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 glomerulosa
  3. CZona reticularis
  4. DZona fasciculata
2.Human anatomyHard

Which structure is found in the posterior mediastinum?

  1. AThymus
  2. BOesophagus
  3. CAscending aorta
  4. DHeart
3.Human physiologyMedium

What is the normal pH range of arterial blood?

  1. A7.00 to 7.20
  2. B7.35 to 7.45
  3. C7.50 to 7.65
  4. D6.80 to 7.00
4.Human physiologyHard

Why is severe hyperkalaemia dangerous for the heart?

  1. AIt speeds up the SA node until tachycardia causes fainting
  2. BIt hyperpolarises cardiac cells, so they can never fire
  3. CIt depolarises cardiac cells, inactivating sodium channels and causing arrhythmias
  4. DIt blocks the binding of calcium to troponin
5.MicrobiologyMedium

In the chain of infection, what is the "reservoir"?

  1. AThe place where the pathogen normally lives and multiplies
  2. BThe route by which the pathogen leaves the infected host's body
  3. CThe way the pathogen enters a new host
  4. DThe person who is most at risk of infection
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 multiply very fast inside the gut and invade the intestinal wall
  3. CThe immune system reacts to the bacteria within minutes
  4. DThe bacteria invade the bloodstream immediately
7.PharmacologyMedium

Which sign is typical of opioid toxicity?

  1. AHigh body temperature
  2. BFast, deep breathing
  3. CWidely dilated pupils
  4. DPinpoint pupils
8.PharmacologyHard

Why do infants absorb more of a topical corticosteroid than adults?

  1. ATheir skin contains no blood vessels
  2. BInfants do not absorb topical drugs at all
  3. CTheir liver changes the cream into a much stronger form
  4. DThey have more skin area per kilogram and thinner skin
9.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 12 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 12 mmol/L
PaCO₂ = mmHg
10.Arterial blood gas interpretationHard

Practice values: Na⁺ 140, Cl⁻ 90 and HCO₃⁻ 15 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.

Na⁺ 140 mmol/LCl⁻ 90 mmol/LHCO₃⁻ 15 mmol/L
delta ratio =
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVatrial fibrillationaccelerated junctional rhythmsupraventricular tachycardia (SVT)ventricular 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 fibrillation
  2. 2accelerated junctional rhythm
  3. 3supraventricular tachycardia (SVT)
  4. 4ventricular tachycardia
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVfirst-degree AV blockthird-degree (complete) AV blocksecond-degree AV block type I (Wenckebach)second-degree AV block type II

This lead II strip shows a conduction problem between the atria and the ventricles. 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. 1first-degree AV block
  2. 2third-degree (complete) AV block
  3. 3second-degree AV block type I (Wenckebach)
  4. 4second-degree AV block type II
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment109241350abcontrol277433710cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 350 patients received a new treatment and 710 received the control treatment. The table shows how many in each group had the outcome (an unwanted event such as a stroke). Find the number needed to treat NNT to prevent one event. Round up to a whole number of patients.

treatment: 109/350control: 277/710
NNT =
14.Evidence-based practice statisticsHard
CER29%EER?RRR 50%

Practice exercise (made-up values, not clinical guidance). A treatment reduces the risk of an event by 50% in relative terms (RRR = 50%). In a patient group the risk without treatment (CER) is 29% 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 = 50%CER = 29%
NNT =

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: B · 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

B · Oesophagus
3.Human physiology

Answer: B · 7.35 to 7.45

Why this is the answer

Arterial pH is normally 7.35–7.45. Below 7.35 is acidaemia and above 7.45 alkalaemia.

Answer

B · 7.35 to 7.45
4.Human physiology

Answer: C · It depolarises cardiac cells, inactivating sodium channels and causing arrhythmias

Why this is the answer

High extracellular potassium makes the resting potential less negative. Many fast sodium channels then become inactivated, slowing conduction and risking fatal arrhythmias.

Answer

C · It depolarises cardiac cells, inactivating sodium channels and causing arrhythmias
5.Microbiology

Answer: A · The place where the pathogen normally lives and multiplies

Why this is the answer

The chain of infection links the agent, reservoir, portal of exit, mode of transmission, portal of entry and susceptible host. Breaking any link stops transmission.

