Free practice paper · 2027 format

HUMAT Test Practice Paper 1

60 questions in the format of today's HUMAT Test, with the answer and a full explanation for every one. Written by IvyTest and modelled on the Humanitas past papers. It is not an official HUMAT paper.

Start at question 1 The full HUMAT Test guide

Before you start

How to sit this paper

Questions
60
Time
120 minutes
Options per question
5 (A to E)
Sections
3, each timed separately
SectionQuestionsTimeMarks (Medicine and Surgery)
Scientific Thinking & Academic Literacy2045 min+22 correct, -5.5 wrong, 0 blank
Biology & Chemistry2035 min+16 correct, -4 wrong, 0 blank
Mathematics & Physics2040 min+10 correct, -2.5 wrong, 0 blank

Sit each section in order against its own clock, and answer on paper before opening any explanation. A wrong answer costs marks and a blank costs nothing, so leave a question blank rather than guess blindly.

Section 1 of 3

Scientific Thinking & Academic Literacy

20 questions · 45 minutes

Question 1

Scientific Thinking · Procedural Thinking · Standard

A hospital pharmacy uses the following (fictional) rule to set the daily dose of a medicine for a child.

Step 1: Start with 15 mg for each kilogram of body mass. Step 2: If the child is younger than 2 years, reduce the result of Step 1 by one third. Step 3: If the result is more than 400 mg, use 400 mg instead. Step 4: Round the result down to the nearest multiple of 25 mg.

What daily dose does the rule give for a child aged 18 months with a body mass of 12 kg?

Show answer and explanation

Answer: A

Step 1: 15 × 12 = 180 mg. Step 2: the child is under 2, so reduce by one third: 180 − 60 = 120 mg. Step 3: 120 mg is below 400 mg, so no change. Step 4: rounding 120 down to a multiple of 25 gives 100 mg. Rounding to the nearest multiple instead of down gives 125 mg (C); skipping Step 2 gives 175 mg (D).

Question 2

Scientific Thinking · Mathematical Thinking · Challenging

The rate Q at which a liquid flows through a narrow tube is given by

Q = k × P × r⁴ ÷ L

where P is the pressure difference between the ends of the tube, r is the radius of the tube, L is its length and k is a constant.

If the radius of the tube is halved and its length is also halved, with the pressure difference unchanged, what happens to Q?

Show answer and explanation

Answer: C

Halving r multiplies r⁴ by (1/2)⁴ = 1/16. Halving L, which is on the bottom of the fraction, doubles Q. Together: 1/16 × 2 = 1/8. Dividing by 2 instead of multiplying gives 1/32 (A); ignoring the change in length gives 1/16 (B).

Question 3

Scientific Thinking · Mathematical Thinking · Standard

A pharmacy records how many flu vaccinations it gives in four consecutive weeks.

Week 1: 120 Week 2: 150 Week 3: 195 Week 4: 180

Which one of the following statements is correct?

Show answer and explanation

Answer: D

Week 1 to week 2: 30 more on 120, a 25% rise. Week 2 to week 3: 45 more on 150, a 30% rise. Week 3 to week 4 is a fall. So the largest rise is from week 2 to week 3. The mean is 645 ÷ 4 = 161.25 (A); week 4 is 15 ÷ 195 ≈ 7.7% below week 3 (B); weeks 1 and 2 total 270 against 375 (C); week 4 is 50% above week 1 (E).

Question 4

Scientific Thinking · Mathematical Thinking · Standard

The rate of an intravenous drip, in drops per minute, is found with

rate = (volume in mL × drop factor) ÷ time in minutes

where the drop factor is the number of drops that make up 1 mL. A patient is to receive 500 mL of fluid over 4 hours through a set with a drop factor of 20 drops/mL.

What drip rate is needed, to the nearest whole number?

Show answer and explanation

Answer: B

4 hours = 240 minutes. (500 × 20) ÷ 240 = 10 000 ÷ 240 ≈ 41.7, which is 42 to the nearest whole number. Leaving the time in hours gives 2500 (D); 41 rounds down instead of to the nearest whole number (E).

Question 5

Scientific Thinking · Procedural Thinking · Standard

A (fictional) triage protocol sorts casualties into three categories.

Step 1: If the casualty is not breathing, the category is Red. Step 2: Otherwise, if the breathing rate is above 30 breaths per minute, the category is Red. Step 3: Otherwise, if the casualty cannot walk, the category is Red if the pulse is above 120 beats per minute and Yellow if it is not. Step 4: Otherwise, the category is Green.

