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 structure is the main bundle of nerve fibres connecting the left and right cerebral hemispheres?

  1. AFornix
  2. BInternal capsule
  3. CCerebral peduncle
  4. DCorpus callosum
2.Human anatomyHard

After an injury at the medial epicondyle of the elbow, a patient has numbness of the little finger and weakness of finger abduction. Which nerve is affected?

  1. ARadial nerve
  2. BUlnar nerve
  3. CMusculocutaneous nerve
  4. DMedian nerve
3.Human physiologyMedium

Vital capacity is the sum of which lung volumes?

  1. AInspiratory reserve volume and residual volume
  2. BTidal volume, inspiratory reserve volume and expiratory reserve volume
  3. CResidual volume and expiratory reserve volume
  4. DTidal volume and residual volume
4.Human physiologyHard

In Graves' disease, what thyroid function results are expected and why?

  1. ALow T4 and high TSH, because antibodies destroy the gland
  2. BHigh T4 and high TSH, because the anterior pituitary gland is overactive
  3. CHigh T4 and low TSH, because antibodies stimulate the TSH receptor
  4. DLow T4 and low TSH, because the hypothalamus fails
5.MicrobiologyMedium

Which organism causes tuberculosis, and what makes it hard to stain with the Gram method?

  1. AStreptococcus pneumoniae, which has a capsule
  2. BMycoplasma pneumoniae, which has no cell wall to take up the stain
  3. CMycobacterium tuberculosis, which has a waxy mycolic acid wall
  4. DLegionella pneumophila, which lives inside amoebae
6.MicrobiologyHard

Why is Chlamydia trachomatis usually diagnosed with nucleic acid amplification tests instead of routine culture on agar?

  1. AIt is an obligate intracellular bacterium that cannot grow on ordinary media
  2. BIt is too large to grow on agar plates
  3. CIt is a virus and has no DNA
  4. DIt dies immediately in the presence of oxygen
7.PharmacologyMedium

A patient has severe kidney impairment. A drug is mainly excreted unchanged in the urine. What is the usual adjustment?

  1. AReduce the dose or lengthen the dosing interval
  2. BNo change is needed, because the liver takes over
  3. CIncrease the dose to make up for poor absorption
  4. DGive the drug orally instead of intravenously
8.PharmacologyHard

In aspirin overdose the urine may be made alkaline with sodium bicarbonate. Why does this increase salicylate excretion?

  1. AAlkaline urine increases glomerular filtration
  2. BMore salicylate is ionised in the tubule, so less is reabsorbed
  3. CBicarbonate speeds up the liver metabolism of salicylate to inactive forms
  4. DBicarbonate binds salicylate and makes it inactive
9.Arterial blood gas interpretationMedium

Practice values: Na⁺ 150 mmol/L, glucose 24 mmol/L and urea 18.2 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 150 mmol/Lglucose 24 mmol/Lurea 18.2 mmol/L
Osm = mOsm/kg
10.Arterial blood gas interpretationHard

Practice values: Na⁺ 133, Cl⁻ 103 and HCO₃⁻ 12 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.

Na⁺ 133 mmol/LCl⁻ 103 mmol/LHCO₃⁻ 12 mmol/L
delta ratio =
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVatrial flutter, 4:1 conductionatrial flutter, 2:1 conductionatrial flutter, 3:1 conductionsinus tachycardia

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, 2:1 conduction
  3. 3atrial flutter, 3:1 conduction
  4. 4sinus tachycardia
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVsinus rhythm with wide QRSpaced rhythm, failure to capturedual-chamber (AV) paced rhythmventricular paced rhythm

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. 1sinus rhythm with wide QRS
  2. 2paced rhythm, failure to capture
  3. 3dual-chamber (AV) paced rhythm
  4. 4ventricular paced rhythm
13.Evidence-based practice statisticsMedium
casescontrolsexposed5530abnot exposed195170cd

Practice exercise (made-up values, not clinical guidance). A case-control study compares 250 patients with a disease (cases) and 200 people without it (controls). The table shows how many in each group were exposed to a risk factor. Find the odds ratio OR for the exposure. Round to two decimal places.

a = 55b = 30c = 195d = 170
OR =
14.Evidence-based practice statisticsHard
pre-test10%post-test?p′LR+

Practice exercise (made-up values, not clinical guidance). A patient has a pre-test probability of 10% for a disease. A test with sensitivity 95% and specificity 63% comes back positive. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 10%Se = 95%Sp = 63%positive
p′ = %

3Solutions

1.Human anatomy

Answer: D · Corpus callosum

Why this is the answer

The corpus callosum is the largest commissure, linking matching areas of the two hemispheres. The internal capsule carries projection fibres up and down instead.

