Medical University of Lodz · oral exam practice

Medical University of Lodz Entrance Exam Practice Questions with Answers (2027)

The Medical University of Lodz's entrance exam is oral: about 30 minutes on Microsoft Teams, in English, before a two-person committee. You answer 12 questions: four in each of the two sciences you chose when you registered, two on socio-medical topics, one on your motivation and one on the Student Code of Ethics. Only four of the twelve have options to choose from; the other eight you answer aloud, and nobody prompts you if your answer is incomplete.

So this is a practice page to use out loud. For each of Biology, Chemistry, Physics and Mathematics there are two mock sets of two closed and two open questions, each open question with a model answer as you could say it and a guide to what earns 1, 2 and 3 points. Then come 17 socio-medical, motivation and Code of Ethics questions with outlines for building your own answer. To sit a whole exam, mix one: pick your two sciences, and the page builds a 12-question set with a 30-minute timer, reads each question aloud, and adds up your score out of 32.

Mix a timed mock exam

From MUL's own rules

How the oral exam is scored

The Medical University of Lodz entrance exam: 12 questions, 32 points (Ordinance 8/2026, §6)
Part	Questions	Points
Science 1 (your choice of Biology, Chemistry, Physics or Mathematics)	2 closed + 2 open	12 (closed 0 or 3 each, open 0-3 each)
Science 2 (your second choice)	2 closed + 2 open	12
Socio-medical topics	2 open	4 (0-2 each)
Motivation, predispositions and interests	1 open	2 (0-2)
The Student Code of Ethics	1 open	2 (0-2)
Total	12	32; the pass mark is 18

That is all MUL's rules say about marking: closed questions score 0 or 3, open science questions 0 to 3, and the four general questions 0 to 2 each (Ordinance 8/2026, §6). Candidates exempt from the science part (holders of a Polish school-leaving certificate and the other documents §7 lists, and PREMED graduates with an average of 4.0 or more) are given the 24 science points automatically, answer only the four general questions and need 5 of their 8 points.

MUL publishes no marking scheme and no answers to its Sample Questions. The guides below are IvyTest's way of using the official scales: a reasonable reading of what a committee looks for, not the committee's own criteria.

Open science questions, 0-3

0: no answer, or an answer that is wrong at its core.
1: some correct, relevant facts, but the main point is missing or there is a real error.
2: the core is correct and in order, with one gap or one imprecision.
3: complete, correct and organised, in the right terms, with the example or the working said aloud.

General questions, 0-2

0: no answer, an answer beside the question, or one that contradicts the Code or a patient's interest.
1: a relevant answer, but generic: a position with no reason, or reasons with no example.
2: a clear position, reasoned, with a specific example, and aware of the other side or of the patient.

Read in MUL's documents on 17 October 2026: Ordinance No. 8/2026: the exam's rules · Range of Knowledge: the official topic list · Sample Questions (2023, no answers) · Students Code of Ethics.

Mix your exam

A timed mock of the whole oral

Pick your two sciences and the page builds a 12-question exam in MUL's proportions, drawn from the questions below: two closed and two open questions in each science, two socio-medical, one motivation and one Code of Ethics question, with a 30-minute timer. Each question is read aloud; closed questions score themselves, and you score the open ones with the guide.

1. Pick the two sciences you chose (or will choose) when you register

I am exempt from the science part (a Polish school-leaving certificate or another document §7 lists, or MUL's PREMED with an average of 4.0 or more): give me the four general questions only.Read each question aloud, as the committee would (your browser's voice).

30 minutes · answer aloud, then score yourself with the guide

Practise with someone acting as the committee if you can: in the real exam two examiners listen, your camera and microphone stay on, and you may use a pen, a blank sheet, a calculator and a periodic table, each shown to the camera.

Science questions

Biology: two mock sets

Biology in the Range of Knowledge is 43 topics, from macromolecules and the cell through genetics and every body system to microbes, ecology and evolution, taught from Campbell Biology. Expect open questions that ask you to describe or compare a process.

Biology, mock set 1

Two closed questions (3 points or 0) and two open questions (0-3): 12 points, as in the exam.

Question 1

Biology · Cell Structure and Organelles · Foundation

Which of these structures is found in both prokaryotic and eukaryotic cells?

Show answer and explanation

Answer: C

Ribosomes are not membrane-bound, and every cell needs them to make proteins: prokaryotes have smaller 70S ribosomes, eukaryotes 80S ribosomes in the cytoplasm and on the rough ER (with 70S-type ribosomes inside mitochondria). A nucleus, mitochondria and a Golgi apparatus are membrane-bound organelles, which prokaryotes lack.

Question 2

Biology · Genetics and Molecular Biology · Standard

A man with an X-linked recessive disorder has children with a woman who neither has the disorder nor carries it. Which statement about their children is true?

Show answer and explanation

Answer: B

A father passes his X chromosome to every daughter and his Y chromosome to every son. Every daughter therefore receives his affected X and her mother's normal X: she is a carrier. Every son receives his mother's normal X, so no son is affected. Options A and D forget that sons never inherit their father's X.

