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 structure is the main bundle of nerve fibres connecting the left and right cerebral hemispheres?

  1. ACerebral peduncle
  2. BInternal capsule
  3. CCorpus callosum
  4. DFornix
2.Human anatomyHard

When inserting a chest drain or needle into the pleural space, why is it placed just above the upper border of a rib?

  1. AThe intercostal vein, artery and nerve run along the lower border of each rib
  2. BThe lung does not reach the area above each rib
  3. CThe pleura is thickest just above each rib
  4. DThe intercostal muscles are absent above each rib
3.Human physiologyMedium

Which protein forms the mesh that stabilises a blood clot?

  1. AThrombin
  2. BAlbumin
  3. CFibrin
  4. DCollagen
4.Human physiologyHard

A patient with small-cell lung cancer has low plasma sodium and low plasma osmolality but inappropriately concentrated urine. What is the most likely explanation?

  1. ASyndrome of inappropriate ADH secretion
  2. BAddison's disease with high aldosterone
  3. CCranial diabetes insipidus
  4. DPrimary hyperaldosteronism
5.MicrobiologyMedium

Transfer of bacterial genes from one bacterium to another by a virus is called:

  1. ATranscription
  2. BConjugation
  3. CTransformation
  4. DTransduction
6.MicrobiologyHard

Why are penicillins ineffective against Mycoplasma pneumoniae?

  1. AIt has a thick waxy mycolic acid layer that blocks entry
  2. BIt produces large amounts of beta-lactamase
  3. CIt lives only inside red blood cells
  4. DIt has no cell wall for penicillin to act on
7.PharmacologyMedium

Which early signs suggest systemic toxicity from a local anaesthetic?

  1. APinpoint pupils and slow, shallow breathing
  2. BItchy rash and swelling only at the injection site
  3. CHeavy sweating, salivation and diarrhoea
  4. DNumbness around the mouth, metallic taste and tinnitus
8.PharmacologyHard

A patient with early aspirin (salicylate) overdose has tinnitus and is breathing fast. Which acid–base pattern is classic?

  1. ARespiratory acidosis with normal bicarbonate
  2. BRespiratory alkalosis followed by metabolic acidosis
  3. CMetabolic alkalosis followed by respiratory acidosis
  4. DPure metabolic alkalosis
9.Arterial blood gas interpretationMedium

Practice values: Na⁺ 147 mmol/L, glucose 14.1 mmol/L and urea 12.2 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 147 mmol/Lglucose 14.1 mmol/Lurea 12.2 mmol/L
Osm = mOsm/kg
10.Arterial blood gas interpretationHard

Practice values: Na⁺ 141, Cl⁻ 114, HCO₃⁻ 18 mmol/L and albumin 18 g/L. Find the albumin-corrected anion gap AGc = AG + 0.25·(40 − albumin).

Na⁺ 141 mmol/LCl⁻ 114 mmol/LHCO₃⁻ 18 mmol/Lalbumin 18 g/L
AGc = mmol/L
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVnormal sinus rhythmsinus bradycardiasinus tachycardiaatrial fibrillation

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. 1normal sinus rhythm
  2. 2sinus bradycardia
  3. 3sinus tachycardia
  4. 4atrial fibrillation
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVfirst-degree AV blockthird-degree (complete) AV blocksecond-degree AV block type I (Wenckebach)junctional rhythm

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. 1first-degree AV block
  2. 2third-degree (complete) AV block
  3. 3second-degree AV block type I (Wenckebach)
  4. 4junctional rhythm
13.Evidence-based practice statisticsMedium
Se85%Sp73%LR+ = ?

Practice exercise (made-up values, not clinical guidance). A test has a sensitivity of 85% and a specificity of 73%. Find the positive likelihood ratio LR+. Round to two decimal places.

Se = 85%Sp = 73%
LR+ =
14.Evidence-based practice statisticsHard
p (%)PPV (%)1%PPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 70% and a specificity of 91%. It is used in a population where the prevalence is 1%. Find the positive predictive value PPV as a percentage. Round to one decimal place.

Se = 70%Sp = 91%p = 1%
PPV = %

3Solutions

1.Human anatomy

Answer: C · Corpus callosum

Why this is the answer

The corpus callosum is the largest commissure, linking matching areas of the two hemispheres. The internal capsule carries projection fibres up and down instead.