Answer

D · Corpus callosum
2.Human anatomy

Answer: B · Ulnar nerve

Why this is the answer

The ulnar nerve passes behind the medial epicondyle. It supplies most intrinsic hand muscles, including the interossei, and the skin of the little finger.

Answer

B · Ulnar nerve
3.Human physiology

Answer: B · Tidal volume, inspiratory reserve volume and expiratory reserve volume

Why this is the answer

Vital capacity = IRV + TV + ERV. It excludes the residual volume, which always stays in the lungs.

Answer

B · Tidal volume, inspiratory reserve volume and expiratory reserve volume
4.Human physiology

Answer: C · High T4 and low TSH, because antibodies stimulate the TSH receptor

Why this is the answer

TSH-receptor antibodies stimulate the thyroid independently of TSH. The resulting high T4 and T3 suppress pituitary TSH by negative feedback.

Answer

C · High T4 and low TSH, because antibodies stimulate the TSH receptor
5.Microbiology

Answer: C · Mycobacterium tuberculosis, which has a waxy mycolic acid wall

Why this is the answer

M. tuberculosis has a cell wall rich in mycolic acids, so it resists Gram staining and is identified with acid-fast stains.

Answer

C · Mycobacterium tuberculosis, which has a waxy mycolic acid wall
6.Microbiology

Answer: A · It is an obligate intracellular bacterium that cannot grow on ordinary media

Why this is the answer

Chlamydia replicates only inside host cells, so it cannot be grown on agar. NAATs such as PCR on urine or swabs are sensitive and are the standard diagnostic test.

Answer

A · It is an obligate intracellular bacterium that cannot grow on ordinary media
7.Pharmacology

Answer: A · Reduce the dose or lengthen the dosing interval

Why this is the answer

When renal clearance falls, drugs excreted by the kidney accumulate. The dose is lowered or given less often, guided by kidney function and, where possible, drug levels.

Answer

A · Reduce the dose or lengthen the dosing interval
8.Pharmacology

Answer: B · More salicylate is ionised in the tubule, so less is reabsorbed

Why this is the answer

Salicylate is a weak acid. In alkaline urine more of it is in the ionised form, which is "trapped" in the tubule and excreted. This is called ion trapping.

Answer

B · More salicylate is ionised in the tubule, so less is reabsorbed
9.Arterial blood gas interpretation

Answer: Osm = 342 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 = 2·150 + 24 + 18.2 = 342.2 ≈ 342 mOsm/kg

Answer

Osm = 342 mOsm/kg
10.Arterial blood gas interpretation

Answer: delta ratio = 0.5

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 = 133 − (103 + 12) = 18

Delta ratio

(18 − 12)/(24 − 12) = 6/12 = 0.5

Answer

delta ratio = 0.5

Below 1: an added normal anion gap acidosis.

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: ventricular paced rhythm

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: R–R = 23 small boxes, 1500 ÷ 23 ≈ 65 per minute.
2. Rhythm: regular, every R–R is 0.92 s.
3. P waves: none visible; a sharp pacing spike comes just before every QRS.
4. PR interval: not measurable.
5. QRS: 0.16 s, wide, and every spike is followed by a QRS (capture).

Interpretation

ventricular paced rhythm

Answer

ventricular paced rhythm

The paced QRS is wide by nature; do not call it a bundle branch block or a ventricular rhythm.

13.Evidence-based practice statistics

Answer: OR = 1.6

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.

Odds of exposure

cases: 55/195 = 0.2821
controls: 30/170 = 0.1765

Odds ratio

OR = (55·170)/(30·195) = 1.598 ≈ 1.6

Answer

OR = 1.6

OR above 1: exposure is more common among the cases.

14.Evidence-based practice statistics

Answer: p′ = 22.2 %

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.

Likelihood ratio

LR+ = 0.95/(1 − 0.63) = 2.568

Pre-test odds

0.1/(1 − 0.1) = 0.1111

Post-test odds

0.1111·2.568 = 0.2853

Post-test probability

p′ = 0.2853/(1 + 0.2853) = 0.222 ≈ 22.2%

Answer

p′ = 22.2%

ExamProblems · examproblems.com/courses/medical-sciences