Medical Sciences: cram pack

Formula sheets, the key method steps for every topic and 14 practice problems, with full solutions at the back.

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1Formulas and methods

Arterial blood gas interpretation

Normal ranges
pH 7.35–7.45, PaCO₂ 35–45 mmHg (4.7–6.0 kPa), HCO₃⁻ 22–26 mmol/L
ROME
Respiratory: PaCO₂ opposite to pH; Metabolic: HCO₃⁻ equal to pH
Winter’s formula
PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2
Metabolic alkalosis
PaCO₂ ≈ 0.7·HCO₃⁻ + 21
Anion gap
AG = Na⁺ − (Cl⁻ + HCO₃⁻) ≈ 8–12
Albumin-corrected gap
AG + 2.5·(4.0 − alb g/dL) = AG + 0.25·(40 − alb g/L)
Delta ratio
(AG − 12)/(24 − HCO₃⁻)
P/F ratio
PaO₂/FiO₂
Alveolar gas equation
PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8
Serum osmolality
2·Na⁺ + glucose + urea (2·Na⁺ + glucose/18 + BUN/2.8)

Method

  1. Read the pH: below 7.35 is acidosis, above 7.45 alkalosis.
  2. Find the value that explains it: PaCO₂ moving opposite to the pH is respiratory, HCO₃⁻ moving with the pH is metabolic.
  3. 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.
  4. In a metabolic acidosis, compare PaCO₂ with Winter’s formula, 1.5·HCO₃⁻ + 8 ± 2, and calculate the anion gap Na⁺ − (Cl⁻ + HCO₃⁻).
  5. Check a high anion gap with the delta ratio and, when albumin is low, with the corrected gap.

ECG rhythm strip interpretation

Paper (25 mm/s, 10 mm/mV)
1 small box = 0.04 s, 1 large box = 0.20 s, 10 mm = 1 mV
Heart rate, regular rhythm
300 ÷ large boxes = 1500 ÷ small boxes = 60 ÷ RR (s)
Heart rate, irregular rhythm
QRS complexes in 6 s × 10
Normal PR interval
0.12–0.20 s
Normal QRS duration
< 0.12 s
QTc (Bazett)
QT/√RR
QTc (Fridericia)
QT/∛RR
QTc (Framingham)
QT + 154·(1 − RR)
Sinus rates
bradycardia < 60, normal 60–100, tachycardia > 100 /min
Escape rates
junctional 40–60, ventricular 20–40 /min
Fast rhythms
SVT 150–250 /min (narrow), VT > 100 /min (wide)

Method

  1. Rate: for a regular rhythm divide 300 by the large boxes or 1500 by the small boxes between two R waves; for an irregular rhythm count the QRS complexes in 6 seconds and multiply by 10.
  2. Rhythm: compare the R–R intervals. Equal is regular; a repeating pattern is regularly irregular; no pattern at all is irregularly irregular.
  3. P waves: is there an upright P wave in lead II before every QRS, all alike? Look for fibrillatory or sawtooth waves, inverted P waves and P waves without a QRS.
  4. PR interval: from the start of P to the start of the QRS, normally 0.12–0.20 s and constant. Watch whether it lengthens, stays fixed before a dropped beat, or varies at random.
  5. QRS duration: below 0.12 s is narrow; 0.12 s or more is wide. Then name the rhythm, and for the QT use QTc = QT/√RR (Bazett) with times in seconds.

Evidence-based practice statistics

Sensitivity and specificity
Se = a/(a + c), Sp = d/(b + d)
Predictive values
PPV = a/(a + b), NPV = d/(c + d)
Accuracy
(a + d)/n
Likelihood ratios
LR+ = Se/(1 − Sp), LR− = (1 − Se)/Sp
PPV at prevalence p
Se·p / (Se·p + (1 − Sp)(1 − p))
Odds
odds = p/(1 − p); p = odds/(1 + odds); post-test odds = pre-test odds × LR
Risk measures
RR = EER/CER, ARR = CER − EER, RRR = ARR/CER
Number needed to treat
NNT = 1/ARR, rounded up; NNH = 1/(EER − CER)
Odds ratio
OR = ad/(bc)
Incidence rate
new cases / person-time

Method

  1. Draw the 2 × 2 table and label a, b, c and d before you calculate.
  2. Read sensitivity and specificity down the columns, predictive values along the rows.
  3. For another prevalence, imagine 10 000 people and fill the table with Se, Sp and the prevalence.
  4. For a likelihood ratio, convert the probability to odds, multiply, and convert back.
  5. For a trial, find EER and CER first; then RR = EER/CER, ARR = CER − EER and NNT = 1/ARR rounded up.