Four casualties are assessed. P: breathing 24 per minute, cannot walk, pulse 130 Q: breathing 32 per minute, can walk, pulse 90 R: breathing 18 per minute, can walk, pulse 125 S: breathing 20 per minute, cannot walk, pulse 100

Which casualties are placed in the Red category?

Show answer and explanation

Answer: E

P is breathing at 24, cannot walk and has a pulse of 130, so Step 3 makes it Red. Q's breathing rate of 32 makes it Red at Step 2, before walking is considered. R can walk, so it reaches Step 4 and is Green despite its fast pulse. S cannot walk but its pulse is 100, so it is Yellow. The pulse only matters for casualties who cannot walk, which is why C is wrong.

Question 6

Scientific Thinking · Procedural Thinking · Foundation

A word is encoded in two steps. First, each letter is replaced by the letter three places later in the alphabet (A becomes D, B becomes E, and so on). Then the order of the letters is reversed.

What does the word CELL become?

Show answer and explanation

Answer: A

C becomes F, E becomes H and each L becomes O, giving FHOO; reversed, that is OOHF. B leaves out the reversal; D and E shift the letters backwards instead of forwards.

Question 7

Scientific Thinking · Visual Thinking · Standard

An analogue clock is seen in a mirror. In the reflection, its hands appear to show 4:20.

What time does the clock actually show?

Show answer and explanation

Answer: C

A mirror swaps left and right, so each hand appears at the mirror-image position, and the real time and the reflected time add up to 12:00: 12:00 − 4:20 = 7:40. Check: at 7:40 the minute hand points at the 8 and appears at the 4 (20 minutes), and the hour hand, two thirds of the way from 7 to 8, appears one third of the way from 4 to 5.

Question 8

Scientific Thinking · Visual Thinking · Challenging

On a standard die, the numbers on opposite faces always add up to 7. A die rests on a table with 2 on the top face and 3 on the face towards you. It is tipped over its far bottom edge, so that it rolls a quarter-turn away from you, three times in a row.

Which number is now on the top face?

Show answer and explanation

Answer: D

Each roll away brings the face that was towards you to the top, and the old bottom face to the front. At the start: top 2, front 3, bottom 5, back 4. After the first roll: top 3, front 5. After the second: top 5, front 4. After the third: top 4.

Question 9

Scientific Thinking · Visual Thinking · Foundation

The capital letter N, written as three straight lines, is rotated 90° clockwise.

Which capital letter does the rotated shape most closely resemble?

Show answer and explanation

Answer: B

The two uprights of the N become horizontal bars at the top and the bottom, and the diagonal, which ran from top left to bottom right, now runs from top right to bottom left: the shape of a Z.

Question 10

Scientific Thinking · Visual Thinking · Standard

Matchsticks are laid out to make a row of squares. One square uses 4 matchsticks, a row of two squares uses 7 and a row of three squares uses 10, because neighbouring squares share a side.

How many matchsticks are needed for a row of 20 squares?

Show answer and explanation

Answer: E

The first square needs 4 matchsticks and each further square adds 3, so a row of n squares needs 3n + 1. For 20 squares: 3 × 20 + 1 = 61. Counting 4 per square gives 80 (C); counting 3 per square with nothing extra gives 60 (A).

Question 11

Academic Literacy · Critical Thinking · Standard

A survey of 2,000 adults found that people who own a fitness tracker exercise on more days each week than people who do not. The manufacturer of one tracker says this proves that wearing a tracker makes people more active.

Which one of the following best expresses the flaw in the manufacturer's reasoning?

Show answer and explanation

Answer: B

The survey shows only that owning a tracker and exercising often go together. The manufacturer reads that as the tracker causing the exercise, but the link could run the other way: keen exercisers are the people most likely to buy one. A 2,000-person sample is not small (E), and the argument makes no claim about health (D).

Question 12

Academic Literacy · Critical Thinking · Standard

The city council wants to reduce traffic in the historic centre. It proposes doubling the price of parking there, arguing that drivers faced with higher charges will leave their cars at home and take the bus instead.

Which one of the following is an assumption on which the council's argument depends?

Show answer and explanation

Answer: D

The plan only works if drivers have somewhere to switch to: if none of them could reach the centre by bus, higher charges would not move anyone onto buses. That is the assumption the argument needs. Stable bus fares (B) might help the plan, but the argument does not depend on them; the others are not needed at all.

Question 13

Academic Literacy · Global Careful Reading · Standard

Which one of the following best expresses the main idea of the passage?

Show answer and explanation

Answer: E

The passage argues that forgetting can be useful, then limits that claim in its last paragraph. A overstates it ('always'), which the dementia example rules out. B and D take a detail for the main idea, and C goes further than the passage, which says only that forgetting used to be seen as a failure.

