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 two regions of the adult spine normally show a lordosis (curve concave towards the back)?

  1. AThoracic and sacral
  2. BCervical and lumbar
  3. CThoracic and lumbar
  4. DCervical and thoracic
2.Human anatomyHard

Why can an inflamed gallbladder that irritates the diaphragm cause pain at the tip of the right shoulder?

  1. AThe gallbladder is attached to the right clavicle
  2. BBile travels up the lymphatics to the shoulder
  3. CThe vagus nerve supplies the skin of the shoulder
  4. DThe phrenic nerve shares spinal segments C3–C5 with the skin of the shoulder
3.Human physiologyMedium

Which receptor is stimulated when the patellar tendon is tapped in the knee-jerk reflex?

  1. ANociceptor
  2. BGolgi tendon organ
  3. CMuscle spindle
  4. DPacinian corpuscle
4.Human physiologyHard

In pernicious anaemia, autoimmune destruction of gastric parietal cells leads to anaemia because:

  1. AIntrinsic factor is lost, so vitamin B12 is not absorbed
  2. BGastrin is lost, so the bone marrow is no longer stimulated
  3. CPepsin is lost, so haemoglobin cannot be made
  4. DAcid is lost, so iron is never absorbed in any form
5.MicrobiologyMedium

Which bacterium causes whooping cough (pertussis)?

  1. AHaemophilus influenzae
  2. BCorynebacterium diphtheriae
  3. CBordetella pertussis
  4. DMycoplasma pneumoniae
6.MicrobiologyHard

Primary syphilis typically presents with:

  1. AA widespread rash on the palms and soles
  2. BA painless ulcer (chancre) at the site of infection
  3. CA painful cluster of small blisters on the genitals or the mouth
  4. DDamage to the heart and brain
7.PharmacologyMedium

In which patient is bupropion contraindicated?

  1. AA patient with high blood cholesterol and a family history of it
  2. BA patient with a seizure disorder or an eating disorder
  3. CA patient who wants to stop smoking
  4. DA patient with seasonal allergies
8.PharmacologyHard

A patient with asthma starts timolol eye drops for glaucoma and soon becomes wheezy. What is the most likely explanation?

  1. ATimolol activates histamine receptors in the lungs
  2. BThe eye drops contain an allergen that causes hay fever and asthma
  3. CThe wheeze is unrelated to the eye drops
  4. DTimolol is absorbed and blocks beta-2 receptors in the airways
9.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 29 mmHg (3.9 kPa). Use the rule that in chronic respiratory alkalosis HCO₃⁻ falls by 5 mmol/L for every 10 mmHg that PaCO₂ is below 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 29 mmHg (3.9 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
10.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 33 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 33 mmol/L
PaCO₂ = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVsinus bradycardiajunctional rhythmnormal sinus rhythmsinus 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. 1sinus bradycardia
  2. 2junctional rhythm
  3. 3normal sinus rhythm
  4. 4sinus tachycardia
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVatrial fibrillationtorsades de pointesatrial flutter, 4:1 conductionventricular fibrillation

Identify the rhythm on this lead II strip. 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. 2torsades de pointes
  3. 3atrial flutter, 4:1 conduction
  4. 4ventricular fibrillation
13.Evidence-based practice statisticsMedium
Se83%Sp86%LR+ = ?

Practice exercise (made-up values, not clinical guidance). A test has a sensitivity of 83% and a specificity of 86%. Find the positive likelihood ratio LR+. Round to two decimal places.

Se = 83%Sp = 86%
LR+ =
14.Evidence-based practice statisticsHard
testdisease presentdisease absenttotalpositive?negativetotal10 000

Practice exercise (made-up values, not clinical guidance). 10 000 people are screened with a test of sensitivity 84% and specificity 93%. The prevalence of the disease is 27%. How many positive results n₊ are expected in total?

N = 10 000p = 27%Se = 84%Sp = 93%
n₊ =

3Solutions

1.Human anatomy

Answer: B · Cervical and lumbar

Why this is the answer

The cervical and lumbar regions are lordotic (secondary curves). The thoracic and sacral regions are kyphotic (primary curves).

Answer

B · Cervical and lumbar
2.Human anatomy

Answer: D · The phrenic nerve shares spinal segments C3–C5 with the skin of the shoulder

Why this is the answer

Diaphragmatic irritation is carried by the phrenic nerve (C3–C5). The brain refers it to skin supplied by the same segments, via the supraclavicular nerves over the shoulder.

