Free practice paper · 2027 format
The whole written test in the format Pilsen uses from 2027/28: 20 Biology, 20 Chemistry and 20 Physics questions, four options and one correct answer each, with the answer and a full explanation for every one. The faculty's own sample tests still contain open-response questions; the live test is single-answer multiple choice only, and so is this paper. Written by IvyTest; it is not an official Charles University paper.
Before you start
| Section | Questions | Time | Marks (Entrance Examination) |
|---|---|---|---|
| Entrance Examination | 60 | 90 min | +1 correct, 0 wrong, 0 blank |
Give yourself 90 minutes for all 60 questions and answer on paper before opening any explanation. Each correct answer scores 1 point and a wrong one costs nothing, so answer everything. From 2027/28 you also need at least 9 points in each subject, whatever your total: the result at the end of the page shows each subject against that minimum.
Section 1 of 1
60 questions · 90 minutes
Which of the following organisms is a prokaryote?
Answer: C
Staphylococcus aureus is a bacterium, and bacteria are prokaryotes: their DNA lies free in the cytoplasm with no nuclear envelope. Yeast is a fungus and Plasmodium and Amoeba are protists, so all three are eukaryotes with a true nucleus, even though they are single-celled.
Which structure in a human cell contains its own circular DNA and 70S ribosomes?
Answer: D
Mitochondria carry their own small circular genome and bacterial-type 70S ribosomes, which is part of the evidence that they descend from engulfed bacteria. The rough endoplasmic reticulum is studded with ribosomes, but these are the cytoplasmic 80S kind and it has no DNA of its own. The Golgi apparatus and lysosomes contain neither.
In which order does a newly made protein hormone such as insulin pass through the cell before it is secreted?
Answer: A
A secreted protein is made on ribosomes bound to the rough ER and enters its lumen, then travels in vesicles to the Golgi apparatus, where it is modified and packed into secretory vesicles that fuse with the plasma membrane. Reversing the ER and Golgi gets the direction of the pathway wrong. Lysosomes are an end point for digestion, not a route out of the cell, and the smooth ER makes lipids rather than handling secreted proteins.
For each molecule of ATP it hydrolyses, the sodium-potassium pump (Na⁺/K⁺-ATPase) moves:
Answer: B
The pump moves three sodium ions out and two potassium ions in per ATP, against both concentration gradients, which keeps sodium high outside and potassium high inside. Because it moves more positive charge out than in, it is electrogenic and adds slightly to the negative resting potential. The other options either swap the numbers or the directions; sodium entering the cell is what happens through channels, not through the pump.
Human red blood cells are placed in a 0.3% sodium chloride solution. What happens to them?
Answer: C
Blood plasma is isotonic with about 0.9% sodium chloride, so a 0.3% solution is hypotonic: it has a higher water potential than the cytoplasm. Water therefore enters the cells by osmosis, and because red cells have no cell wall they swell and can burst. Crenation is what happens in a hypertonic solution, and the sodium pump moves sodium out, not in.
Cyanide blocks cytochrome c oxidase, the last complex of the mitochondrial electron transport chain. What is the immediate consequence for a cell?
Answer: A
Cytochrome c oxidase passes electrons to oxygen, the final acceptor, so blocking it stops electron flow, oxygen use and proton pumping. Without a proton gradient, oxidative phosphorylation fails and the cell falls back on glycolysis, regenerating NAD⁺ by reducing pyruvate to lactate. Glycolysis takes place in the cytoplasm and does not need the chain, so it continues and even speeds up; the gradient collapses rather than steepens, and a reversed ATP synthase would consume ATP, not make it.
At which stage does crossing over between homologous chromosomes take place?
Answer: B
Crossing over happens while homologous chromosomes are paired as bivalents in prophase I of meiosis, and the points of exchange are seen as chiasmata. Homologues do not pair in mitosis, so there is nothing to cross over with. By anaphase I the homologues are being pulled apart, and in meiosis II there are no homologous pairs left in the cell.