Question 14

Academic Literacy · Word- and Sentence-Level Processes · Foundation
Show the passage · Forgetting

For most of the twentieth century, forgetting was treated as a failure: a sign that information had been stored badly, or had simply faded with time. Recent research has encouraged a different view. Studies in both mice and humans suggest that the brain actively clears away some memories, and that this clearing is not a defect but a feature.

A memory system that kept every detail would be slow to search and would struggle to generalise. By discarding specifics, the brain can hold on to the patterns that stay useful when circumstances change. Someone who cannot recall exactly where they parked last Tuesday is not showing a weakness: that detail stopped mattering once the car was collected.

Researchers are careful, however, not to overstate the point. Forgetting can still do great harm, as in dementia, where the loss is neither selective nor useful.

In the sentence 'Researchers are careful, however, not to overstate the point', what does the word 'however' signal?

Show answer and explanation

Answer: C

'However' introduces a contrast. Here it qualifies what came before: having argued that forgetting can be useful, the passage now warns against taking that too far, and gives dementia as a case where forgetting is harmful. The topic stays the same, so E is wrong.

Question 15

Academic Literacy · Critical Thinking · Standard

Last year a town introduced a 20 km/h speed limit on the roads around its schools. In the twelve months since, the number of children injured on those roads fell from 14 to 9. The council concludes that the lower speed limit has made the roads around its schools safer for children.

Which one of the following, if true, most weakens the council's conclusion?

Show answer and explanation

Answer: B

If two of the five schools closed, far fewer children use the roads around the town's schools, which could explain the fall in injuries without the speed limit having any effect. A makes the fall more striking, so it strengthens the conclusion rather than weakening it; C, D and E say nothing about why injuries fell.

Question 16

Academic Literacy · Critical Thinking · Standard

Many people assume that a food labelled 'natural' must be healthier than a processed alternative. Yet for most foods, in many countries, the word has no legal definition, so manufacturers are free to use it as they like. Moreover, some natural substances, such as certain mushrooms, are highly toxic, while many processed foods are fortified with vitamins that prevent deficiency diseases. Shoppers should therefore judge a food by its list of ingredients and its nutritional content, not by whether it claims to be natural.

Which one of the following best expresses the main conclusion of the above argument?

Show answer and explanation

Answer: E

The final sentence, introduced by 'therefore', is what the rest of the passage argues for; A and B are two of the reasons given for it. C goes further than the passage, which says only that some processed foods are fortified, and D is never claimed.

Question 17

Academic Literacy · Local Expeditious Reading · Foundation

According to the passage, what did Laennec compare his notes on patients' chest sounds with?

Show answer and explanation

Answer: A

Paragraph 2: 'when they died, compared his notes with what he found at autopsy'. None of the other sources is mentioned in the passage.

Question 18

Academic Literacy · Global Expeditious Reading · Foundation
Show the passage · The listening tube

Before 1816, a doctor who wanted to hear a patient's heart had one option: to press an ear directly against the patient's chest. The method, known as immediate auscultation, was awkward for both doctor and patient and often told the doctor little, particularly when the patient was overweight. In that year the French physician René Laennec, examining a young woman whose symptoms suggested heart disease, rolled a sheaf of paper into a tube, placed one end on her chest and put the other to his ear. He was surprised to find that her heartbeat sounded clearer than it ever had through direct contact.

Laennec spent the next three years refining the device, eventually settling on a hollow wooden cylinder about 25 centimetres long, and, more importantly, learning what the sounds meant. He listened to hundreds of patients and, when they died, compared his notes with what he found at autopsy. In 1819 he published a treatise linking particular sounds to particular diseases of the lungs and heart. It was this work of classification, rather than the tube itself, that made the stethoscope useful: an instrument that carries sound is of little value to a doctor who cannot interpret it.

The stethoscope was not adopted at once. Some physicians objected that it put a barrier between doctor and patient, and others doubted that sound could reveal anything that touch and observation could not. By the middle of the century, however, it had become standard equipment, and binaural designs, with a tube for each ear, had begun to replace Laennec's single wooden cylinder.

Which one of the following would be the best title for the passage?

Show answer and explanation

Answer: D

The passage follows the stethoscope from Laennec's rolled paper to standard equipment. A and C cover only part of paragraph 3; B names the method the stethoscope replaced; E is what Laennec's treatise did, not what the passage does.

