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 part of the adrenal gland secretes adrenaline?

  1. AAdrenal medulla
  2. BZona fasciculata
  3. CZona reticularis
  4. DZona glomerulosa
2.Human anatomyHard

A large central disc prolapse at L4–L5 causes saddle anaesthesia, urinary retention and bilateral leg weakness. Which structure is compressed?

  1. AThoracic spinal cord
  2. BSciatic nerve in the buttock
  3. CCauda equina
  4. DFemoral nerve
3.Human physiologyMedium

Since action potentials are all-or-none, how does a neuron signal a stronger stimulus?

  1. ABy making each action potential larger
  2. BBy firing action potentials more often
  3. CBy changing the neurotransmitter it releases
  4. DBy making each action potential longer
4.Human physiologyHard

Which substance's clearance is used as the gold standard to measure glomerular filtration rate?

  1. ACreatinine
  2. BUrea
  3. CGlucose
  4. DInulin
5.MicrobiologyMedium

Which vaccine contains live attenuated (weakened) viruses?

  1. AInactivated influenza injection
  2. BHepatitis B vaccine
  3. CMMR (measles, mumps, rubella)
  4. DTetanus vaccine
6.MicrobiologyHard

Joseph Lister reduced infection after surgery in the 1860s. What was his main innovation?

  1. AUsing steam autoclaves to sterilise all surgical instruments before each operation
  2. BUsing carbolic acid (phenol) as an antiseptic on wounds and instruments
  3. CVaccinating surgeons against staphylococci
  4. DGiving sulfonamide antibiotics after every operation
7.PharmacologyMedium

A patient starting sulfasalazine should be told about which harmless effect?

  1. AGreen colouring of the sweat
  2. BWhite spots on the nails
  3. COrange-yellow colouring of the urine
  4. DBlue colouring of the tongue and gums
8.PharmacologyHard

Which heart failure drug improves symptoms and reduces hospital admissions but has not been shown to reduce mortality?

  1. AA mineralocorticoid receptor antagonist such as spironolactone
  2. BA beta blocker such as bisoprolol
  3. CDigoxin
  4. DAn ACE inhibitor
9.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 16 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 16 mmol/L
PaCO₂ = mmHg
10.Arterial blood gas interpretationHard
pH7.357.457.23PaCO₂mmHg354564HCO₃⁻mmol/L222626acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.23, PaCO₂ 64 mmHg (8.5 kPa), HCO₃⁻ 26 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 7.23PaCO₂ 64 mmHg (8.5 kPa)HCO₃⁻ 26 mmol/L
  1. 1acute
  2. 2chronic
  3. 3acute on chronic
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mV

This lead II strip shows atrial flutter. How many flutter waves per QRS complex are there (the n of n:1 conduction)?

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
flutter waves per QRS =
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVasystolepulseless electrical activity (PEA)ventricular fibrillationnormal sinus rhythm

A monitored patient is found unresponsive and not breathing normally, and no carotid pulse can be felt. The monitor shows this organised rhythm. What is this situation called? 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. 1asystole
  2. 2pulseless electrical activity (PEA)
  3. 3ventricular fibrillation
  4. 4normal sinus rhythm
13.Evidence-based practice statisticsMedium
casescontrolsexposed29109abnot exposed301571cd

Practice exercise (made-up values, not clinical guidance). A case-control study compares 330 patients with a disease (cases) and 680 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 = 29b = 109c = 301d = 571
OR =
14.Evidence-based practice statisticsHard
p (%)PPV (%)3%PPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 83% and a specificity of 85%. It is used in a population where the prevalence is 3%. Find the positive predictive value PPV as a percentage. Round to one decimal place.

Se = 83%Sp = 85%p = 3%
PPV = %

3Solutions

1.Human anatomy

Answer: A · Adrenal medulla

Why this is the answer

The adrenal medulla releases adrenaline and noradrenaline in response to sympathetic stimulation. The three zones of the cortex make steroid hormones.

Answer

A · Adrenal medulla
2.Human anatomy

Answer: C · Cauda equina

Why this is the answer

Below L1–L2 the canal holds the cauda equina. Central compression of these lumbar and sacral roots causes cauda equina syndrome, a surgical emergency.

Answer

C · Cauda equina
3.Human physiology

Answer: B · By firing action potentials more often

Why this is the answer

Stimulus strength is coded by the frequency of action potentials and by how many neurons are recruited, not by their amplitude.

