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 part of the brainstem contains the main cardiovascular and respiratory centres?

  1. ACerebellum
  2. BMedulla oblongata
  3. CPons
  4. DMidbrain
2.Human anatomyHard

Which structure is found in the posterior mediastinum?

  1. AThymus
  2. BAscending aorta
  3. COesophagus
  4. DHeart
3.Human physiologyMedium

How is the ejection fraction calculated?

  1. AEnd-diastolic volume ÷ end-systolic volume
  2. BStroke volume ÷ end-diastolic volume
  3. CEnd-systolic volume ÷ stroke volume
  4. DCardiac output ÷ heart rate
4.Human physiologyHard

Which change shifts the oxygen–haemoglobin dissociation curve to the right?

  1. AHigher temperature
  2. BLower CO₂
  3. CHigher pH
  4. DLower 2,3-BPG
5.MicrobiologyMedium

Which vaccine contains live attenuated (weakened) viruses?

  1. AMMR (measles, mumps, rubella)
  2. BTetanus vaccine
  3. CInactivated influenza injection
  4. DHepatitis B vaccine
6.MicrobiologyHard

Which bacterial toxin causes the muscle spasms of tetanus?

  1. AEndotoxin from the outer membrane
  2. BTetanospasmin, which blocks inhibitory neurotransmitter release
  3. CBotulinum toxin, which blocks acetylcholine release at the neuromuscular junction
  4. DCholera toxin, which activates adenylate cyclase
7.PharmacologyMedium

A patient is due the first dose of IV cefuroxime. Which question is most important before giving it?

  1. A"Have you ever had a reaction to penicillin or another antibiotic?"
  2. B"Do you prefer the drip in your left arm or in your right arm?"
  3. C"Have you eaten anything in the last two hours?"
  4. D"Have you taken paracetamol today?"
8.PharmacologyHard

Probenecid has been used to raise plasma penicillin levels. How does it do this?

  1. AIt blocks the tubular secretion of penicillin in the kidney
  2. BIt inhibits the liver metabolism of penicillin
  3. CIt displaces penicillin from plasma proteins
  4. DIt increases the absorption of penicillin from the small intestine
9.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 18 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 18 mmol/L
PaCO₂ = mmHg
10.Arterial blood gas interpretationHard
pH7.357.457.31PaCO₂mmHg354531HCO₃⁻mmol/L222615added normal-gap acidosispure high-gap acidosisadded metabolic alkalosis

A practice gas shows pH 7.31, PaCO₂ 31 mmHg (4.1 kPa) and HCO₃⁻ 15 mmol/L, with Na⁺ 142 and Cl⁻ 88 mmol/L. Use the anion gap and the delta ratio to click the best interpretation.

pH 7.31PaCO₂ 31 mmHg (4.1 kPa)HCO₃⁻ 15 mmol/LNa⁺ 142 mmol/LCl⁻ 88 mmol/L
  1. 1added normal-gap acidosis
  2. 2pure high-gap acidosis
  3. 3added metabolic alkalosis
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mV

This lead II strip shows sinus rhythm with one pause. Measure the pause, the R–R interval across it, in seconds.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
pause = s
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mV

This lead II strip shows an AV block, so the atria and the ventricles beat at different rates. Measure the P–P interval and find the atrial rate in beats per minute (1500 method, whole number).

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
atrial rate = bpm
13.Evidence-based practice statisticsMedium
casescontrolsexposed63299abnot exposed147351cd

Practice exercise (made-up values, not clinical guidance). A case-control study compares 210 patients with a disease (cases) and 650 people without it (controls). The table shows how many in each group were exposed to a risk factor. Find the odds ratio OR for the exposure. Round to two decimal places.

a = 63b = 299c = 147d = 351
OR =
14.Evidence-based practice statisticsHard
CER9%EER?RRR 48%

Practice exercise (made-up values, not clinical guidance). A treatment reduces the risk of an event by 48% in relative terms (RRR = 48%). In a patient group the risk without treatment (CER) is 9% over five years. Find the number needed to treat NNT for five years to prevent one event. Round up to a whole number of patients.

RRR = 48%CER = 9%
NNT =

3Solutions

1.Human anatomy

Answer: B · Medulla oblongata

Why this is the answer

The medulla oblongata contains the vital centres that regulate heart rate, blood pressure and breathing rhythm.

Answer

B · Medulla oblongata
2.Human anatomy

Answer: C · Oesophagus

Why this is the answer

The posterior mediastinum contains the oesophagus, descending aorta, azygos veins and thoracic duct. The heart and ascending aorta are in the middle mediastinum; the thymus is in the superior and anterior mediastinum.

