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. AFacial nerve (VII)
  2. BAccessory nerve (XI)
  3. CVagus nerve (X)
  4. DHypoglossal nerve (XII)
2.Human anatomyHard

After a stroke, a patient speaks fluently but uses meaningless words and cannot understand speech. Where is the lesion most likely to be?

  1. AInferior frontal gyrus of the dominant hemisphere
  2. BCerebellar hemisphere
  3. CPosterior superior temporal gyrus of the dominant hemisphere
  4. DPrecentral gyrus of the non-dominant hemisphere
3.Human physiologyMedium

Mean arterial pressure is approximately equal to:

  1. ACardiac output × total peripheral resistance
  2. BHeart rate × stroke volume
  3. CCardiac output ÷ heart rate
  4. DStroke volume × total peripheral vascular resistance
4.Human physiologyHard

In a patient with primary hypothyroidism, you would expect:

  1. ALow TSH and low free T4
  2. BHigh TSH and high free T4
  3. CHigh TSH and low free T4
  4. DLow TSH and high free T4
5.MicrobiologyMedium

In the chain of infection, what is the "reservoir"?

  1. AThe place where the pathogen normally lives and multiplies
  2. BThe way the pathogen enters a new host
  3. CThe route by which the pathogen leaves the infected host's body
  4. DThe person who is most at risk of infection
6.MicrobiologyHard

After eating home-canned vegetables, a patient develops double vision, difficulty swallowing and a descending flaccid paralysis. What is the most likely cause?

  1. AEndotoxin from Gram-negative bacteria
  2. BTetanus toxin, which blocks inhibitory neurotransmitters
  3. CA viral infection of the motor neurons
  4. DBotulinum toxin, which blocks acetylcholine release
7.PharmacologyMedium

Which approach is usually recommended to prevent constipation in a patient on regular opioids?

  1. AAn antidiarrhoeal drug at night to slow the gut
  2. BA stimulant laxative such as senna, often with a stool softener
  3. CNo laxative until the patient has not opened the bowels for a week
  4. DBulk-forming fibre alone, with fluid intake restricted
8.PharmacologyHard

Some receptors show activity even without an agonist. How does an inverse agonist differ from a neutral antagonist at such receptors?

  1. AIt increases activity above the baseline
  2. BIt reduces activity below the baseline level
  3. CIt has no effect when given alone
  4. DIt destroys the receptor permanently
9.Arterial blood gas interpretationMedium
pH7.357.457.29PaCO₂mmHg354563HCO₃⁻mmol/L222629uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.29, PaCO₂ 63 mmHg (8.4 kPa) and HCO₃⁻ 29 mmol/L. The primary disorder is respiratory acidosis. How far is it compensated? Click your answer.

pH 7.29PaCO₂ 63 mmHg (8.4 kPa)HCO₃⁻ 29 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard
pH7.357.457.31PaCO₂mmHg354572HCO₃⁻mmol/L222635acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.31, PaCO₂ 72 mmHg (9.6 kPa), HCO₃⁻ 35 mmol/L. Use the rules ‘HCO₃⁻ rises 1 mmol/L per 10 mmHg (acute) or 3.5 mmol/L per 10 mmHg (chronic)’ to classify it. Click your answer.

pH 7.31PaCO₂ 72 mmHg (9.6 kPa)HCO₃⁻ 35 mmol/L
  1. 1acute
  2. 2chronic
  3. 3acute on chronic
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVatrial flutter, 3:1 conductionnormal sinus rhythmatrial fibrillationsinus tachycardia

Interpret this lead II rhythm strip. 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. 1atrial flutter, 3:1 conduction
  2. 2normal sinus rhythm
  3. 3atrial fibrillation
  4. 4sinus tachycardia
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
Se86%Sp82%LR+ = ?

Practice exercise (made-up values, not clinical guidance). A test has a sensitivity of 86% and a specificity of 82%. Find the positive likelihood ratio LR+. Round to two decimal places.

Se = 86%Sp = 82%
LR+ =
14.Evidence-based practice statisticsHard
testdisease presentdisease absenttotalpositive?negativetotal10 000

Practice exercise (made-up values, not clinical guidance). 10 000 people are screened with a test of sensitivity 95% and specificity 92%. The prevalence of the disease is 3%. How many true-positive results TP are expected?

N = 10 000p = 3%Se = 95%Sp = 92%
TP =

3Solutions

1.Human anatomy

Answer: B · Accessory nerve (XI)

Why this is the answer

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

Answer

B · Accessory nerve (XI)
2.Human anatomy

Answer: C · Posterior superior temporal gyrus of the dominant hemisphere

Why this is the answer

This is Wernicke's (receptive) aphasia, caused by damage to Wernicke's area in the posterior superior temporal gyrus. Broca's area in the inferior frontal gyrus causes non-fluent aphasia.

