Free practice paper · 2027 format

Campus Bio-Medico Admission Test Practice Paper 1, with Answers

60 questions in the format of UCBM's call: 20 Biology, 20 Chemistry and 20 Physics, five options each, with the answer and a full explanation for every one. One test admits to both English-taught degrees, Medicine and Surgery and Medicine and Surgery – MedTech, so this paper prepares you for either. Written by IvyTest; it is not an official Campus Bio-Medico paper.

Before you start

How to sit this paper

Questions
60
Time
100 minutes
Options per question
5 (A to E)
Sections
3, against one overall time
SectionQuestionsTimeMarks (Medicine and Surgery Admission Test)
Biology20–+1 correct, -0.2 wrong, 0 blank
Chemistry20–+1 correct, -0.2 wrong, 0 blank
Physics20–+1 correct, -0.2 wrong, 0 blank

Give yourself 100 minutes for all 60 questions, with no calculator, and answer on paper before opening any explanation. A correct answer scores 1 point, a wrong one loses 0.2 and a blank scores 0, out of 60; you need at least 12 to be ranked. Guess only when you can rule out at least one option.

Section 1 of 3

Biology

20 questions

Question 1

Biology · The Chemistry of Living Organisms · Foundation

Water has an unusually high specific heat capacity and a high surface tension for such a small molecule. Which interaction is mainly responsible for these properties?

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Answer: C

Each water molecule can form hydrogen bonds with its neighbours, and energy must be spent breaking these weak bonds before the molecules can move faster or separate at the surface. The covalent O–H bonds are much stronger, but they hold each molecule together rather than linking molecules to one another, and they are not broken when water is heated or stretched.

Question 2

Biology · The Chemistry of Living Organisms · Standard

Which statement correctly describes a competitive inhibitor of an enzyme?

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Answer: A

A competitive inhibitor resembles the substrate and competes with it for the active site, so a large excess of substrate wins most of the binding events and the enzyme approaches its normal maximum rate. Binding to a separate allosteric site and lowering the maximum rate whatever the substrate concentration describe a non-competitive inhibitor instead.

Question 3

Biology · Cell Biology · Foundation

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

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Answer: E

All cells make proteins, so all have ribosomes: prokaryotes have smaller 70S ribosomes and eukaryotes 80S ribosomes in their cytoplasm. Prokaryotes have no membrane-bound organelles, so they lack a nuclear envelope, mitochondria, endoplasmic reticulum and Golgi apparatus; their DNA lies in a nucleoid region, not a nucleus.

Question 4

Biology · Cell Biology · Standard

Human red blood cells, whose cytoplasm is isotonic with 0.9% NaCl, are placed in a 0.3% NaCl solution. What happens to them?

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Answer: B

The 0.3% solution is hypotonic to the cells, so water moves by osmosis from the solution, where it is more concentrated, into the cells; with no cell wall to resist, they swell and can burst (haemolysis). Shrinking would happen in a hypertonic solution, and aquaporins are channels for water, not for salt.

Question 5

Biology · Cell Biology · Challenging

Pancreatic cells that secrete digestive enzymes are given a radioactively labelled amino acid for a few minutes, and the label is then followed over time. In which order does the label appear in these structures before it leaves the cell?

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Answer: D

A secreted protein is built by ribosomes on the rough endoplasmic reticulum, carried in transport vesicles to the Golgi apparatus to be modified and sorted, and then packed into secretory vesicles that release it by exocytosis. The nucleus holds the gene and makes the mRNA, but amino acids are joined in the cytoplasm, so the labelled amino acid never passes through it; the Golgi comes before, not after, the secretory vesicles.

Question 6

Biology · Cell Cycle and Cell Division · Standard

In an animal species with 2n = 12, a body cell in G1 contains 8 pg of DNA. How many chromosomes, and how much DNA, does each gamete produced at the end of meiosis II contain?

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Answer: D

The DNA doubles to 16 pg in S phase; meiosis I separates homologous chromosomes, giving cells with 6 chromosomes of two chromatids each and 8 pg, and meiosis II separates the chromatids, giving gametes with 6 chromosomes and 4 pg. Six chromosomes with 8 pg describes a cell at the end of meiosis I, and 2 pg comes from halving the doubled amount three times instead of twice.

