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

Which spinal nerve roots form the brachial plexus?

  1. AC1 to C4
  2. BC3 to C7
  3. CC5 to T1
  4. DT1 to T5
2.Human anatomyHard

In which part of the small intestine are vitamin B12 and bile salts mainly absorbed?

  1. ACaecum
  2. BJejunum
  3. CTerminal ileum
  4. DDuodenum
3.Human physiologyMedium

Which receptor is stimulated when the patellar tendon is tapped in the knee-jerk reflex?

  1. APacinian corpuscle
  2. BNociceptor
  3. CMuscle spindle
  4. DGolgi tendon organ
4.Human physiologyHard

A patient with small-cell lung cancer has low plasma sodium and low plasma osmolality but inappropriately concentrated urine. What is the most likely explanation?

  1. ASyndrome of inappropriate ADH secretion
  2. BCranial diabetes insipidus
  3. CAddison's disease with high aldosterone
  4. DPrimary hyperaldosteronism
5.MicrobiologyMedium

Which bacterium causes whooping cough (pertussis)?

  1. ACorynebacterium diphtheriae
  2. BMycoplasma pneumoniae
  3. CHaemophilus influenzae
  4. DBordetella pertussis
6.MicrobiologyHard

Staphylococcus aureus food poisoning starts only 1–6 hours after eating. Why so fast?

  1. AThe bacteria made a heat-stable toxin in the food before it was eaten
  2. BThe bacteria invade the bloodstream immediately
  3. CThe bacteria multiply very fast inside the gut and invade the intestinal wall
  4. DThe immune system reacts to the bacteria within minutes
7.PharmacologyMedium

Which signs suggest early lithium toxicity?

  1. ADiarrhoea, vomiting, coarse tremor and drowsiness
  2. BHair loss and dark urine only
  3. CPinpoint pupils and slow breathing
  4. DVery high blood pressure and a severe headache
8.PharmacologyHard

A patient on simvastatin is prescribed gemfibrozil. What is the main concern?

  1. AA sharp rise in LDL cholesterol and triglycerides
  2. BSevere hypoglycaemia
  3. CA much higher risk of myopathy and rhabdomyolysis
  4. DLoss of all lipid-lowering effect
9.Arterial blood gas interpretationMedium

Practice values: Na⁺ 145 mmol/L, glucose 13.3 mmol/L and urea 6.2 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 145 mmol/Lglucose 13.3 mmol/Lurea 6.2 mmol/L
Osm = mOsm/kg
10.Arterial blood gas interpretationHard
pH7.357.457.24PaCO₂mmHg354577HCO₃⁻mmol/L222632acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.24, PaCO₂ 77 mmHg (10.3 kPa), HCO₃⁻ 32 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 7.24PaCO₂ 77 mmHg (10.3 kPa)HCO₃⁻ 32 mmol/L
  1. 1acute
  2. 2chronic
  3. 3acute on chronic
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mV

Measure the QT interval and the R–R interval on this regular lead II strip, then calculate the rate-corrected QTc with Bazett’s formula QTc = QT/√RR (both in seconds). Give the answer in seconds to three decimals.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
QTc = s
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVsecond-degree AV block type IIdual-chamber (AV) paced rhythmidioventricular rhythmpaced rhythm, failure to capture

This patient has a pacemaker. Interpret the 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. 1second-degree AV block type II
  2. 2dual-chamber (AV) paced rhythm
  3. 3idioventricular rhythm
  4. 4paced rhythm, failure to capture
13.Evidence-based practice statisticsMedium
testdisease presentdisease absenttotalpositive158617775abnegative8212531335cdtotal24018702110

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 negative likelihood ratio LR−. Round to two decimal places.

a = 158b = 617c = 82d = 1253
LR− =
14.Evidence-based practice statisticsHard
testdisease presentdisease absenttotalpositive?negativetotal10 000

Practice exercise (made-up values, not clinical guidance). 10 000 people are screened with a test of sensitivity 90% and specificity 90%. The prevalence of the disease is 10%. How many true-positive results TP are expected?

N = 10 000p = 10%Se = 90%Sp = 90%
TP =

3Solutions

1.Human anatomy

Answer: C · C5 to T1

Why this is the answer

The brachial plexus is formed by the ventral rami of C5, C6, C7, C8 and T1. It gives rise to the main nerves of the arm.

Answer

C · C5 to T1
2.Human anatomy

Answer: C · Terminal ileum

Why this is the answer

The terminal ileum absorbs vitamin B12 (bound to intrinsic factor) and reabsorbs bile salts. The duodenum mainly absorbs iron.

