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 9/min, SpO₂ 95% on room air, blood pressure 124/74 mmHg, pulse 44/min, alert, temperature 38.4 °C. What is the NEWS2 total score?
RR 9SpO₂ 95%airSBP 124HR 44AT 38.4 °C
NEWS2 =
2.Clinical assessment scoresHard
Practice exercise (made-up values, not clinical guidance). Use the NEWS2 chart (SpO₂ scale 1) for these observations: respiration rate 16/min, SpO₂ 97% on room air, blood pressure 88/52 mmHg, pulse 88/min, alert, temperature 38.4 °C. Which clinical risk group does the patient fall into? Click it.
RR 16SpO₂ 97%airSBP 88HR 88AT 38.4 °C
1low
2low–medium
3medium
4high
3.Arterial blood gas interpretationMedium
Practice values: Na⁺ 130 mmol/L, glucose 25.9 mmol/L and urea 14.2 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.
Na⁺ 130 mmol/Lglucose 25.9 mmol/Lurea 14.2 mmol/L
Osm = mOsm/kg
4.Arterial blood gas interpretationHard
Practice values: Na⁺ 140, Cl⁻ 95 and HCO₃⁻ 18 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.
Na⁺ 140 mmol/LCl⁻ 95 mmol/LHCO₃⁻ 18 mmol/L
delta ratio =
5.Nursing fundamentalsMedium
What is the correct order of assessment in the ABCDE approach?
Why can a patient with a high fever be in negative fluid balance even when measured intake equals measured output?
AFever makes the kidneys produce extra urine that cannot be measured
BFever causes the body to make extra water from fat
CFever increases unmeasured fluid loss through sweating and breathing
DFever has no effect on the body's water balance
7.Nursing math & unit conversionsMedium
Practice exercise (made-up values, not clinical guidance). A drip-rate calculation gives 181.096 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?
181.096 gtt/min
x = gtt/min
8.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion delivers 5 mcg/min. Express this dose rate D in mg/h.
5 mcg/min1 h = 60 min1 mg = 1000 mcg
D = mg/h
3Solutions
1.Clinical assessment scores
Answer: NEWS2 = 4
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 9/min → 1
SpO₂ 95% → 1
on air → 0
SBP 124 mmHg → 0
HR 44/min → 1
alert (A) → 0
T 38.4 °C → 1
Add
NEWS2 = 1 + 1 + 0 + 0 + 1 + 0 + 1 = 4
Answer
NEWS2 = 4
2.Clinical assessment scores
Answer: low–medium
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 16/min → 0
SpO₂ 97% → 0
on air → 0
SBP 88 mmHg → 3
HR 88/min → 0
alert (A) → 0
T 38.4 °C → 1
Total and red scores
NEWS2 = 0 + 0 + 0 + 3 + 0 + 0 + 1 = 4
At least one parameter scores 3.
Risk group
low–medium
Answer
low–medium
A single score of 3 needs an urgent review even when the total is low.
3.Arterial blood gas interpretation
Answer: Osm = 300 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 = 2·130 + 25.9 + 14.2 = 300.1 ≈ 300 mOsm/kg
Answer
Osm = 300 mOsm/kg
4.Arterial blood gas interpretation
Answer: delta ratio = 2.5
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 = 140 − (95 + 18) = 27
Delta ratio
(27 − 12)/(24 − 18) = 15/6 = 2.5
Answer
delta ratio = 2.5
Above 2: an added metabolic alkalosis.
5.Nursing fundamentals
Answer: A · Airway, Breathing, Circulation, Disability, Exposure
Why this is the answer
ABCDE assesses Airway, Breathing, Circulation, Disability (neurology, glucose) and Exposure, fixing each problem before moving on.
Answer
A · Airway, Breathing, Circulation, Disability, Exposure
6.Nursing fundamentals
Answer: C · Fever increases unmeasured fluid loss through sweating and breathing
Why this is the answer
Insensible losses through the skin and lungs are not measured and rise with fever and fast breathing. A balanced chart can therefore hide a real fluid deficit.
Answer
C · Fever increases unmeasured fluid loss through sweating and breathing
7.Nursing math & unit conversions
Answer: x = 181 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
181.096 → 1
Only the next digit decides
181.096 → 0
0 is 4 or less, so 1 stays.
The digits after it (96) are ignored: round once, never step by step.
Round
x = 181 gtt/min
Answer
x = 181 gtt/min
8.Nursing math & unit conversions
Answer: D = 0.3 mg/h
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.