Medical Sciences: cram pack

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

New problemsBack to the course

In the print window, choose “Save as PDF” to keep a copy on your device.

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

The sympathetic nervous system leaves the central nervous system from which spinal segments?

  1. ASacral only (S2–S4)
  2. BCervical only
  3. CThoracic and upper lumbar (T1–L2)
  4. DCranial and sacral
2.Human anatomyHard

Which coronary artery most often supplies the sinoatrial (SA) node?

  1. ALeft anterior descending artery
  2. BRight coronary artery
  3. CCircumflex artery
  4. DLeft main coronary artery
3.Human physiologyMedium

What is the main effect of vagus nerve stimulation on the heart?

  1. AIt slows the heart rate
  2. BIt increases ventricular contractility strongly
  3. CIt constricts the coronary arteries
  4. DIt increases the heart rate
4.Human physiologyHard

In pernicious anaemia, autoimmune destruction of gastric parietal cells leads to anaemia because:

  1. AIntrinsic factor is lost, so vitamin B12 is not absorbed
  2. BGastrin is lost, so the bone marrow is no longer stimulated
  3. CPepsin is lost, so haemoglobin cannot be made
  4. DAcid is lost, so iron is never absorbed in any form
5.MicrobiologyMedium

Why are Gram-negative bacteria often harder to treat with antibiotics?

  1. ATheir outer membrane blocks many drugs
  2. BThey have a thicker peptidoglycan layer
  3. CThey divide much more slowly
  4. DThey have no ribosomes
6.MicrobiologyHard

An older adult develops a painful blistering rash in a band on one side of the chest. What explains this pattern?

  1. ABacteria spread along the lymphatic vessels of the chest
  2. BA new chickenpox infection spreads through the blood to one side
  3. CVaricella-zoster virus reactivates from one sensory ganglion and travels along its nerve
  4. DAn allergic reaction to clothing affects one dermatome
7.PharmacologyMedium

Which receptor do beta blockers such as metoprolol mainly block?

  1. ABeta-1 adrenergic receptors in the heart
  2. BAlpha-1 receptors in blood vessels
  3. CBeta-3 receptors in fat tissue
  4. DMuscarinic receptors in the heart
8.PharmacologyHard

A patient who takes clonidine stopped it suddenly two days ago. He is now agitated, has a headache and his blood pressure is very high. What is the most likely explanation?

  1. ARebound hypertension from abrupt clonidine withdrawal
  2. BClonidine toxicity due to slow excretion by the kidneys
  3. CNormal variation unrelated to the medication
  4. DAn allergic reaction to clonidine
9.Arterial blood gas interpretationMedium

Practice values: Na⁺ 149 mmol/L, glucose 20.4 mmol/L and urea 3.9 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 149 mmol/Lglucose 20.4 mmol/Lurea 3.9 mmol/L
Osm = mOsm/kg
10.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 28% oxygen shows PaO₂ 70 mmHg (9.3 kPa) and PaCO₂ 46 mmHg (6.1 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 28%PaO₂ 70 mmHg (9.3 kPa)PaCO₂ 46 mmHg (6.1 kPa)
A–a gradient = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVatrial fibrillationsinus rhythm with PVCsatrial flutter, 4:1 conductionsinus arrhythmia

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 fibrillation
  2. 2sinus rhythm with PVCs
  3. 3atrial flutter, 4:1 conduction
  4. 4sinus arrhythmia
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVventricular tachycardiasinus tachycardiaatrial fibrillationatrial flutter, 2:1 conduction

Identify the rhythm on this lead II strip. 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. 1ventricular tachycardia
  2. 2sinus tachycardia
  3. 3atrial fibrillation
  4. 4atrial flutter, 2:1 conduction
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment259541800abcontrol58262320cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 800 patients received a new treatment and 320 received the control treatment. The table shows how many in each group had a side effect. Find the number needed to harm NNH: how many patients must be treated for one extra patient to have the side effect? Round up to a whole number of patients.

treatment: 259/800control: 58/320
NNH =
14.Evidence-based practice statisticsHard
control34%treatment?

Practice exercise (made-up values, not clinical guidance). Without a drug, 34% of patients have a certain side effect during a year. The drug raises this risk with a relative risk of RR = 1.98. Find the number needed to harm NNH: how many patients must take the drug for a year for one extra patient to have the side effect? Round up to a whole number of patients.

control 34%RR = 1.98
NNH =

3Solutions

1.Human anatomy

Answer: C · Thoracic and upper lumbar (T1–L2)

Why this is the answer

Sympathetic preganglionic neurons lie in the lateral horn from T1 to L2. The parasympathetic system has a craniosacral outflow.

Answer

C · Thoracic and upper lumbar (T1–L2)
2.Human anatomy

Answer: B · Right coronary artery

Why this is the answer

The SA nodal artery arises from the right coronary artery in roughly 60% of people and from the circumflex artery in the rest.

