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

The rotator cuff consists of supraspinatus, infraspinatus, teres minor and which other muscle?

  1. ASubscapularis
  2. BTeres major
  3. CDeltoid
  4. DLatissimus dorsi
2.Human anatomyHard

A pituitary tumour grows upwards and causes loss of both outer (temporal) halves of the visual field. Where is the visual pathway compressed?

  1. ALeft optic tract
  2. BRight optic nerve
  3. COptic chiasm
  4. DOccipital cortex
3.Human physiologyMedium

How does glucagon raise blood glucose?

  1. AIt slows glucose absorption from the gut
  2. BIt blocks insulin receptors on fat cells
  3. CIt stimulates glycogen breakdown and gluconeogenesis in the liver
  4. DIt stimulates glucose uptake by muscle
4.Human physiologyHard

Hodgkin and Huxley's classic studies of the ionic basis of the action potential used which preparation?

  1. AThe squid giant axon
  2. BThe frog sciatic nerve–muscle preparation
  3. CThe cat spinal cord
  4. DCultured human cortical neurons
5.MicrobiologyMedium

What is endotoxin?

  1. AThe lipopolysaccharide in the outer membrane of Gram-negative bacteria
  2. BA toxin produced only inside human cells
  3. CA protein toxin secreted by Gram-positive bacteria into the surrounding tissue
  4. DA toxin made by fungi in damp buildings
6.MicrobiologyHard

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

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

Ipratropium is a bronchodilator used in COPD. How does it work?

  1. AIt reduces inflammation like a corticosteroid
  2. BIt blocks muscarinic receptors in airway smooth muscle
  3. CIt stimulates beta-2 adrenergic receptors in the airways
  4. DIt blocks leukotriene receptors
8.PharmacologyHard

A patient with latent tuberculosis feels well and is not infectious. Why is treatment such as isoniazid still offered?

  1. ATo produce a negative skin test quickly
  2. BTo prevent progression to active TB later
  3. CTo stop the patient spreading TB at the moment
  4. DTo cure an active lung infection
9.Arterial blood gas interpretationMedium

Practice values: Na⁺ 148 mmol/L, glucose 31.8 mmol/L and urea 21.2 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 148 mmol/Lglucose 31.8 mmol/Lurea 21.2 mmol/L
Osm = mOsm/kg
10.Arterial blood gas interpretationHard
pH7.357.457.18PaCO₂mmHg354578HCO₃⁻mmol/L222628acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.18, PaCO₂ 78 mmHg (10.4 kPa), HCO₃⁻ 28 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 7.18PaCO₂ 78 mmHg (10.4 kPa)HCO₃⁻ 28 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 sinus rhythm with one pause. Measure the pause, the R–R interval across it, in seconds.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
pause = s
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mV

This lead II strip shows an AV block, so the atria and the ventricles beat at different rates. Measure the P–P interval and find the atrial rate in beats per minute (1500 method, whole number).

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
atrial rate = bpm
13.Evidence-based practice statisticsMedium
casescontrolsexposed5176abnot exposed79464cd

Practice exercise (made-up values, not clinical guidance). A case-control study compares 130 patients with a disease (cases) and 540 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 = 51b = 76c = 79d = 464
OR =
14.Evidence-based practice statisticsHard
p (%)NPV (%)5%NPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 79% and a specificity of 94%. It is used in a population where the prevalence is 5%. Find the negative predictive value NPV as a percentage. Round to one decimal place.

Se = 79%Sp = 94%p = 5%
NPV = %

3Solutions

1.Human anatomy

Answer: A · Subscapularis

Why this is the answer

SITS: supraspinatus, infraspinatus, teres minor and subscapularis. Teres major is close by but is not part of the cuff.

Answer

A · Subscapularis
2.Human anatomy

Answer: C · Optic chiasm

Why this is the answer

Bitemporal hemianopia results from compression of the crossing nasal fibres at the optic chiasm, which lies directly above the pituitary gland.

Answer

C · Optic chiasm
3.Human physiology

Answer: C · It stimulates glycogen breakdown and gluconeogenesis in the liver

Why this is the answer

Glucagon from alpha cells acts on the liver to break down glycogen and make new glucose from non-carbohydrate sources.

Answer

C · It stimulates glycogen breakdown and gluconeogenesis in the liver
4.Human physiology

Answer: A · The squid giant axon

Why this is the answer

The squid giant axon is up to about 1 mm wide, so voltage-clamp electrodes could be inserted. This showed that sodium inflow and potassium outflow produce the action potential.

Answer

A · The squid giant axon
5.Microbiology

Answer: A · The lipopolysaccharide in the outer membrane of Gram-negative bacteria

Why this is the answer

Endotoxin is lipid A of lipopolysaccharide. It triggers strong immune responses with fever and, in large amounts, septic shock.

Answer

A · The lipopolysaccharide in the outer membrane of Gram-negative bacteria
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: B · It blocks muscarinic receptors in airway smooth muscle

Why this is the answer

Ipratropium is an inhaled antimuscarinic. It blocks vagally mediated bronchoconstriction and mucus secretion, which is especially useful in COPD.

Answer

B · It blocks muscarinic receptors in airway smooth muscle
8.Pharmacology

Answer: B · To prevent progression to active TB later

Why this is the answer

People with latent TB carry dormant bacteria that can reactivate, especially if immunity weakens. Treatment reduces the risk of active disease, which would be infectious.

Answer

B · To prevent progression to active TB later
9.Arterial blood gas interpretation

Answer: Osm = 349 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 = 2·148 + 31.8 + 21.2 = 349 ≈ 349 mOsm/kg

Answer

Osm = 349 mOsm/kg
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 + 1·3.8 = 27.8 mmol/L
chronic: 24 + 3.5·3.8 = 37.3 mmol/L

Compare

measured: 28 mmol/L → acute

Answer

acute
11.ECG rhythm strip interpretation

Answer: pause = 1.68 s

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).

Measure

42 small boxes from R to R across the pause

Convert

pause = 42 × 0.04 s = 1.68 s

Compare with P–P

1.68 ÷ 0.72 ≈ 2.3 P–P cycles, not a whole number

Answer

pause = 1.68 s

No P wave appears in the pause, and the pause is not a whole number of P–P cycles: sinus arrest. A pause of exactly two or three cycles would point to sinus exit block.

12.ECG rhythm strip interpretation

Answer: atrial rate = 100 bpm

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.

Atrial rate

P–P = 15 small boxes = 0.60 s → 1500 ÷ 15 = 100 ≈ 100 per minute

Ventricular rate

R–R = 34 small boxes = 1.36 s → 1500 ÷ 34 = 44.12 ≈ 44 per minute

Answer

atrial rate = 100 bpm

Answer

atrial rate = 100 bpm

Third-degree block with a narrow-complex junctional escape (usually 40–60 per minute).

13.Evidence-based practice statistics

Answer: OR = 3.94

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: 51/79 = 0.6456
controls: 76/464 = 0.1638

Odds ratio

OR = (51·464)/(76·79) = 3.941 ≈ 3.94

Answer

OR = 3.94

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

14.Evidence-based practice statistics

Answer: NPV = 98.8 %

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 negatives (per person)

Sp·(1 − p) = 0.94·0.95 = 0.893
(1 − Se)·p = 0.21·0.05 = 0.0105

Negative predictive value

NPV = 0.893/(0.893 + 0.0105) = 0.9884 ≈ 98.8%

Answer

NPV = 98.8%

ExamProblems · examproblems.com/courses/medical-sciences