Question 3 · open · 0-3 points

Cell Communication and the Cell Cycle

Compare mitosis and meiosis: what is each for, and how do their products differ?

Model spoken answer and marking guide

Mitosis is for growth, repair and asexual reproduction. It is one division that gives two daughter cells, each diploid and genetically identical to the parent cell, because the sister chromatids of each chromosome are separated.

Meiosis makes gametes. It is two divisions that give four haploid cells, each genetically different. In meiosis I the homologous chromosomes pair up and separate, which halves the chromosome number; in meiosis II the sister chromatids separate, as in mitosis.

The variation comes from two events in meiosis I: crossing over between homologous chromosomes in prophase I, and independent assortment of the pairs at metaphase I. Fertilisation then restores the diploid number.

What earns the points

0: no answer, or an answer that is wrong at its core.
1: One correct contrast, for example two cells against four, or diploid against haploid.
2: The purpose and the products of both are right, but the source of variation is missing or muddled.
3: Purpose, number and ploidy of the products, homologues versus chromatids separating, and crossing over and independent assortment as the source of variation.

Question 4 · open · 0-3 points

Genetics and Molecular Biology

What is a mutation? Distinguish a gene mutation from a chromosome mutation, with an example of each, and say what mutations mean for disease and for evolution.

Model spoken answer and marking guide

A mutation is a permanent change in the DNA sequence. A gene mutation changes one gene: a substitution, insertion or deletion of bases. A substitution can be silent, change one amino acid, as in sickle cell anaemia, where one base change replaces glutamic acid with valine in beta-globin, or create a stop codon. An insertion or deletion that is not a multiple of three shifts the reading frame.

A chromosome mutation changes the structure or number of whole chromosomes: deletions, duplications, inversions and translocations, or an extra or missing chromosome after non-disjunction. Trisomy 21, Down syndrome, is the classic example.

In disease, mutations cause inherited disorders and, when they accumulate in somatic cells, cancer. In evolution they are the original source of all genetic variation: most are neutral or harmful, but the few that help an organism survive and reproduce are spread by natural selection.

What earns the points

0: no answer, or an answer that is wrong at its core.
1: A correct definition, or one correct example, but no clear distinction between the two kinds.
2: Definition and the distinction with examples, but disease or evolution left out.
3: Definition, both kinds with a correct example each, and both consequences: disease (including cancer) and variation for natural selection.

Biology, mock set 2

Two closed questions (3 points or 0) and two open questions (0-3): 12 points, as in the exam.

Question 5

Biology · Human Anatomy and Physiology · Foundation

Which vessel carries oxygenated blood from the lungs to the heart?

Show answer and explanation

Answer: B

Arteries carry blood away from the heart and veins carry it towards it, whatever its oxygen content. The pulmonary veins bring oxygenated blood from the lungs to the left atrium; the pulmonary artery is the exception the other way, taking deoxygenated blood from the right ventricle to the lungs. The aorta leaves the left ventricle, and the superior vena cava returns deoxygenated blood from the upper body.

Question 6

Biology · Macromolecules and Enzymes · Standard

Which statement describes a competitive inhibitor of an enzyme?

Show answer and explanation

Answer: B

A competitive inhibitor resembles the substrate and competes with it for the active site, so enough extra substrate outcompetes it: the maximum rate is unchanged, but more substrate is needed to reach it. Binding elsewhere and changing the active site describes non-competitive (allosteric) inhibition; lowering activation energy is what the enzyme itself does.

Question 7 · open · 0-3 points

Human Anatomy and Physiology

Describe how a nephron forms urine.

Model spoken answer and marking guide

Urine is made in three steps. First, filtration: blood pressure in the glomerulus forces water and small solutes, such as glucose, amino acids, ions and urea, into Bowman's capsule. Cells and large proteins stay in the blood.

Second, reabsorption. In the proximal convoluted tubule nearly all the glucose and amino acids and most of the sodium and water go back into the blood. The loop of Henle builds a salt gradient in the medulla, which later lets water be drawn out. In the distal tubule and collecting duct, hormones fine-tune the rest: ADH makes the collecting duct more permeable to water, and aldosterone increases sodium reabsorption.

Third, secretion: substances such as hydrogen and potassium ions and some drugs are added to the tubule. What is left is urine: water, urea, creatinine and salts, normally with no glucose and no protein.

What earns the points

0: no answer, or an answer that is wrong at its core.
1: Names filtration, or the glomerulus, but cannot explain what happens in the tubule.
2: Filtration and reabsorption explained correctly, but no hormonal control or no secretion.
3: Filtration, reabsorption by segment, the loop of Henle's role, control by ADH or aldosterone, and what normal urine contains.

Question 8 · open · 0-3 points

Metabolism and Cellular Respiration

Outline glycolysis: where it happens, what goes in and comes out, and what happens to pyruvate with and without oxygen.