2Practice problems

1.Human anatomyMedium

Which cranial nerve supplies the trapezius and sternocleidomastoid muscles?

  1. AVagus nerve (X)
  2. BHypoglossal nerve (XII)
  3. CAccessory nerve (XI)
  4. DFacial nerve (VII)
2.Human anatomyHard

What is the correct order of structures that urine passes through after leaving the collecting ducts?

  1. AMinor calyx, renal pelvis, major calyx, ureter
  2. BRenal pelvis, minor calyx, major calyx, ureter
  3. CMinor calyx, major calyx, renal pelvis, ureter
  4. DMajor calyx, minor calyx, renal pelvis, ureter
3.Human physiologyMedium

Where does the final activation step of vitamin D (1-alpha hydroxylation) take place?

  1. ASkin
  2. BKidney
  3. CLiver
  4. DSmall intestine
4.Human physiologyHard

What is the main reason the ventricles do not contract at the same moment as the atria?

  1. AThe SA node fires twice per beat
  2. BThe Purkinje fibres conduct slowly
  3. CConduction is delayed at the atrioventricular node
  4. DThe ventricles have a longer refractory period only
5.MicrobiologyMedium

Which infection is a typical complication of broad-spectrum antibiotic use, causing severe diarrhoea?

  1. AClostridioides difficile infection
  2. BSalmonella infection
  3. CHelicobacter pylori infection
  4. DHepatitis A
6.MicrobiologyHard

How do high-risk HPV types contribute to cervical cancer?

  1. AThe virus kills cells so quickly that they are replaced by cancer cells
  2. BThe virus destroys CD4 T cells in the cervix
  3. CViral E6 and E7 proteins inactivate the tumour suppressors p53 and Rb
  4. DThe virus produces an endotoxin that damages DNA
7.PharmacologyMedium

Why is IV promethazine given with great caution?

  1. AIt is a strong opioid that causes addiction
  2. BIt causes immediate kidney failure
  3. CIt can cause severe tissue injury if it leaks or enters an artery
  4. DIt causes a severe rise in blood pressure when it is given intravenously
8.PharmacologyHard

A patient on digoxin is started on amiodarone. What change should the nurse expect?

  1. ANo interaction is expected
  2. BDigoxin levels fall sharply, so the digoxin dose is doubled
  3. CAmiodarone levels fall to zero
  4. DDigoxin levels rise, so the digoxin dose is often reduced
9.Arterial blood gas interpretationMedium
pH7.357.457.51PaCO₂mmHg354531HCO₃⁻mmol/L222624uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.51, PaCO₂ 31 mmHg (4.1 kPa) and HCO₃⁻ 24 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.51PaCO₂ 31 mmHg (4.1 kPa)HCO₃⁻ 24 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

Practice values: Na⁺ 140, Cl⁻ 97 and HCO₃⁻ 15 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.

Na⁺ 140 mmol/LCl⁻ 97 mmol/LHCO₃⁻ 15 mmol/L
delta ratio =
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mV

Measure the QT interval on this lead II strip, in seconds.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
QT = s
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVsecond-degree AV block type I (Wenckebach)first-degree AV blockthird-degree (complete) AV blocksecond-degree AV block type II

This lead II strip shows a conduction problem between the atria and the ventricles. Which rhythm is it? Click your answer.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
  1. 1second-degree AV block type I (Wenckebach)
  2. 2first-degree AV block
  3. 3third-degree (complete) AV block
  4. 4second-degree AV block type II
13.Evidence-based practice statisticsMedium
testdisease presentdisease absenttotalpositive103241344abnegative2710291056cdtotal13012701400

Practice exercise (made-up values, not clinical guidance). A new test was compared with the reference standard in a study (see the 2 × 2 table). Find the negative likelihood ratio LR−. Round to two decimal places.

a = 103b = 241c = 27d = 1029
LR− =
14.Evidence-based practice statisticsHard
p (%)NPV (%)30%NPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 87% and a specificity of 83%. It is used in a population where the prevalence is 30%. Find the negative predictive value NPV as a percentage. Round to one decimal place.