A human body cell has 46 chromosomes. How many chromatids are there in one cell at metaphase II of meiosis?
Answer: D
Meiosis I separates homologous pairs, so each cell entering meiosis II has 23 chromosomes; the sister chromatids have not yet separated, so each chromosome still has two chromatids, giving 23 × 2 = 46. Twenty-three is the count after meiosis II, when the chromatids have parted, and 92 is the count of a diploid cell after DNA replication, before meiosis I.
The template strand of a short stretch of DNA reads 3′-TAC GGA-5′. What is the sequence of the mRNA transcribed from it?
Answer: A
RNA polymerase builds mRNA complementary and antiparallel to the template: T pairs with A, A with U, C with G and G with C, so 3′-TAC GGA-5′ gives 5′-AUG CCU-3′. Copying the template letters unchanged gives UAC GGA, and ATG CCT contains thymine, which RNA does not. UCC GUA is the right base pairing read in the wrong direction.
A single base substitution changes the codon UAU (tyrosine) to UAA. What type of mutation is this?
Answer: C
UAA is a stop codon, so translation ends at this point and the protein is cut short: that is a nonsense mutation. A silent mutation would give another codon for tyrosine, and a missense mutation a codon for a different amino acid. A frameshift needs an insertion or deletion of bases that is not a multiple of three; a substitution keeps the reading frame.
A mother with blood group A (genotype IᴬI⁰) and a father with blood group B (genotype IᴮI⁰) have children. Which blood groups are possible among their children?
Answer: D
Each parent passes on one of two alleles with equal probability, so the children can be IᴬIᴮ (AB), IᴬI⁰ (A), IᴮI⁰ (B) or I⁰I⁰ (O), each with probability 1/4. The tempting answer leaves out O, but both parents carry the recessive I⁰ allele, so a child can inherit it from each of them.
Cystic fibrosis is autosomal recessive. Two healthy parents are both carriers. Their first child does not have the disease. What is the probability that this child is a carrier?
Answer: C
A cross of two carriers gives 1 AA : 2 Aa : 1 aa. We know the child is not aa, so only the three healthy outcomes remain, and two of those three are carriers: 2/3. The answer 1/2 is the carrier probability for any child before we know it is healthy, and 1/4 is the probability of an affected child.
Which cells secrete antibodies into the blood?
Answer: B
Plasma cells are activated B lymphocytes that have differentiated into antibody factories. Helper T cells coordinate the response and help B cells become activated, but they do not make antibodies themselves. Neutrophils destroy microbes by phagocytosis, and erythrocytes carry oxygen.
Which type of epithelium lines the alveoli of the lungs?
Answer: A
Gas exchange needs the shortest possible diffusion distance, and the alveolar wall is built of a single layer of flat cells: simple squamous epithelium. Pseudostratified ciliated epithelium lines the trachea and bronchi, not the alveoli. Keratinised stratified epithelium is the epidermis of the skin, and columnar cells with microvilli line the small intestine.
When a skeletal muscle fibre is stimulated, calcium ions released from the sarcoplasmic reticulum bind to which protein?
Answer: D
Calcium binds to troponin, which changes shape and pulls tropomyosin away from the myosin-binding sites on actin, so cross-bridges can form. Tropomyosin is the protein that is moved, not the one calcium binds to. Actin and myosin are the contractile filaments themselves.
The producers in a food chain fix 50,000 kJ of energy. If about 10% of the energy passes from each trophic level to the next, how much reaches the secondary consumers?
Answer: B
Primary consumers receive 10% of 50,000 kJ, which is 5,000 kJ, and secondary consumers receive 10% of that, 500 kJ. The answer 5,000 kJ stops one step early at the primary consumers, and 50 kJ goes one step too far, to the tertiary consumers.
Which vessels carry oxygenated blood into the left atrium?