Question 19

Academic Literacy · Global Careful Reading · Standard
Show the passage · The listening tube

Before 1816, a doctor who wanted to hear a patient's heart had one option: to press an ear directly against the patient's chest. The method, known as immediate auscultation, was awkward for both doctor and patient and often told the doctor little, particularly when the patient was overweight. In that year the French physician René Laennec, examining a young woman whose symptoms suggested heart disease, rolled a sheaf of paper into a tube, placed one end on her chest and put the other to his ear. He was surprised to find that her heartbeat sounded clearer than it ever had through direct contact.

Laennec spent the next three years refining the device, eventually settling on a hollow wooden cylinder about 25 centimetres long, and, more importantly, learning what the sounds meant. He listened to hundreds of patients and, when they died, compared his notes with what he found at autopsy. In 1819 he published a treatise linking particular sounds to particular diseases of the lungs and heart. It was this work of classification, rather than the tube itself, that made the stethoscope useful: an instrument that carries sound is of little value to a doctor who cannot interpret it.

The stethoscope was not adopted at once. Some physicians objected that it put a barrier between doctor and patient, and others doubted that sound could reveal anything that touch and observation could not. By the middle of the century, however, it had become standard equipment, and binaural designs, with a tube for each ear, had begun to replace Laennec's single wooden cylinder.

According to the passage, what made the stethoscope useful to doctors?

Show answer and explanation

Answer: C

Paragraph 2 says that it was 'this work of classification, rather than the tube itself, that made the stethoscope useful'. B describes the tube's advantage, which the passage says was not enough on its own; E is what the sceptics in paragraph 3 doubted, not the passage's explanation.

Question 20

Academic Literacy · Word- and Sentence-Level Processes · Standard
Show the passage · The listening tube

Before 1816, a doctor who wanted to hear a patient's heart had one option: to press an ear directly against the patient's chest. The method, known as immediate auscultation, was awkward for both doctor and patient and often told the doctor little, particularly when the patient was overweight. In that year the French physician René Laennec, examining a young woman whose symptoms suggested heart disease, rolled a sheaf of paper into a tube, placed one end on her chest and put the other to his ear. He was surprised to find that her heartbeat sounded clearer than it ever had through direct contact.

Laennec spent the next three years refining the device, eventually settling on a hollow wooden cylinder about 25 centimetres long, and, more importantly, learning what the sounds meant. He listened to hundreds of patients and, when they died, compared his notes with what he found at autopsy. In 1819 he published a treatise linking particular sounds to particular diseases of the lungs and heart. It was this work of classification, rather than the tube itself, that made the stethoscope useful: an instrument that carries sound is of little value to a doctor who cannot interpret it.

The stethoscope was not adopted at once. Some physicians objected that it put a barrier between doctor and patient, and others doubted that sound could reveal anything that touch and observation could not. By the middle of the century, however, it had become standard equipment, and binaural designs, with a tube for each ear, had begun to replace Laennec's single wooden cylinder.

In paragraph 2, what does the phrase 'more importantly' tell the reader about the writer's view?

Show answer and explanation

Answer: B

'More importantly' ranks the second activity, learning what the sounds meant, above the first, refining the device. It is the writer's judgement, not a claim about Laennec's own view (C), and the paragraph's last sentence makes the same point.

Section 2 of 3

Biology & Chemistry

20 questions · 35 minutes

Question 21

Biology · Reproduction and Inheritance · Standard

In a species of plant, the allele for red flowers (R) is dominant to the allele for white flowers (r), and the allele for tall stems (T) is dominant to the allele for short stems (t). The two genes are on different chromosomes.

A plant heterozygous for both genes is crossed with a plant that has white flowers and short stems.

What proportion of the offspring is expected to have a phenotype different from both parents?

Show answer and explanation

Answer: D

The cross is RrTt × rrtt. The first parent makes four kinds of gamete in equal numbers (RT, Rt, rT, rt) and the second makes only rt, so the offspring are red tall, red short, white tall and white short, a quarter each. The parents are red tall and white short, so the new phenotypes are red short and white tall: 1/4 + 1/4 = 1/2.

Question 22

Biology · Chemistry of Living Things · Standard

Which of the following statements about proteins is/are correct?

1 The primary structure of a protein is its sequence of amino acids. 2 An α-helix is held in shape by hydrogen bonds between groups in the polypeptide backbone. 3 Denaturing a protein by heating it breaks the peptide bonds between its amino acids.

Show answer and explanation

Answer: A

Statements 1 and 2 are correct. Heat denatures a protein by breaking the weak interactions that hold its shape (hydrogen bonds, ionic and hydrophobic interactions); the covalent peptide bonds survive, so the primary structure is unchanged. That is why 3 is wrong.

Question 23

Biology · Cell as the Basis of Life · Foundation

Which one of the following structures is found in both prokaryotic and eukaryotic cells?