Answer

C · Posterior superior temporal gyrus of the dominant hemisphere
3.Human physiology

Answer: A · Cardiac output × total peripheral resistance

Why this is the answer

Pressure = flow × resistance, so MAP ≈ CO × TPR. Changes in either cardiac output or vascular resistance change blood pressure.

Answer

A · Cardiac output × total peripheral resistance
4.Human physiology

Answer: C · High TSH and low free T4

Why this is the answer

When the thyroid fails, low T4 removes negative feedback and the pituitary raises TSH. Low TSH with low T4 would point to secondary (pituitary) hypothyroidism.

Answer

C · High TSH and low free T4
5.Microbiology

Answer: A · The place where the pathogen normally lives and multiplies

Why this is the answer

The chain of infection links the agent, reservoir, portal of exit, mode of transmission, portal of entry and susceptible host. Breaking any link stops transmission.

Answer

A · The place where the pathogen normally lives and multiplies
6.Microbiology

Answer: D · Botulinum toxin, which blocks acetylcholine release

Why this is the answer

Clostridium botulinum can grow in poorly canned, low-acid foods and produce botulinum toxin. The toxin blocks acetylcholine release at nerve endings, causing descending flaccid paralysis.

Answer

D · Botulinum toxin, which blocks acetylcholine release
7.Pharmacology

Answer: B · A stimulant laxative such as senna, often with a stool softener

Why this is the answer

Opioid-induced constipation does not usually resolve with time, so a laxative is started with the opioid. Stimulant laxatives counter reduced motility; bulk-forming laxatives alone can worsen symptoms if fluid intake is low.

Answer

B · A stimulant laxative such as senna, often with a stool softener
8.Pharmacology

Answer: B · It reduces activity below the baseline level

Why this is the answer

A neutral antagonist simply blocks agonists and leaves baseline activity unchanged. An inverse agonist stabilises the inactive receptor state, so constitutive activity falls below baseline.

Answer

B · It reduces activity below the baseline level
9.Arterial blood gas interpretation

Answer: partially compensated

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 7.29: acidaemia (below 7.35)
PaCO₂ 63 mmHg: high (35–45)
HCO₃⁻ 29 mmol/L: high (22–26)

Compensation

partially compensated

Answer

partially compensated
10.Arterial blood gas interpretation

Answer: chronic

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.

Expected HCO₃⁻

acute: 24 + 1·3.2 = 27.2 mmol/L
chronic: 24 + 3.5·3.2 = 35.2 mmol/L

Compare

measured: 35 mmol/L → chronic

Answer

chronic
11.ECG rhythm strip interpretation

Answer: atrial flutter, 3:1 conduction

Rhythm criteria (lead II): sinus rhythm has an upright P wave before every QRS, a constant PR of 0.12–0.20 s and a narrow QRS: normal sinus rhythm at 60–100/min, sinus bradycardia below 60, sinus tachycardia above 100. Atrial fibrillation: no P waves, a fibrillatory baseline and an irregularly irregular R–R. Atrial flutter: sawtooth flutter waves at about 250–350/min with a fixed conduction ratio such as 2:1 or 4:1. First-degree AV block: sinus rhythm with a constant PR above 0.20 s. Junctional rhythm: narrow QRS at 40–60/min with absent or inverted P waves (PR below 0.12 s, or P after the QRS). A PVC is an early, wide (0.12 s or more), bizarre QRS without a P wave, with the T wave in the opposite direction and usually a full compensatory pause; in bigeminy every second beat is a PVC.

Five steps

1. Rate: R–R = 18 small boxes, 1500 ÷ 18 ≈ 83 per minute.
2. Rhythm: regular, every R–R is 0.72 s.
3. P waves: none; regular sawtooth flutter waves every 0.24 s (250 per minute), 3 for each QRS.
4. PR interval: not measurable.
5. QRS: 0.06 s, narrow (below 0.12 s).

Interpretation

atrial flutter, 3:1 conduction

Answer

atrial flutter, 3:1 conduction
12.ECG rhythm strip interpretation

Answer: atrial rate = 79 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 = 19 small boxes = 0.76 s → 1500 ÷ 19 = 78.95 ≈ 79 per minute

Ventricular rate

R–R = 42 small boxes = 1.68 s → 1500 ÷ 42 = 35.71 ≈ 36 per minute

Answer

atrial rate = 79 bpm

Answer

atrial rate = 79 bpm

Third-degree block with a wide-complex ventricular escape (usually 20–40 per minute).

13.Evidence-based practice statistics

Answer: LR+ = 4.78

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.

Positive likelihood ratio

LR+ = 0.86/(1 − 0.82) = 4.778 ≈ 4.78

Answer

LR+ = 4.78
14.Evidence-based practice statistics

Answer: TP = 285

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.

With and without the disease

10 000·0.03 = 300
10 000 − 300 = 9700

True positives

TP = 300·0.95 = 285

Answer

TP = 285

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