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 is the largest nerve in the human body?

  1. AMedian nerve
  2. BFemoral nerve
  3. CSciatic nerve
  4. DVagus nerve
2.Human anatomyHard

Which structure is found in the posterior mediastinum?

  1. AHeart
  2. BAscending aorta
  3. CThymus
  4. DOesophagus
3.Human physiologyMedium

Why can cardiac muscle not be tetanised like skeletal muscle?

  1. AIt has no calcium in the sarcoplasmic reticulum
  2. BIt is not striated
  3. CIts long refractory period lasts almost as long as the contraction
  4. DIt is controlled only by hormones
4.Human physiologyHard

Which change shifts the oxygen–haemoglobin dissociation curve to the right?

  1. AHigher temperature
  2. BLower CO₂
  3. CHigher pH
  4. DLower 2,3-BPG
5.MicrobiologyMedium

Which laboratory test separates Staphylococcus aureus from most other staphylococci?

  1. AThe coagulase test
  2. BThe catalase test
  3. CThe acid-fast stain
  4. DThe Gram stain
6.MicrobiologyHard

A positive blood culture shows Gram-positive cocci in clusters. Which organism is most likely?

  1. AEnterococcus in short chains
  2. BStaphylococcus
  3. CStreptococcus
  4. DNeisseria
7.PharmacologyMedium

Which adverse effect is typical of metoclopramide, especially in young people?

  1. ALow blood glucose
  2. BExtrapyramidal movement disorders such as acute dystonia
  3. CDry cough
  4. DSevere constipation
8.PharmacologyHard

Why is the TPMT enzyme often tested before azathioprine is started?

  1. ALow TPMT activity causes toxic levels and marrow suppression
  2. BTPMT testing shows whether the patient has tuberculosis
  3. CTPMT is needed to absorb azathioprine from the gut
  4. DHigh TPMT activity causes an allergic reaction to azathioprine
9.Arterial blood gas interpretationMedium
pH7.357.457.25PaCO₂mmHg354540HCO₃⁻mmol/L222617uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.25, PaCO₂ 40 mmHg (5.3 kPa) and HCO₃⁻ 17 mmol/L. The primary disorder is metabolic acidosis. How far is it compensated? Click your answer.

pH 7.25PaCO₂ 40 mmHg (5.3 kPa)HCO₃⁻ 17 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 30% oxygen shows PaO₂ 82 mmHg (10.9 kPa) and PaCO₂ 60 mmHg (8.0 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 30%PaO₂ 82 mmHg (10.9 kPa)PaCO₂ 60 mmHg (8.0 kPa)
A–a gradient = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVatrial flutter, 4:1 conductionatrial flutter, 3:1 conductionatrial flutter, 2:1 conductionnormal sinus rhythm

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 flutter, 4:1 conduction
  2. 2atrial flutter, 3:1 conduction
  3. 3atrial flutter, 2:1 conduction
  4. 4normal sinus rhythm
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
eventno eventtotaltreatment20400420abcontrol10160170cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 420 patients received a new treatment and 170 received the control treatment. The table shows how many in each group had the outcome (an unwanted event such as a stroke). Find the relative risk reduction RRR as a percentage. Round to one decimal place.

treatment: 20/420control: 10/170
RRR = %
14.Evidence-based practice statisticsHard
CER4%EER?RRR 34%

Practice exercise (made-up values, not clinical guidance). A treatment reduces the risk of an event by 34% in relative terms (RRR = 34%). In a patient group the risk without treatment (CER) is 4% over five years. Find the number needed to treat NNT for five years to prevent one event. Round up to a whole number of patients.

RRR = 34%CER = 4%
NNT =

3Solutions

1.Human anatomy

Answer: C · Sciatic nerve

Why this is the answer

The sciatic nerve (L4–S3) leaves the pelvis through the greater sciatic foramen and supplies the hamstrings and all the muscles below the knee. Skin on the inner side of the leg is supplied by the saphenous nerve instead.

Answer

C · Sciatic nerve
2.Human anatomy

Answer: D · Oesophagus

Why this is the answer

The posterior mediastinum contains the oesophagus, descending aorta, azygos veins and thoracic duct. The heart and ascending aorta are in the middle mediastinum; the thymus is in the superior and anterior mediastinum.

Answer

D · Oesophagus
3.Human physiology

Answer: C · Its long refractory period lasts almost as long as the contraction

Why this is the answer

The plateau of the cardiac action potential gives a long refractory period, so the muscle relaxes before it can be excited again. This allows the heart to refill.