Question 7

Biology · Cell Cycle and Cell Division · Challenging

Three genes, A, B and C, lie on the same chromosome. Their recombination frequencies are: A–B 12%, B–C 5%, A–C 7%. What is the order of the genes on the chromosome map?

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Answer: B

Recombination frequency grows with the distance between genes (1% = 1 map unit), so the two genes furthest apart, A and B at 12 units, are at the ends and C lies between them: 7 + 5 = 12. Genes on different chromosomes assort independently and recombine at 50%, so 12% shows that A and B are linked, not that they are separate.

Question 8

Biology · Bioenergetics · Foundation

In aerobic respiration, what is the final acceptor of the electrons passed along the electron transport chain?

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Answer: A

At the end of the chain in the inner mitochondrial membrane, electrons are passed to oxygen, which combines with H⁺ ions to form water. NAD⁺ accepts electrons earlier, in glycolysis and the Krebs cycle, and hands them to the start of the chain as NADH, so it is a carrier rather than the final acceptor.

Question 9

Biology · Bioenergetics · Challenging

A plant is given carbon dioxide whose oxygen atoms are the isotope ¹⁸O, together with ordinary water. Ignoring any exchange of oxygen atoms between CO₂ and water, where will the ¹⁸O be found after photosynthesis?

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Answer: E

The O₂ given off comes from the splitting of water in the light-dependent reactions, so it carries no oxygen from CO₂. The CO₂ is fixed in the Calvin cycle, and its oxygen atoms end up in the sugar and in the water formed by the overall reaction 6CO₂ + 12H₂O → C₆H₁₂O₆ + 6O₂ + 6H₂O; the label would appear in the O₂ only if the water had been labelled instead.

Question 10

Biology · Reproduction and Mendelian Genetics · Foundation

In pea plants, purple flowers (P) are dominant over white flowers (p). A purple-flowered plant is crossed with a white-flowered plant in a test cross. If the purple plant is heterozygous, what ratio of offspring is expected?

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Answer: C

The cross Pp × pp gives Pp and pp offspring in equal numbers, so half are purple and half white; a homozygous PP plant would give only purple offspring, which is how the test cross tells the two apart. The 3 : 1 ratio is what two heterozygotes give when crossed with each other.

Question 11

Biology · Reproduction and Mendelian Genetics · Standard

In plants whose life cycle shows alternation of generations, gametes are produced by:

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Answer: A

In plants, meiosis takes place in the diploid sporophyte and produces haploid spores, which grow by mitosis into the haploid gametophyte; that gametophyte, already haploid, makes its gametes by mitosis. Meiosis cannot halve a cell that is already haploid, and making gametes directly by meiosis is the animal pattern, not the plant one.

Question 12

Biology · Reproduction and Mendelian Genetics · Challenging

Three genes on different chromosomes each have a dominant and a recessive allele. A plant AaBbCc is crossed with a plant aaBbCc. What fraction of the offspring is expected to show the dominant phenotype for all three traits?

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Answer: E

The genes assort independently, so the probabilities multiply: Aa × aa gives the dominant phenotype with probability 1/2, and Bb × Bb and Cc × Cc each give it with probability 3/4, so 1/2 × 3/4 × 3/4 = 9/32. The figure 27/64 would apply only if both parents were heterozygous at all three loci, which ignores that the second parent is aa.

Question 13

Biology · Molecular and Human Genetics · Standard

To make human insulin in bacteria, the gene is inserted into a plasmid as complementary DNA (cDNA), copied from the insulin mRNA by reverse transcriptase, rather than as the gene cut from human chromosomes. Why?

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Answer: C

Human genes are interrupted by introns, which eukaryotic cells splice out of the pre-mRNA; bacteria have no splicing machinery, so they would translate the introns too. Mature mRNA has already been spliced, so its cDNA copy is an uninterrupted coding sequence. The genetic code is nearly universal, so bacterial ribosomes read human codons perfectly well.

Question 14

Biology · Molecular and Human Genetics · Standard

Translation of the mRNA 5′-GCAUGGCUUACGAAUGACCGUAA-3′ begins at the first AUG. The stop codons are UAA, UAG and UGA. How many amino acids does the resulting polypeptide contain?

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Answer: B

Reading in triplets from the first AUG gives AUG–GCU–UAC–GAA and then UGA, a stop codon, so the polypeptide has 4 amino acids; the stop codon itself codes for none. Counting 6 means reading past UGA to the final UAA, and the second AUG in the sequence lies in a different reading frame, so it is never read as a codon.