Answer: C
Blood oxygenated in the lungs returns to the heart through the pulmonary veins, which open into the left atrium. They are the main veins that carry oxygen-rich blood. The pulmonary arteries carry deoxygenated blood from the right ventricle to the lungs, and the venae cavae and coronary sinus drain deoxygenated blood into the right atrium.
The left ventricle of a resting adult holds 120 mL at the end of diastole and 50 mL at the end of systole. The heart rate is 80 beats per minute. What is the cardiac output?
Answer: D
Stroke volume is the volume ejected per beat: 120 − 50 = 70 mL. Cardiac output is stroke volume times heart rate: 70 mL × 80 = 5,600 mL/min = 5.6 L/min. Using the end-diastolic volume alone gives 9.6 L/min and the end-systolic volume alone 4.0 L/min, but neither is the volume actually pumped out on each beat.
A patient's posterior pituitary releases almost no antidiuretic hormone (ADH). What would you expect?
Answer: B
ADH inserts aquaporins into the collecting duct so that water is reabsorbed and urine is concentrated. Without it the collecting duct stays poorly permeable to water, so large amounts of dilute urine are lost (diabetes insipidus). Glucose in the urine points to diabetes mellitus, an insulin problem, and water retention is what too much ADH would cause.
Which of the following is an effect of stimulating the parasympathetic nervous system?
Answer: A
The parasympathetic system, largely through the vagus nerve and acetylcholine, governs "rest and digest": it increases gut motility and the secretion of digestive juices. Dilated pupils, a faster heart and wider bronchi are all sympathetic "fight or flight" effects; parasympathetic stimulation does the opposite, constricting the pupils, slowing the heart and narrowing the bronchi.
Iron has atomic number 26. How many protons, neutrons and electrons does the ion ⁵⁶Fe³⁺ contain?
Answer: B
The atomic number gives 26 protons, the neutrons are 56 − 26 = 30, and a 3+ charge means three electrons have been lost, leaving 26 − 3 = 23. Twenty-six electrons would describe the neutral atom, and 29 electrons would be an anion with a 3− charge. The mass number counts protons and neutrons together, so it cannot itself be the number of neutrons.
Iodine-131, used to treat thyroid disease, has a half-life of 8 days. A sample contains 80 mg of iodine-131. How much is left after 24 days?
Answer: C
Twenty-four days is three half-lives, and each one halves the amount: 80 → 40 → 20 → 10 mg. Dividing 80 by 3 treats decay as linear, which it is not, and 20 mg is the amount after only two half-lives. Radioactive decay never reaches exactly zero in a whole number of half-lives.
How many moles of glucose, C₆H₁₂O₆, are in 45 g? (Ar: C = 12, H = 1, O = 16)
Answer: A
The molar mass of glucose is 6 × 12 + 12 × 1 + 6 × 16 = 180 g/mol, so n = m / M = 45 / 180 = 0.25 mol. The answer 4 mol comes from dividing the molar mass by the mass, the wrong way round.
What volume of oxygen, measured at standard conditions (molar volume 22.4 L/mol), is needed to burn 4.6 g of ethanol, C₂H₅OH, completely to carbon dioxide and water? (Ar: C = 12, H = 1, O = 16)
Answer: D
The balanced equation is C₂H₅OH + 3 O₂ → 2 CO₂ + 3 H₂O. Ethanol's molar mass is 46 g/mol, so 4.6 g is 0.1 mol and needs 0.3 mol of oxygen, which occupies 0.3 × 22.4 = 6.72 L. The answer 2.24 L assumes a 1 : 1 ratio, 4.48 L is the volume of carbon dioxide produced, and 67.2 L is ten times too large.
Which of the following substances forms hydrogen bonds between its own molecules?
Answer: B
A hydrogen bond needs a hydrogen atom bonded directly to N, O or F, and ethanol has one in its O–H group. Dimethyl ether contains oxygen, but all its hydrogens are on carbon, so its molecules cannot hydrogen-bond to each other. Sulfur is not electronegative enough for strong hydrogen bonds, and methane has only weak dispersion forces.