Show answer and explanation

Answer: C

Every cell makes proteins, so every cell has ribosomes: smaller (70S) ones in prokaryotes and 80S ones in the cytoplasm of eukaryotes. A nucleus and membrane-bound organelles such as mitochondria, the endoplasmic reticulum and the Golgi apparatus are found only in eukaryotic cells.

Question 24

Biology · Cell as the Basis of Life · Foundation

A sample of human red blood cells is placed in distilled water.

What happens to the cells?

Show answer and explanation

Answer: B

Distilled water has a higher water potential than the cytoplasm, so water moves into the cells by osmosis. Animal cells have no cell wall (D describes a plant cell), so they swell until the membrane ruptures: haemolysis.

Question 25

Biology · Bioenergetics · Foundation

In which part of a human cell does glycolysis take place?

Show answer and explanation

Answer: E

Glycolysis, which splits glucose into two molecules of pyruvate, happens in the cytoplasm and does not need oxygen. The link reaction and the Krebs cycle happen in the mitochondrial matrix (A), and oxidative phosphorylation on the inner mitochondrial membrane (B).

Question 26

Biology · Bioenergetics · Challenging

During intense exercise, when the supply of oxygen is insufficient, human muscle cells convert pyruvate into lactate.

What is the main importance of this reaction?

Show answer and explanation

Answer: D

Glycolysis needs NAD⁺ to accept electrons. Without oxygen the electron transport chain cannot reoxidise NADH, so reducing pyruvate to lactate is how the cell regenerates NAD⁺ and keeps getting the small yield of ATP from glycolysis. The reaction itself makes no ATP (A) and releases no carbon dioxide (B).

Question 27

Biology · Reproduction and Inheritance · Standard

A man with blood group AB and a woman with blood group O have a child.

Which blood groups could the child have?

Show answer and explanation

Answer: A

The man's genotype is IᴬIᴮ and the woman's is ii. Every child receives i from the mother and either Iᴬ or Iᴮ from the father, so is Iᴬi (group A) or Iᴮi (group B), each with a probability of 1/2. No child of this couple can be AB or O.

Question 28

Biology · Evolution and Selection · Standard

Which one of the following is an example of natural selection?

Show answer and explanation

Answer: C

Natural selection needs inherited variation and differences in survival and reproduction caused by the environment, which is what C describes. A is the inheritance of acquired characteristics, which does not happen; B is artificial selection; D is an acquired change, not an inherited one; and mutations arise at random, not in response to need (E).

Question 29

Biology · Anatomy, Physiology and Homeostasis · Foundation

Which blood vessel carries deoxygenated blood away from the heart?

Show answer and explanation

Answer: E

The right ventricle pumps deoxygenated blood to the lungs through the pulmonary artery, the only artery in an adult that carries deoxygenated blood. The pulmonary vein brings oxygenated blood back to the heart (B), and the venae cavae bring deoxygenated blood to the heart, not away from it (C).

Question 30

Biology · Anatomy, Physiology and Homeostasis · Standard

Shortly after a meal rich in carbohydrate, the concentration of glucose in a person's blood rises.

Which response returns it towards its normal level?

Show answer and explanation

Answer: B

A rise in blood glucose is detected by the β cells of the islets of Langerhans, which release insulin. Insulin increases the uptake of glucose by cells and its conversion to glycogen in the liver and muscles. A and E describe responses that raise blood glucose; insulin comes from the pancreas, and healthy kidneys do not excrete glucose (C).

Question 31

Chemistry · Stoichiometry and Chemical Reactions · Challenging

4.8 g of magnesium is heated with 1.6 g of oxygen gas until no further reaction takes place.

2Mg + O₂ → 2MgO

Which row correctly gives the mass of magnesium oxide formed and the reactant left over? (Relative atomic masses: Mg = 24, O = 16)

Show answer and explanation

Answer: A

Moles of Mg = 4.8 ÷ 24 = 0.20. Moles of O₂ = 1.6 ÷ 32 = 0.050. 0.050 mol of O₂ reacts with 0.10 mol of Mg, so oxygen runs out first and 0.10 mol of Mg is left over. 0.10 mol of MgO forms: 0.10 × 40 = 4.0 g. Adding the two masses (B) ignores the leftover magnesium; treating magnesium as the limiting reactant gives 8.0 g (C).

Question 32

Chemistry · Structure of Matter and the Periodic Table · Foundation

An atom of iron has atomic number 26 and mass number 56.

How many neutrons does it contain?

Show answer and explanation

Answer: D

Neutrons = mass number − atomic number = 56 − 26 = 30. 26 is the number of protons, and of electrons in the neutral atom; 82 adds the two numbers instead of subtracting them.

