Medical Sciences: cram pack

Formula sheets, the key method steps for every topic and 14 practice problems, with full solutions at the back.

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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 valve lies between the left atrium and the left ventricle?

  1. AAortic valve
  2. BPulmonary valve
  3. CTricuspid valve
  4. DMitral (bicuspid) valve
2.Human anatomyHard

Injury to the common fibular (peroneal) nerve at the neck of the fibula typically causes:

  1. AWeak hip abduction
  2. BFoot drop
  3. CLoss of sensation on the sole of the foot
  4. DInability to flex the knee
3.Human physiologyMedium

Which ABO blood group has both anti-A and anti-B antibodies in the plasma?

  1. AGroup O
  2. BGroup B
  3. CGroup A
  4. DGroup AB
4.Human physiologyHard

Why can a patient with carbon monoxide poisoning have a normal PaO₂ but severe tissue hypoxia?

  1. ACO occupies haemoglobin binding sites, so oxygen content falls
  2. BCO blocks diffusion across the alveolar wall
  3. CCO stops oxygen from dissolving in plasma
  4. DCO lowers the barometric pressure in the alveoli
5.MicrobiologyMedium

Which bacterium causes whooping cough (pertussis)?

  1. ABordetella pertussis
  2. BCorynebacterium diphtheriae
  3. CMycoplasma pneumoniae
  4. DHaemophilus influenzae
6.MicrobiologyHard

Why are beta-lactamase inhibitors such as clavulanic acid combined with amoxicillin?

  1. AThey protect amoxicillin from bacterial enzymes that destroy it
  2. BThey kill bacteria by themselves through the cell membrane
  3. CThey slow the excretion of amoxicillin by the kidneys, raising its level
  4. DThey make amoxicillin active against viruses
7.PharmacologyMedium

Benzathine benzylpenicillin (penicillin G benzathine) is ordered. Which route is correct?

  1. AIntravenous push
  2. BDeep intramuscular only
  3. CIntravenous infusion over 30 minutes
  4. DSubcutaneous in the abdomen
8.PharmacologyHard

A toddler swallowed many of his mother's iron tablets. He has vomiting and bloody diarrhoea. Which drug may be used to bind iron?

  1. ADeferoxamine (desferrioxamine)
  2. BNaloxone
  3. CActivated charcoal given by mouth
  4. DAcetylcysteine
9.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 10 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

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

Practice values: Na⁺ 137, Cl⁻ 115, HCO₃⁻ 14 mmol/L and albumin 19 g/L. Find the albumin-corrected anion gap AGc = AG + 0.25·(40 − albumin).

Na⁺ 137 mmol/LCl⁻ 115 mmol/LHCO₃⁻ 14 mmol/Lalbumin 19 g/L
AGc = mmol/L
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mV

Measure the QT interval on this lead II strip, in seconds.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
QT = s
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVraterhythmP wavesPR intervalQRS duration

Interpret this lead II strip with the five steps in order: rate, rhythm, P waves, PR interval, QRS duration. At which step do you find the first abnormal finding? Click it.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
  1. 1rate
  2. 2rhythm
  3. 3P waves
  4. 4PR interval
  5. 5QRS duration
13.Evidence-based practice statisticsMedium
casescontrolsexposed214118abnot exposed116192cd

Practice exercise (made-up values, not clinical guidance). A case-control study compares 330 patients with a disease (cases) and 310 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 = 214b = 118c = 116d = 192
OR =
14.Evidence-based practice statisticsHard
CER39%EER?RRR 44%

Practice exercise (made-up values, not clinical guidance). A treatment reduces the risk of an event by 44% in relative terms (RRR = 44%). In a patient group the risk without treatment (CER) is 39% 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 = 44%CER = 39%
NNT =

3Solutions

1.Human anatomy

Answer: D · Mitral (bicuspid) valve

Why this is the answer

The mitral (bicuspid) valve separates the left atrium and left ventricle; the tricuspid valve does the same on the right side.