Which molecule contains polar bonds but is non-polar overall?
Answer: D
Each C=O bond in carbon dioxide is polar, but the molecule is linear, so the two bond dipoles point in opposite directions and cancel. Water is bent and ammonia is trigonal pyramidal, so their bond dipoles add up to a net dipole. Hydrogen chloride has only one polar bond, so nothing can cancel it.
Which of these elements is an alkaline earth metal?
Answer: A
The alkaline earth metals are group 2: beryllium, magnesium, calcium, strontium, barium and radium. Sodium is an alkali metal in group 1, aluminium is in group 13, and chlorine is a halogen in group 17.
Which of these atoms has the largest atomic radius?
Answer: C
Atomic radius increases down a group, as electrons fill a new shell, and decreases across a period, as the growing nuclear charge pulls the same shell inwards. Potassium is in period 4 and at the start of it, so it is larger than sodium (period 3) and larger than bromine, which sits at the far end of period 4. Chlorine is small on both counts.
What is the formula of calcium phosphate?
Answer: D
Calcium forms Ca²⁺ and phosphate is PO₄³⁻, so the charges balance with three calcium ions (+6) and two phosphate ions (−6): Ca₃(PO₄)₂. Ca₂(PO₄)₃ has the subscripts swapped and would carry a net charge of −5, and the other two formulas do not balance either.
What is the average oxidation state of sulfur in sodium thiosulfate, Na₂S₂O₃?
Answer: A
Sodium is +1 and oxygen −2, and the compound is neutral, so 2(+1) + 2x + 3(−2) = 0, giving 2x = 4 and x = +2. The answer +4 forgets that there are two sulfur atoms to share the charge, and +6 is sulfur's oxidation state in sulfate. Sulfur is −2 only in sulfides.
Physiological saline is 0.9% sodium chloride (mass per volume, g per 100 mL). How much sodium chloride is in a 500 mL bag?
Answer: B
A 0.9% (m/V) solution holds 0.9 g in every 100 mL, so 500 mL holds 5 × 0.9 = 4.5 g. The answer 9.0 g is the amount in a full litre, and 0.45 g and 45 g are out by a factor of ten.
200 mL of a 0.5 mol/L glucose solution is mixed with 300 mL of a 1.0 mol/L glucose solution. What is the concentration of the mixture?
Answer: C
Add the amounts: 0.2 L × 0.5 mol/L = 0.1 mol and 0.3 L × 1.0 mol/L = 0.3 mol, so 0.4 mol in a total of 0.5 L, which is 0.8 mol/L. The simple average of the two concentrations, 0.75 mol/L, ignores that more of the stronger solution was used, and 1.5 mol/L adds the concentrations, which is never right.
Which statement about a catalyst is correct?
Answer: D
A catalyst provides a pathway of lower activation energy, so both directions of a reversible reaction speed up by the same factor and equilibrium is reached sooner. Because both directions are affected equally, the position of equilibrium does not change, and the enthalpy change depends only on the reactants and products, so it is unchanged too. A catalyst is regenerated at the end of each cycle.
In acidic solution, permanganate oxidises iron(II): MnO₄⁻ is reduced to Mn²⁺ and Fe²⁺ is oxidised to Fe³⁺. How many moles of Fe²⁺ are oxidised by 1 mol of MnO₄⁻?
Answer: B
Manganese goes from +7 in MnO₄⁻ to +2 in Mn²⁺, gaining 5 electrons, while each Fe²⁺ loses only 1 electron. Electrons gained must equal electrons lost, so 1 mol of permanganate oxidises 5 mol of iron(II): MnO₄⁻ + 8 H⁺ + 5 Fe²⁺ → Mn²⁺ + 5 Fe³⁺ + 4 H₂O. The 8 in the equation belongs to the hydrogen ions, not to iron.
