Practice

Adenine, thymine, guanine, cytosine. A pairs with T; G pairs with C.

Body cell: $46$ chromosomes. Gamete: $23$ chromosomes.

Gene -- a length of DNA coding for a trait. Allele -- one version of a gene. Genotype -- the pair of alleles carried. Phenotype -- the observable trait.

Heterozygous (two different alleles).

Growth and repair of tissues; replacing old cells (e.g. skin, blood).

Mitosis produces two identical diploid cells; meiosis produces four genetically different haploid gametes.

$3 : 1$ brown to blue.

All offspring $Bb$; all brown.

$1 : 1$ tall to short.

$\dfrac{1}{4}$, or $25\%$.

All children will have attached earlobes. Both parents are $ee$, so every child must inherit $e$ from each parent.

Her mother was $ww$, so the woman inherited $w$ from mother and $W$ from her widow's-peak parent; genotype $Ww$. Cross $Ww \times ww$: $\dfrac{1}{2}$ widow's peak, $\dfrac{1}{2}$ straight.

Expected $\dfrac{1}{4} \times 4 = 1$ affected child. The actual number can differ because each child is an independent event; outcomes follow a binomial distribution, not a guaranteed quota.

Offspring genotypes $BB : Bb : bb = 1 : 2 : 1$. Because $BB$ and $Bb$ share the dominant phenotype, the three "brown" outcomes combine, giving $3 : 1$.

Father is $X^c Y$, mother is $X^C X^C$. All daughters are $X^C X^c$ (carriers, not colour-blind). All sons are $X^C Y$ (not colour-blind).

Ratio $\approx 3 : 1$ suggests both parents are heterozygous $Rr$. Punnett: $RR, Rr, Rr, rr$, giving $3$ red $: 1$ white.

Meiosis shuffles maternal and paternal chromosomes by independent assortment and crossing over, producing gametes with new combinations. Random fertilisation then pairs two such gametes, so each child represents one of millions of possible genotypes.

$4$ chromosomes per gamete; $4$ gametes from one starting cell.

Son has haemophilia with probability $\dfrac{1}{2}$. Daughter is a carrier with probability $\dfrac{1}{2}$ (the other $\dfrac{1}{2}$ are $X^H X^H$).

$1 : 2 : 1$ red : pink : white.

Each conception is independent; meiosis in the father randomly produces an $X$-bearing or $Y$-bearing sperm with probability $\tfrac{1}{2}$. Previous children do not change the odds for the next.

His father must have been $Hh$ (or he could not pass the allele), so the son's probability of being $Hh$ is $\dfrac{1}{2}$. If he is $Hh$, each child has probability $\dfrac{1}{2}$ of inheriting $H$.

Ratio $9 : 3 : 3 : 1$ (both dominant : yellow round; yellow wrinkled; green round; green wrinkled). The $9$ comes from $\dfrac{3}{4} \times \dfrac{3}{4} = \dfrac{9}{16}$ having at least one dominant allele for each gene.

(i) With $23$ chromosome pairs, independent assortment gives $2^{23} \approx 8.4 \times 10^6$ gamete combinations per parent. (ii) Random fertilisation squares this: $\approx 7 \times 10^{13}$ possible zygote genotypes, before crossing over. Variation fuels adaptation to changing environments.

Variation; selection pressure; differential survival and reproduction; heritability.

Adaptation -- an inherited trait that improves survival or reproduction in a given environment. Fitness -- the number of viable offspring an individual contributes. Selection pressure -- an environmental factor (predator, climate, disease, food supply) that favours some variants over others.

Homologous: same underlying structure, different function (human arm and whale flipper share bones). Analogous: same function, different origin (butterfly wing and bat wing).

A structure that no longer serves its original function (e.g. human appendix, wisdom teeth, tailbone).

A group whose members can interbreed in nature to produce fertile offspring.

A physical barrier splits a population; the separated groups diverge until they can no longer interbreed.

Fossil record, biogeography, comparative anatomy (homologous structures), molecular (DNA/protein) similarity. (Also embryology, direct observation.)

They show intermediate features between ancestral and modern groups, matching the predictions of common descent.

About $98.8\%$.

The continents were isolated for tens of millions of years; mammals evolved along separate lines on each land mass.