Model spoken answer and marking guide

Glycolysis happens in the cytoplasm and does not need oxygen. One glucose molecule, with six carbons, is split into two molecules of pyruvate, with three carbons each. Two ATP are used at the start and four are made, so the net gain is two ATP and two NADH.

With oxygen, pyruvate enters the mitochondria, is converted to acetyl-CoA and goes into the Krebs cycle; the NADH and FADH2 then feed the electron transport chain, where most of the ATP is made.

Without oxygen, in human muscle, pyruvate is reduced to lactate. That earns no extra ATP, but it regenerates NAD+, so glycolysis can keep going. Yeast makes ethanol and carbon dioxide instead.

What earns the points

0: no answer, or an answer that is wrong at its core.
1: Glucose to pyruvate, but the place, the yield or the fate of pyruvate is wrong or missing.
2: Place, inputs and products with the net yield, and one fate of pyruvate.
3: Place, the net two ATP and two NADH, the aerobic route into the mitochondria, and lactate in its purpose of regenerating NAD+.

Science questions

Chemistry: two mock sets

Chemistry follows the 17 chapters of Timberlake's Chemistry: An Introduction to General, Organic, and Biological Chemistry, from measurement and the mole through acids, bases and buffers to biomolecules and metabolism. Calculations come up, so say your working aloud.

Chemistry, mock set 1

Two closed questions (3 points or 0) and two open questions (0-3): 12 points, as in the exam.

Question 9

Chemistry · Acids, Bases and Equilibrium · Foundation

What is the pH of a 0.001 mol/L solution of hydrochloric acid at 25 °C?

Show answer and explanation

Answer: C

HCl is a strong acid and dissociates completely, so [H+] = 0.001 = 10^-3 mol/L, and pH = -log[H+] = 3. 11 would be the pH of 0.001 mol/L NaOH.

Question 10

Chemistry · Ionic and Molecular Compounds · Standard

Which of these molecules is polar?

Show answer and explanation

Answer: C

Polarity needs polar bonds and a shape in which their dipoles do not cancel. Water is bent, because of the oxygen's two lone pairs, so its O-H dipoles add up. CO2 is linear and CH4 and CCl4 are tetrahedral and symmetrical, so their bond dipoles cancel.

Question 11 · open · 0-3 points

Biomolecules

Describe the four levels of protein structure and the bonds that hold each one.

Model spoken answer and marking guide

The primary structure is the sequence of amino acids, joined by peptide bonds, which are covalent. The sequence decides everything else.

The secondary structure is the folding of the backbone into alpha-helices and beta-pleated sheets, held by hydrogen bonds between the C=O and N-H groups of the backbone.

The tertiary structure is the three-dimensional shape of the whole chain, held by interactions between the side chains: hydrogen bonds, ionic bonds, hydrophobic interactions and covalent disulfide bridges between cysteines.

The quaternary structure exists only in proteins of more than one chain, such as haemoglobin with its four subunits, held by the same kinds of interaction. Heat or a change of pH breaks the weaker bonds and denatures the protein, while the peptide bonds survive.

What earns the points

0: no answer, or an answer that is wrong at its core.
1: The levels named, or the primary structure explained, but the bonds are missing or wrong.
2: All four levels with most of the bonds, with one error or omission (often the disulfide bridge).
3: All four levels, the right bonds for each, and an example such as haemoglobin.

Question 12 · open · 0-3 points

Gases and Solutions

State Boyle's law and Charles's law, explain them with the kinetic theory of gases, and give an example from the human body.

Model spoken answer and marking guide

Boyle's law: at constant temperature, the pressure of a fixed amount of gas is inversely proportional to its volume, so pressure times volume stays constant. Charles's law: at constant pressure, the volume is directly proportional to the absolute temperature, in kelvin.

The kinetic theory explains both. Gas pressure is the result of particles colliding with the walls. Halve the volume and the particles hit the walls twice as often, so the pressure doubles. Heat the gas and the particles move faster, so at constant pressure the gas has to expand.

Breathing is Boyle's law at work: when the diaphragm contracts and the ribs rise, the volume of the chest increases, the pressure in the lungs falls below atmospheric pressure, and air flows in. Breathing out reverses it.

What earns the points

0: no answer, or an answer that is wrong at its core.
1: One law stated correctly, with no explanation.
2: Both laws stated correctly and explained, but no example, or an example that does not fit.
3: Both laws with their conditions, the kinetic explanation, temperature in kelvin, and breathing or another real example.

Chemistry, mock set 2

Two closed questions (3 points or 0) and two open questions (0-3): 12 points, as in the exam.

Question 13

Chemistry · Chemical Quantities and Reactions · Foundation

How many moles of water are there in 9.0 g of water? (H = 1, O = 16)

Show answer and explanation

Answer: B

The molar mass of H2O is 2 × 1 + 16 = 18 g/mol, so 9.0 g ÷ 18 g/mol = 0.5 mol.

Question 14

Chemistry · Atoms, Elements and Nuclear Chemistry · Standard

A radioisotope used in medicine has a half-life of 6 hours. What fraction of it remains after 24 hours?