Answer

B · Right coronary artery
3.Human physiology

Answer: A · It slows the heart rate

Why this is the answer

The vagus releases acetylcholine on muscarinic receptors in the SA and AV nodes, slowing pacemaker firing and AV conduction.

Answer

A · It slows the heart rate
4.Human physiology

Answer: A · Intrinsic factor is lost, so vitamin B12 is not absorbed

Why this is the answer

Parietal cells secrete intrinsic factor, needed for B12 absorption in the terminal ileum. B12 deficiency impairs DNA synthesis and causes megaloblastic anaemia.

Answer

A · Intrinsic factor is lost, so vitamin B12 is not absorbed
5.Microbiology

Answer: A · Their outer membrane blocks many drugs

Why this is the answer

The outer membrane of Gram-negative bacteria, with lipopolysaccharide and porins, keeps many antibiotics out and adds efflux and enzyme defences.

Answer

A · Their outer membrane blocks many drugs
6.Microbiology

Answer: C · Varicella-zoster virus reactivates from one sensory ganglion and travels along its nerve

Why this is the answer

After chickenpox, VZV stays latent in a dorsal root or cranial nerve ganglion. When immunity weakens it can reactivate, travelling down that nerve to cause shingles in its dermatome.

Answer

C · Varicella-zoster virus reactivates from one sensory ganglion and travels along its nerve
7.Pharmacology

Answer: A · Beta-1 adrenergic receptors in the heart

Why this is the answer

Cardioselective beta blockers block beta-1 receptors, lowering heart rate, contractility and renin release.

Answer

A · Beta-1 adrenergic receptors in the heart
8.Pharmacology

Answer: A · Rebound hypertension from abrupt clonidine withdrawal

Why this is the answer

Clonidine is a central alpha-2 agonist. Stopping it suddenly lets sympathetic activity surge, causing rebound hypertension, so it is tapered gradually.

Answer

A · Rebound hypertension from abrupt clonidine withdrawal
9.Arterial blood gas interpretation

Answer: Osm = 322 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 = 2·149 + 20.4 + 3.9 = 322.3 ≈ 322 mOsm/kg

Answer

Osm = 322 mOsm/kg
10.Arterial blood gas interpretation

Answer: A–a gradient = 72.14 mmHg

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.

Alveolar oxygen

PAO₂ = 0.28·713 − 46/0.8 = 199.6 − 57.5 = 142.1 mmHg

Gradient

A–a = 142.1 − 70 = 72.14 mmHg

Answer

A–a gradient = 72.14 mmHg
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: 8 QRS complexes in 6 s, × 10 = 80 per minute.
2. Rhythm: irregularly irregular, R–R from 0.54 to 1.00 s with no pattern.
3. P waves: none; the baseline shows small irregular fibrillatory waves.
4. PR interval: not measurable.
5. QRS: 0.08 s, narrow (below 0.12 s).

Interpretation

atrial fibrillation

Answer

atrial fibrillation
12.ECG rhythm strip interpretation

Answer: ventricular tachycardia

Ventricular rhythms: ventricular tachycardia is a run of three or more wide (0.12 s or more) complexes in a row at more than 100/min, usually 150–250/min, regular, without related P waves. Ventricular fibrillation is a chaotic, irregular waveform with no identifiable P waves, QRS complexes or T waves and no countable rate. Asystole is an almost flat line with no ventricular activity; a flat line is always confirmed by checking the patient, the leads and the gain and a second lead. In resuscitation guidelines VF and pulseless VT are the shockable rhythms and asystole is not.

Five steps

1. Rate: R–R = 10 small boxes, 1500 ÷ 10 ≈ 150 per minute.
2. Rhythm: regular, every R–R is 0.40 s.
3. P waves: none identifiable.
4. PR interval: not measurable.
5. QRS: 0.16 s, wide (0.12 s or more).

Interpretation

ventricular tachycardia

Answer

ventricular tachycardia

In resuscitation guidelines VF and pulseless VT are the shockable rhythms. This is identification practice only.

13.Evidence-based practice statistics

Answer: NNH = 8

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.

Event rates

EER = 259/800 = 0.3237
CER = 58/320 = 0.1812

Number needed to harm

ARI = 0.3237 − 0.1812 = 0.1425
NNH = 1/0.1425 = 7.018 → 8

Answer

NNH = 8

About one in every 8 treated patients has the side effect because of the treatment.

14.Evidence-based practice statistics

Answer: NNH = 4

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.

Risk with the drug

0.34·1.98 = 0.6732

Absolute risk increase

ARI = 0.6732 − 0.34 = 0.3332

Number needed to harm

NNH = 1/0.3332 = 3.001 → 4

Answer

NNH = 4

ExamProblems · examproblems.com/courses/medical-sciences