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 two regions of the adult spine normally show a lordosis (curve concave towards the back)?

  1. ACervical and lumbar
  2. BThoracic and lumbar
  3. CThoracic and sacral
  4. DCervical and thoracic
2.Human anatomyHard

Why does a displaced fracture of the femoral neck carry a high risk of avascular necrosis of the femoral head?

  1. AIt damages the sciatic nerve that controls blood flow
  2. BIt tears the retinacular branches of the medial circumflex femoral artery
  3. CIt cuts the main trunk of the femoral artery
  4. DIt blocks the femoral vein and causes congestion
3.Human physiologyMedium

Which receptors respond mainly to a fall in arterial oxygen levels?

  1. ABaroreceptors in the carotid sinus
  2. BPeripheral chemoreceptors in the carotid and aortic bodies
  3. CCentral chemoreceptors in the medulla
  4. DStretch receptors in the lungs
4.Human physiologyHard

What is the main reason the ventricles do not contract at the same moment as the atria?

  1. AThe Purkinje fibres conduct slowly
  2. BConduction is delayed at the atrioventricular node
  3. CThe ventricles have a longer refractory period only
  4. DThe SA node fires twice per beat
5.MicrobiologyMedium

Which white blood cells are the main phagocytes in an acute bacterial infection and the main component of pus?

  1. ANeutrophils
  2. BEosinophils
  3. CB lymphocytes
  4. DBasophils
6.MicrobiologyHard

Which mechanism of antibiotic resistance does a bacterium use when it pumps the drug out of the cell?

  1. AEnzymatic inactivation
  2. BTarget modification
  3. CEfflux pumps
  4. DReduced porin uptake only
7.PharmacologyMedium

A child weighing 20 kg is prescribed a drug at 15 mg/kg per dose. What is the dose?

  1. A150 mg
  2. B300 mg
  3. C35 mg
  4. D3000 mg
8.PharmacologyHard

A patient taking metoprolol is also started on verapamil. Which adverse effect is most likely?

  1. ASevere bradycardia and heart block
  2. BHyperkalaemia and muscle weakness
  3. CHypoglycaemia and weight gain
  4. DRebound tachycardia and hypertension
9.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 10 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 10 mmol/L
PaCO₂ = mmHg
10.Arterial blood gas interpretationHard

Practice values: Na⁺ 143, Cl⁻ 106, HCO₃⁻ 19 mmol/L and albumin 35 g/L. Find the albumin-corrected anion gap AGc = AG + 0.25·(40 − albumin).

Na⁺ 143 mmol/LCl⁻ 106 mmol/LHCO₃⁻ 19 mmol/Lalbumin 35 g/L
AGc = mmol/L
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mV

Measure the QT interval on this lead II strip, in seconds.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
QT = 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
eventno eventtotaltreatment13267280abcontrol42308350cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 280 patients received a new treatment and 350 received the control treatment. The table shows how many in each group had the outcome (an unwanted event such as a stroke). Find the number needed to treat NNT to prevent one event. Round up to a whole number of patients.

treatment: 13/280control: 42/350
NNT =
14.Evidence-based practice statisticsHard
testdisease presentdisease absenttotalpositivenegative?total10 000

Practice exercise (made-up values, not clinical guidance). 10 000 people are screened with a test of sensitivity 82% and specificity 78%. The prevalence of the disease is 24%. How many people with the disease are missed by the test (false negatives, FN)?

N = 10 000p = 24%Se = 82%Sp = 78%
FN =

3Solutions

1.Human anatomy

Answer: A · Cervical and lumbar

Why this is the answer

The cervical and lumbar regions are lordotic (secondary curves). The thoracic and sacral regions are kyphotic (primary curves).

Answer

A · Cervical and lumbar
2.Human anatomy

Answer: B · It tears the retinacular branches of the medial circumflex femoral artery

Why this is the answer

The femoral head is supplied mainly by retinacular branches of the medial circumflex femoral artery running along the neck. A displaced neck fracture tears them and the head can die.

Answer

B · It tears the retinacular branches of the medial circumflex femoral artery
3.Human physiology

Answer: B · Peripheral chemoreceptors in the carotid and aortic bodies

Why this is the answer

The carotid and aortic bodies detect low PaO₂ (and also high CO₂ and H⁺). The central chemoreceptors respond to CO₂ but not directly to oxygen.

Answer

B · Peripheral chemoreceptors in the carotid and aortic bodies
4.Human physiology

Answer: B · Conduction is delayed at the atrioventricular node

Why this is the answer

The AV node conducts slowly (about 0.1 s delay), so atrial contraction completes ventricular filling before ventricular depolarisation begins.

Answer

B · Conduction is delayed at the atrioventricular node
5.Microbiology

Answer: A · Neutrophils

Why this is the answer

Neutrophils arrive quickly at sites of infection and engulf bacteria. Dead neutrophils, bacteria and tissue debris form pus.

Answer

A · Neutrophils
6.Microbiology

Answer: C · Efflux pumps

Why this is the answer

Efflux pumps actively export antibiotics such as tetracyclines and fluoroquinolones, keeping the inside concentration too low to work.

Answer

C · Efflux pumps
7.Pharmacology

Answer: B · 300 mg

Why this is the answer

20 kg × 15 mg/kg = 300 mg. The result is also checked against the safe dose range and the adult maximum.

Answer

B · 300 mg
8.Pharmacology

Answer: A · Severe bradycardia and heart block

Why this is the answer

Beta blockers and non-dihydropyridine calcium channel blockers (verapamil, diltiazem) both slow heart rate and AV conduction. Together they can cause severe bradycardia, heart block and heart failure.

Answer

A · Severe bradycardia and heart block
9.Arterial blood gas interpretation

Answer: PaCO₂ = 23 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 = 1.5·10 + 8 = 23 mmHg
range: 21–25 mmHg

Answer

PaCO₂ = 23 mmHg
10.Arterial blood gas interpretation

Answer: AGc = 19.25 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 = 143 − (106 + 19) = 18

Correction for albumin

18 + 0.25·(40 − 35) = 19.25 mmol/L

Answer

AGc = 19.25 mmol/L

Above about 12 after correction: a high anion gap.

11.ECG rhythm strip interpretation

Answer: QT = 0.42 s

QT and QTc: the QT interval runs from the start of the QRS complex to the end of the T wave. It shortens as the heart rate rises, so it is corrected for rate with the R–R interval in seconds: Bazett QTc = QT/√RR and Fridericia QTc = QT/∛RR. Bazett is the formula most textbooks use; it over-corrects at fast rates, where Fridericia is preferred. Limits differ between references: a QTc above about 0.45 s in men or 0.46 s in women is usually called prolonged, and above 0.50 s markedly prolonged.

Measure

10.5 small boxes from the start of the QRS to the end of the T wave

Convert

QT = 10.5 × 0.04 s = 0.42 s

Answer

QT = 0.42 s

A rough rule: at normal rates the QT should be less than half the R–R interval (here R–R = 0.80 s).

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: NNT = 14

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 = 13/280 = 0.04643
CER = 42/350 = 0.12

Number needed to treat

ARR = 0.12 − 0.04643 = 0.07357
NNT = 1/0.07357 = 13.59 → 14

Answer

NNT = 14

Treating 14 patients prevents about one event.

14.Evidence-based practice statistics

Answer: FN = 432

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

10 000·0.24 = 2400
10 000 − 2400 = 7600

False negatives

FN = 2400·0.18 = 432

Answer

FN = 432

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