Question 33

Chemistry · Structure of Matter and the Periodic Table · Standard

Which element has the ground-state electron configuration 1s² 2s² 2p⁶ 3s² 3p⁴?

Show answer and explanation

Answer: A

The electrons add up to 2 + 2 + 6 + 2 + 4 = 16, the atomic number of sulfur. Oxygen (8) and selenium (34) have the same outer arrangement, s²p⁴, but in the second and fourth shells.

Question 34

Chemistry · Chemical Bonding and Properties of Matter · Standard

Which one of the following molecules is non-polar, even though it contains polar bonds?

Show answer and explanation

Answer: E

Each C=O bond is polar, but CO₂ is linear, so the two bond dipoles point in opposite directions and cancel. Water is bent and ammonia is pyramidal, so their bond dipoles do not cancel; HCl has a single polar bond; and in CH₃Cl the C–Cl dipole is not balanced by the C–H bonds.

Question 35

Chemistry · Stoichiometry and Chemical Reactions · Standard

What volume of 0.20 mol/L sodium hydroxide solution exactly neutralises 25.0 mL of 0.10 mol/L sulfuric acid?

H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O

Show answer and explanation

Answer: C

Moles of H₂SO₄ = 0.0250 L × 0.10 mol/L = 0.0025 mol. The equation needs twice as much NaOH: 0.0050 mol. Volume = 0.0050 ÷ 0.20 = 0.025 L = 25.0 mL. Ignoring the 1 : 2 ratio gives 12.5 mL (B).

Question 36

Chemistry · Chemical Bonding and Properties of Matter · Standard

According to VSEPR theory, what is the shape of a molecule of ammonia, NH₃?

Show answer and explanation

Answer: B

Nitrogen has three bonding pairs and one lone pair: four electron pairs arranged roughly tetrahedrally. Describing only the positions of the atoms, the molecule is a trigonal pyramid, with H–N–H angles of about 107°. Tetrahedral (C) is the arrangement of the electron pairs, not the shape of the molecule.

Question 37

Chemistry · Equilibria, Acids-Bases and Redox · Standard

A solution of hydrochloric acid has a pH of 2. It is diluted with water until its volume is 100 times greater.

What is the pH of the diluted solution?

Show answer and explanation

Answer: D

A pH of 2 means [H⁺] = 10⁻² mol/L. Diluting 100 times gives 10⁻⁴ mol/L, so the pH is 4. Each tenfold dilution of a strong acid raises the pH by 1, so a hundredfold dilution raises it by 2, not 1 (C). Dilution alone can bring an acid close to 7 but never past it (E).

Question 38

Chemistry · Equilibria, Acids-Bases and Redox · Standard

In the reaction

Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)

which one of the following statements is correct?

Show answer and explanation

Answer: A

Zinc goes from an oxidation number of 0 to +2: it loses two electrons, so it is oxidised, and by giving those electrons to Cu²⁺ it acts as the reducing agent. Copper goes from +2 to 0, a decrease, which D has the wrong way round.

Question 39

Chemistry · Fundamentals of Organic Chemistry · Standard

How many structural isomers have the molecular formula C₄H₁₀?

Show answer and explanation

Answer: E

Four carbon atoms can form an unbranched chain (butane) or a three-carbon chain with a methyl branch on the middle carbon (2-methylpropane). Putting the branch on an end carbon just makes butane again, so there are two.

Question 40

Chemistry · Fundamentals of Organic Chemistry · Foundation

Which one of the following compounds is an ester?

Show answer and explanation

Answer: C

An ester contains the –COO– group with a carbon atom on each side: CH₃COOCH₃ is methyl ethanoate. A is an alcohol (ethanol), B a ketone (propanone), D a carboxylic acid (ethanoic acid) and E an aldehyde (ethanal).

Section 3 of 3

Mathematics & Physics

20 questions · 40 minutes

Question 41

Mathematics · Probability, Statistics and Combinatorics · Standard

A bag contains 4 red counters and 6 blue counters. Two counters are taken out at random, one after the other, without replacement.

What is the probability that the two counters are different colours?

Show answer and explanation

Answer: E

Red then blue: 4/10 × 6/9 = 24/90. Blue then red: 6/10 × 4/9 = 24/90. Total: 48/90 = 8/15. Counting only one order gives 4/15 (A); drawing with replacement gives 2 × 0.4 × 0.6 = 12/25 (C).

Question 42

Mathematics · Functions · Foundation

If 3ˣ⁺¹ = 81, what is the value of x?

