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

The circle of Willis at the base of the brain connects which two arterial supplies?

  1. AInternal carotid and vertebrobasilar systems
  2. BJugular and vertebral systems
  3. CLeft and right external carotid arteries
  4. DExternal carotid and subclavian arterial systems
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. APrecentral gyrus of the non-dominant hemisphere
  2. BCerebellar hemisphere
  3. CPosterior superior temporal gyrus of the dominant hemisphere
  4. DInferior frontal gyrus of the dominant hemisphere
3.Human physiologyMedium

What causes the first heart sound (S1)?

  1. AClosure of the aortic and pulmonary valves
  2. BOpening of the aortic valve
  3. CBlood filling the atria
  4. DClosure of the mitral and tricuspid valves
4.Human physiologyHard

At the start of a fever, a patient shivers and feels cold even though body temperature is rising. Why?

  1. APyrogens raise the hypothalamic set point above the current body temperature
  2. BThe body has lost its ability to produce heat
  3. CThe thermoreceptors in the skin are destroyed
  4. DSweating has already cooled the body too much
5.MicrobiologyMedium

Why does high vaccination coverage also protect babies too young to be vaccinated?

  1. AFewer people can pass on the infection, so it spreads less
  2. BBabies are naturally immune to all vaccine-preventable diseases
  3. CVaccinated people pass antibodies to everyone they meet
  4. DVaccines kill the pathogen in the environment
6.MicrobiologyHard

Why must a negative-sense RNA virus such as influenza carry its own RNA-dependent RNA polymerase into the host cell?

  1. AThe polymerase protects the virus from antibodies
  2. BHost ribosomes cannot read any viral genes
  3. CThe polymerase is needed to integrate the genome into host DNA
  4. DHost cells cannot make mRNA from an RNA template
7.PharmacologyMedium

How should oral potassium chloride tablets be taken?

  1. ALying down straight after the dose
  2. BCrushed and dissolved under the tongue
  3. CWith food and plenty of water, swallowed whole if slow-release
  4. DOn an empty stomach with only a small sip of water, then lie down
8.PharmacologyHard

A woman using the combined oral contraceptive pill starts carbamazepine for epilepsy. What is the main concern?

  1. AContraceptive failure because the hormones are metabolised faster
  2. BNo concern, because the drugs do not interact
  3. CSevere hypoglycaemia from the combination
  4. DCarbamazepine toxicity because the pill strongly blocks its metabolism
9.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 6 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 6 mmol/L
PaCO₂ = mmHg
10.Arterial blood gas interpretationHard
pH7.357.457.32PaCO₂mmHg354566HCO₃⁻mmol/L222633acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.32, PaCO₂ 66 mmHg (8.8 kPa), HCO₃⁻ 33 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 7.32PaCO₂ 66 mmHg (8.8 kPa)HCO₃⁻ 33 mmol/L
  1. 1acute
  2. 2chronic
  3. 3acute on chronic
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVsinus bradycardianormal sinus rhythmatrial fibrillationsinus 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. 1sinus bradycardia
  2. 2normal sinus rhythm
  3. 3atrial fibrillation
  4. 4sinus arrhythmia
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVraterhythmP wavesPR intervalQRS duration

Interpret this lead II strip with the five steps in order: rate, rhythm, P waves, PR interval, QRS duration. At which step do you find the first abnormal finding? Click it.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
  1. 1rate
  2. 2rhythm
  3. 3P waves
  4. 4PR interval
  5. 5QRS duration
13.Evidence-based practice statisticsMedium
testdisease presentdisease absenttotalpositive351131482abnegative3910591098cdtotal39011901580

Practice exercise (made-up values, not clinical guidance). A new test was compared with the reference standard in a study (see the 2 × 2 table). Find the positive likelihood ratio LR+. Round to two decimal places.

a = 351b = 131c = 39d = 1059
LR+ =
14.Evidence-based practice statisticsHard
p (%)PPV (%)0.5%PPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 78% and a specificity of 88%. It is used in a population where the prevalence is 0.5%. Find the positive predictive value PPV as a percentage. Round to one decimal place.

Se = 78%Sp = 88%p = 0.5%
PPV = %

3Solutions

1.Human anatomy

Answer: A · Internal carotid and vertebrobasilar systems

Why this is the answer

The circle of Willis links the internal carotid arteries with the basilar artery (formed by the vertebral arteries), allowing some collateral flow.