Answer

C · Corpus callosum
2.Human anatomy

Answer: A · The intercostal vein, artery and nerve run along the lower border of each rib

Why this is the answer

The intercostal neurovascular bundle (vein, artery, nerve from above down) lies in the costal groove under each rib. Going just above the rib below avoids it.

Answer

A · The intercostal vein, artery and nerve run along the lower border of each rib
3.Human physiology

Answer: C · Fibrin

Why this is the answer

Thrombin converts soluble fibrinogen into insoluble fibrin strands, which bind the platelet plug and trap red cells to form a stable clot.

Answer

C · Fibrin
4.Human physiology

Answer: A · Syndrome of inappropriate ADH secretion

Why this is the answer

In SIADH excess ADH makes the kidneys retain water, diluting the plasma while urine stays concentrated. Small-cell lung cancer can secrete ADH.

Answer

A · Syndrome of inappropriate ADH secretion
5.Microbiology

Answer: D · Transduction

Why this is the answer

In transduction a bacteriophage accidentally packages bacterial DNA and delivers it to the next cell it infects. Transformation is uptake of free DNA and conjugation uses direct contact.

Answer

D · Transduction
6.Microbiology

Answer: D · It has no cell wall for penicillin to act on

Why this is the answer

Mycoplasma lacks a cell wall, so beta-lactams have no target. Macrolides or tetracyclines, which act on the ribosome, are used instead.

Answer

D · It has no cell wall for penicillin to act on
7.Pharmacology

Answer: D · Numbness around the mouth, metallic taste and tinnitus

Why this is the answer

Local anaesthetic toxicity starts with central nervous system signs such as perioral numbness, metallic taste, tinnitus and agitation. It can progress to seizures, arrhythmias and cardiac arrest.

Answer

D · Numbness around the mouth, metallic taste and tinnitus
8.Pharmacology

Answer: B · Respiratory alkalosis followed by metabolic acidosis

Why this is the answer

Salicylates stimulate breathing, causing respiratory alkalosis early. They then disturb cell metabolism, causing a metabolic acidosis with a raised anion gap. Adults often show a mixed picture.

Answer

B · Respiratory alkalosis followed by metabolic acidosis
9.Arterial blood gas interpretation

Answer: Osm = 320 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 = 2·147 + 14.1 + 12.2 = 320.3 ≈ 320 mOsm/kg

Answer

Osm = 320 mOsm/kg
10.Arterial blood gas interpretation

Answer: AGc = 14.5 mmol/L

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 = 141 − (114 + 18) = 9

Correction for albumin

9 + 0.25·(40 − 18) = 14.5 mmol/L

Answer

AGc = 14.5 mmol/L

Above about 12 after correction: a high anion gap.

11.ECG rhythm strip interpretation

Answer: sinus tachycardia

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 = 14 small boxes, 1500 ÷ 14 ≈ 107 per minute.
2. Rhythm: regular, every R–R is 0.56 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.14 s, constant, within 0.12–0.20 s.
5. QRS: 0.08 s, narrow (below 0.12 s).

Interpretation

sinus tachycardia

Answer

sinus tachycardia
12.ECG rhythm strip interpretation

Answer: third-degree (complete) AV block

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: R–R = 30 small boxes, 1500 ÷ 30 ≈ 50 per minute.
2. Rhythm: R–R regular (1.20 s) and P–P regular (0.76 s), but the two are independent.
3. P waves: upright and regular at 79 per minute, but not linked to the QRS complexes; some hide in a QRS or a T wave.
4. PR interval: varies from beat to beat; there is no fixed relation.
5. QRS: 0.10 s, narrow (below 0.12 s).

Interpretation

third-degree (complete) AV block

Answer

third-degree (complete) AV block

Type II and third-degree blocks are the ones that can suddenly progress, so textbooks rank them as more serious than type I.

13.Evidence-based practice statistics

Answer: LR+ = 3.15

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+ = 0.85/(1 − 0.73) = 3.148 ≈ 3.15

Answer

LR+ = 3.15
14.Evidence-based practice statistics

Answer: PPV = 7.3 %

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 positives (per person)

Se·p = 0.7·0.01 = 0.007
(1 − Sp)·(1 − p) = 0.09·0.99 = 0.0891

Positive predictive value

PPV = 0.007/(0.007 + 0.0891) = 0.07284 ≈ 7.3%

Answer

PPV = 7.3%

The lower the prevalence, the lower the PPV of the same test.

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