Question 15

Biology · Molecular and Human Genetics · Challenging

Red–green colour blindness is an X-linked recessive trait. A colour-blind man has a child with a woman who has normal vision but whose father was colour-blind. If the child is a daughter, what is the probability that she is colour-blind?

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Answer: D

The woman received her colour-blind father's X, so she is a carrier (XᴺXⁿ); the man is XⁿY. A daughter always receives her father's Xⁿ and has a 1/2 chance of receiving her mother's Xⁿ, so the probability is 1/2. The figure 1/4 is the chance that a child of unknown sex is a colour-blind daughter, not the chance for a daughter.

Question 16

Biology · Mutations and Evolution · Standard

A single base substitution in a gene changes the mRNA codon UAU, which codes for tyrosine, into UAA. What kind of mutation is this?

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Answer: E

UAA is a stop codon, so translation ends at this point and a shortened, usually non-functional, protein is made: a nonsense mutation. A missense mutation swaps one amino acid for another, and a frameshift needs an insertion or deletion of bases that is not a multiple of three, not a substitution.

Question 17

Biology · Mutations and Evolution · Standard

In a population in Hardy–Weinberg equilibrium for a gene with two alleles, 16% of individuals show the recessive phenotype. What percentage of the population is heterozygous?

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Answer: C

The recessive phenotype frequency is q² = 0.16, so q = 0.4 and p = 0.6, and the heterozygotes are 2pq = 2 × 0.6 × 0.4 = 0.48, or 48%. The figure 36% is p², the homozygous dominant individuals, and 84% is everyone with the dominant phenotype, heterozygotes and homozygotes together.

Question 18

Biology · Anatomy and Physiology of Man · Foundation

Which blood vessels carry oxygenated blood from the lungs back to the heart?

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Answer: D

The pulmonary veins return oxygen-rich blood from the lungs to the left atrium. The pulmonary arteries carry blood the other way, from the right ventricle to the lungs, and it is deoxygenated: arteries and veins are named by the direction of flow relative to the heart, not by their oxygen content.

Question 19

Biology · Anatomy and Physiology of Man · Standard

After a long run without drinking, the osmotic concentration of a person's blood plasma rises. Which response restores it?

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Answer: A

Osmoreceptors in the hypothalamus detect the rise, and the posterior pituitary releases ADH, which inserts aquaporins into the collecting ducts so more water returns to the blood: a negative feedback loop. ADH acts on reabsorption in the collecting ducts, not on filtration at the glomerulus, and its effect is less, more concentrated urine.

Question 20

Biology · Anatomy and Physiology of Man · Foundation

Which tissue forms the walls of the alveoli and the lining of the capillaries, where substances must cross quickly by diffusion?

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Answer: B

Simple squamous epithelium is a single layer of very flat cells, giving the shortest possible diffusion path for gases and solutes. Ciliated columnar epithelium lines the larger airways, where it moves mucus, and its tall cells would slow diffusion; stratified squamous epithelium has many layers and protects surfaces such as the skin.

Section 2 of 3

Chemistry

20 questions

Question 21

Chemistry · The Constitution of Matter · Foundation

Which of the following is a homogeneous mixture?

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Answer: C

Dissolved sodium chloride is spread evenly through the water as ions, so the solution has the same composition everywhere and shows a single phase: a homogeneous mixture. Distilled water is also uniform, but it is a pure compound, not a mixture; granite, sand in water and oil with vinegar all have visibly separate phases.

Question 22

Chemistry · The Constitution of Matter · Standard

A fixed amount of an ideal gas occupies 6.0 L at 300 K and 100 kPa. The temperature is raised to 450 K and, at the same time, the pressure is raised to 150 kPa. What volume does the gas now occupy?

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Answer: A

From the combined gas law, V₂ = V₁ × (T₂/T₁) × (p₁/p₂) = 6.0 × (450/300) × (100/150) = 6.0 × 1.5 × 2/3 = 6.0 L: the expansion caused by heating is exactly cancelled by the compression. Applying only the temperature change gives 9.0 L, and multiplying by both ratios instead of dividing by the pressure ratio gives 13.5 L.