Answer

B · By firing action potentials more often
4.Human physiology

Answer: D · Inulin

Why this is the answer

Inulin is filtered freely and is not reabsorbed or secreted, so its clearance equals GFR exactly. Creatinine is slightly secreted, so it overestimates GFR a little.

Answer

D · Inulin
5.Microbiology

Answer: C · MMR (measles, mumps, rubella)

Why this is the answer

MMR contains weakened live viruses that replicate a little and give strong, long-lasting immunity. Tetanus is a toxoid and hepatitis B a subunit vaccine.

Answer

C · MMR (measles, mumps, rubella)
6.Microbiology

Answer: B · Using carbolic acid (phenol) as an antiseptic on wounds and instruments

Why this is the answer

Lister applied carbolic acid to wounds, dressings and instruments, which greatly reduced post-operative infection. This started antiseptic surgery.

Answer

B · Using carbolic acid (phenol) as an antiseptic on wounds and instruments
7.Pharmacology

Answer: C · Orange-yellow colouring of the urine

Why this is the answer

Sulfasalazine can colour urine and sometimes skin and contact lenses orange-yellow. More serious adverse effects include blood disorders and rash, so blood counts are monitored.

Answer

C · Orange-yellow colouring of the urine
8.Pharmacology

Answer: C · Digoxin

Why this is the answer

ACE inhibitors (or ARBs/ARNI), beta blockers, mineralocorticoid antagonists and SGLT2 inhibitors reduce mortality in heart failure with reduced ejection fraction. Digoxin improves symptoms and reduces admissions without reducing mortality.

Answer

C · Digoxin
9.Arterial blood gas interpretation

Answer: PaCO₂ = 32 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 = 1.5·16 + 8 = 32 mmHg
range: 30–34 mmHg

Answer

PaCO₂ = 32 mmHg
10.Arterial blood gas interpretation

Answer: acute

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 + 1·2.4 = 26.4 mmol/L
chronic: 24 + 3.5·2.4 = 32.4 mmol/L

Compare

measured: 26 mmol/L → acute

Answer

acute
11.ECG rhythm strip interpretation

Answer: flutter waves per QRS = 3

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.

Flutter waves

F–F = 5 small boxes = 0.20 s → 1500 ÷ 5 = 300 per minute

QRS complexes

R–R = 15 small boxes = 0.60 s → 1500 ÷ 15 = 100 per minute
conduction ratio = 300 ÷ 100 = 3:1

Answer

flutter waves per QRS = 3
12.ECG rhythm strip interpretation

Answer: pulseless electrical activity (PEA)

Pulseless electrical activity (PEA): PEA cannot be seen on a strip. The monitor shows organised electrical activity (a rhythm other than VF, VT or asystole) but the patient has no palpable pulse, so it is recognised by checking the patient. In adult resuscitation guidelines PEA and asystole are the non-shockable cardiac arrest rhythms: high-quality CPR, epinephrine as soon as possible and a search for reversible causes (the Hs and Ts, such as hypovolaemia, hypoxia, tension pneumothorax and cardiac tamponade). VF and pulseless VT are the shockable rhythms.

What the strip shows

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: upright, one before every QRS, all alike.
4. PR interval: 0.14 s, constant, within 0.12–0.20 s.
5. QRS: 0.08 s, narrow (below 0.12 s).
normal sinus rhythm

What the patient shows

no pulse despite organised electrical activity: pulseless electrical activity (PEA), a non-shockable cardiac arrest rhythm

Answer

pulseless electrical activity (PEA)

Answer

pulseless electrical activity (PEA)

PEA is recognised at the bedside, never from the strip alone. This is exam practice, not clinical guidance.

13.Evidence-based practice statistics

Answer: OR = 0.5

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: 29/301 = 0.09635
controls: 109/571 = 0.1909

Odds ratio

OR = (29·571)/(109·301) = 0.5047 ≈ 0.5

Answer

OR = 0.5

OR below 1: exposure is less common among the cases, which suggests a protective effect.

14.Evidence-based practice statistics

Answer: PPV = 14.6 %

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 = 0.83·0.03 = 0.0249
(1 − Sp)·(1 − p) = 0.15·0.97 = 0.1455

Positive predictive value

PPV = 0.0249/(0.0249 + 0.1455) = 0.1461 ≈ 14.6%

Answer

PPV = 14.6%

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

ExamProblems · examproblems.com/courses/medical-sciences