Show answer and explanation

Answer: C

24 hours is four half-lives, and each halves what is left: 1/2 × 1/2 × 1/2 × 1/2 = 1/16. 1/4 is the answer after two half-lives only.

Question 15 · open · 0-3 points

Acids, Bases and Equilibrium

What is a buffer? Explain how the bicarbonate buffer keeps the pH of blood near 7.4.

Model spoken answer and marking guide

A buffer is a solution that resists a change in pH when a small amount of acid or base is added. It is a weak acid with its conjugate base, or a weak base with its conjugate acid.

In blood, the main buffer is carbonic acid and the hydrogen carbonate ion: H2CO3 is in equilibrium with H+ and HCO3-. If acid is added, hydrogen carbonate takes up the extra H+ and becomes carbonic acid, which breaks down into carbon dioxide and water; the lungs breathe out the carbon dioxide. If a base is added, carbonic acid gives up H+ to neutralise the OH-.

Blood pH is normally 7.35 to 7.45. The lungs adjust carbon dioxide within minutes and the kidneys adjust hydrogen carbonate and excrete H+ over hours to days, so the buffer works with both.

What earns the points

0: no answer, or an answer that is wrong at its core.
1: A correct definition of a buffer, but no mechanism.
2: The definition and the bicarbonate pair with the reaction one way (acid added or base added).
3: The definition, both directions, the link to carbon dioxide and the lungs, and the normal pH range or the kidneys' role.

Question 16 · open · 0-3 points

Chemical Quantities and Reactions

What is an oxidation-reduction reaction? In Zn + Cu2+ → Zn2+ + Cu, say what is oxidised and what is reduced, and give an example from metabolism.

Model spoken answer and marking guide

A redox reaction transfers electrons: oxidation is the loss of electrons and reduction is their gain, and they always happen together.

In this reaction zinc loses two electrons and becomes Zn2+: zinc is oxidised and is the reducing agent. The copper ion gains those two electrons and becomes copper metal: Cu2+ is reduced and is the oxidising agent.

In metabolism, glycolysis and the Krebs cycle oxidise fuel molecules and reduce NAD+ to NADH. In the electron transport chain NADH is oxidised again, and the electrons end up on oxygen, the final electron acceptor, which is reduced to water.

What earns the points

0: no answer, or an answer that is wrong at its core.
1: A correct definition, but the zinc and copper are the wrong way round or unexplained.
2: Definition and the zinc-copper example right, with no metabolic example, or the reverse.
3: Definition, both species with the electrons counted, the agents named, and NAD+/NADH or oxygen in the electron transport chain.

Science questions

Physics: two mock sets

Physics follows the 25 chapters of Giancoli's Physics: Principles with Applications, from kinematics and Newton's laws through fluids, heat, waves and circuits to optics. You may use a calculator and a sheet of paper, both shown to the camera.

Physics, mock set 1

Two closed questions (3 points or 0) and two open questions (0-3): 12 points, as in the exam.

Question 17

Physics · Measurement and Kinematics · Foundation

A car accelerates uniformly from rest to 20 m/s in 5 s. How far does it travel in that time?

Show answer and explanation

Answer: B

Under uniform acceleration the average speed is (0 + 20) ÷ 2 = 10 m/s, so the distance is 10 m/s × 5 s = 50 m. Using s = ½at² with a = 4 m/s² gives the same: ½ × 4 × 25 = 50 m. 100 m multiplies the final speed by the time.

Question 18

Physics · Electric Charge, Potential and DC Circuits · Foundation

Two 6 Ω resistors are connected in parallel. What is their combined resistance?

Show answer and explanation

Answer: C

In parallel, 1/R = 1/6 + 1/6 = 1/3, so R = 3 Ω. 12 Ω is the series value, and 1/3 Ω forgets to invert the sum.

Question 19 · open · 0-3 points

Dynamics, Gravitation and Circular Motion

State Newton's three laws of motion and give an example of each from the human body or from medicine.

Model spoken answer and marking guide

The first law: a body stays at rest or keeps moving at constant velocity unless a resultant force acts on it. In a car crash, the passenger keeps moving forward when the car stops, which is why seat belts and airbags exist, and why the brain can strike the inside of the skull.

The second law: the resultant force equals mass times acceleration, F = ma, or more generally the rate of change of momentum. Stopping the same body over a longer time, on a crumple zone or by bending the knees on landing, means a smaller force and less injury.

The third law: when one body exerts a force on another, the second exerts an equal and opposite force on the first. When you walk, your foot pushes back on the ground and the ground pushes you forward.

What earns the points

0: no answer, or an answer that is wrong at its core.
1: One or two laws stated correctly, with no examples.
2: All three laws stated correctly, with one or two fitting examples.
3: All three laws stated precisely, F = ma with resultant force, and a fitting example for each.

Question 20 · open · 0-3 points

Fluids, Heat and Thermodynamics

What is the difference between heat and temperature? Describe the ways heat is transferred, and how the body uses them to lose heat.