Question 23

Chemistry · Atomic Structure and the Periodic System · Foundation

Chlorine has atomic number 17. How many protons, neutrons and electrons does the ion ³⁷Cl⁻ contain?

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Answer: E

The atomic number fixes 17 protons; the mass number 37 is protons plus neutrons, so there are 37 − 17 = 20 neutrons; and the single negative charge means one electron more than the protons, 18. Keeping 17 electrons ignores the charge, which changes only the number of electrons, never the number of protons or neutrons.

Question 24

Chemistry · Atomic Structure and the Periodic System · Standard

Moving from left to right across period 3, from sodium to chlorine, which statement is correct?

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Answer: B

Across a period the nuclear charge rises while the electrons are added to the same shell, so they are pulled closer (smaller radius) and are harder to remove (higher ionisation energy, with small dips such as at aluminium and sulfur). Thinking that more electrons make a bigger atom gives the opposite trend; a new shell is started only at the beginning of the next period, and metallic character decreases from sodium to chlorine.

Question 25

Chemistry · Chemical Bonding · Foundation

Which of the following substances is made up of ions held together by ionic bonds?

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Answer: D

Potassium, an alkali metal of very low electronegativity, transfers its outer electron to fluorine, the most electronegative element, forming K⁺ and F⁻ ions held in a lattice. Hydrogen chloride is tempting because it ionises in water, but the pure substance consists of molecules with a polar covalent H–Cl bond; CH₄, Cl₂ and NH₃ are covalent molecules too.

Question 26

Chemistry · Inorganic Compounds and Nomenclature · Foundation

What is the formula of iron(III) sulfate?

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Answer: A

Iron(III) is Fe³⁺ and sulfate is SO₄²⁻; balancing the charges needs two Fe³⁺ (+6) for three SO₄²⁻ (−6), giving Fe₂(SO₄)₃. FeSO₄ is iron(II) sulfate, and Fe₂(SO₃)₃ has the right ratio but contains sulfite, SO₃²⁻, not sulfate.

Question 27

Chemistry · Reactions and Stoichiometry · Standard

How many oxygen atoms are there in 11 g of carbon dioxide, CO₂? (Relative atomic masses: C = 12, O = 16; Avogadro's number = 6.0 × 10²³ mol⁻¹)

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Answer: C

The molar mass of CO₂ is 12 + 2 × 16 = 44 g/mol, so 11 g is 0.25 mol of molecules; each molecule has two oxygen atoms, giving 0.50 mol of O, that is 0.50 × 6.0 × 10²³ = 3.0 × 10²³ atoms. Stopping at the number of molecules gives 1.5 × 10²³, and counting every atom, carbon included, gives 4.5 × 10²³.

Question 28

Chemistry · Solutions, Equilibria and Kinetics · Standard

What mass of sodium hydroxide, NaOH, is needed to prepare 250 mL of a 0.40 mol/L solution? (Relative atomic masses: Na = 23, O = 16, H = 1)

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Answer: E

The amount needed is concentration × volume = 0.40 mol/L × 0.250 L = 0.10 mol, and with a molar mass of 23 + 16 + 1 = 40 g/mol that is 0.10 × 40 = 4.0 g. Multiplying the concentration by the molar mass alone gives 16 g, which would be right only for a full litre of solution.

Question 29

Chemistry · Acids, Bases and Redox · Standard

Potassium cyanide, KCN, is dissolved in pure water. HCN is a weak acid. What is the resulting solution like?

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Answer: B

CN⁻ is the conjugate base of a weak acid, so it undergoes hydrolysis, CN⁻ + H₂O ⇌ HCN + OH⁻, and the extra OH⁻ makes the solution basic; K⁺, from the strong base KOH, does not react with water. Assuming every salt is neutral holds only for salts of a strong acid with a strong base, such as NaCl, and KCN contains no hydroxide of its own.

Question 30

Chemistry · Organic Chemistry · Foundation

Which functional group does butanone, CH₃COCH₂CH₃, contain?

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Answer: D

The –CO– in the middle of the chain is a carbonyl group with a carbon atom on each side, which is what defines a ketone, and the -one ending of the name says so. An aldehyde also has a carbonyl group, but at the end of the chain, bonded to a hydrogen atom (–CHO).

