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 nerve supplies the diaphragm?

  1. AVagus nerve
  2. BPhrenic nerve
  3. CAccessory nerve
  4. DIntercostal nerves
2.Human anatomyHard

After a stroke, a patient speaks fluently but uses meaningless words and cannot understand speech. Where is the lesion most likely to be?

  1. AInferior frontal gyrus of the dominant hemisphere
  2. BPosterior superior temporal gyrus of the dominant hemisphere
  3. CCerebellar hemisphere
  4. DPrecentral gyrus of the non-dominant hemisphere
3.Human physiologyMedium

Cardiac output equals heart rate multiplied by:

  1. AEjection fraction
  2. BStroke volume
  3. CPeripheral resistance
  4. DBlood pressure
4.Human physiologyHard

Why does a deep sea diver risk decompression sickness when surfacing quickly?

  1. AOxygen becomes toxic at the surface
  2. BThe lungs collapse when the pressure falls
  3. CNitrogen dissolved at high pressure forms bubbles as the pressure falls
  4. DCarbon dioxide cannot leave the lungs fast enough
5.MicrobiologyMedium

Pneumocystis jirovecii pneumonia in a person with advanced HIV is an example of:

  1. AAn opportunistic infection
  2. BA food-borne infection
  3. CA vector-borne infection
  4. DA zoonotic infection
6.MicrobiologyHard

Why are penicillins ineffective against Mycoplasma pneumoniae?

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

Which patient should usually not use the combined oral contraceptive pill?

  1. AA 25-year-old woman with heavy periods
  2. BA 22-year-old non-smoker with acne
  3. CA 38-year-old woman who smokes 20 cigarettes a day
  4. DA 30-year-old non-smoker with no medical problems
8.PharmacologyHard

A patient receives high-dose IV aciclovir for herpes encephalitis. Which nursing action reduces the main risk to the kidneys?

  1. AKeep the patient well hydrated and give the infusion slowly
  2. BRestrict oral and IV fluids to prevent brain swelling
  3. CGive the infusion as a rapid push
  4. DGive a loop diuretic before each dose
9.Arterial blood gas interpretationMedium

Practice values: Na⁺ 145 mmol/L, glucose 15.3 mmol/L and urea 3.3 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 145 mmol/Lglucose 15.3 mmol/Lurea 3.3 mmol/L
Osm = mOsm/kg
10.Arterial blood gas interpretationHard
pH7.357.457.31PaCO₂mmHg354579HCO₃⁻mmol/L222638acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.31, PaCO₂ 79 mmHg (10.5 kPa), HCO₃⁻ 38 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 7.31PaCO₂ 79 mmHg (10.5 kPa)HCO₃⁻ 38 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/mVsinus tachycardiasupraventricular tachycardia (SVT)ventricular tachycardiatorsades de pointes

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. 1sinus tachycardia
  2. 2supraventricular tachycardia (SVT)
  3. 3ventricular tachycardia
  4. 4torsades de pointes
13.Evidence-based practice statisticsMedium
casescontrolsexposed4058abnot exposed240172cd

Practice exercise (made-up values, not clinical guidance). A case-control study compares 280 patients with a disease (cases) and 230 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 = 40b = 58c = 240d = 172
OR =
14.Evidence-based practice statisticsHard
CER10%EER?RRR 31%

Practice exercise (made-up values, not clinical guidance). A treatment reduces the risk of an event by 31% in relative terms (RRR = 31%). In a patient group the risk without treatment (CER) is 10% 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 = 31%CER = 10%
NNT =

3Solutions

1.Human anatomy

Answer: B · Phrenic nerve

Why this is the answer

The phrenic nerve (roots C3–C5) is the motor supply to the diaphragm. High cervical cord injury above C3 therefore stops spontaneous breathing.

Answer

B · Phrenic nerve
2.Human anatomy

Answer: B · Posterior superior temporal gyrus of the dominant hemisphere

Why this is the answer

This is Wernicke's (receptive) aphasia, caused by damage to Wernicke's area in the posterior superior temporal gyrus. Broca's area in the inferior frontal gyrus causes non-fluent aphasia.

Answer

B · Posterior superior temporal gyrus of the dominant hemisphere
3.Human physiology

Answer: B · Stroke volume

Why this is the answer

CO = HR × SV. At rest about 70 beats/min × 70 mL ≈ 5 L/min.

Answer

B · Stroke volume
4.Human physiology

Answer: C · Nitrogen dissolved at high pressure forms bubbles as the pressure falls

Why this is the answer

At depth more nitrogen dissolves in the tissues. If pressure falls too fast it comes out of solution as bubbles in tissues and blood, causing "the bends".

Answer

C · Nitrogen dissolved at high pressure forms bubbles as the pressure falls
5.Microbiology

Answer: A · An opportunistic infection

Why this is the answer

Opportunistic infections take advantage of a weakened immune system. In HIV they become common when the CD4 count falls to low levels.

Answer

A · An opportunistic infection
6.Microbiology

Answer: B · 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

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

Answer: C · A 38-year-old woman who smokes 20 cigarettes a day

Why this is the answer

Smoking over the age of 35 greatly increases the risk of myocardial infarction and stroke with combined hormonal contraception. Progestogen-only or non-hormonal methods are preferred.

Answer

C · A 38-year-old woman who smokes 20 cigarettes a day
8.Pharmacology

Answer: A · Keep the patient well hydrated and give the infusion slowly

Why this is the answer

Aciclovir can crystallise in the tubules and cause acute kidney injury. Good hydration, slow infusion and monitoring of kidney function reduce this risk.

Answer

A · Keep the patient well hydrated and give the infusion slowly
9.Arterial blood gas interpretation

Answer: Osm = 309 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 = 2·145 + 15.3 + 3.3 = 308.6 ≈ 309 mOsm/kg

Answer

Osm = 309 mOsm/kg
10.Arterial blood gas interpretation

Answer: chronic

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 + 1·3.9 = 27.9 mmol/L
chronic: 24 + 3.5·3.9 = 37.65 mmol/L

Compare

measured: 38 mmol/L → chronic

Answer

chronic
11.ECG rhythm strip interpretation

Answer: pause = 1.84 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

46 small boxes from R to R across the pause

Convert

pause = 46 × 0.04 s = 1.84 s

Compare with P–P

1.84 ÷ 0.80 ≈ 2.3 P–P cycles, not a whole number

Answer

pause = 1.84 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: ventricular tachycardia

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: R–R = 10 small boxes, 1500 ÷ 10 ≈ 150 per minute.
2. Rhythm: regular, every R–R is 0.40 s.
3. P waves: none identifiable.
4. PR interval: not measurable.
5. QRS: 0.14 s, wide (0.12 s or more).

Interpretation

ventricular tachycardia

Answer

ventricular tachycardia

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

13.Evidence-based practice statistics

Answer: OR = 0.49

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: 40/240 = 0.1667
controls: 58/172 = 0.3372

Odds ratio

OR = (40·172)/(58·240) = 0.4943 ≈ 0.49

Answer

OR = 0.49

OR below 1: exposure is less common among the cases, which suggests a protective effect.

14.Evidence-based practice statistics

Answer: NNT = 33

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 = 0.1·0.31 = 0.031

Number needed to treat

NNT = 1/0.031 = 32.26 → 33

Answer

NNT = 33

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

ExamProblems · examproblems.com/courses/medical-sciences