Model spoken answer and marking guide

Temperature measures the average kinetic energy of the particles in a body. Heat is energy transferred from a hotter body to a colder one because of their difference in temperature. A bath of warm water holds far more heat than a cup at the same temperature.

Heat moves by conduction, through direct contact between particles, as into a cold chair; by convection, when a moving fluid carries it away, as air or blood does; and by radiation, as infrared waves that need no medium. A fourth way the body uses is evaporation, which takes the latent heat of vaporisation.

The body loses most of its heat by radiation at rest. When it is hot, the skin's blood vessels dilate to bring more warm blood to the surface, and sweat evaporates. In exercise, evaporation of sweat becomes the main way of losing heat.

What earns the points

0: no answer, or an answer that is wrong at its core.
1: Names the ways of transfer, but confuses heat with temperature.
2: The distinction right and the three ways explained, with little on the body.
3: The distinction, conduction, convection and radiation with examples, and evaporation of sweat with vasodilation.

Physics, mock set 2

Two closed questions (3 points or 0) and two open questions (0-3): 12 points, as in the exam.

Question 21

Physics · Work, Energy and Momentum · Foundation

A 2 kg object is lifted 5 m. By how much does its gravitational potential energy increase? (g = 10 m/s²)

Show answer and explanation

Answer: C

ΔE = mgh = 2 kg × 10 m/s² × 5 m = 100 J.

Question 22

Physics · Optics and the Nature of Light · Standard

A lens has an optical power of +4 dioptres. What is its focal length?

Show answer and explanation

Answer: B

Power in dioptres is the reciprocal of the focal length in metres, so f = 1/4 = 0.25 m, or 25 cm. The positive sign means a converging lens; -0.25 m would be a diverging lens of -4 D.

Question 23 · open · 0-3 points

Oscillation, Waves and Sound

What is ultrasound, and how does an ultrasound scanner use it to form an image?

Model spoken answer and marking guide

Ultrasound is sound above the range of human hearing, which is above 20 kilohertz. Medical scanners use frequencies of a few megahertz. Sound is a longitudinal wave, so it needs a medium.

A probe sends short pulses into the body. At every boundary between tissues with different acoustic properties, part of the wave is reflected back to the probe. The scanner measures the time each echo takes to return and, knowing the speed of sound in soft tissue, about 1,540 metres per second, works out the depth of the boundary, then builds the image from many echoes.

A gel is put on the skin because air would reflect almost all the sound before it entered the body. Higher frequencies give finer detail but penetrate less deeply. Ultrasound uses no ionising radiation, which is why it is used in pregnancy.

What earns the points

0: no answer, or an answer that is wrong at its core.
1: A correct definition of ultrasound, but no account of how the image is formed.
2: The definition and reflection at boundaries, with the time-to-depth idea only loosely.
3: The definition, the pulse-echo principle with the time and the speed of sound, and a practical point: the gel, resolution against depth, or no ionising radiation.

Question 24 · open · 0-3 points

Electric Charge, Potential and DC Circuits

State Ohm's law. How do resistors combine in series and in parallel, and why are the appliances in a house wired in parallel?

Model spoken answer and marking guide

Ohm's law: the current through a conductor is directly proportional to the potential difference across it, at constant temperature, so V = IR.

In series the same current flows through every resistor, and the total resistance is the sum: R = R1 + R2. In parallel every branch has the same voltage, the currents add up, and the reciprocals add: 1/R = 1/R1 + 1/R2, so the total is less than the smallest resistance.

Appliances are wired in parallel so that each one gets the full mains voltage and can be switched on and off on its own. In series, one switched-off or broken appliance would cut the current to all of them, and they would share the voltage.

What earns the points

0: no answer, or an answer that is wrong at its core.
1: Ohm's law stated, but the series and parallel rules wrong or missing.
2: Ohm's law and both rules correct, with no explanation of the household wiring.
3: Ohm's law with its condition, both rules with what is shared in each, and the reasons for parallel wiring.

Science questions

Mathematics: two mock sets

Mathematics follows Calculus for the Life Sciences (Greenwell, Ritchey and Lial): algebra, functions, exponentials and logarithms, derivatives, integration, multivariable calculus and probability. MUL's own sample questions are all multiple choice and lean on number reasoning; an open question here means talking through a calculation.

Mathematics, mock set 1

Two closed questions (3 points or 0) and two open questions (0-3): 12 points, as in the exam.

Question 25

Mathematics · Limits and the Derivative · Foundation

At what value of x does f(x) = x² - 4x + 1 have its minimum?

Show answer and explanation

Answer: C

f'(x) = 2x - 4 = 0 gives x = 2, and f''(x) = 2 > 0, so it is a minimum (f(2) = -3). Completing the square gives the same: (x - 2)² - 3.

Question 26

Mathematics · Exponentials, Logarithms and Trigonometry · Foundation

What is log₂ 32 - log₂ 4?