Question 31

Chemistry · Solutions, Equilibria and Kinetics · Challenging

Barium sulfate has a solubility product Ksp = 1.0 × 10⁻¹⁰ at 25 °C. What is its molar solubility in a 0.010 mol/L solution of sodium sulfate at the same temperature?

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Answer: D

Ksp = [Ba²⁺][SO₄²⁻]; the sulfate already present (0.010 mol/L) is far more than the little BaSO₄ adds, so s = Ksp / 0.010 = 1.0 × 10⁻¹⁰ / 1.0 × 10⁻² = 1.0 × 10⁻⁸ mol/L. The value 1.0 × 10⁻⁵ mol/L is the solubility in pure water: the common ion shifts the equilibrium towards the solid and lowers it a thousandfold.

Question 32

Chemistry · Acids, Bases and Redox · Challenging

Consider the reaction 2H₂S + SO₂ → 3S + 2H₂O. Which statement is correct?

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Answer: A

Sulfur goes from −2 in H₂S to 0 (oxidised, so H₂S is the reducing agent) and from +4 in SO₂ to 0 (reduced, so SO₂ is the oxidising agent), while hydrogen stays at +1 throughout. Calling SO₂ the reducing agent confuses the species that is reduced with the one that does the reducing: the oxidising agent is the one that is itself reduced.

Question 33

Chemistry · Inorganic Compounds and Nomenclature · Standard

Which pair lists a basic oxide followed by an acidic oxide, in that order?

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Answer: B

Metal oxides such as BaO react with water to give hydroxides (Ba(OH)₂) and are basic, while non-metal oxides such as N₂O₅ give oxyacids (HNO₃) and are acidic. CO₂ with CaO and Cl₂O₇ with Na₂O do contain one of each, but in the reverse order; SO₂ and P₄O₁₀ are both acidic, Li₂O and MgO both basic.

Question 34

Chemistry · Reactions and Stoichiometry · Standard

Which of the following reactions is both a combination (synthesis) reaction and a redox reaction?

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Answer: E

Magnesium and oxygen combine into one product, and in doing so magnesium goes from 0 to +2 and oxygen from 0 to −2, so electrons are transferred. The reaction of CaO with water is also a combination, but every element keeps its oxidation number (Ca +2, O −2, H +1), so it is not a redox reaction; the others are a precipitation, a decomposition and a neutralisation.

Question 35

Chemistry · Chemical Bonding · Standard

Using these Pauling electronegativities, which bond is the most polar? (H = 2.1, C = 2.5, N = 3.0, O = 3.5, F = 4.0, Cl = 3.0)

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Answer: C

Bond polarity grows with the difference in electronegativity: 1.9 for H–F, against 1.4 for O–H, 0.9 for N–H, 0.5 for C–Cl and 0.4 for C–H. O–H is tempting because water is the familiar example of a polar molecule, but fluorine pulls the shared pair even more strongly than oxygen.

Question 36

Chemistry · Solutions, Equilibria and Kinetics · Foundation

A catalyst increases the rate of a reaction because it…

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Answer: C

A catalyst opens a different reaction pathway whose energy barrier is lower, so a larger fraction of collisions has enough energy to react; it is recovered unchanged at the end. Raising the particles' kinetic energy is what heating does, and since a catalyst speeds up the forward and reverse reactions equally, it changes neither the equilibrium constant nor the enthalpy change.

Question 37

Chemistry · Acids, Bases and Redox · Challenging

0.20 mol of a weak monoprotic acid HA (Ka = 1.0 × 10⁻⁴) and 0.10 mol of NaOH are dissolved together in water and made up to 1.0 L. What is the pH of the solution?

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Answer: E

NaOH converts 0.10 mol of HA into A⁻, leaving 0.10 mol HA and 0.10 mol A⁻: a buffer in which [H⁺] = Ka × [HA]/[A⁻] = 1.0 × 10⁻⁴ × 1 = 1.0 × 10⁻⁴ mol/L, so pH = 4.0. Expecting pH 7.0 assumes the base has neutralised all the acid, but only half of it has reacted; treating the remaining HA as a strong acid gives 1.0.

Question 38

Chemistry · Organic Chemistry · Standard

Which pair of compounds are structural isomers of each other?