Answer

D · The phrenic nerve shares spinal segments C3–C5 with the skin of the shoulder
3.Human physiology

Answer: C · Muscle spindle

Why this is the answer

Tapping the tendon stretches quadriceps muscle spindles. Their afferents synapse directly on motor neurons in a monosynaptic reflex that contracts the muscle.

Answer

C · Muscle spindle
4.Human physiology

Answer: A · Intrinsic factor is lost, so vitamin B12 is not absorbed

Why this is the answer

Parietal cells secrete intrinsic factor, needed for B12 absorption in the terminal ileum. B12 deficiency impairs DNA synthesis and causes megaloblastic anaemia.

Answer

A · Intrinsic factor is lost, so vitamin B12 is not absorbed
5.Microbiology

Answer: C · 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

C · Bordetella pertussis
6.Microbiology

Answer: B · A painless ulcer (chancre) at the site of infection

Why this is the answer

Treponema pallidum causes a painless chancre in the primary stage. The secondary stage brings rash and systemic symptoms, and tertiary syphilis can damage the heart and nervous system. Painful blisters suggest herpes.

Answer

B · A painless ulcer (chancre) at the site of infection
7.Pharmacology

Answer: B · A patient with a seizure disorder or an eating disorder

Why this is the answer

Bupropion increases the risk of seizures, especially with bulimia or anorexia, where electrolyte disturbances are common. It is used for depression and as a smoking cessation aid.

Answer

B · A patient with a seizure disorder or an eating disorder
8.Pharmacology

Answer: D · Timolol is absorbed and blocks beta-2 receptors in the airways

Why this is the answer

Ophthalmic timolol is a non-selective beta blocker and can reach the circulation in amounts that cause bronchospasm or bradycardia. It is generally avoided in asthma.

Answer

D · Timolol is absorbed and blocks beta-2 receptors in the airways
9.Arterial blood gas interpretation

Answer: HCO₃⁻ = 18.5 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.

Change in PaCO₂

|29 − 40| = 11 mmHg → 1.1 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 − 5·1.1 = 18.5 mmol/L

Answer

HCO₃⁻ = 18.5 mmol/L
10.Arterial blood gas interpretation

Answer: PaCO₂ = 44.1 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.

Expected PaCO₂

0.7·33 + 21 = 44.1 mmHg

Answer

PaCO₂ = 44.1 mmHg

The rise has a limit: PaCO₂ rarely goes above about 55 mmHg from compensation alone.

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 = 32 small boxes, 1500 ÷ 32 ≈ 47 per minute.
2. Rhythm: regular, every R–R is 1.28 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.18 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: ventricular fibrillation

Ventricular rhythms: ventricular tachycardia is a run of three or more wide (0.12 s or more) complexes in a row at more than 100/min, usually 150–250/min, regular, without related P waves. Ventricular fibrillation is a chaotic, irregular waveform with no identifiable P waves, QRS complexes or T waves and no countable rate. Asystole is an almost flat line with no ventricular activity; a flat line is always confirmed by checking the patient, the leads and the gain and a second lead. In resuscitation guidelines VF and pulseless VT are the shockable rhythms and asystole is not.

Five steps

1. Rate: no countable ventricular rate.
2. Rhythm: chaotic, no repeating pattern.
3. P waves: none identifiable.
4. PR interval: not measurable.
5. QRS: no QRS complexes.

Interpretation

ventricular fibrillation

Answer

ventricular fibrillation

In resuscitation guidelines VF and pulseless VT are the shockable rhythms. This is identification practice only.

13.Evidence-based practice statistics

Answer: LR+ = 5.93

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.

Positive likelihood ratio

LR+ = 0.83/(1 − 0.86) = 5.929 ≈ 5.93

Answer

LR+ = 5.93
14.Evidence-based practice statistics

Answer: n₊ = 2779

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.

With and without the disease

10 000·0.27 = 2700
10 000 − 2700 = 7300

All positive results

TP = 2700·0.84 = 2268
FP = 7300·0.07 = 511
n₊ = 2268 + 511 = 2779

Answer

n₊ = 2779

Of the 2779 positives only 2268 have the disease (PPV 81.6%).

ExamProblems · examproblems.com/courses/medical-sciences