What is the pH of a 0.01 mol/L solution of hydrochloric acid?
Answer: A
Hydrochloric acid is a strong acid and dissociates completely, so [H₃O⁺] = 0.01 = 10⁻² mol/L and pH = −log 10⁻² = 2. The value 0.01 is the concentration, not the pH, and 12 is the pH of a 0.01 mol/L strong base.
What is the pH of a 0.005 mol/L solution of barium hydroxide, Ba(OH)₂, at 25 °C? Assume complete dissociation.
Answer: C
Each Ba(OH)₂ releases two hydroxide ions, so [OH⁻] = 2 × 0.005 = 0.01 mol/L, pOH = 2 and pH = 14 − 2 = 12. Forgetting the factor of two gives [OH⁻] = 0.005 mol/L and a pH of about 11.7. A pH of 2 is the pOH mistaken for the pH.
How many structural isomers have the formula C₅H₁₂?
Answer: B
There are three: pentane (an unbranched chain), 2-methylbutane and 2,2-dimethylpropane. Structures such as 3-methylbutane or 1-methylbutane only look new: numbered the right way round or drawn straight, they are 2-methylbutane and pentane again.
Propan-2-ol is oxidised with acidified potassium dichromate. What is the organic product?
Answer: C
Propan-2-ol is a secondary alcohol, and oxidising a secondary alcohol gives a ketone, here propanone (acetone). Propanal and propanoic acid are the products of oxidising the primary alcohol propan-1-ol. Propene comes from dehydration with a hot acid catalyst, which is not an oxidation.
Which of these proteinogenic amino acids is not chiral?
Answer: D
Glycine's side chain is a hydrogen atom, so its alpha carbon carries two identical hydrogens and is not a stereocentre. Alanine, serine and cysteine have a methyl, a CH₂OH and a CH₂SH side chain respectively, so their alpha carbons bear four different groups and are chiral.
Hydrolysis of sucrose gives which monosaccharides?
Answer: A
Sucrose, table sugar, is a disaccharide of glucose joined to fructose by a glycosidic bond, and hydrolysis splits it into those two. Glucose and galactose make lactose, and two glucose units make maltose. No common disaccharide is made of fructose and galactose.
Which of the following expresses the joule in SI base units?
Answer: B
Work is force times distance, so 1 J = 1 N × 1 m. A newton is 1 kg m s⁻², so 1 J = 1 kg m s⁻² × 1 m = 1 kg m² s⁻². kg m s⁻² is the newton itself, kg m² s⁻³ is the watt (a joule per second), and kg m⁻¹ s⁻² is the pascal (a newton per square metre).
A car accelerates uniformly from 10 m/s to 30 m/s in 4.0 s. How far does it travel in this time?
Answer: C
For uniform acceleration the average speed is the mean of the initial and final speeds, (10 + 30) / 2 = 20 m/s, so the distance is 20 m/s × 4.0 s = 80 m. Checking another way: a = (30 − 10) / 4 = 5 m/s², and s = ut + ½at² = 10 × 4 + ½ × 5 × 16 = 40 + 40 = 80 m. 120 m assumes the car moved at 30 m/s throughout, 40 m uses only the initial speed (or only the ½at² term), and 60 m treats the car as starting from rest, averaging 15 m/s.
A ball is thrown vertically upwards at 20 m/s. Ignoring air resistance and taking g = 10 m/s², at what time after launch is the ball 15 m above the launch point for the second time?
Answer: D
Taking upwards as positive, h = ut − ½gt², so 15 = 20t − 5t², which rearranges to t² − 4t + 3 = 0, or (t − 1)(t − 3) = 0. The ball passes 15 m on the way up at t = 1 s and on the way down at t = 3 s; the question asks for the second time, 3 s. 1 s is the first passage, 2 s is the time to reach the top (20 / 10), where the ball is 20 m up, and 1.7 s comes from √(2 × 15 / 10), which treats the ball as falling from rest.