Answer

C · Its long refractory period lasts almost as long as the contraction
4.Human physiology

Answer: A · Higher temperature

Why this is the answer

Higher temperature, CO₂, H⁺ (lower pH) and 2,3-BPG lower haemoglobin's affinity and shift the curve right, releasing more oxygen to active tissues.

Answer

A · Higher temperature
5.Microbiology

Answer: A · The coagulase test

Why this is the answer

S. aureus produces coagulase, which converts fibrinogen to fibrin. All staphylococci are Gram-positive and catalase-positive, so those tests do not separate them.

Answer

A · The coagulase test
6.Microbiology

Answer: B · Staphylococcus

Why this is the answer

Staphylococci grow in grape-like clusters; streptococci and enterococci in chains or pairs. Neisseria are Gram-negative diplococci.

Answer

B · Staphylococcus
7.Pharmacology

Answer: B · Extrapyramidal movement disorders such as acute dystonia

Why this is the answer

Metoclopramide is a dopamine D2 antagonist. Blocking dopamine in the basal ganglia can cause dystonia and other extrapyramidal effects, more often in young adults.

Answer

B · Extrapyramidal movement disorders such as acute dystonia
8.Pharmacology

Answer: A · Low TPMT activity causes toxic levels and marrow suppression

Why this is the answer

Thiopurine methyltransferase helps inactivate azathioprine and mercaptopurine. People with low or absent TPMT activity need much lower doses or another drug to avoid life-threatening myelosuppression.

Answer

A · Low TPMT activity causes toxic levels and marrow suppression
9.Arterial blood gas interpretation

Answer: uncompensated

Reading a blood gas (ROME): first the pH: below 7.35 is acidaemia, above 7.45 alkalaemia. Then find the value that explains it. PaCO₂ (normal 35–45 mmHg, 4.7–6.0 kPa) is the respiratory part and moves Opposite to the pH in a respiratory disorder; HCO₃⁻ (normal 22–26 mmol/L) is the metabolic part and moves in the same direction as the pH (Respiratory Opposite, Metabolic Equal). The other value shows the compensation: normal means uncompensated; abnormal in the direction that pulls the pH back while the pH is still abnormal means partially compensated; a normal pH with both values abnormal means fully compensated. Ranges differ slightly between laboratories; these are practice values.

ROME, value by value

pH 7.25: acidaemia (below 7.35)
PaCO₂ 40 mmHg: normal (35–45)
HCO₃⁻ 17 mmol/L: low (22–26)

Compensation

Clinically, also check the expected compensation: Winter’s formula expects PaCO₂ 31.5–35.5 mmHg, so the measured 40 mmHg points to an additional respiratory acidosis (a mixed disorder). The answer above is the ROME exam classification.

uncompensated

Answer

uncompensated
10.Arterial blood gas interpretation

Answer: A–a gradient = 56.9 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 = 0.3·713 − 60/0.8 = 213.9 − 75 = 138.9 mmHg

Gradient

A–a = 138.9 − 82 = 56.9 mmHg

Answer

A–a gradient = 56.9 mmHg
11.ECG rhythm strip interpretation

Answer: atrial flutter, 3:1 conduction

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 = 15 small boxes, 1500 ÷ 15 ≈ 100 per minute.
2. Rhythm: regular, every R–R is 0.60 s.
3. P waves: none; regular sawtooth flutter waves every 0.20 s (300 per minute), 3 for each QRS.
4. PR interval: not measurable.
5. QRS: 0.08 s, narrow (below 0.12 s).

Interpretation

atrial flutter, 3:1 conduction

Answer

atrial flutter, 3:1 conduction
12.ECG rhythm strip interpretation

Answer: QRS duration

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 = 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: 0.18 s, constant, within 0.12–0.20 s.
5. QRS: 0.12 s, wide (0.12 s or more).

First abnormal step

QRS duration → sinus rhythm with wide QRS

Answer

QRS duration
13.Evidence-based practice statistics

Answer: RRR = 19 %

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 = 20/420 = 0.04762
CER = 10/170 = 0.05882

Relative risk reduction

ARR = 0.05882 − 0.04762 = 0.0112
RRR = 0.0112/0.05882 = 0.1905 ≈ 19%

Answer

RRR = 19%
14.Evidence-based practice statistics

Answer: NNT = 74

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.

Absolute risk reduction

ARR = 0.04·0.34 = 0.0136

Number needed to treat

NNT = 1/0.0136 = 73.53 → 74

Answer

NNT = 74

The same relative effect gives a smaller NNT when the baseline risk is higher.

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