Show answer and explanation

Answer: B

81 = 3⁴, so x + 1 = 4 and x = 3. C gives the exponent itself rather than x; D comes from treating the power as a product, 3(x + 1) = 81.

Question 43

Mathematics · Algebra and Number Sets · Foundation

The price of a coat is increased by 20%. Later, the new price is reduced by 20%.

How does the final price compare with the original price?

Show answer and explanation

Answer: A

Percentage changes multiply: 1.20 × 0.80 = 0.96, so the final price is 96% of the original, 4% lower. The 20% reduction is taken from a larger amount than the 20% rise was, which is why the two do not cancel (B).

Question 44

Mathematics · Functions · Standard

What is the minimum value of the function f(x) = x² − 6x + 5?

Show answer and explanation

Answer: D

Completing the square: x² − 6x + 5 = (x − 3)² − 4. The square is never negative and is 0 when x = 3, so the minimum value is −4. 3 is where the minimum occurs, not its value (B).

Question 45

Mathematics · Algebra and Number Sets · Standard

Which values of x satisfy |2x − 3| < 5?

Show answer and explanation

Answer: C

|2x − 3| < 5 means −5 < 2x − 3 < 5. Adding 3 throughout gives −2 < 2x < 8, so −1 < x < 4. D is the solution of the opposite inequality, |2x − 3| > 5.

Question 46

Mathematics · Geometry and Trigonometry · Challenging

A right-angled triangle has shorter sides of 6 cm and 8 cm. A circle passes through all three of its vertices.

What is the area of the circle?

Show answer and explanation

Answer: E

The hypotenuse is √(6² + 8²) = 10 cm. The angle in a semicircle is a right angle, so the hypotenuse of a right-angled triangle is a diameter of the circle through its vertices: the radius is 5 cm and the area 25π cm². Taking 10 cm as the radius gives 100π (D); 24 cm² is the area of the triangle (B).

Question 47

Mathematics · Geometry and Trigonometry · Standard

An acute angle θ has sin θ = 3/5.

What is the value of tan θ?

Show answer and explanation

Answer: A

cos²θ = 1 − (3/5)² = 16/25, and cos θ is positive for an acute angle, so cos θ = 4/5. Then tan θ = sin θ ÷ cos θ = (3/5) ÷ (4/5) = 3/4: the familiar 3-4-5 triangle with 3 opposite θ.

Question 48

Mathematics · Logic and Mathematical Reasoning · Standard

Which one of the following is the negation of the statement 'All the students passed the exam'?

Show answer and explanation

Answer: D

The negation of 'every student passed' is 'not every student passed', which means that at least one did not. A and B are much stronger claims: in a class where most students passed and one failed, 'all passed' is false, yet A and B are false too.

Question 49

Mathematics · Logic and Mathematical Reasoning · Challenging

Which one of the following is logically equivalent to 'If it rains, the match is cancelled'?

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Answer: B

B is the contrapositive (if not Q, then not P), which always has the same truth value as the original statement. A is the converse and C the inverse: the match could be cancelled for some other reason. The statement is also equivalent to 'it does not rain, or the match is cancelled', which is not what E says.

Question 50

Mathematics · Probability, Statistics and Combinatorics · Standard

The mean of five numbers is 12. Four of the numbers are 10, 11, 14 and 15.

What is the median of the five numbers?

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Answer: C

The five numbers add up to 5 × 12 = 60. The four given add up to 50, so the fifth is 10. In order they are 10, 10, 11, 14, 15, and the middle one is 11. 12 is the mean, not the median (B).

Question 51

Physics · Dynamics · Standard

A car of mass 1200 kg is travelling at 20 m/s. The driver brakes, and the car comes to rest in a distance of 40 m.

Assuming the braking force is constant, what is its size?

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Answer: C

From v² = u² + 2as: 0 = 20² + 2a × 40, so a = −400 ÷ 80 = −5 m/s². The force is F = ma = 1200 × 5 = 6000 N. Leaving out the 2 in 2as gives 10 m/s² and 12 000 N (D).

Question 52

Physics · Measures and Kinematics · Foundation

Which one of the following expresses the newton in SI base units?

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Answer: E

From F = ma, one newton gives a mass of 1 kg an acceleration of 1 m/s²: kg·m·s⁻². A is the unit of momentum and B the unit of energy, the joule; D uses CGS units and is the dyne.

Question 53

Physics · Measures and Kinematics · Standard

A ball is dropped from rest from a height of 20 m. Air resistance is negligible and g = 10 m/s².

How long does the ball take to reach the ground, and how fast is it moving when it lands?