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Answer: A

Isomers share a molecular formula but differ in structure: cyclohexane (a ring) and hex-1-ene (a chain with one C=C) are both C₆H₁₂. Cyclohexane and benzene both have six-carbon rings, but benzene is C₆H₆; the other pairs differ in hydrogen or oxygen atoms (C₂H₆O and C₂H₄O, C₄H₁₀ and C₄H₈, C₃H₈O and C₃H₆O₂).

Question 39

Chemistry · Reactions and Stoichiometry · Challenging

Hydrogen burns according to 2H₂ + O₂ → 2H₂O. If 4.0 g of H₂ and 16 g of O₂ react until one of them runs out, what mass of water forms? (Relative atomic masses: H = 1, O = 16)

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Answer: D

4.0 g of H₂ is 2.0 mol and 16 g of O₂ is 0.50 mol; 2.0 mol of H₂ would need 1.0 mol of O₂, so oxygen is the limiting reagent, and 0.50 mol O₂ gives 1.0 mol H₂O, that is 18 g. Basing the answer on the hydrogen gives 36 g, and adding the two masses gives 20 g, which ignores the 2.0 g of hydrogen left unreacted.

Question 40

Chemistry · Atomic Structure and the Periodic System · Challenging

A neutral atom in its ground state has the electron configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁶ 4s². Which statement about this element is correct?

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Answer: B

The atom has 26 electrons (iron) and its last electrons enter the 3d subshell, which makes it a d-block transition element; its outermost shell is n = 4, so it sits in period 4. The 4s² is tempting, but it is filled before the 3d in every period-4 transition element; the configuration gives the number of protons, not of neutrons, and the outermost shell (n = 4) holds only two electrons.

Section 3 of 3

Physics

20 questions

Question 41

Physics · Measurement and Units · Foundation

Which of the following is a base (fundamental) quantity of the International System of Units (SI)?

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Answer: C

The seven SI base quantities are length, mass, time, electric current, thermodynamic temperature, amount of substance (unit: the mole) and luminous intensity. Electric charge is tempting, but it is derived: the coulomb is one ampere flowing for one second, and it is the current that is the base quantity.

Question 42

Physics · Measurement and Units · Standard

In the CGS system the unit of energy is the erg, equal to 1 g·cm²/s². How many ergs are there in 1 joule?

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Answer: A

1 J = 1 kg·m²/s², and 1 kg = 10³ g while 1 m² = (10² cm)² = 10⁴ cm², so 1 J = 10³ × 10⁴ g·cm²/s² = 10⁷ erg. The answer 10⁵ comes from converting the metre only once instead of squaring it (it is the number of dynes in a newton), and 10⁻⁷ is the conversion turned upside down.

Question 43

Physics · Measurement and Units · Standard

Which of the following products or quotients has the same physical dimensions as energy?

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Answer: D

Pressure × volume has units (N/m²) × m³ = N·m = J, so its dimensions are those of energy, [M L² T⁻²]. Force × velocity is tempting because it contains a force, but a force times a distance per unit time is energy per unit time, which is power; mass × velocity is momentum and force ÷ area is pressure.

Question 44

Physics · Kinematics · Foundation

A cyclist travelling at 12 m/s brakes with a constant deceleration and comes to rest in 4.0 s. How far does she travel while braking?

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Answer: B

With constant deceleration the average velocity is (12 + 0)/2 = 6.0 m/s, so the distance is 6.0 m/s × 4.0 s = 24 m. The answer 48 m treats the initial 12 m/s as if it lasted the whole 4.0 s, ignoring that the speed falls steadily to zero.

Question 45

Physics · Kinematics · Standard

A coin sits on a turntable 0.25 m from its axis. The turntable turns at a steady 2.0 revolutions per second and the coin does not slip. What is the centripetal acceleration of the coin?

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Answer: E

The angular velocity is ω = 2π × 2.0 = 4π rad/s, so a = ω²r = 16π² × 0.25 = 4π² m/s² (about 39 m/s²). Equivalently v = ωr = π m/s and a = v²/r = π²/0.25 = 4π² m/s²; stopping at v² gives π² m/s², and forgetting to multiply ω² by the radius gives 16π² m/s².

Question 46

Physics · Kinematics · Challenging

A particle moves in simple harmonic motion along a straight line with an amplitude of 10 cm and an angular frequency of 10 rad/s. What is its speed when it is 5.0 cm from the centre of its motion?