False. Mutations arise randomly, independent of the environment. Selection then acts on the variation already present.

Mutations produce rare resistant cells; the antibiotic kills susceptible cells; resistant cells survive, reproduce rapidly (every $\sim 20$ min), and pass resistance to daughter cells; within weeks resistant strains dominate.

When soot darkened the trees, birds preyed on conspicuous light moths; dark moths survived and reproduced more, raising the frequency of the dark allele. After clean-air laws pale bark returned, reversing the advantage.

Selection pressure changes with rainfall; the trait that maximises fitness changes each year, so the mean beak size tracks the current food supply.

Prey speed is a selection pressure; faster cheetahs caught more prey and raised more cubs; the fastest heritable traits (long legs, flexible spine, large heart and lungs) accumulated over many generations.

Mutation produces rare resistant individuals; pesticide kills susceptible ones; survivors breed; resistance spreads. Strategies: rotate between pesticides with different modes of action; leave "refuge" areas untreated so susceptible genes persist in the population.

Consistent with selection, but a one-off survival event could be chance. Confidence requires heritability (do offspring of survivors also tend to be larger?) and repeatability across generations or populations.

Yes, effectively. Behavioural isolation (mate recognition) is a reproductive barrier; gene flow has stopped. They are on their way to being recognised as distinct species even if still anatomically similar.

Vestigial limbs and embryonic hind-limb buds are expected if whales descended from four-legged ancestors. Genetic programs for limbs persist but are no longer expressed fully.

Direct: transitional forms (light-sensitive patches in flatworms, cup eyes in snails, pinhole eyes in nautiluses, full lens eyes in vertebrates) show a gradient of working intermediate eyes. Logic: each small improvement in light detection confers survival advantage, so intermediate eyes are favoured -- not disadvantageous.

Grow a large bacterial culture; plate onto agar with and without low-dose antibiotic. Selection pressure: the antibiotic. Heritable variation: resistance alleles from spontaneous mutation. Measure fitness by counting colonies; track allele frequency by repeated subculturing.

Evolution is not directional. The horse fossil record is a branching bush with many extinct side lineages -- not a straight march to Equus. Modern horses are one surviving branch; most lineages went extinct.

Fraction expressing dark phenotype $= q^2 = 0.01$ (1%). If only $q^2$ survives, the new allele frequency is $q = 1$ (the dark allele fixes at $100\%$) since only homozygous dark individuals remain.

Urban birds changing songs to cut through city noise; tuskless elephants becoming more common under ivory poaching pressure; peppered moth; antibiotic-resistant bacteria; herbicide-resistant weeds; salmon reaching sexual maturity earlier under heavy fishing of large fish. (Any two.)

A group is a vertical column; a period is a horizontal row. Group members share valence-electron count; period members share their outermost shell number.

Hydrogen, lithium, sodium, potassium, rubidium. (H is sometimes placed separately.)

Helium, neon, argon, krypton.

Metals: left and centre. Non-metals: upper right.

Elements on the diagonal "staircase" with some metallic and some non-metallic properties. Examples: silicon, germanium, boron.

Their outer electron shells are full, so they have no tendency to gain, lose or share electrons.

(a) C: $2, 4$. (b) O: $2, 6$. (c) Ne: $2, 8$. (d) Na: $2, 8, 1$.

Group 16. Sulfur.

Group 1. Potassium.

$5$ valence electrons.

Mg ($2, 8, 2$): two electrons in inner shell, eight in second, two in outer.

Group 1: $+1$. Group 2: $+2$.

Group 17: $-1$. Group 16: $-2$.

Ionic -- a metal (Na) bonded with a non-metal (Cl); electrons transfer.

Covalent -- both elements are non-metals (C and H); electrons are shared.

MgO.

Down Group 1, outer electrons are further from the nucleus and more easily lost, so metals become more reactive. Down Group 17, atoms are larger and less able to attract an extra electron, so non-metal reactivity falls.

Sodium is more reactive. Na loses $1$ electron to form Na$^+$; Mg must lose $2$ electrons to form Mg$^{2+}$, which requires more energy.

They have the same number of valence electrons; chemistry is determined by the outer shell.

Atoms form ions to reach a full outer shell (the noble-gas configuration), which is energetically stable.

