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 type of epithelium lines most of the trachea?

  1. APseudostratified ciliated columnar epithelium
  2. BTransitional epithelium
  3. CSimple cuboidal epithelium
  4. DStratified squamous epithelium
2.Human anatomyHard

Why does an inhaled foreign body more often lodge in the right main bronchus than the left?

  1. AThe right bronchus is wider, shorter and more vertical
  2. BThe right lung has stronger airflow due to the heart's position
  3. CThe left bronchus is closed by the epiglottis
  4. DThe right bronchus is narrower and more horizontal
3.Human physiologyMedium

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

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

Which transporter in the thick ascending limb of the loop of Henle is key to building the medullary concentration gradient?

  1. AThe Na⁺–K⁺–2Cl⁻ cotransporter (NKCC2)
  2. BThe epithelial sodium channel (ENaC)
  3. CThe sodium–glucose cotransporter (SGLT2)
  4. DAquaporin-2 water channels
5.MicrobiologyMedium

In the lysogenic cycle of a bacteriophage, what happens to the phage DNA?

  1. AIt is destroyed by the bacterium
  2. BIt leaves the cell through the pilus
  3. CIt is integrated into the bacterial chromosome as a prophage
  4. DIt is immediately used to make new phages that burst the cell
6.MicrobiologyHard

Why are penicillins ineffective against Mycoplasma pneumoniae?

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

A patient is starting olanzapine. Which monitoring is most important over the following months?

  1. AHearing tests and vision tests every month
  2. BINR and platelet count
  3. CPeak expiratory flow
  4. DWeight, blood glucose and blood lipids
8.PharmacologyHard

Codeine is converted to morphine by CYP2D6. What happens in a patient who is a CYP2D6 ultra-rapid metaboliser?

  1. ACodeine is excreted unchanged in the urine
  2. BCodeine is converted to an inactive compound only
  3. CCodeine gives almost no pain relief because little morphine is formed
  4. DMore morphine is formed, increasing the risk of opioid toxicity
9.Arterial blood gas interpretationMedium

Practice values: Na⁺ 145 mmol/L, glucose 24.7 mmol/L and urea 22.3 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 145 mmol/Lglucose 24.7 mmol/Lurea 22.3 mmol/L
Osm = mOsm/kg
10.Arterial blood gas interpretationHard
pH7.357.457.16PaCO₂mmHg354549HCO₃⁻mmol/L222617appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.16, PaCO₂ 49 mmHg (6.5 kPa), HCO₃⁻ 17 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.16PaCO₂ 49 mmHg (6.5 kPa)HCO₃⁻ 17 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVjunctional rhythmsinus tachycardiasinus bradycardiafirst-degree AV block

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. 1junctional rhythm
  2. 2sinus tachycardia
  3. 3sinus bradycardia
  4. 4first-degree AV block
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. The QRS complexes are regular: find the ventricular 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
ventricular rate = bpm
13.Evidence-based practice statisticsMedium
testdisease presentdisease absenttotalpositive68212280abnegative12318330cdtotal80530610

Practice exercise (made-up values, not clinical guidance). A new test was compared with the reference standard in a study (see the 2 × 2 table). Find the negative likelihood ratio LR−. Round to two decimal places.

a = 68b = 212c = 12d = 318
LR− =
14.Evidence-based practice statisticsHard
CER12%EER?RRR 32%

Practice exercise (made-up values, not clinical guidance). A treatment reduces the risk of an event by 32% in relative terms (RRR = 32%). In a patient group the risk without treatment (CER) is 12% 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 = 32%CER = 12%
NNT =

3Solutions

1.Human anatomy

Answer: A · Pseudostratified ciliated columnar epithelium

Why this is the answer

Respiratory epithelium is pseudostratified ciliated columnar with goblet cells. Mucus traps particles and cilia move it up towards the pharynx.

Answer

A · Pseudostratified ciliated columnar epithelium
2.Human anatomy

Answer: A · The right bronchus is wider, shorter and more vertical

Why this is the answer

The right main bronchus is wider, shorter and continues more directly in line with the trachea, so aspirated objects tend to fall into it.

Answer

A · The right bronchus is wider, shorter and more vertical
3.Human physiology

Answer: C · 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

C · Group O
4.Human physiology

Answer: A · The Na⁺–K⁺–2Cl⁻ cotransporter (NKCC2)

Why this is the answer

NKCC2 moves Na⁺, K⁺ and Cl⁻ out of the tubule into the interstitium without water, building the medullary gradient. Loop diuretics such as furosemide block it.

Answer

A · The Na⁺–K⁺–2Cl⁻ cotransporter (NKCC2)
5.Microbiology

Answer: C · It is integrated into the bacterial chromosome as a prophage

Why this is the answer

In lysogeny the phage genome integrates into the host chromosome and is copied with it. Later it may switch to the lytic cycle, making new phages and lysing the cell.

Answer

C · It is integrated into the bacterial chromosome as a prophage
6.Microbiology

Answer: A · 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

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

Answer: D · Weight, blood glucose and blood lipids

Why this is the answer

Olanzapine and several other atypical antipsychotics cause weight gain, insulin resistance and dyslipidaemia. Weight, waist size, glucose and lipids are checked regularly.

Answer

D · Weight, blood glucose and blood lipids
8.Pharmacology

Answer: D · More morphine is formed, increasing the risk of opioid toxicity

Why this is the answer

Ultra-rapid metabolisers convert more codeine to morphine, which can cause respiratory depression. Poor metabolisers form little morphine and get poor pain relief. This is a classic example of pharmacogenetics.

Answer

D · More morphine is formed, increasing the risk of opioid toxicity
9.Arterial blood gas interpretation

Answer: Osm = 337 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 + 24.7 + 22.3 = 337 ≈ 337 mOsm/kg

Answer

Osm = 337 mOsm/kg
10.Arterial blood gas interpretation

Answer: added respiratory acidosis

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

1.5·17 + 8 = 33.5 → 31.5–35.5 mmHg

Compare

measured: 49 mmHg → added respiratory acidosis

Answer

added respiratory acidosis
11.ECG rhythm strip interpretation

Answer: first-degree AV block

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 = 21 small boxes, 1500 ÷ 21 ≈ 71 per minute.
2. Rhythm: regular, every R–R is 0.84 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.34 s, constant, longer than 0.20 s.
5. QRS: 0.06 s, narrow (below 0.12 s).

Interpretation

first-degree AV block

Answer

first-degree AV block
12.ECG rhythm strip interpretation

Answer: ventricular rate = 54 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 = 20 small boxes = 0.80 s → 1500 ÷ 20 = 75 ≈ 75 per minute

Ventricular rate

R–R = 28 small boxes = 1.12 s → 1500 ÷ 28 = 53.57 ≈ 54 per minute

Answer

ventricular rate = 54 bpm

Answer

ventricular rate = 54 bpm

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

13.Evidence-based practice statistics

Answer: LR− = 0.25

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.

Sensitivity and specificity

Se = 68/80 = 0.85
Sp = 318/530 = 0.6

Negative likelihood ratio

LR− = (1 − 0.85)/0.6 = 0.25

Answer

LR− = 0.25
14.Evidence-based practice statistics

Answer: NNT = 27

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 = 0.12·0.32 = 0.0384

Number needed to treat

NNT = 1/0.0384 = 26.04 → 27

Answer

NNT = 27

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

ExamProblems · examproblems.com/courses/medical-sciences