Answer

D · Mitral (bicuspid) valve
2.Human anatomy

Answer: B · Foot drop

Why this is the answer

The common fibular nerve supplies the dorsiflexors and evertors. Damage at the fibular neck causes foot drop and a high-stepping gait. The sole is supplied by the tibial nerve.

Answer

B · Foot drop
3.Human physiology

Answer: A · Group O

Why this is the answer

Group O people have no A or B antigens and make both anti-A and anti-B. Group AB has both antigens and neither antibody.

Answer

A · Group O
4.Human physiology

Answer: A · CO occupies haemoglobin binding sites, so oxygen content falls

Why this is the answer

CO binds haemoglobin far more strongly than oxygen and shifts the curve left. Dissolved O₂ (PaO₂) is normal, but total oxygen content and release to tissues drop sharply.

Answer

A · CO occupies haemoglobin binding sites, so oxygen content falls
5.Microbiology

Answer: A · 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

A · Bordetella pertussis
6.Microbiology

Answer: A · They protect amoxicillin from bacterial enzymes that destroy it

Why this is the answer

Beta-lactamases hydrolyse the beta-lactam ring. Clavulanic acid binds these enzymes, so amoxicillin stays active against beta-lactamase-producing bacteria.

Answer

A · They protect amoxicillin from bacterial enzymes that destroy it
7.Pharmacology

Answer: B · Deep intramuscular only

Why this is the answer

Benzathine penicillin is a depot suspension given deep IM. Accidental intravenous injection can cause cardiorespiratory arrest and death.

Answer

B · Deep intramuscular only
8.Pharmacology

Answer: A · Deferoxamine (desferrioxamine)

Why this is the answer

Iron poisoning can cause GI bleeding, shock, metabolic acidosis and liver failure. Deferoxamine chelates iron and is used in serious poisoning; activated charcoal does not bind iron.

Answer

A · Deferoxamine (desferrioxamine)
9.Arterial blood gas interpretation

Answer: PaCO₂ = 23 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 = 1.5·10 + 8 = 23 mmHg
range: 21–25 mmHg

Answer

PaCO₂ = 23 mmHg
10.Arterial blood gas interpretation

Answer: AGc = 13.25 mmol/L

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 = 137 − (115 + 14) = 8

Correction for albumin

8 + 0.25·(40 − 19) = 13.25 mmol/L

Answer

AGc = 13.25 mmol/L

Above about 12 after correction: a high anion gap.

11.ECG rhythm strip interpretation

Answer: QT = 0.44 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

11 small boxes from the start of the QRS to the end of the T wave

Convert

QT = 11 × 0.04 s = 0.44 s

Answer

QT = 0.44 s

A rough rule: at normal rates the QT should be less than half the R–R interval (here R–R = 0.88 s).

12.ECG rhythm strip interpretation

Answer: QRS duration

Five steps for every strip: 1. rate (300 or 1500 method, or the 6-second method if irregular); 2. rhythm: are the R–R intervals equal; 3. P waves: present, upright in lead II, one before every QRS and all alike; 4. PR interval: 0.12–0.20 s and constant; 5. QRS duration: below 0.12 s. Only after the five steps name the rhythm. Normal sinus rhythm passes all five: 60–100/min, regular, upright P before every QRS, PR 0.12–0.20 s, QRS below 0.12 s.

Five steps

1. Rate: R–R = 19 small boxes, 1500 ÷ 19 ≈ 79 per minute.
2. Rhythm: regular, every R–R is 0.76 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.16 s, constant, within 0.12–0.20 s.
5. QRS: 0.14 s, wide (0.12 s or more).

First abnormal step

QRS duration → sinus rhythm with wide QRS

Answer

QRS duration
13.Evidence-based practice statistics

Answer: OR = 3

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: 214/116 = 1.845
controls: 118/192 = 0.6146

Odds ratio

OR = (214·192)/(118·116) = 3.002 ≈ 3

Answer

OR = 3

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

14.Evidence-based practice statistics

Answer: NNT = 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.

Absolute risk reduction

ARR = 0.39·0.44 = 0.1716

Number needed to treat

NNT = 1/0.1716 = 5.828 → 6

Answer

NNT = 6

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

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