Show answer and explanation

Answer: A

log₂ 32 - log₂ 4 = log₂ (32 ÷ 4) = log₂ 8 = 3. Option B stops at 32 ÷ 4 = 8; option D is log₂ 32 alone.

Question 27 · open · 0-3 points

Limits and the Derivative

What does the derivative of a function tell you? Find the stationary points of f(x) = 2x³ - 3x² - 12x + 1 and say which is a maximum and which a minimum.

Model spoken answer and marking guide

The derivative is the instantaneous rate of change of the function: the gradient of its graph at each point. Where it is zero the graph is flat, at a stationary point.

Here f'(x) = 6x² - 6x - 12 = 6(x² - x - 2) = 6(x - 2)(x + 1), which is zero at x = 2 and x = -1.

The second derivative is f''(x) = 12x - 6. At x = -1 it is -18, negative, so that is a local maximum, where f(-1) = 8. At x = 2 it is 18, positive, so that is a local minimum, where f(2) = -19.

What earns the points

0: no answer, or an answer that is wrong at its core.
1: A correct meaning of the derivative, or the correct f'(x), but no stationary points.
2: Both stationary points found, but not classified, or classified with an arithmetic slip.
3: The meaning, f'(x) factorised, both points with their values of f, and a correct test for which is the maximum and which the minimum.

Question 28 · open · 0-3 points

Exponentials, Logarithms and Trigonometry

A bacterial culture doubles every 20 minutes and starts with 500 bacteria. Write a formula for the number after t hours, and find when it reaches 64,000.

Model spoken answer and marking guide

It doubles three times an hour, so after t hours N(t) = 500 × 2^(3t).

For 64,000: 2^(3t) = 64,000 ÷ 500 = 128, and 128 is 2^7, so 3t = 7 and t = 7/3 hours, which is 2 hours and 20 minutes.

Check it in doublings: seven doublings of 20 minutes each are 140 minutes. If the number were not a power of two, I would take logarithms: 3t = log₂ 128, or t = ln 128 ÷ (3 ln 2).

What earns the points

0: no answer, or an answer that is wrong at its core.
1: An exponential idea, but the wrong formula (for example doubling once an hour).
2: The right formula, with a slip in solving for t, or the right time with no formula.
3: N(t) = 500 × 2^(3t), the time of 2 hours 20 minutes, and a check or the logarithmic method.

Mathematics, mock set 2

Two closed questions (3 points or 0) and two open questions (0-3): 12 points, as in the exam.

Question 29

Mathematics · Probability and Random Variables · Foundation

Two fair dice are rolled. What is the probability that their total is 7?

Show answer and explanation

Answer: B

Of the 36 equally likely outcomes, six give 7: (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1). 6/36 = 1/6.

Question 30

Mathematics · Integration · Foundation

What is the value of the integral of 3x² from x = 0 to x = 2?

Show answer and explanation

Answer: B

An antiderivative of 3x² is x³, so the integral is 2³ - 0³ = 8. Option C evaluates 3x² at x = 2 instead of integrating.

Question 31 · open · 0-3 points

Probability and Random Variables

A disease affects 1% of a population. A test detects it in 90% of people who have it, and gives a false positive in 5% of people who don't. If someone tests positive, what is the probability they have the disease?

Model spoken answer and marking guide

Take 10,000 people. 100 have the disease, and the test is positive in 90 of them. Of the 9,900 who do not, 5% test positive anyway: 495 people.

So 90 + 495 = 585 people test positive, and only 90 of them are ill: the probability is 90 ÷ 585, about 0.15, or 15%. In conditional probability terms, that is P(disease and positive) ÷ P(positive) = 0.009 ÷ 0.0585.

The point for a doctor: when a disease is rare, most positive results from a screening test are false positives, so a positive screen is followed by a more specific test before anyone is diagnosed.

What earns the points

0: no answer, or an answer that is wrong at its core.
1: Answers 90%, the test's sensitivity, but recognises some of the information.
2: The right method, with an arithmetic slip, or the right answer with the reasoning unclear.
3: About 15%, the working said aloud (counts or P(A and B) ÷ P(B)), and what it means for screening.

Question 32 · open · 0-3 points

Algebra and Expressions

Solve the inequality x² - 5x + 6 < 0 and explain the answer with a sketch of the graph.

Model spoken answer and marking guide

First the roots: x² - 5x + 6 = (x - 2)(x - 3), which is zero at x = 2 and x = 3.

The graph of y = x² - 5x + 6 is a parabola opening upwards, because the coefficient of x² is positive. It crosses the x-axis at 2 and 3 and lies below it between them.

So the expression is negative for 2 < x < 3. The end points are not included because the inequality is strict; for ≤ 0 they would be.

What earns the points

0: no answer, or an answer that is wrong at its core.
1: The roots found, but the wrong region chosen (x < 2 or x > 3).
2: The correct interval, with no explanation of why.
3: Factorisation, the interval 2 < x < 3, the parabola's shape as the reason, and the strict inequality's end points.