Two blocks, of mass 2.0 kg and 3.0 kg, sit in contact on a frictionless horizontal surface. A horizontal force of 20 N pushes the 2.0 kg block, which in turn pushes the 3.0 kg block. What force does the 2.0 kg block exert on the 3.0 kg block?
Answer: A
The two blocks move together, so a = 20 N / (2.0 + 3.0) kg = 4.0 m/s². The only horizontal force on the 3.0 kg block is the push from the 2.0 kg block, so that push is ma = 3.0 × 4.0 = 12 N. 8 N is the net force on the 2.0 kg block (2.0 × 4.0), which is 20 − 12; 10 N splits the force equally regardless of mass; 20 N would be passed on only if the front block had no mass.
A planet has twice the mass and twice the radius of the Earth. Taking the gravitational field strength at the Earth's surface as 10 m/s², what is it at the surface of this planet?
Answer: B
Surface field strength is g = GM / R². Doubling M doubles g, and doubling R divides it by 2² = 4, so g changes by a factor of 2 / 4 = ½: 10 × ½ = 5 m/s². 10 m/s² divides by R rather than R², 20 m/s² doubles the mass and ignores the radius, and 2.5 m/s² applies the radius but forgets the extra mass.
A motor lifts a 50 kg load vertically through 12 m at constant speed in 20 s. Taking g = 10 m/s², what useful power does the motor deliver?
Answer: D
At constant speed the motor's force equals the weight, mg = 50 × 10 = 500 N. The work done is 500 N × 12 m = 6000 J, delivered in 20 s, so P = 6000 / 20 = 300 W. 6000 is the work in joules, not divided by the time; 500 is the weight in newtons, not a power; 30 W comes from leaving out g (50 × 12 / 20).
A 2.0 kg block is released from rest at the top of a ramp 9.0 m long whose top is 5.0 m above its bottom. It reaches the bottom at 8.0 m/s. Taking g = 10 m/s², what is the average friction force acting on the block along the ramp?
Answer: A
The block loses potential energy mgh = 2.0 × 10 × 5.0 = 100 J and gains kinetic energy ½mv² = ½ × 2.0 × 8.0² = 64 J. The other 100 − 64 = 36 J is work done against friction over the 9.0 m of ramp, so the friction force is 36 / 9.0 = 4.0 N. 36 N treats the energy lost in joules as the force; 7.1 N divides the kinetic energy by the length (64 / 9.0); 11 N divides the potential energy by the length (100 / 9.0). Note that the distance is the 9.0 m along the ramp, not the 5.0 m height, because friction acts along the surface.
What is the total (absolute) pressure 3.0 m below the surface of a lake? Take the density of water as 1000 kg/m³, g = 10 m/s² and atmospheric pressure as 100 kPa.
Answer: C
The water adds ρgh = 1000 × 10 × 3.0 = 30 000 Pa = 30 kPa, and the atmosphere presses on the surface with 100 kPa, so the total is 100 + 30 = 130 kPa. 30 kPa is the gauge pressure only, 100 kPa is the atmosphere alone, and 103 kPa adds 3 kPa, a slip of a factor of ten in converting 30 000 Pa.
Water (density 1000 kg/m³) flows at 2.0 m/s through a horizontal pipe that then narrows to half its original radius. Treating the water as an ideal fluid, how much lower is the pressure in the narrow section than in the wide section?
Answer: B
Halving the radius divides the cross-sectional area by 2² = 4, so by continuity (A₁v₁ = A₂v₂) the speed rises by 4, to 8.0 m/s. For a horizontal pipe, Bernoulli's equation gives p₁ − p₂ = ½ρ(v₂² − v₁²) = ½ × 1000 × (64 − 4) = 30 000 Pa = 30 kPa. 6 kPa only doubles the speed, as if area were proportional to radius; 60 kPa forgets the ½; 18 kPa uses ½ρ(v₂ − v₁)², squaring the difference of the speeds instead of taking the difference of their squares.
