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 artery is most commonly used to feel the pulse at the wrist?

  1. AAxillary artery
  2. BBrachial artery
  3. CRadial artery
  4. DUlnar artery
2.Human anatomyHard

Which structure passes through the inguinal canal in males?

  1. AFemoral artery
  2. BObturator nerve
  3. CSpermatic cord
  4. DGreat saphenous vein
3.Human physiologyMedium

Vital capacity is the sum of which lung volumes?

  1. ATidal volume and residual volume
  2. BInspiratory reserve volume and residual volume
  3. CResidual volume and expiratory reserve volume
  4. DTidal volume, inspiratory reserve volume and expiratory reserve volume
4.Human physiologyHard

A young woman has muscle weakness that gets worse with repeated use and improves with an acetylcholinesterase inhibitor. What is the most likely mechanism?

  1. AA defect in the dystrophin protein of muscle
  2. BDemyelination of central nervous system tracts
  3. CLoss of motor neurons in the spinal cord
  4. DAntibodies against acetylcholine receptors at the neuromuscular junction
5.MicrobiologyMedium

How does an mRNA vaccine produce immunity?

  1. AThe mRNA is inserted permanently into human DNA
  2. BThe mRNA kills the virus directly in the blood
  3. CThe mRNA contains weakened live virus
  4. DBody cells use the mRNA to make a viral protein that the immune system learns to recognise
6.MicrobiologyHard

What is the key difference between bactericidal and bacteriostatic antibiotics?

  1. ABactericidal drugs work only outside the body
  2. BBactericidal drugs kill bacteria; bacteriostatic drugs stop growth and rely on the immune system to clear them
  3. CBactericidal drugs work only on viruses; bacteriostatic drugs work on bacteria
  4. DBacteriostatic drugs always work faster than bactericidal drugs
7.PharmacologyMedium

How is adenosine given for supraventricular tachycardia?

  1. AAs a rapid IV push followed by a fast saline flush
  2. BAs a tablet under the tongue
  3. CAs an intramuscular injection into the outer thigh muscle
  4. DAs a slow infusion over one hour
8.PharmacologyHard

A patient with an epidural infusion of local anaesthetic becomes hypotensive. What is the most likely mechanism?

  1. ABlockade of sympathetic nerves causes vasodilation
  2. BThe local anaesthetic causes a severe allergic reaction
  3. CThe epidural catheter has caused heavy bleeding
  4. DThe drug increases urine output and causes dehydration
9.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 12 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 12 mmol/L
PaCO₂ = mmHg
10.Arterial blood gas interpretationHard
pH7.357.457.26PaCO₂mmHg354572HCO₃⁻mmol/L222631acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.26, PaCO₂ 72 mmHg (9.6 kPa), HCO₃⁻ 31 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 7.26PaCO₂ 72 mmHg (9.6 kPa)HCO₃⁻ 31 mmol/L
  1. 1acute
  2. 2chronic
  3. 3acute on chronic
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVsinus rhythm with PVCsatrial flutter, 4:1 conductionatrial fibrillationatrial flutter, 2:1 conduction

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. 1sinus rhythm with PVCs
  2. 2atrial flutter, 4:1 conduction
  3. 3atrial fibrillation
  4. 4atrial flutter, 2:1 conduction
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVsynchronised cardioversiontranscutaneous pacingCPR (non-shockable rhythm)immediate defibrillation

A patient without a palpable pulse has this organised rhythm on the monitor (pulseless electrical activity). Which treatment do adult resuscitation guidelines name for 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. 1synchronised cardioversion
  2. 2transcutaneous pacing
  3. 3CPR (non-shockable rhythm)
  4. 4immediate defibrillation
13.Evidence-based practice statisticsMedium
Se64%Sp76%LR+ = ?

Practice exercise (made-up values, not clinical guidance). A test has a sensitivity of 64% and a specificity of 76%. Find the positive likelihood ratio LR+. Round to two decimal places.

Se = 64%Sp = 76%
LR+ =
14.Evidence-based practice statisticsHard
pre-test50%post-test?p′LR−

Practice exercise (made-up values, not clinical guidance). A patient has a pre-test probability of 50% for a disease. A test with sensitivity 84% and specificity 87% comes back negative. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 50%Se = 84%Sp = 87%negative
p′ = %

3Solutions

1.Human anatomy

Answer: C · Radial artery

Why this is the answer

The radial artery lies superficially on the thumb side of the wrist, against the radius, which makes the pulse easy to feel.

Answer

C · Radial artery
2.Human anatomy

Answer: C · Spermatic cord

Why this is the answer

The inguinal canal carries the spermatic cord in males and the round ligament in females. The femoral vessels pass below the inguinal ligament instead.