Se = 87%Sp = 83%p = 30%
NPV = %

3Solutions

1.Human anatomy

Answer: C · Accessory nerve (XI)

Why this is the answer

The accessory nerve (XI) supplies sternocleidomastoid and trapezius. Damage weakens head turning and shoulder shrugging.

Answer

C · Accessory nerve (XI)
2.Human anatomy

Answer: C · Minor calyx, major calyx, renal pelvis, ureter

Why this is the answer

Collecting ducts open at the renal papillae into minor calyces, which join to form major calyces, which empty into the renal pelvis and then the ureter.

Answer

C · Minor calyx, major calyx, renal pelvis, ureter
3.Human physiology

Answer: B · Kidney

Why this is the answer

Vitamin D is made in the skin or eaten, hydroxylated in the liver, and then activated to calcitriol in the kidney. Kidney failure therefore causes vitamin D deficiency.

Answer

B · Kidney
4.Human physiology

Answer: C · Conduction is delayed at the atrioventricular node

Why this is the answer

The AV node conducts slowly (about 0.1 s delay), so atrial contraction completes ventricular filling before ventricular depolarisation begins.

Answer

C · Conduction is delayed at the atrioventricular node
5.Microbiology

Answer: A · Clostridioides difficile infection

Why this is the answer

Antibiotics kill normal gut bacteria, letting toxin-producing C. difficile overgrow. Its spores are not killed by alcohol gel, so soap and water handwashing is needed.

Answer

A · Clostridioides difficile infection
6.Microbiology

Answer: C · Viral E6 and E7 proteins inactivate the tumour suppressors p53 and Rb

Why this is the answer

E6 promotes the breakdown of p53 and E7 binds Rb, removing controls on cell division and DNA repair. Infected cells can then accumulate mutations and become cancerous over years.

Answer

C · Viral E6 and E7 proteins inactivate the tumour suppressors p53 and Rb
7.Pharmacology

Answer: C · It can cause severe tissue injury if it leaks or enters an artery

Why this is the answer

Promethazine is a vesicant. Deep intramuscular injection is the preferred parenteral route, and if given IV it is diluted, given slowly into a well-running large vein, and stopped at once if the patient reports burning or pain.

Answer

C · It can cause severe tissue injury if it leaks or enters an artery
8.Pharmacology

Answer: D · Digoxin levels rise, so the digoxin dose is often reduced

Why this is the answer

Amiodarone inhibits P-glycoprotein and reduces digoxin clearance, so digoxin levels rise. The digoxin dose is often reduced, and the patient is monitored for bradycardia and toxicity; amiodarone also raises warfarin levels.

Answer

D · Digoxin levels rise, so the digoxin dose is often reduced
9.Arterial blood gas interpretation

Answer: uncompensated

Reading a blood gas (ROME): first the pH: below 7.35 is acidaemia, above 7.45 alkalaemia. Then find the value that explains it. PaCO₂ (normal 35–45 mmHg, 4.7–6.0 kPa) is the respiratory part and moves Opposite to the pH in a respiratory disorder; HCO₃⁻ (normal 22–26 mmol/L) is the metabolic part and moves in the same direction as the pH (Respiratory Opposite, Metabolic Equal). The other value shows the compensation: normal means uncompensated; abnormal in the direction that pulls the pH back while the pH is still abnormal means partially compensated; a normal pH with both values abnormal means fully compensated. Ranges differ slightly between laboratories; these are practice values.