200 g of water at 80 °C is mixed with 300 g of water at 20 °C in an insulated container. Ignoring the heat taken by the container, what is the final temperature?
Answer: A
Heat lost by the hot water equals heat gained by the cold, and the specific heat capacity is the same for both, so 200 × (80 − T) = 300 × (T − 20). That gives 16 000 − 200T = 300T − 6000, so 500T = 22 000 and T = 44 °C. 50 °C is the plain average, which would be right only for equal masses; 56 °C swaps the masses, giving the larger share to the hot water; 60 °C is the temperature difference, not a temperature.
A gas is supplied with 1000 J of heat and expands at a constant pressure of 200 kPa from a volume of 2.0 L to 5.0 L. What is the change in the internal energy of the gas?
Answer: D
The work done by the gas is W = pΔV = 200 × 10³ Pa × (5.0 − 2.0) × 10⁻³ m³ = 600 J (1 L = 10⁻³ m³). By the first law, ΔU = Q − W = 1000 − 600 = 400 J: part of the heat goes into pushing back the surroundings. 600 J is the work, not the change in internal energy; 1000 J ignores the work; 1600 J adds the work instead of subtracting it, a sign error (work is done by the gas, so it leaves the gas's energy).
Two point charges a distance r apart repel each other with a force F. Both charges are doubled and the distance between them is also doubled. What is the new force?
Answer: C
By Coulomb's law F = kq₁q₂ / r². Doubling both charges multiplies the numerator by 2 × 2 = 4, and doubling r multiplies the denominator by 2² = 4, so the force is unchanged: F. 4F applies the charges but forgets the distance; F/4 applies the distance but forgets the charges; F/2 doubles only one of the two charges.
A 20 µF capacitor is charged to a potential difference of 50 V. How much energy does it store?
Answer: B
E = ½CV² = ½ × 20 × 10⁻⁶ F × (50 V)² = ½ × 20 × 10⁻⁶ × 2500 = 0.025 J = 25 mJ. 50 mJ forgets the ½; 1.0 mJ is the number for the charge, Q = CV = 1.0 mC, not an energy; 0.50 mJ is ½CV, which is half the charge, again not an energy.
A 6 Ω resistor and a 3 Ω resistor are connected in parallel, and this pair is connected in series with a 4 Ω resistor across a 12 V supply of negligible internal resistance. What current flows from the supply?
Answer: D
The parallel pair has resistance (6 × 3) / (6 + 3) = 18 / 9 = 2 Ω. Adding the 4 Ω in series gives 6 Ω in total, so I = V / R = 12 / 6 = 2.0 A. 0.92 A puts all three resistors in series (12 / 13); 3.0 A ignores the parallel pair (12 / 4); 1.3 A is the current in the 3 Ω branch only (the pair has 2.0 A × 2 Ω = 4 V across it, and 4 / 3 ≈ 1.3 A), not the current from the supply.
A 12 V battery drives a current of 0.50 A through a lamp for 10 minutes. How much energy does the battery transfer?
Answer: C
E = VIt, with the time in seconds: 10 min = 600 s, so E = 12 × 0.50 × 600 = 3600 J = 3.6 kJ. 60 J leaves the time in minutes; 300 J is the charge that flows, Q = It = 0.50 × 600 = 300 C, which is in coulombs, not joules; 1.8 kJ halves the answer, as the ½ in a capacitor's energy would, but the battery keeps a constant voltage, so no ½ applies.
A straight wire 0.50 m long carries a current of 4.0 A in a uniform magnetic field of 0.20 T. The wire makes an angle of 30° with the field. What is the magnitude of the magnetic force on the wire?