General questions

Socio-medical questions

Two of the twelve questions are on socio-medical topics: treatment and prevention, lifestyle and environmental risks, the challenges of medicine, donation, vaccination and alternative medicine, and health problems seen globally and locally. These are questions of opinion: the outlines give you a structure, and the content has to be yours.

Question 33 · Socio-medical · 0-2 points

Treatment and Prevention

“Is prevention more important than treatment?”

How to build your answer

Take a position, and qualify it: both are needed, but prevention reaches more people for less.
Give one concrete example of prevention that works: vaccination, smoking bans, screening for cervical or colon cancer.
Say where treatment cannot be replaced: accidents, the conditions that are not preventable, and the patient in front of you today.
Close with the doctor's part in both, for example advice in every consultation.

Avoid: Answering in slogans without one real example.

Question 34 · Socio-medical · 0-2 points

Lifestyle and Environmental Risk Factors

“Which lifestyle or environmental factors damage health most where you live, and what could be done about them?”

How to build your answer

Name two factors you actually know about where you live (smoking, diet and obesity, inactivity, alcohol, air pollution), and say why they matter.
Link each to diseases: cardiovascular disease, type 2 diabetes, cancers, COPD.
Say what could be done at two levels: the individual (a doctor's advice) and society (taxes, urban planning, education).

Avoid: A list of every risk factor with no link to diseases or to action.

Question 35 · Socio-medical · 0-2 points

Challenges in the Medical Field

“What do you think is the biggest challenge facing medicine in the next twenty years?”

How to build your answer

Choose one challenge and explain it: an ageing population, antimicrobial resistance, shortages of doctors and nurses, the cost of new treatments, or the use of AI.
Say why it matters for patients, with a figure or an example you are sure of.
Suggest what doctors or health systems could do, and admit what is hard about it.

Avoid: Naming five challenges and explaining none.

Question 36 · Socio-medical · 0-2 points

Donation, Vaccination and Alternative Medicine

“Should organ donation be opt-out, so that everyone is a donor unless they refuse?”

How to build your answer

Explain the two systems in one sentence each: opt-in and opt-out (presumed consent).
Give the argument for: more organs and fewer deaths on waiting lists. Then the argument against: autonomy, trust, and the role of the family.
Reach your own view and say what would make the system work either way: information, registration and talking with families.

Avoid: Ignoring consent, which is the heart of the question.

Question 37 · Socio-medical · 0-2 points

Donation, Vaccination and Alternative Medicine

“A parent tells you they do not want their child vaccinated. How would you respond?”

How to build your answer

Start by listening: ask what worries them, without judging.
Explain the facts simply: how vaccines protect the child and, through herd immunity, others who cannot be vaccinated; side effects are real but serious ones are rare.
Respect the decision-making process: offer information, time and a further conversation; involve the child's doctor.
Say why it matters for public health, for example the return of measles where vaccination rates fall.

Avoid: Lecturing or dismissing the parent: the committee is listening for how you treat a worried person.

Question 38 · Socio-medical · 0-2 points

Donation, Vaccination and Alternative Medicine

“What is your opinion of alternative medicine, such as homeopathy?”

How to build your answer

Distinguish what has evidence from what has not: some complementary approaches help with wellbeing or symptoms, while remedies like homeopathy have shown no effect beyond placebo.
Name the risk: delaying effective treatment, or interactions with medicines.
Say how you would talk to a patient who uses it: with respect, asking what they take, and keeping them on the treatment that works.

Avoid: Mocking patients who use it.

Question 39 · Socio-medical · 0-2 points

Global and Local Health Problems

“Choose a major health problem and explain how it looks different globally and locally.”

How to build your answer

Choose one problem: antimicrobial resistance, obesity, tuberculosis, mental health, or access to care.
The global picture: who is affected most and why (income, health systems, climate).
The local picture where you live or in Poland: how it shows up and what is being done.
One thing that would help on both levels.

Avoid: Staying abstract: one country and one example make the answer.

General questions

Motivation questions

One question is about your motivation, predispositions and interests. No outline here is an answer to learn by heart: a committee hears hundreds of rehearsed answers, and the points go to the specific and the honest.

Question 40 · Motivation · 0-2 points

Motivation and Expectations of Study

“Why do you want to study medicine?”

How to build your answer

One or two reasons that are really yours, each tied to something you did or saw: a job, volunteering, a family experience, a subject that fascinated you.
Show you know what the work is like: long training, responsibility, night shifts, and patients you cannot cure.
End with what kind of doctor you want to become.

Avoid: "I want to help people" with nothing behind it: say how, and why medicine rather than nursing or research.

Question 41 · Motivation · 0-2 points

Motivation and Expectations of Study

“Why the Medical University of Lodz, and what do you expect from studying here?”

How to build your answer

Reasons that are specific and true: the programme in English, the Medical Simulation Centre, the clinical training in its own teaching hospitals, the recognition of the degree, the city.
What you expect of yourself: the workload, learning Polish for patients, adapting to a new system.
What you would bring to the student community.