ROME, value by value

pH 7.51: alkalaemia (above 7.45)
PaCO₂ 31 mmHg: low (35–45)
HCO₃⁻ 24 mmol/L: normal (22–26)

Compensation

uncompensated

Answer

uncompensated
10.Arterial blood gas interpretation

Answer: delta ratio = 1.778

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 − (97 + 15) = 28

Delta ratio

(28 − 12)/(24 − 15) = 16/9 = 1.778

Answer

delta ratio = 1.778

Between 1 and 2: a pure high anion gap acidosis.

11.ECG rhythm strip interpretation

Answer: QT = 0.38 s

QT and QTc: the QT interval runs from the start of the QRS complex to the end of the T wave. It shortens as the heart rate rises, so it is corrected for rate with the R–R interval in seconds: Bazett QTc = QT/√RR and Fridericia QTc = QT/∛RR. Bazett is the formula most textbooks use; it over-corrects at fast rates, where Fridericia is preferred. Limits differ between references: a QTc above about 0.45 s in men or 0.46 s in women is usually called prolonged, and above 0.50 s markedly prolonged.

Measure

9.5 small boxes from the start of the QRS to the end of the T wave

Convert

QT = 9.5 × 0.04 s = 0.38 s

Answer

QT = 0.38 s

A rough rule: at normal rates the QT should be less than half the R–R interval (here R–R = 0.72 s).

12.ECG rhythm strip interpretation

Answer: second-degree AV block type I (Wenckebach)

AV blocks: march out the P waves and check which ones are followed by a QRS. First-degree: every P conducted, PR constant and above 0.20 s. Second-degree type I (Mobitz I, Wenckebach): the PR lengthens from beat to beat until one P wave is not conducted, then the cycle starts again (group beating). Second-degree type II (Mobitz II): the PR of the conducted beats stays constant, and P waves are suddenly not conducted; the QRS is often wide. Third-degree (complete) block: P waves and QRS complexes are each regular but independent, the PR varies at random and the atrial rate is faster than the escape rate (junctional 40–60/min with a narrow QRS, ventricular 20–40/min with a wide QRS). A 2:1 block cannot be called type I or type II from one strip.

Five steps

1. Rate: 4 QRS complexes in 6 s, × 10 = 40 per minute.
2. Rhythm: regularly irregular, the QRS complexes come in groups separated by a pause (group beating).
3. P waves: upright and regular (P–P 1.00 s, 60 per minute); one P in every 3 is not followed by a QRS.
4. PR interval: lengthens 0.20 → 0.32 s, then a P wave is not conducted.
5. QRS: 0.08 s, narrow (below 0.12 s).

Interpretation

second-degree AV block type I (Wenckebach)

Answer

second-degree AV block type I (Wenckebach)
13.Evidence-based practice statistics

Answer: LR− = 0.26

Likelihood ratios and risk measures: LR+ = sensitivity/(1 − specificity), LR− = (1 − sensitivity)/specificity. In a trial, EER and CER are the event rates with and without treatment: RR = EER/CER, ARR = CER − EER, RRR = ARR/CER and NNT = 1/ARR, rounded up. In a case-control study only the odds ratio OR = ad/(bc) can be used. An incidence rate = new cases/person-time.

Sensitivity and specificity

Se = 103/130 = 0.7923
Sp = 1029/1270 = 0.8102

Negative likelihood ratio

LR− = (1 − 0.7923)/0.8102 = 0.2563 ≈ 0.26

Answer

LR− = 0.26
14.Evidence-based practice statistics

Answer: NPV = 93.7 %

Predictive values depend on prevalence: PPV = Se·p/(Se·p + (1 − Sp)(1 − p)) and NPV = Sp(1 − p)/(Sp(1 − p) + (1 − Se)p). With likelihood ratios: pre-test odds = p/(1 − p), post-test odds = pre-test odds × LR, probability = odds/(1 + odds). For a population of N, true positives = N·p·Se and false positives = N·(1 − p)·(1 − Sp). NNT = 1/(CER × RRR), rounded up.

True and false negatives (per person)

Sp·(1 − p) = 0.83·0.7 = 0.581
(1 − Se)·p = 0.13·0.3 = 0.039

Negative predictive value

NPV = 0.581/(0.581 + 0.039) = 0.9371 ≈ 93.7%

Answer

NPV = 93.7%

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