Answer

A · The place where the pathogen normally lives and multiplies
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: D · Pinpoint pupils

Why this is the answer

Opioid toxicity classically causes pinpoint pupils, slow or shallow breathing and reduced consciousness. Naloxone reverses these effects.

Answer

D · Pinpoint pupils
8.Pharmacology

Answer: D · They have more skin area per kilogram and thinner skin

Why this is the answer

Infants have a high surface area-to-weight ratio and a thinner skin barrier, so topical drugs reach higher systemic levels. Nappies can act as an occlusive dressing and increase absorption further.

Answer

D · They have more skin area per kilogram and thinner skin
9.Arterial blood gas interpretation

Answer: PaCO₂ = 26 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 = 1.5·12 + 8 = 26 mmHg
range: 24–28 mmHg

Answer

PaCO₂ = 26 mmHg
10.Arterial blood gas interpretation

Answer: delta ratio = 2.556

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 = 140 − (90 + 15) = 35

Delta ratio

(35 − 12)/(24 − 15) = 23/9 = 2.556

Answer

delta ratio = 2.556

Above 2: an added metabolic alkalosis.

11.ECG rhythm strip interpretation

Answer: supraventricular tachycardia (SVT)

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. Narrow-complex tachycardia and pauses: supraventricular tachycardia (SVT) is a regular tachycardia at about 150–250/min with narrow QRS complexes; the P waves are usually not visible because they are hidden in the QRS complex or the T wave. Sinus tachycardia in an adult at rest is usually below about 150/min and has a visible P wave before every QRS; atrial flutter with 2:1 conduction often runs at about 150/min and shows sawtooth waves. In sinus arrest the sinus node stops firing for a moment: a pause with no P wave and no QRS whose length is not a whole number of P–P cycles (a pause of exactly two or three cycles points to sinus exit block instead).

Five steps

1. Rate: R–R = 6 small boxes, 1500 ÷ 6 ≈ 250 per minute.
2. Rhythm: regular, every R–R is 0.24 s.
3. P waves: none visible; at this rate they are hidden in the QRS complexes or the T waves.
4. PR interval: not measurable.
5. QRS: 0.06 s, narrow (below 0.12 s), so the rhythm starts above the ventricles.

Interpretation

supraventricular tachycardia (SVT)

Answer

supraventricular tachycardia (SVT)
12.ECG rhythm strip interpretation

Answer: second-degree AV block type II

AV blocks: march out the P waves and check which ones are followed by a QRS. First-degree: every P conducted, PR constant and above 0.20 s. Second-degree type I (Mobitz I, Wenckebach): the PR lengthens from beat to beat until one P wave is not conducted, then the cycle starts again (group beating). Second-degree type II (Mobitz II): the PR of the conducted beats stays constant, and P waves are suddenly not conducted; the QRS is often wide. Third-degree (complete) block: P waves and QRS complexes are each regular but independent, the PR varies at random and the atrial rate is faster than the escape rate (junctional 40–60/min with a narrow QRS, ventricular 20–40/min with a wide QRS). A 2:1 block cannot be called type I or type II from one strip.

Five steps

1. Rate: 6 QRS complexes in 6 s, × 10 = 60 per minute.
2. Rhythm: the P waves are regular; R–R is regular except for a long pause where a QRS is missing.
3. P waves: upright and regular (P–P 0.84 s, 71 per minute); one P in every 4 is not followed by a QRS.
4. PR interval: constant at 0.16 s in the conducted beats.
5. QRS: 0.14 s, wide (0.12 s or more).

Interpretation

second-degree AV block type II

Answer

second-degree AV block type II

Type II and third-degree blocks are the ones that can suddenly progress, so textbooks rank them as more serious than type I.

13.Evidence-based practice statistics

Answer: NNT = 13

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 = 109/350 = 0.3114
CER = 277/710 = 0.3901

Number needed to treat

ARR = 0.3901 − 0.3114 = 0.07871
NNT = 1/0.07871 = 12.7 → 13

Answer

NNT = 13

Treating 13 patients prevents about one event.

14.Evidence-based practice statistics

Answer: NNT = 7

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 = 0.29·0.5 = 0.145

Number needed to treat

NNT = 1/0.145 = 6.897 → 7

Answer

NNT = 7

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

ExamProblems · examproblems.com/courses/medical-sciences