CPR and call the cardiac arrest team
DLeave the patient and ask the family to wait outside until the doctor comes
7.Nursing math & unit conversionsMedium
Practice exercise (made-up values, not clinical guidance). A drip-rate calculation gives 67.819 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?
67.819 gtt/min
x = gtt/min
8.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads 1 tsp of an oral suspension every 6 hours for 5 days. The suspension comes in 150 mL bottles. Using 1 tsp = 5 mL, how many whole bottles N must be supplied so the course is complete?
1 tspevery 6 hours5 days150 mL1 tsp = 5 mL
N =
3Solutions
1.Clinical assessment scores
Answer: SI = 1.12
Blood pressure values: pulse pressure PP = SBP − DBP. Mean arterial pressure MAP ≈ (SBP + 2·DBP)/3 = DBP + PP/3, an estimate based on the heart spending about two thirds of each beat in diastole at a normal heart rate (less accurate when the heart rate is fast); a MAP of at least about 65 mmHg is a common target for organ perfusion. The shock index SI = heart rate/SBP is normally about 0.5–0.7; a value above about 1 is a warning sign of shock.
Shock index
SI = 133/119 = 1.118 ≈ 1.12
Answer
SI = 1.12
1 or more: a warning sign of shock in this practice case.
2.Clinical assessment scores
Answer: obesity class III
Body mass index: BMI = weight (kg)/height (m)², with the height converted to metres first. With pounds and inches, BMI = 703 × weight (lb)/height (in)². WHO adult categories: below 18.5 underweight, 18.5–24.9 healthy weight, 25.0–29.9 overweight, 30.0–34.9 obesity class I, 35.0–39.9 obesity class II and 40 or more obesity class III.
BMI
BMI = 112/1.5² = 49.78
Category
obesity class III
Answer
obesity class III
3.Arterial blood gas interpretation
Answer: Osm = 296 mOsm/kg
Derived values: calculated serum osmolality is 2·Na⁺ + glucose + urea with all values in mmol/L (2·Na⁺ + glucose/18 + BUN/2.8 with glucose and BUN in mg/dL); normal is about 275–295 mOsm/kg. The P/F ratio is PaO₂ divided by FiO₂ as a fraction. The alveolar oxygen pressure is PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 mmHg at sea level, and the A–a gradient is PAO₂ − PaO₂.
Calculated osmolality
Osm = 2·129 + 30.3 + 7.8 = 296.1 ≈ 296 mOsm/kg
Answer
Osm = 296 mOsm/kg
4.Arterial blood gas interpretation
Answer: A–a gradient = 105.9 mmHg
Derived values: calculated serum osmolality is 2·Na⁺ + glucose + urea with all values in mmol/L (2·Na⁺ + glucose/18 + BUN/2.8 with glucose and BUN in mg/dL); normal is about 275–295 mOsm/kg. The P/F ratio is PaO₂ divided by FiO₂ as a fraction. The alveolar oxygen pressure is PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 mmHg at sea level, and the A–a gradient is PAO₂ − PaO₂.
Alveolar oxygen
PAO₂ = 0.3·713 − 40/0.8 = 213.9 − 50 = 163.9 mmHg
Gradient
A–a = 163.9 − 58 = 105.9 mmHg
Answer
A–a gradient = 105.9 mmHg
5.Nursing fundamentals
Answer: C · The risk of malnutrition
Why this is the answer
MUST combines body mass index, unplanned weight loss and acute disease effect into a score that shows the risk of malnutrition and guides nutritional care.
Answer
C · The risk of malnutrition
6.Nursing fundamentals
Answer: B · Not start CPR, note the time, inform the team and support the family
Why this is the answer
CPR is not attempted when a valid DNACPR decision applies. The nurse notes the time, follows local policy for verifying death, informs the medical team and supports the family.
Answer
B · Not start CPR, note the time, inform the team and support the family
7.Nursing math & unit conversions
Answer: x = 68 gtt/min
Rounding: look at the digit just after the place you round to: 5 or more rounds up, 4 or less leaves the digit as it is. Round only the final answer, never the steps. Typical exam rules: volumes of 1 mL or more to the nearest tenth, volumes below 1 mL to the nearest hundredth, drip rates to whole drops and weights to one decimal place; always follow the rule the question states.
Digit in the ones place
67.819 → 7
Only the next digit decides
67.819 → 8
8 is 5 or more, so round 7 up.
The digits after it (19) are ignored: round once, never step by step.
Round
x = 68 gtt/min
Answer
x = 68 gtt/min
8.Nursing math & unit conversions
Answer: N = 1
Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.