Helium has only $2$ electrons, but its outer shell ($1$s) is full at $2$. It is chemically inert like the other noble gases, so it belongs in Group 18 by behaviour.

Lithium is the lightest metal and has the highest energy-to-mass ratio; it is also less violently reactive than sodium or potassium when managed in non-aqueous electrolytes, and its ion is small enough to move quickly between electrodes.

Argon is inert -- it will not react with the hot filament. Oxygen would oxidise (burn) the filament; nitrogen is less reactive but still less safe than argon.

HF is most vigorous; going down Group 17 reactivity decreases, so F $>$ Cl $>$ Br.

(a) KCl, ionic. (b) CaO, ionic. (c) CO$_2$, covalent. (d) NH$_3$, covalent.

The table's pattern meant each gap had predictable properties from its neighbours (mass, melting point, reactivity). The switch to atomic number resolved anomalies (e.g. tellurium and iodine appear out of order by mass but in the right order by proton count), and atomic number reflects the true physical basis of chemistry.

Group 1 and 17 elements are typically one electron away from a noble-gas configuration, giving one clearly preferred ion. Transition metals have inner-shell (d-orbital) electrons of similar energy that can also be removed, giving multiple stable ions.

Na loses its one outer-shell electron, collapsing to the inner $2, 8$ shell -- much smaller. Cl gains an electron into its outer shell; electron-electron repulsion and a weaker effective nuclear pull per electron expand the radius.

Water is polar: the O end is slightly negative, the H end slightly positive. Polar water molecules surround the Na$^+$ and Cl$^-$ ions, pulling them out of the crystal lattice -- dissolution.

In a chemical reaction, the total mass of reactants equals the total mass of products -- atoms are rearranged, not created or destroyed.

Hydrogen + oxygen $\to$ water.

$2\text{H}_2\text{O} \to 2\text{H}_2 + \text{O}_2$.

Reactants: zinc, hydrochloric acid. Products: zinc chloride, hydrogen.

There are $2$ water molecules (so $4$ H atoms and $2$ O atoms in total from that term).

$\text{H}_2 + \text{Cl}_2 \to 2\text{HCl}$.

$4\text{Na} + \text{O}_2 \to 2\text{Na}_2\text{O}$.

$4\text{Al} + 3\text{O}_2 \to 2\text{Al}_2\text{O}_3$.

$\text{Mg} + 2\text{HCl} \to \text{MgCl}_2 + \text{H}_2$.

$2\text{C}_2\text{H}_6 + 7\text{O}_2 \to 4\text{CO}_2 + 6\text{H}_2\text{O}$.

$2\text{Fe}_2\text{O}_3 + 3\text{C} \to 4\text{Fe} + 3\text{CO}_2$.

$16$ g.

$10 - 5.6 = 4.4$ g.

$5 - 3 = 2$ g.

$4.6 + 3.55 = 8.15$ g.

$28.6 - 20 = 8.6$ g.

(a) Synthesis. (b) Decomposition. (c) Displacement. (d) Combustion.

Subscripts describe what the molecule is. Changing them changes the compound (water to hydrogen peroxide). Only coefficients (whole-number multiples of molecules) may be changed.

No. Iron combines with oxygen from the air; the added mass is oxygen. Mass of iron + oxygen consumed = mass of rust formed.

Mass was converted to CO$_2$ and water vapour that escaped into the air. If the candle burned in a sealed system, no mass would be lost.

$88 + 36 = 124$ g total products.

CO$_2$ mass: $5 - 3.2 = 1.8$ g. Equation: $\text{CuCO}_3 \to \text{CuO} + \text{CO}_2$.

$\text{Zn} + \text{CuSO}_4 \to \text{ZnSO}_4 + \text{Cu}$. Displacement (Zn is more reactive than Cu).

$2\text{C}_4\text{H}_{10} + 13\text{O}_2 \to 8\text{CO}_2 + 10\text{H}_2\text{O}$.

$2\text{Na} + 2\text{H}_2\text{O} \to 2\text{NaOH} + \text{H}_2$.

Perform the reaction in a closed, weighed flask fitted with a balloon or sealed gas collection. The total mass of the sealed system before and after the reaction will be equal. Alternatively, measure the masses of CaO produced and CO$_2$ collected separately and sum them.

