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 connects the middle ear to the nasopharynx?

  1. AExternal acoustic meatus
  2. BAuditory (Eustachian) tube
  3. CCochlear duct
  4. DNasolacrimal duct
2.Human anatomyHard

Which muscle is the main flexor of the hip joint?

  1. AGluteus maximus
  2. BBiceps femoris
  3. CIliopsoas
  4. DAdductor magnus
3.Human physiologyMedium

What causes the first heart sound (S1)?

  1. AOpening of the aortic valve
  2. BBlood filling the atria
  3. CClosure of the mitral and tricuspid valves
  4. DClosure of the aortic and pulmonary valves
4.Human physiologyHard

Why does a person with a high spinal cord injury above T1 risk low blood pressure?

  1. AThe vagus nerve is cut, so the heart rate rises
  2. BThe sympathetic outflow to the vessels and heart is cut off
  3. CThe phrenic nerve can no longer control the tone of the arteries
  4. DRenin release from the kidney stops completely
5.MicrobiologyMedium

MRSA is resistant to methicillin because it has:

  1. AAn efflux pump for every antibiotic
  2. BA polysaccharide capsule that blocks the entry of all beta-lactams
  3. CNo cell wall at all
  4. DAn altered penicillin-binding protein (PBP2a)
6.MicrobiologyHard

Why are penicillins ineffective against Mycoplasma pneumoniae?

  1. AIt has a thick waxy mycolic acid layer that blocks entry
  2. BIt produces large amounts of beta-lactamase
  3. CIt has no cell wall for penicillin to act on
  4. DIt lives only inside red blood cells
7.PharmacologyMedium

Which description fits tardive dyskinesia?

  1. AHigh fever with lead-pipe rigidity and confusion
  2. BA sudden painful spasm of the neck muscles and upward rolling of the eyes within days of the first dose
  3. CA low white cell count with sore throat and fever
  4. DInvoluntary movements of the lips, tongue and face after long-term antipsychotic use
8.PharmacologyHard

In myxoedema coma, why is hydrocortisone often given before or with thyroid hormone?

  1. AHydrocortisone prevents the hypoglycaemia caused by levothyroxine
  2. BThyroid hormone is inactive unless hydrocortisone is given
  3. CThyroid hormone can trigger adrenal crisis if cortisol is also low
  4. DHydrocortisone makes thyroid hormone work faster
9.Arterial blood gas interpretationMedium
pH7.357.457.37PaCO₂mmHg354532HCO₃⁻mmol/L222618uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.37, PaCO₂ 32 mmHg (4.3 kPa) and HCO₃⁻ 18 mmol/L. The primary disorder is metabolic acidosis. How far is it compensated? Click your answer.

pH 7.37PaCO₂ 32 mmHg (4.3 kPa)HCO₃⁻ 18 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
10.Arterial blood gas interpretationHard
pH7.357.457.25PaCO₂mmHg354521HCO₃⁻mmol/L22269appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.25, PaCO₂ 21 mmHg (2.8 kPa), HCO₃⁻ 9 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.25PaCO₂ 21 mmHg (2.8 kPa)HCO₃⁻ 9 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVjunctional rhythmsinus bradycardiasinus tachycardiafirst-degree AV block

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. 1junctional rhythm
  2. 2sinus bradycardia
  3. 3sinus tachycardia
  4. 4first-degree AV block
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVventricular fibrillationpulseless electrical activity (PEA)asystolenormal 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. 1ventricular fibrillation
  2. 2pulseless electrical activity (PEA)
  3. 3asystole
  4. 4normal sinus rhythm
13.Evidence-based practice statisticsMedium
peopleyears190521204new cases36

Practice exercise (made-up values, not clinical guidance). In a cohort, groups of people were followed for different lengths of time (see the table: number of people and years of follow-up for each). During follow-up, 36 new cases occurred. Find the incidence rate IR per 1000 person-years. Round to one decimal place.

90 × 5 years120 × 4 years36 new cases
IR = per 1000 person-years
14.Evidence-based practice statisticsHard
control2%treatment?