Avoid: Reasons that would fit any university, or that are only about the fees.

Question 42 · Motivation · 0-2 points

Duties and Responsibilities of Doctors

“What are a doctor's most important responsibilities, apart from treating disease?”

How to build your answer

Choose two or three: confidentiality, honesty with patients, informed consent, working in a team, keeping up to date, caring for one's own health.
Explain each with a short example of what it means in practice.
Link them to trust: why patients and society depend on them.

Avoid: A list of words with no explanation.

Question 43 · Motivation · 0-2 points

Studying and Living Abroad

“How will you cope with studying and living in Poland, far from home?”

How to build your answer

Be honest about what will be hard: the language, the climate, distance from family, cultural differences, managing money and time alone.
Show evidence you can adapt: a time you lived away from home, moved schools or took responsibility.
Say what you will do: learn Polish, join student life, keep a routine, ask for help early.

Avoid: Saying it will not be difficult at all.

Question 44 · Motivation · 0-2 points

Hobbies, Interests and Future Plans

“Tell us about an interest outside school, and what it says about you.”

How to build your answer

One interest, described concretely: what you do, how often, for how long.
What it has taught you that matters in medicine: discipline, teamwork, coping with pressure, communication.
How you will keep it going during your studies, for balance.

Avoid: Listing several hobbies without depth.

General questions

Student Code of Ethics questions

One question is on the Student Code of Ethics, a three-page document MUL links from its exam page. Read it before the exam: an answer that names what the Code actually says, and applies it, stands out from one that only lists good values.

Question 45 · Code of Ethics · 0-2 points

The Student Code of Ethics

“During an online test, a classmate sends you the answers. What do you do, and why?”

How to build your answer

Say plainly that you would not use them: the Code calls it unethical to write a test non-independently, by consulting others or using devices to receive data (§5.1).
Explain why it matters in medicine: grades are meant to show what you know, and patients will rely on that knowledge.
Say what you would do about the classmate: the Code asks students to oppose dishonesty in a lawful manner and report it to the relevant authorities (§3.3). Talk about how you would handle it with tact.

Avoid: Saying you would simply ignore it: the Code says a student is not indifferent to unethical actions (§4.3). · The Code, §3.3, §4.3, §5.1

Question 46 · Code of Ethics · 0-2 points

The Student Code of Ethics

“What does MUL's Student Code of Ethics expect from you in how you treat other students and the university's staff?”

How to build your answer

Towards students: relations based on respect, solidarity, loyalty and cooperation (§4.2), and tolerance of other beliefs and traditions without discrimination (§3.2).
Towards staff: due respect, and good manners; the Code names lateness, disrupting classes, insults and attending under the influence of intoxicants as reprehensible (§5.2).
Add why it matters in an international university and in a future clinical team.

Avoid: Answering with general values without showing you have read the Code. · The Code, §3.2, §4.2, §5.2

Question 47 · Code of Ethics · 0-2 points

The Student Code of Ethics

“You see fellow students mocking another student because of where they come from. What would you do?”

How to build your answer

Name it: discrimination by nationality, which the Code asks students to prevent (§3.2), and an action that humiliates a member of the academic community (§4.4).
Say what you would do, in order: support the student, speak to the others calmly, and report it if it continues (§3.3).
Link it to medicine: a doctor treats every patient equally.

Avoid: An answer that only condemns, without saying what you would actually do. · The Code, §3.2, §3.3, §4.4

Question 48 · Code of Ethics · 0-2 points

The Student Code of Ethics

“Why should a medical university have a code of ethics for its students, and not only for its doctors?”

How to build your answer

Its purpose, in the Code's words: a guide in difficult situations of moral dilemma and a statement of the student's ethical obligations (§1.2).
Students already work with patients, in classes and summer training, and the habits formed now (honesty, respect, responsibility) are those of the future doctor.
The Code has consequences: breaking it can lead to disciplinary measures, from an admonition to expulsion (§7).

Avoid: Treating the Code as a formality. · The Code, §1.2, §7

Question 49 · Code of Ethics · 0-2 points

The Student Code of Ethics

“A relative of yours works at the university and offers to help you with an exam. What do you answer?”

How to build your answer

Refuse, and say why: the Code lists exploiting family relationships as unethical (§5.1), and a student must not engage in anything that could affect the objective assessment of their knowledge (§4.2).
Explain the principle behind it: fairness to the other students, and honesty in everything ("absolute honesty", §5.1).
Say how you would decline without damaging the relationship, and what kind of help you would accept, such as advice on how to study.

Avoid: Saying it would depend on the help offered. · The Code, §4.2, §5.1

Next step

Know the rules as well as the science

Every question here is IvyTest's, written to the Range of Knowledge and the Code; none is one of MUL's. The guide covers the rest: who is invited to the exam, the dates for 2027, fees and the documents.

The full Medical University of Lodz entrance exam guide The annotated topic checklist (syllabus)Medical University of Lodz: fees, location and curriculum MUL's exam page