Answer

C · Terminal ileum
3.Human physiology

Answer: C · Muscle spindle

Why this is the answer

Tapping the tendon stretches quadriceps muscle spindles. Their afferents synapse directly on motor neurons in a monosynaptic reflex that contracts the muscle.

Answer

C · Muscle spindle
4.Human physiology

Answer: A · Syndrome of inappropriate ADH secretion

Why this is the answer

In SIADH excess ADH makes the kidneys retain water, diluting the plasma while urine stays concentrated. Small-cell lung cancer can secrete ADH.

Answer

A · Syndrome of inappropriate ADH secretion
5.Microbiology

Answer: D · Bordetella pertussis

Why this is the answer

Bordetella pertussis causes long coughing fits with a "whoop". It is most dangerous for young babies, which is why vaccination in pregnancy is offered in many countries.

Answer

D · Bordetella pertussis
6.Microbiology

Answer: A · The bacteria made a heat-stable toxin in the food before it was eaten

Why this is the answer

S. aureus produces enterotoxins in food left at warm temperatures. The toxin is already there when the food is eaten and survives reheating, so symptoms start quickly.

Answer

A · The bacteria made a heat-stable toxin in the food before it was eaten
7.Pharmacology

Answer: A · Diarrhoea, vomiting, coarse tremor and drowsiness

Why this is the answer

Early lithium toxicity causes GI upset, a coarse tremor, sluggishness and unsteadiness. Higher levels cause confusion, seizures and arrhythmias, so the drug is held and the level checked.

Answer

A · Diarrhoea, vomiting, coarse tremor and drowsiness
8.Pharmacology

Answer: C · A much higher risk of myopathy and rhabdomyolysis

Why this is the answer

Gemfibrozil reduces statin clearance and adds its own muscle toxicity. The combination greatly increases the risk of rhabdomyolysis and is generally avoided.

Answer

C · A much higher risk of myopathy and rhabdomyolysis
9.Arterial blood gas interpretation

Answer: Osm = 310 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 = 2·145 + 13.3 + 6.2 = 309.5 ≈ 310 mOsm/kg

Answer

Osm = 310 mOsm/kg
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 + 1·3.7 = 27.7 mmol/L
chronic: 24 + 3.5·3.7 = 36.95 mmol/L

Compare

measured: 32 mmol/L → acute on chronic

Answer

acute on chronic
11.ECG rhythm strip interpretation

Answer: QTc = 0.5 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

QT = 13 × 0.04 = 0.52 s
RR = 27 × 0.04 = 1.08 s

Bazett’s formula

QTc = 0.52/√1.08 = 0.52/1.039 = 0.5 s

Answer

QTc = 0.5 s

Above the usual limits for both men (about 0.45 s) and women (about 0.46 s): prolonged. (500 ms)

12.ECG rhythm strip interpretation

Answer: paced rhythm, failure to capture

Paced rhythms: a pacemaker impulse shows as a narrow vertical pacing spike. After a ventricular spike the QRS is wide (0.12 s or more), because the impulse spreads from the lead through the muscle instead of the conduction system; with right-ventricular pacing it is often mostly negative in lead II. A spike before each P wave means atrial pacing, and a dual-chamber (AV) pacemaker shows an atrial spike and a P wave, then, after the programmed AV delay, a ventricular spike and a wide QRS. Capture means every spike is followed by a depolarisation. Failure to capture is a spike without a P wave or QRS after it; failure to sense (spikes that ignore the patient’s own beats) and failure to pace (no spike when one is due) are the other classic malfunctions.

Five steps

1. Rate: 5 QRS complexes in 6 s, × 10 = 50 per minute.
2. Rhythm: the pacing spikes are regular (every 0.96 s), but the R–R is not, because a QRS is missing after some spikes.
3. P waves: none visible.
4. PR interval: not measurable.
5. QRS: 0.16 s and wide after the captured spikes; one spike is not followed by a QRS (no capture).

Interpretation

paced rhythm, failure to capture

Answer

paced rhythm, failure to capture

Failure to capture: the pacemaker fires but the heart does not respond. Textbooks treat it as urgent to report, because the patient may depend on the pacemaker.

13.Evidence-based practice statistics

Answer: LR− = 0.51

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 = 158/240 = 0.6583
Sp = 1253/1870 = 0.6701

Negative likelihood ratio

LR− = (1 − 0.6583)/0.6701 = 0.5099 ≈ 0.51

Answer

LR− = 0.51
14.Evidence-based practice statistics

Answer: TP = 900

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

10 000·0.1 = 1000
10 000 − 1000 = 9000

True positives

TP = 1000·0.9 = 900

Answer

TP = 900

ExamProblems · examproblems.com/courses/medical-sciences