Answer

C · Spermatic cord
3.Human physiology

Answer: D · Tidal volume, inspiratory reserve volume and expiratory reserve volume

Why this is the answer

Vital capacity = IRV + TV + ERV. It excludes the residual volume, which always stays in the lungs.

Answer

D · Tidal volume, inspiratory reserve volume and expiratory reserve volume
4.Human physiology

Answer: D · Antibodies against acetylcholine receptors at the neuromuscular junction

Why this is the answer

In myasthenia gravis, autoantibodies reduce the number of functional acetylcholine receptors. Blocking acetylcholinesterase leaves more ACh to bind the remaining receptors.

Answer

D · Antibodies against acetylcholine receptors at the neuromuscular junction
5.Microbiology

Answer: D · Body cells use the mRNA to make a viral protein that the immune system learns to recognise

Why this is the answer

The mRNA is translated by cells into an antigen, such as a coronavirus spike protein. The immune system responds to it. The mRNA is broken down and does not enter the nucleus.

Answer

D · Body cells use the mRNA to make a viral protein that the immune system learns to recognise
6.Microbiology

Answer: B · Bactericidal drugs kill bacteria; bacteriostatic drugs stop growth and rely on the immune system to clear them

Why this is the answer

Bacteriostatic drugs halt multiplication so host defences can eliminate the bacteria. Bactericidal drugs are preferred when defences are weak or hard to reach, such as in endocarditis or neutropenia.

Answer

B · Bactericidal drugs kill bacteria; bacteriostatic drugs stop growth and rely on the immune system to clear them
7.Pharmacology

Answer: A · As a rapid IV push followed by a fast saline flush

Why this is the answer

Adenosine must reach the heart quickly, so it is pushed rapidly into a large vein and flushed. Patients are warned about brief flushing, chest tightness and a short pause in the heartbeat.

Answer

A · As a rapid IV push followed by a fast saline flush
8.Pharmacology

Answer: A · Blockade of sympathetic nerves causes vasodilation

Why this is the answer

Epidural local anaesthetics block sympathetic fibres as well as sensory nerves. This dilates blood vessels and lowers blood pressure, so fluids, position changes or vasopressors may be needed.

Answer

A · Blockade of sympathetic nerves causes vasodilation
9.Arterial blood gas interpretation

Answer: PaCO₂ = 26 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 = 1.5·12 + 8 = 26 mmHg
range: 24–28 mmHg

Answer

PaCO₂ = 26 mmHg
10.Arterial blood gas interpretation

Answer: acute on 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: 31 mmol/L → acute on chronic

Answer

acute on chronic
11.ECG rhythm strip interpretation

Answer: atrial fibrillation

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: 10 QRS complexes in 6 s, × 10 = 100 per minute.
2. Rhythm: irregularly irregular, R–R from 0.44 to 0.76 s with no pattern.
3. P waves: none; the baseline shows small irregular fibrillatory waves.
4. PR interval: not measurable.
5. QRS: 0.06 s, narrow (below 0.12 s).

Interpretation

atrial fibrillation

Answer

atrial fibrillation
12.ECG rhythm strip interpretation

Answer: CPR (non-shockable rhythm)

Pulseless electrical activity (PEA): PEA cannot be seen on a strip. The monitor shows organised electrical activity (a rhythm other than VF, VT or asystole) but the patient has no palpable pulse, so it is recognised by checking the patient. In adult resuscitation guidelines PEA and asystole are the non-shockable cardiac arrest rhythms: high-quality CPR, epinephrine as soon as possible and a search for reversible causes (the Hs and Ts, such as hypovolaemia, hypoxia, tension pneumothorax and cardiac tamponade). VF and pulseless VT are the shockable rhythms.

What the strip shows

1. Rate: R–R = 21 small boxes, 1500 ÷ 21 ≈ 71 per minute.
2. Rhythm: regular, every R–R is 0.84 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: 0.06 s, narrow (below 0.12 s).
normal sinus rhythm

What the patient shows

no pulse despite organised electrical activity: pulseless electrical activity (PEA), a non-shockable cardiac arrest rhythm

Answer

CPR (non-shockable rhythm)

Answer

CPR (non-shockable rhythm)

PEA is recognised at the bedside, never from the strip alone. This is exam practice, not clinical guidance.

13.Evidence-based practice statistics

Answer: LR+ = 2.67

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+ = 0.64/(1 − 0.76) = 2.667 ≈ 2.67

Answer

LR+ = 2.67
14.Evidence-based practice statistics

Answer: p′ = 15.5 %

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.

Likelihood ratio

LR− = (1 − 0.84)/0.87 = 0.1839

Pre-test odds

0.5/(1 − 0.5) = 1

Post-test odds

1·0.1839 = 0.1839

Post-test probability

p′ = 0.1839/(1 + 0.1839) = 0.1553 ≈ 15.5%

Answer

p′ = 15.5%

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