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 practice chart records GCS 7, with E2 and V3. What motor score M was recorded, and which response does it describe? Give the number.
GCS 7E2V3
M =
2.Clinical assessment scoresHard
Practice exercise (made-up values, not clinical guidance). The team aims for a mean arterial pressure of at least 65 mmHg. A patient’s systolic pressure is 107 mmHg. Using MAP = (SBP + 2·DBP)/3, what is the lowest diastolic pressure DBP that still gives a MAP of 65 mmHg?
MAP 65 mmHgSBP 107 mmHg
DBP = mmHg
3.Arterial blood gas interpretationMedium
A practice gas shows a metabolic acidosis with HCO₃⁻ 6 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.
HCO₃⁻ 6 mmol/L
PaCO₂ = mmHg
4.Arterial blood gas interpretationHard
Practice values: Na⁺ 136, Cl⁻ 110 and HCO₃⁻ 10 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.
Na⁺ 136 mmol/LCl⁻ 110 mmol/LHCO₃⁻ 10 mmol/L
delta ratio =
5.Nursing fundamentalsMedium
How is a 24-hour urine collection started?
AOnly urine passed at night is collected
BThe first urine of the morning is discarded and the time noted, then all urine is kept
CThe first urine of the morning is kept and the rest of the day's urine is discarded
DA sample is taken every four hours and the rest discarded
6.Nursing fundamentalsHard
Before giving a PRN dose of oral morphine, which assessment is most important?
AThe patient's last bowel movement
BThe patient's blood glucose level
CThe patient's weight and height, recorded on admission
DThe respiratory rate and level of sedation
7.Nursing math & unit conversionsMedium
Practice exercise (made-up values, not clinical guidance). A patient’s temperature is 100.7 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
100.7 °F
T = °C
8.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 18:40 and finishes at 04:05 the next morning (24-hour clock). How many hours t did it run? Give the answer in hours as a decimal, rounded to two decimal places.
18:4004:05
t = h
3Solutions
1.Clinical assessment scores
Answer: M = 2
Glasgow Coma Scale: add the best response in three areas. Eye opening E: 4 spontaneous, 3 to sound or speech, 2 to pressure, 1 none. Verbal V: 5 oriented, 4 confused, 3 inappropriate words, 2 incomprehensible sounds, 1 none. Motor M: 6 obeys commands, 5 localises, 4 normal flexion (withdraws), 3 abnormal flexion, 2 extension, 1 none. The total runs from 3 to 15. After a head injury, 13–15 is usually called mild, 9–12 moderate and 3–8 severe.
Motor score
M = 7 − 2 − 3 = 2
M2: extension of the arms and legs (abnormal extension)
Answer
M = 2
2.Clinical assessment scores
Answer: DBP = 44 mmHg
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.
Rearrange
DBP = (3·MAP − SBP)/2
Substitute
DBP = (3·65 − 107)/2 = 88/2 = 44 mmHg
Answer
DBP = 44 mmHg
3.Arterial blood gas interpretation
Answer: PaCO₂ = 17 mmHg
Expected compensation: in metabolic acidosis Winter’s formula predicts PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2 mmHg; a measured value above that range points to an additional respiratory acidosis, below it to an additional respiratory alkalosis. The anion gap AG = Na⁺ − (Cl⁻ + HCO₃⁻), normally about 8–12 mmol/L, separates high-gap from normal-gap metabolic acidosis; low albumin hides a high gap (add 2.5 per g/dL that albumin is below 4.0). The delta ratio (AG − 12)/(24 − HCO₃⁻) between about 0.8 and 2 fits a pure high-gap acidosis (some texts use 1 instead of 0.8), below that an added normal-gap acidosis, and above 2 an added metabolic alkalosis.
Winter’s formula
PaCO₂ = 1.5·6 + 8 = 17 mmHg
range: 15–19 mmHg
Answer
PaCO₂ = 17 mmHg
4.Arterial blood gas interpretation
Answer: delta ratio = 0.2857
Expected compensation: in metabolic acidosis Winter’s formula predicts PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2 mmHg; a measured value above that range points to an additional respiratory acidosis, below it to an additional respiratory alkalosis. The anion gap AG = Na⁺ − (Cl⁻ + HCO₃⁻), normally about 8–12 mmol/L, separates high-gap from normal-gap metabolic acidosis; low albumin hides a high gap (add 2.5 per g/dL that albumin is below 4.0). The delta ratio (AG − 12)/(24 − HCO₃⁻) between about 0.8 and 2 fits a pure high-gap acidosis (some texts use 1 instead of 0.8), below that an added normal-gap acidosis, and above 2 an added metabolic alkalosis.
Anion gap
AG = 136 − (110 + 10) = 16
Delta ratio
(16 − 12)/(24 − 10) = 4/14 = 0.2857
Answer
delta ratio = 0.2857
Below 1: an added normal anion gap acidosis.
5.Nursing fundamentals
Answer: B · The first urine of the morning is discarded and the time noted, then all urine is kept
Why this is the answer
The patient empties the bladder at the start and that urine is discarded. All urine for the next 24 hours is kept, including a final void at the end time.
Answer
B · The first urine of the morning is discarded and the time noted, then all urine is kept
6.Nursing fundamentals
Answer: D · The respiratory rate and level of sedation
Why this is the answer
Opioids can cause sedation and respiratory depression. Checking breathing and alertness before each dose, as well as the pain score, keeps the patient safe.
Answer
D · The respiratory rate and level of sedation
7.Nursing math & unit conversions
Answer: T = 38.2 °C
Temperature: °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32. Subtract 32 before you multiply when going from °F, and add 32 after you multiply when going from °C. A quick check: 37 °C is 98.6 °F, and every 1 °C is 1.8 °F.
Subtract 32
100.7 − 32 = 68.7
Multiply by 5/9
T = 68.7·5/9 = 38.17 ≈ 38.2 °C
Answer
T = 38.2 °C
8.Nursing math & unit conversions
Answer: t = 9.42 h
24-hour clock: from 1 PM onwards add 12 to the hour (3:45 PM = 15:45). Midnight to 12:59 AM is 00:00–00:59, and 12:00–12:59 PM stays 12:00–12:59. Going back, subtract 12 from hours 13–23 and add PM; hours 00 become 12 AM. Count time across midnight in two parts: up to 24:00 (00:00), then from 00:00 on.