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). Use the NEWS2 chart (SpO₂ scale 1) for these observations: respiration rate 14/min, SpO₂ 97% on supplemental oxygen, blood pressure 112/68 mmHg, pulse 104/min, alert, temperature 36.1 °C. What is the NEWS2 total score?
RR 14SpO₂ 97%O₂SBP 112HR 104AT 36.1 °C
NEWS2 =
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 103 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 103 mmHg
DBP = mmHg
3.Arterial blood gas interpretationMedium
A practice gas shows a metabolic acidosis with HCO₃⁻ 12 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.
HCO₃⁻ 12 mmol/L
PaCO₂ = mmHg
4.Arterial blood gas interpretationHard
Practice values: Na⁺ 133, Cl⁻ 86 and HCO₃⁻ 18 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.
Na⁺ 133 mmol/LCl⁻ 86 mmol/LHCO₃⁻ 18 mmol/L
delta ratio =
5.Nursing fundamentalsMedium
While being helped to eat, a patient with dysphagia coughs and their voice sounds wet and gurgly. What should the nurse do?
AGive a drink of water to wash the food down
BStop feeding and report for a swallowing assessment
CFeed more quickly so the meal is finished before they tire
DLie the patient flat to rest
6.Nursing fundamentalsHard
The family of a patient with terminal cancer worries that morphine will make the patient addicted. What is the best response?
AExplain that addiction is uncommon when morphine is used for pain
BSuggest giving the morphine only once a day
CAgree that the morphine should be stopped to protect the patient
DTell them that addiction does not matter at this stage
7.Nursing math & unit conversionsMedium
Practice exercise (made-up values, not clinical guidance). A patient’s temperature is 98.7 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
98.7 °F
T = °C
8.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 20:40 and finishes at 08:25 the next morning (24-hour clock). How many minutes t did it run?
20:4008:25
t = min
3Solutions
1.Clinical assessment scores
Answer: NEWS2 = 3
NEWS2 (National Early Warning Score 2, Royal College of Physicians 2017): score each of the seven parameters with the chart (respiration rate, SpO₂ on scale 1, air or supplemental oxygen, systolic blood pressure, pulse, consciousness on the ACVPU scale and temperature) and add the scores. Clinical risk: 0–4 low; a score of 3 in any single parameter low–medium; 5–6 medium; 7 or more high. A total of 5 or more needs an urgent response.
Score each parameter
RR 14/min → 0
SpO₂ 97% → 0
on oxygen → 2
SBP 112 mmHg → 0
HR 104/min → 1
alert (A) → 0
T 36.1 °C → 0
Add
NEWS2 = 0 + 0 + 2 + 0 + 1 + 0 + 0 = 3
Answer
NEWS2 = 3
2.Clinical assessment scores
Answer: DBP = 46 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 − 103)/2 = 92/2 = 46 mmHg
Answer
DBP = 46 mmHg
3.Arterial blood gas interpretation
Answer: PaCO₂ = 26 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 = 1.5·12 + 8 = 26 mmHg
range: 24–28 mmHg
Answer
PaCO₂ = 26 mmHg
4.Arterial blood gas interpretation
Answer: delta ratio = 2.833
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 = 133 − (86 + 18) = 29
Delta ratio
(29 − 12)/(24 − 18) = 17/6 = 2.833
Answer
delta ratio = 2.833
Above 2: an added metabolic alkalosis.
5.Nursing fundamentals
Answer: B · Stop feeding and report for a swallowing assessment
Why this is the answer
Coughing, choking and a wet voice during meals suggest food or drink is entering the airway. Feeding stops, the patient sits upright and a speech and language therapist assesses them.
Answer
B · Stop feeding and report for a swallowing assessment
6.Nursing fundamentals
Answer: A · Explain that addiction is uncommon when morphine is used for pain
Why this is the answer
When opioids are used for pain under supervision, addiction is uncommon. Gentle explanation of tolerance, side effects and the goal of comfort helps the family support good pain control.
Answer
A · Explain that addiction is uncommon when morphine is used for pain
7.Nursing math & unit conversions
Answer: T = 37.1 °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
98.7 − 32 = 66.7
Multiply by 5/9
T = 66.7·5/9 = 37.06 ≈ 37.1 °C
Answer
T = 37.1 °C
8.Nursing math & unit conversions
Answer: t = 705 min
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.