Answer: A
F = BIL sin θ, where θ is the angle between the wire and the field: F = 0.20 × 4.0 × 0.50 × sin 30° = 0.40 × 0.5 = 0.20 N. 0.40 N would apply only if the wire were at right angles to the field; 0.35 N uses cos 30° instead of sin 30°; 0.80 N leaves out the length (0.20 × 4.0).
A flat coil of 200 turns, each of area 0.010 m², lies at right angles to a uniform magnetic field. The field falls steadily from 0.50 T to 0.10 T in 0.20 s. What is the magnitude of the emf induced in the coil?
Answer: B
By Faraday's law, emf = N ΔΦ / Δt = N A ΔB / Δt = 200 × 0.010 × (0.50 − 0.10) / 0.20 = 200 × 0.010 × 0.40 / 0.20 = 4.0 V. 0.020 V leaves out the 200 turns; 5.0 V uses the starting field of 0.50 T as if it fell to zero; 6.0 V adds the two fields (0.60 T) instead of taking their difference.
An object is placed 15 cm in front of a thin converging lens of focal length 10 cm. Which statement describes the image?
Answer: C
With the lens equation 1/f = 1/u + 1/v (real distances positive), 1/v = 1/10 − 1/15 = 3/30 − 2/30 = 1/30, so v = +30 cm: a real image on the far side of the lens. The magnification is v / u = 30 / 15 = 2, and a real image formed by a single lens is inverted. 6.0 cm adds 1/10 and 1/15 instead of subtracting; the virtual, upright image would need the object inside the focal length (closer than 10 cm), and this object is between f and 2f; half the size inverts the magnification to u / v.
A laser emits light of wavelength 500 nm with an output power of 2.0 mW. About how many photons does it emit per second? Take h = 6.6 × 10⁻³⁴ J s and c = 3.0 × 10⁸ m/s.
Answer: D
Each photon carries E = hc / λ = (6.6 × 10⁻³⁴ × 3.0 × 10⁸) / (500 × 10⁻⁹) = 1.98 × 10⁻²⁵ / 5.0 × 10⁻⁷ ≈ 4.0 × 10⁻¹⁹ J. The laser emits 2.0 × 10⁻³ J each second, so the number per second is 2.0 × 10⁻³ / 4.0 × 10⁻¹⁹ ≈ 5 × 10¹⁵. 5 × 10¹⁸ takes the power as 2.0 W, forgetting the milli; 5 × 10¹² takes it as 2.0 µW; 2 × 10⁻¹⁶ divides the photon energy by the power, the wrong way round, and cannot be a count of photons.
A 500 Hz sound wave passes from air, where sound travels at 340 m/s, into water, where it travels at 1500 m/s. What are its frequency and wavelength in the water?
Answer: A
The frequency is set by the source and does not change when a wave crosses into a new medium, so it stays 500 Hz. The speed changes, so the wavelength does: λ = v / f = 1500 / 500 = 3.0 m. 0.68 m is the wavelength in air (340 / 500); the two options that change the frequency (500 × 1500 / 340 ≈ 2200 Hz, or 500 × 340 / 1500 ≈ 110 Hz) wrongly keep or scale the wavelength instead of the frequency.
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The Faculty of Medicine in Pilsen publishes no past papers. Its admission page links three free sample tests as PDFs, one each for Biology, Chemistry and Physics: 20 questions apiece, the same length as each subject on the 2027/28 paper, most with four options A to D and some open-response (a definition, a balanced equation, a compound name), with the solutions at the end of each file. The same page gives the full syllabus of each subject and a short list of A-level study guides. IvyTest's free practice paper, with every answer explained, follows the live format.
This paper keeps the format Pilsen states for 2027/28 (60 questions, 20 each in Biology, Chemistry and Physics, one correct answer, no penalty, at least 9 points per subject) and the subjects of its official syllabi. Every question is new, and every one has its answer explained.
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One paper shows where you are today. Take the free diagnostic next, or read the Charles University Pilsen Entrance Exam guide for the syllabus, dates and scoring in full.