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Answer: B

In simple harmonic motion v = ω√(A² − x²) = 10 × √(0.010 − 0.0025) = 10 × √0.0075 = 10 × 0.05√3 = (√3/2) m/s. The answer 0.50 m/s assumes the speed falls in proportion to the distance from the centre, but the maximum speed Aω = 1.0 m/s falls off with the square root, so halfway out the particle still has most of its speed.

Question 47

Physics · Dynamics, Work and Energy · Standard

A planet has twice the mass of the Earth and twice the Earth's radius. An astronaut has a mass of 80 kg on Earth, where g = 10 m/s². What are her mass and her weight on the surface of the planet?

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Answer: D

Surface gravity is g = GM/R², so doubling M doubles g but doubling R divides it by four: g on the planet is 10 × 2/4 = 5.0 m/s², and the weight is 80 × 5.0 = 400 N. Mass is the amount of matter and stays 80 kg everywhere; 800 N comes from assuming the doubled mass and doubled radius cancel, forgetting that the radius is squared.

Question 48

Physics · Dynamics, Work and Energy · Standard

A mechanic pulls on a spanner 0.50 m from the centre of a bolt with a force of 40 N. The force lies in the plane of rotation and makes an angle of 30° with the spanner's handle. What is the moment of the force about the bolt? (sin 30° = 0.50, cos 30° ≈ 0.87)

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Answer: A

Only the component of the force perpendicular to the handle turns the bolt: M = F·r·sin θ = 40 × 0.50 × 0.50 = 10 N·m. Using cos 30° (about 17 N·m) takes the component along the handle, which pulls straight through the bolt and has no turning effect; 20 N·m ignores the angle altogether.

Question 49

Physics · Dynamics, Work and Energy · Challenging

A 0.20 kg ball travelling horizontally at 15 m/s hits a vertical wall head-on and rebounds along the same line at 10 m/s. The contact lasts 0.010 s. What is the average force exerted by the wall on the ball?

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Answer: C

Momentum is a vector, so the velocity changes from +15 m/s to −10 m/s, a change of 25 m/s: the impulse is 0.20 × 25 = 5.0 kg·m/s, and F = Δp/Δt = 5.0/0.010 = 500 N. The answer 100 N subtracts the speeds (15 − 10 = 5 m/s) as if the ball had kept moving the same way.

Question 50

Physics · Dynamics, Work and Energy · Foundation

A ball of mass 0.50 kg is thrown vertically upwards at 10 m/s. Neglecting air resistance and taking g = 10 m/s², how high does it rise above the point of release?

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Answer: E

Energy is conserved: ½mv² = mgh, so the mass cancels and h = v²/2g = 100/20 = 5.0 m. Forgetting the ½ in the kinetic energy gives 10 m, and the mass of 0.50 kg is irrelevant to the height reached.

Question 51

Physics · Fluid Mechanics · Foundation

In a hydraulic lift the small piston has an area of 10 cm² and the large piston an area of 500 cm². What force on the small piston holds up a car of weight 15 000 N resting on the large piston? (Neglect the pistons' weight and any difference in height between them.)

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Answer: A

By Pascal's law the pressure is the same on both pistons, so F₁/A₁ = F₂/A₂ and F₁ = 15 000 × 10/500 = 300 N. Multiplying by the area ratio instead of dividing gives 750 000 N, and 15 000 N assumes the press passes on the force rather than the pressure.

Question 52

Physics · Fluid Mechanics · Standard

A diver is 20 m below the surface of a lake. Atmospheric pressure at the surface is 1.0 × 10⁵ Pa (about 1 atm), the density of the water is 1000 kg/m³ and g = 10 m/s². What is the total (absolute) pressure on the diver?

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Answer: C

By Stevin's law p = p₀ + ρgh = 1.0 × 10⁵ + 1000 × 10 × 20 = 3.0 × 10⁵ Pa, about 3 atm: every 10 m of water adds about 1 atm. The answer 2 atm is the pressure due to the water alone (the gauge pressure), leaving out the atmosphere pressing on the lake's surface.

Question 53

Physics · Fluid Mechanics · Challenging

A stone hangs from a spring balance. The balance reads 5.0 N with the stone in air, 3.0 N with the stone fully immersed in water (density 1000 kg/m³) and 3.4 N with it fully immersed in a liquid X. What is the density of liquid X?