Answer

A · Internal carotid and vertebrobasilar systems
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: D · Closure of the mitral and tricuspid valves

Why this is the answer

S1 ("lub") is caused by closure of the atrioventricular valves at the start of systole. S2 ("dub") is closure of the semilunar valves.

Answer

D · Closure of the mitral and tricuspid valves
4.Human physiology

Answer: A · Pyrogens raise the hypothalamic set point above the current body temperature

Why this is the answer

Pyrogens trigger prostaglandin E₂ in the hypothalamus, raising the set point. Until body temperature reaches the new set point, heat-gain responses such as shivering occur.

Answer

A · Pyrogens raise the hypothalamic set point above the current body temperature
5.Microbiology

Answer: A · Fewer people can pass on the infection, so it spreads less

Why this is the answer

When enough people are immune, chains of transmission break and the pathogen rarely reaches susceptible people, such as young babies or immunosuppressed patients.

Answer

A · Fewer people can pass on the infection, so it spreads less
6.Microbiology

Answer: D · Host cells cannot make mRNA from an RNA template

Why this is the answer

A negative-sense genome must first be copied into positive-sense mRNA. Human cells have no enzyme that copies RNA from RNA, so the virus brings its own polymerase.

Answer

D · Host cells cannot make mRNA from an RNA template
7.Pharmacology

Answer: C · With food and plenty of water, swallowed whole if slow-release

Why this is the answer

Oral potassium can cause nausea and, if a tablet lodges, ulceration of the oesophagus or gut. Taking it with food and plenty of water and staying upright reduces this; levels are monitored.

Answer

C · With food and plenty of water, swallowed whole if slow-release
8.Pharmacology

Answer: A · Contraceptive failure because the hormones are metabolised faster

Why this is the answer

Carbamazepine induces CYP3A4, speeding up the breakdown of oestrogen and progestogen. Contraceptive levels fall and pregnancy can occur, so another method is advised.

Answer

A · Contraceptive failure because the hormones are metabolised faster
9.Arterial blood gas interpretation

Answer: PaCO₂ = 17 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 = 1.5·6 + 8 = 17 mmHg
range: 15–19 mmHg

Answer

PaCO₂ = 17 mmHg
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 + 1·2.6 = 26.6 mmol/L
chronic: 24 + 3.5·2.6 = 33.1 mmol/L

Compare

measured: 33 mmol/L → chronic

Answer

chronic
11.ECG rhythm strip interpretation

Answer: sinus arrhythmia

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: 7 QRS complexes in 6 s, × 10 = 70 per minute.
2. Rhythm: irregular, R–R from 0.78 to 1.06 s, lengthening and shortening gradually.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.16 s, constant, within 0.12–0.20 s.
5. QRS: 0.08 s, narrow (below 0.12 s).

Interpretation

sinus arrhythmia

Answer

sinus arrhythmia
12.ECG rhythm strip interpretation

Answer: PR interval

Five steps for every strip: 1. rate (300 or 1500 method, or the 6-second method if irregular); 2. rhythm: are the R–R intervals equal; 3. P waves: present, upright in lead II, one before every QRS and all alike; 4. PR interval: 0.12–0.20 s and constant; 5. QRS duration: below 0.12 s. Only after the five steps name the rhythm. Normal sinus rhythm passes all five: 60–100/min, regular, upright P before every QRS, PR 0.12–0.20 s, QRS below 0.12 s.

Five steps

1. Rate: R–R = 19 small boxes, 1500 ÷ 19 ≈ 79 per minute.
2. Rhythm: regular, every R–R is 0.76 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.26 s, constant, longer than 0.20 s.
5. QRS: 0.06 s, narrow (below 0.12 s).

First abnormal step

PR interval → first-degree AV block

Answer

PR interval
13.Evidence-based practice statistics

Answer: LR+ = 8.18

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.

Sensitivity and specificity

Se = 351/390 = 0.9
Sp = 1059/1190 = 0.8899

Positive likelihood ratio

LR+ = 0.9/(1 − 0.8899) = 8.176 ≈ 8.18

Answer

LR+ = 8.18
14.Evidence-based practice statistics

Answer: PPV = 3.2 %

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 = 0.78·0.005 = 0.0039
(1 − Sp)·(1 − p) = 0.12·0.995 = 0.1194

Positive predictive value

PPV = 0.0039/(0.0039 + 0.1194) = 0.03163 ≈ 3.2%

Answer

PPV = 3.2%

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

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