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 structure produces most of the cerebrospinal fluid?

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

During contraction of a skeletal muscle sarcomere, which band stays the same length?

  1. AA band
  2. BI band
  3. CThe whole sarcomere
  4. DH zone
4.Human physiologyHard

Which mechanism mainly creates the concentration gradient in the medulla of the kidney?

  1. AADH acting on the descending limb
  2. BGlomerular filtration
  3. CSecretion of urea into the proximal tubule
  4. DThe countercurrent multiplier of the loop of Henle
5.MicrobiologyMedium

Toxoplasma gondii is a risk in pregnancy. Which advice reduces exposure?

  1. AAvoid contact with dogs
  2. BAvoid all fruit and vegetables
  3. CAvoid swimming pools and all other public bathing areas
  4. DAvoid cleaning cat litter and avoid undercooked meat
6.MicrobiologyHard

Why are penicillins ineffective against Mycoplasma pneumoniae?

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

A patient wants to stop paroxetine suddenly. What should the nurse explain?

  1. AStopping suddenly causes dangerous low blood sugar
  2. BStopping suddenly causes the drug to work better for a while
  3. CIt can be stopped at any time, as antidepressants cause no withdrawal effects
  4. DIt can cause dizziness, "electric shock" feelings and irritability
8.PharmacologyHard

Why are patients on long-acting nitrates advised to have a nitrate-free period of several hours each day?

  1. ATo prevent tolerance to the nitrate
  2. BTo let the liver recover from toxicity
  3. CTo reduce the risk of bleeding
  4. DTo avoid nitrate accumulation in fat tissue
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

At sea level, a practice gas taken on 30% oxygen shows PaO₂ 73 mmHg (9.7 kPa) and PaCO₂ 29 mmHg (3.9 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 30%PaO₂ 73 mmHg (9.7 kPa)PaCO₂ 29 mmHg (3.9 kPa)
A–a gradient = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVfirst-degree AV blocknormal sinus rhythmjunctional 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. 1first-degree AV block
  2. 2normal sinus rhythm
  3. 3junctional rhythm
  4. 4sinus tachycardia
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mV

This lead II strip shows second-degree AV block type I (Wenckebach). Measure the PR interval of the last conducted beat before a non-conducted P wave (the longest PR), in seconds.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
longest PR = s
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment31249280abcontrol118302420cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 280 patients received a new treatment and 420 received the control treatment. The table shows how many in each group had the outcome (an unwanted event such as a stroke). Find the number needed to treat NNT to prevent one event. Round up to a whole number of patients.

treatment: 31/280control: 118/420
NNT =
14.Evidence-based practice statisticsHard
p (%)PPV (%)3%PPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 76% and a specificity of 89%. It is used in a population where the prevalence is 3%. Find the positive predictive value PPV as a percentage. Round to one decimal place.

Se = 76%Sp = 89%p = 3%
PPV = %

3Solutions

1.Human anatomy

Answer: D · Choroid plexus

Why this is the answer

The choroid plexus in the ventricles secretes most CSF. CSF is reabsorbed into venous blood through the arachnoid granulations.

Answer

D · Choroid plexus
2.Human anatomy

Answer: C · 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

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

Answer: A · A band

Why this is the answer

In the sliding filament model, filaments slide past each other without shortening. The A band (myosin length) stays the same while the I band and H zone shorten.

Answer

A · A band
4.Human physiology

Answer: D · The countercurrent multiplier of the loop of Henle

Why this is the answer

The ascending limb actively transports NaCl into the interstitium without letting water follow, and the countercurrent flow multiplies this into a steep gradient that ADH then uses to concentrate urine.

Answer

D · The countercurrent multiplier of the loop of Henle
5.Microbiology

Answer: D · Avoid cleaning cat litter and avoid undercooked meat

Why this is the answer

Toxoplasma oocysts are shed in cat faeces and cysts are found in undercooked meat. Infection during pregnancy can damage the fetal brain and eyes.

Answer

D · Avoid cleaning cat litter and avoid undercooked meat
6.Microbiology

Answer: D · 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

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

Answer: D · It can cause dizziness, "electric shock" feelings and irritability

Why this is the answer

Antidepressant discontinuation syndrome is common with short half-life drugs such as paroxetine and venlafaxine. The dose is tapered gradually under supervision.

Answer

D · It can cause dizziness, "electric shock" feelings and irritability
8.Pharmacology

Answer: A · To prevent tolerance to the nitrate

Why this is the answer

Tolerance to nitrates develops quickly with constant levels. An asymmetric dosing schedule or removing patches overnight keeps them effective.

Answer

A · To prevent tolerance to the nitrate
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: A–a gradient = 104.7 mmHg

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.

Alveolar oxygen

PAO₂ = 0.3·713 − 29/0.8 = 213.9 − 36.25 = 177.7 mmHg

Gradient

A–a = 177.7 − 73 = 104.7 mmHg

Answer

A–a gradient = 104.7 mmHg
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 = 23 small boxes, 1500 ÷ 23 ≈ 65 per minute.
2. Rhythm: regular, every R–R is 0.92 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.24 s, constant, longer than 0.20 s.
5. QRS: 0.08 s, narrow (below 0.12 s).

Interpretation

first-degree AV block

Answer

first-degree AV block
12.ECG rhythm strip interpretation

Answer: longest PR = 0.38 s

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.

March out the P waves

P–P = 0.96 s, regular; one P wave in every 4 is not conducted

PR in each group

PR₁ = 0.18 s, PR₂ = 0.30 s, PR₃ = 0.38 s

Answer

longest PR = 0.38 s

The biggest step in PR comes between the first and second beats of a group; later steps are smaller, which is why the R–R intervals shorten before the pause.

13.Evidence-based practice statistics

Answer: NNT = 6

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.

Event rates

EER = 31/280 = 0.1107
CER = 118/420 = 0.281

Number needed to treat

ARR = 0.281 − 0.1107 = 0.1702
NNT = 1/0.1702 = 5.874 → 6

Answer

NNT = 6

Treating 6 patients prevents about one event.

14.Evidence-based practice statistics

Answer: PPV = 17.6 %

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.

True and false positives (per person)

Se·p = 0.76·0.03 = 0.0228
(1 − Sp)·(1 − p) = 0.11·0.97 = 0.1067

Positive predictive value

PPV = 0.0228/(0.0228 + 0.1067) = 0.1761 ≈ 17.6%

Answer

PPV = 17.6%

The lower the prevalence, the lower the PPV of the same test.

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