Practice exercise (made-up values, not clinical guidance). Without a drug, 2% of patients have a certain side effect during a year. The drug raises this risk with a relative risk of RR = 2.33. Find the number needed to harm NNH: how many patients must take the drug for a year for one extra patient to have the side effect? Round up to a whole number of patients.

control 2%RR = 2.33
NNH =

3Solutions

1.Human anatomy

Answer: B · Auditory (Eustachian) tube

Why this is the answer

The auditory tube equalises air pressure on both sides of the eardrum. In children it is shorter and more horizontal, which favours middle ear infections.

Answer

B · Auditory (Eustachian) tube
2.Human anatomy

Answer: C · Iliopsoas

Why this is the answer

Iliopsoas (psoas major and iliacus) is the strongest hip flexor. Gluteus maximus extends the hip.

Answer

C · Iliopsoas
3.Human physiology

Answer: C · 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

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

Answer: B · The sympathetic outflow to the vessels and heart is cut off

Why this is the answer

Sympathetic outflow leaves the cord at T1–L2. A lesion above it removes vasomotor tone and cardiac sympathetic drive while the vagus still works, causing hypotension and bradycardia (neurogenic shock).

Answer

B · The sympathetic outflow to the vessels and heart is cut off
5.Microbiology

Answer: D · An altered penicillin-binding protein (PBP2a)

Why this is the answer

The mecA gene codes for PBP2a, which has low affinity for beta-lactams, so the bacterium can keep building its cell wall despite methicillin.

Answer

D · An altered penicillin-binding protein (PBP2a)
6.Microbiology

Answer: C · It has no cell wall for penicillin to act on

Why this is the answer

Mycoplasma lacks a cell wall, so beta-lactams have no target. Macrolides or tetracyclines, which act on the ribosome, are used instead.

Answer

C · It has no cell wall for penicillin to act on
7.Pharmacology

Answer: D · Involuntary movements of the lips, tongue and face after long-term antipsychotic use

Why this is the answer

Tardive dyskinesia develops after months or years of dopamine-blocking drugs and may be permanent. Patients are screened regularly so that treatment can be changed early.

Answer

D · Involuntary movements of the lips, tongue and face after long-term antipsychotic use
8.Pharmacology

Answer: C · Thyroid hormone can trigger adrenal crisis if cortisol is also low

Why this is the answer

Restoring thyroid hormone increases metabolic rate and cortisol clearance. If adrenal reserve is also low, this can precipitate adrenal crisis, so steroid cover is given until adrenal insufficiency is excluded.

Answer

C · Thyroid hormone can trigger adrenal crisis if cortisol is also low
9.Arterial blood gas interpretation

Answer: fully compensated

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 7.37: within 7.35–7.45
PaCO₂ 32 mmHg: low (35–45)
HCO₃⁻ 18 mmol/L: low (22–26)

Compensation

Clinically, also check the expected compensation: Winter’s formula expects PaCO₂ 33–37 mmHg, so the measured 32 mmHg points to an additional respiratory alkalosis (a mixed disorder). The answer above is the ROME exam classification.

fully compensated

Answer

fully compensated
10.Arterial blood gas interpretation

Answer: appropriate compensation

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 PaCO₂

1.5·9 + 8 = 21.5 → 19.5–23.5 mmHg

Compare

measured: 21 mmHg → appropriate compensation

Answer

appropriate compensation
11.ECG rhythm strip interpretation

Answer: sinus bradycardia

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 = 34 small boxes, 1500 ÷ 34 ≈ 44 per minute.
2. Rhythm: regular, every R–R is 1.36 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.12 s, constant, within 0.12–0.20 s.
5. QRS: 0.08 s, narrow (below 0.12 s).

Interpretation

sinus bradycardia

Answer

sinus bradycardia
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 = 17 small boxes, 1500 ÷ 17 ≈ 88 per minute.
2. Rhythm: regular, every R–R is 0.68 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.20 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: IR = 38.7 per 1000 person-years

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.

Person-years

PY = 90·5 + 120·4 = 930

Incidence rate

IR = 36/930·1000 = 38.7 per 1000 person-years

Answer

IR = 38.7 per 1000 person-years
14.Evidence-based practice statistics

Answer: NNH = 38

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.

Risk with the drug

0.02·2.33 = 0.0466

Absolute risk increase

ARI = 0.0466 − 0.02 = 0.0266

Number needed to harm

NNH = 1/0.0266 = 37.59 → 38

Answer

NNH = 38

ExamProblems · examproblems.com/courses/medical-sciences