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Answer: E

The upthrust is the loss of apparent weight: 2.0 N in water and 1.6 N in liquid X. The stone displaces the same volume in both, and by Archimedes' principle the upthrust is proportional to the liquid's density, so ρ = 1000 × 1.6/2.0 = 800 kg/m³. Taking the ratio the other way up gives 1250 kg/m³, a denser liquid, which cannot be right because liquid X buoys the stone less than water does.

Question 54

Physics · Thermology and Thermodynamics · Foundation

In a pan of water heated from below, the warmed water rises and cooler water sinks to replace it, carrying energy through the liquid. What is this mechanism of heat transfer called?

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Answer: D

Convection transfers energy by the bulk movement of a fluid, driven by the lower density of the warmer part. Conduction also happens in the water, but it passes energy from particle to particle without the material itself flowing, which is not what the rising and sinking currents describe.

Question 55

Physics · Thermology and Thermodynamics · Standard

How much heat is needed to melt 0.20 kg of ice at 0 °C and then warm the meltwater to 20 °C? (Latent heat of fusion of ice = 330 kJ/kg; specific heat capacity of water = 4.2 kJ/(kg·°C).)

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Answer: B

Melting takes mL = 0.20 × 330 = 66 kJ with no change in temperature, and warming the water takes mcΔT = 0.20 × 4.2 × 20 = 16.8 kJ, a total of 82.8 kJ. Stopping at 66 kJ forgets the warming, and 16.8 kJ forgets that melting needs latent heat even though the temperature stays at 0 °C.

Question 56

Physics · Thermology and Thermodynamics · Challenging

A fixed mass of ideal gas occupies 6.0 L at 27 °C and 1.0 × 10⁵ Pa. It is compressed to 2.0 L and at the same time heated to 327 °C. What is its new pressure?

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Answer: B

From pV/T = constant, with temperatures in kelvin (300 K and 600 K), p₂ = 1.0 × 10⁵ × (6.0/2.0) × (600/300) = 6.0 × 10⁵ Pa. Using the Celsius temperatures instead gives a factor of 327/27 ≈ 12 in place of 2, and so 3.6 × 10⁶ Pa; 3.0 × 10⁵ Pa allows for the compression but not the heating.

Question 57

Physics · Electrostatics and Electrodynamics · Standard

A metal wire has a resistance of 8.0 Ω. A second wire, of the same metal and at the same temperature, is twice as long and has twice the diameter. What is its resistance?

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Answer: E

R = ρL/A, and the cross-sectional area grows with the square of the diameter, so doubling the diameter makes the area four times larger: R = 8.0 × 2/4 = 4.0 Ω. The answer 8.0 Ω assumes doubling the diameter only doubles the area, so that it cancels the doubled length.

Question 58

Physics · Electrostatics and Electrodynamics · Standard

A 3.0 µF capacitor and a 6.0 µF capacitor are connected in series across a 12 V battery. Once they are fully charged, what charge is stored on each capacitor?

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Answer: A

In series 1/C = 1/3.0 + 1/6.0 = 1/2.0, so the combination is 2.0 µF and Q = CV = 2.0 × 12 = 24 µC; capacitors in series all carry the same charge. The answer 108 µC adds the capacitances (9.0 µF), which is the rule for capacitors in parallel, not in series.

Question 59

Physics · Electrostatics and Electrodynamics · Challenging

Two point charges, +4.0 µC and +1.0 µC, are fixed 3.0 m apart in a vacuum. At what point on the line segment between them is the electric field zero?

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Answer: D

The two fields point in opposite directions between like charges, and they cancel where k(4.0)/x² = k(1.0)/(3.0 − x)², that is where x/(3.0 − x) = 2, so x = 2.0 m from the larger charge (1.0 m from the smaller). The answer 2.4 m comes from making the field fall with the distance rather than its square, and the point cannot be nearer the larger charge, whose field is stronger there.

Question 60

Physics · Electrostatics and Electrodynamics · Foundation

A strong bar magnet is held at rest inside a coil of wire whose ends are connected to a sensitive ammeter. Which statement is correct?

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Answer: C

By Faraday's law of electromagnetic induction the induced emf equals the rate of change of magnetic flux through the coil; with the magnet at rest the flux is constant, so there is no emf and no current. Being in a magnetic field is not enough: a current is induced only while the magnet, or the coil, moves or the field changes.

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