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Answer: A

From h = ½gt²: 20 = 5t², so t = 2.0 s. Then v = gt = 10 × 2.0 = 20 m/s (or, from v² = 2gh, v² = 400). Leaving out the ½ gives t² = 2 and t ≈ 1.4 s (D).

Question 54

Physics · Dynamics · Standard

A block of mass 2.0 kg rests on a smooth horizontal surface. It is pulled by a force of 10 N directed at 60° above the horizontal, and it stays on the surface.

What is its acceleration? (cos 60° = 0.50, sin 60° ≈ 0.87)

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Answer: D

Only the horizontal component of the force accelerates the block along the surface: 10 × cos 60° = 5.0 N. So a = F ÷ m = 5.0 ÷ 2.0 = 2.5 m/s². Using the sine gives 4.3 m/s² (B); using the whole force gives 5.0 m/s² (A).

Question 55

Physics · Fluid Mechanics and Optics · Standard

By how much is the pressure 5.0 m below the surface of a lake greater than the pressure at the surface? (Density of water = 1000 kg/m³, g = 10 m/s²)

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Answer: B

By Stevino's law, the extra pressure is ρgh = 1000 × 10 × 5.0 = 50 000 Pa = 50 kPa. 150 kPa (C) is roughly the total pressure at that depth, including about 100 kPa from the atmosphere above the lake; the question asks only for the difference.

Question 56

Physics · Fluid Mechanics and Optics · Standard

Light passes from air into glass.

Which of the following statements about the light is/are correct?

1 Its speed decreases. 2 Its frequency decreases. 3 Its wavelength decreases.

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Answer: C

Glass has a higher refractive index than air, so light travels more slowly in it. The frequency is set by the source and does not change at a boundary, and since v = fλ, a lower speed at the same frequency means a shorter wavelength.

Question 57

Physics · Thermodynamics · Foundation

A kettle heats 1.5 kg of water from 15 °C to 75 °C. Assuming no energy is lost to the surroundings, how much energy does the water gain? (Take the specific heat capacity of water as 4.2 kJ per kg per °C.)

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Answer: E

Q = mcΔT = 1.5 × 4.2 × 60 = 378 kJ. Using the final temperature, 75 °C, instead of the change gives about 473 kJ (C); leaving out the mass gives 252 kJ (B).

Question 58

Physics · Thermodynamics · Standard

A fixed mass of ideal gas is kept at constant volume while its temperature is raised from 27 °C to 327 °C.

What happens to its pressure?

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Answer: A

At constant volume, the pressure of an ideal gas is proportional to its absolute temperature. 27 °C = 300 K and 327 °C = 600 K, so the temperature doubles and so does the pressure. The ratio 327 ÷ 27 ≈ 12 (B) comes from using degrees Celsius, which is not an absolute scale.

Question 59

Physics · Electrostatics and Electrodynamics · Standard

Resistors of 6.0 Ω and 3.0 Ω are connected in parallel across a 12 V supply of negligible internal resistance.

What current is drawn from the supply?

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Answer: D

In parallel, 1/R = 1/6.0 + 1/3.0 = 1/2.0, so R = 2.0 Ω and I = V ÷ R = 12 ÷ 2.0 = 6.0 A. Equivalently, the branches carry 2.0 A and 4.0 A, which add up to 6.0 A. Treating the resistors as if they were in series gives 12 ÷ 9 ≈ 1.3 A (A).

Question 60

Physics · Electrostatics and Electrodynamics · Standard

Two small charged spheres repel each other with a force F. The distance between them is tripled, and the charge on one of the spheres is doubled.

What is the new force between them?

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Answer: B

By Coulomb's law, F is proportional to q₁q₂/r². Doubling one charge doubles the force, and tripling the distance divides it by 3² = 9, so the new force is 2F/9. Dividing by 3 instead of 9 gives 2F/3 (C).

About this paper

HUMAT Test past papers

Humanitas's admissions pages publish no past papers or sample test. What Humanitas does publish: the official syllabus (Syllabi 2027, posted on its Apply page in October 2026), the points and section minimums for each ranking, and a technical guide; registered candidates also get a demo on Politecnico di Milano's portal to check their computer. Its archive of calls shows why old papers mislead: the EU calls for 2014/15 to 2017/18 describe a 100-minute paper test with general culture and logical reasoning, arranged with Cambridge Assessment (the non-EU calls differed: computer-based in 2015/16, the UKCAT in 2017/18), and the 2020/21 to 2025/26 calls a test of Scientific Thinking and Academic Literacy only, with four options. Today's six subjects in three timed sections date from the 2026 tests. The practice paper on this page is IvyTest's own, in that format.

This paper keeps the kinds of question those papers asked and sets them in today's format. Every question on it is new.

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