Answer

C · Oesophagus
3.Human physiology

Answer: B · Stroke volume ÷ end-diastolic volume

Why this is the answer

Ejection fraction is the proportion of blood in the full ventricle that is ejected per beat. A normal value is about 55–70%.

Answer

B · Stroke volume ÷ end-diastolic volume
4.Human physiology

Answer: A · Higher temperature

Why this is the answer

Higher temperature, CO₂, H⁺ (lower pH) and 2,3-BPG lower haemoglobin's affinity and shift the curve right, releasing more oxygen to active tissues.

Answer

A · Higher temperature
5.Microbiology

Answer: A · MMR (measles, mumps, rubella)

Why this is the answer

MMR contains weakened live viruses that replicate a little and give strong, long-lasting immunity. Tetanus is a toxoid and hepatitis B a subunit vaccine.

Answer

A · MMR (measles, mumps, rubella)
6.Microbiology

Answer: B · Tetanospasmin, which blocks inhibitory neurotransmitter release

Why this is the answer

Tetanospasmin from Clostridium tetani blocks the release of GABA and glycine from inhibitory interneurons, causing spastic paralysis. Botulinum toxin, by contrast, causes flaccid paralysis.

Answer

B · Tetanospasmin, which blocks inhibitory neurotransmitter release
7.Pharmacology

Answer: A · "Have you ever had a reaction to penicillin or another antibiotic?"

Why this is the answer

Allergy history must be checked before any first antibiotic dose. Cephalosporins share the beta-lactam ring with penicillins, so a history of severe penicillin allergy is important.

Answer

A · "Have you ever had a reaction to penicillin or another antibiotic?"
8.Pharmacology

Answer: A · It blocks the tubular secretion of penicillin in the kidney

Why this is the answer

Penicillins are excreted largely by organic anion transporters in the proximal tubule. Probenecid competes for these transporters, so penicillin is excreted more slowly and its level stays higher.

Answer

A · It blocks the tubular secretion of penicillin in the kidney
9.Arterial blood gas interpretation

Answer: PaCO₂ = 35 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 = 1.5·18 + 8 = 35 mmHg
range: 33–37 mmHg

Answer

PaCO₂ = 35 mmHg
10.Arterial blood gas interpretation

Answer: added metabolic alkalosis

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 = 142 − (88 + 15) = 39

Delta ratio

(39 − 12)/(24 − 15) = 3
added metabolic alkalosis

Answer

added metabolic alkalosis
11.ECG rhythm strip interpretation

Answer: pause = 1.92 s

Narrow-complex tachycardia and pauses: supraventricular tachycardia (SVT) is a regular tachycardia at about 150–250/min with narrow QRS complexes; the P waves are usually not visible because they are hidden in the QRS complex or the T wave. Sinus tachycardia in an adult at rest is usually below about 150/min and has a visible P wave before every QRS; atrial flutter with 2:1 conduction often runs at about 150/min and shows sawtooth waves. In sinus arrest the sinus node stops firing for a moment: a pause with no P wave and no QRS whose length is not a whole number of P–P cycles (a pause of exactly two or three cycles points to sinus exit block instead).

Measure

48 small boxes from R to R across the pause

Convert

pause = 48 × 0.04 s = 1.92 s

Compare with P–P

1.92 ÷ 0.84 ≈ 2.3 P–P cycles, not a whole number

Answer

pause = 1.92 s

No P wave appears in the pause, and the pause is not a whole number of P–P cycles: sinus arrest. A pause of exactly two or three cycles would point to sinus exit block.

12.ECG rhythm strip interpretation

Answer: atrial rate = 83 bpm

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.

Atrial rate

P–P = 18 small boxes = 0.72 s → 1500 ÷ 18 = 83.33 ≈ 83 per minute

Ventricular rate

R–R = 27 small boxes = 1.08 s → 1500 ÷ 27 = 55.56 ≈ 56 per minute

Answer

atrial rate = 83 bpm

Answer

atrial rate = 83 bpm

Third-degree block with a narrow-complex junctional escape (usually 40–60 per minute).

13.Evidence-based practice statistics

Answer: OR = 0.5

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.

Odds of exposure

cases: 63/147 = 0.4286
controls: 299/351 = 0.8519

Odds ratio

OR = (63·351)/(299·147) = 0.5031 ≈ 0.5

Answer

OR = 0.5

OR below 1: exposure is less common among the cases, which suggests a protective effect.

14.Evidence-based practice statistics

Answer: NNT = 24

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.

Absolute risk reduction

ARR = 0.09·0.48 = 0.0432

Number needed to treat

NNT = 1/0.0432 = 23.15 → 24

Answer

NNT = 24

The same relative effect gives a smaller NNT when the baseline risk is higher.

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