Balanced equation: $2\text{H}_2 + \text{O}_2 \to 2\text{H}_2\text{O}$. $3.0$ g H$_2$ needs $24.0$ g O$_2$ (stoichiometric ratio $4 : 32 = 1 : 8$), so both are fully consumed. Mass of water $= 3.0 + 24.0 = 27.0$ g. The ampoule contains only water (as liquid/vapour).

$\text{C}_2\text{H}_5\text{OH} + 3\text{O}_2 \to 2\text{CO}_2 + 3\text{H}_2\text{O}$. Check: C $2 = 2$; H $6 = 6$; O $1 + 6 = 2 + 3$, i.e. $7 = 7$. Balanced.

Open vessels allow gases to enter or leave, making "before" and "after" masses disagree. Examples: (i) a burning candle -- mass appears to decrease as CO$_2$ and water vapour escape; (ii) iron rusting in open air -- mass appears to increase as it absorbs oxygen from the atmosphere.

(a) Decomposition. (b) Synthesis. (c) Displacement.

(a) No: silver is below copper, so Ag cannot displace Cu. (b) Yes: magnesium is above zinc in the reactivity series, so Mg displaces Zn.

$2\text{Mg} + \text{O}_2 \to 2\text{MgO}$.

$\text{CaCO}_3 \to \text{CaO} + \text{CO}_2$.

Particles must collide, with enough energy (activation energy), and with the correct orientation.

Higher temperature, higher concentration, greater surface area, adding a catalyst.

No -- "concentration" refers to dissolved or gaseous reactants. For a solid, surface area is the equivalent lever.

Powdered sugar has a far greater surface area exposed to oxygen; more collisions per second support rapid combustion.

A substance that speeds up a reaction by providing a lower-activation-energy pathway without being consumed overall.

Exothermic: releases energy (e.g. combustion of methane). Endothermic: absorbs energy (e.g. photosynthesis).

The products are at a lower energy than the reactants -- the curve ends below where it started.

The minimum energy that colliding particles need to react; it is the peak of the energy profile above the reactant level.

False. A catalyst lowers activation energy; the overall energy change between reactants and products is unchanged.

Lower temperature means slower particles, fewer successful collisions per second, so spoilage (a reaction) is slower.

Rate increases -- more marble surface is exposed to acid, so more particle collisions per second.

Higher concentration means more reactant particles per unit volume, giving more collisions per second with the metal.

A small rise in average kinetic energy roughly doubles the fraction of particles above the activation-energy threshold, even though $E_a$ itself is unchanged. (The Maxwell-Boltzmann distribution steepens in the high-energy tail with temperature.)

The catalyst participates in intermediate steps but is regenerated by the end of the reaction. It offers a new route with a lower energy barrier.

The sparkler has fine metal particles (large surface area) and burns at high temperature, meeting many oxygen molecules per second; the lump of iron has very little exposed surface and stays cool.

Endothermic -- it absorbs solar energy. Respiration (combustion of glucose) is the reverse, so it is exothermic, releasing the stored energy.

(a) $40\,^\circ\text{C}$: more CO$_2$ per second on average. (b) Yes -- same amount of CaCO$_3$, same amount of HCl, same total CO$_2$.

(a) MnO$_2$ is a catalyst -- it lowers the activation energy for H$_2$O$_2$ decomposition. (b) Its mass is unchanged; it is not consumed.

Doubling concentration does not change the distribution of molecular speeds, so the fraction of collisions with enough energy is the same. However, the total number of collisions per second doubles, so the rate doubles.

The catalyst surface adsorbs exhaust gases and brings them into reactive proximity at a lower activation energy. Pt/Pd/Rh are used because they resist high temperatures, bind the gases with ideal strength (strong enough to hold but weak enough to release products), and are not consumed.

Exothermic: curve from high reactants, up to $E_a$, down to low products; with catalyst the peak is lower but start and end heights unchanged. Endothermic: curve from low reactants, up to $E_a$, down to a level higher than start.

Higher T speeds up the reaction (collision theory) but reduces equilibrium yield because the forward reaction is exothermic (Le Chatelier). The $400$ - $500\,^\circ\text{C}$ range is a compromise -- fast enough to produce useful amounts per hour while keeping yield economically worthwhile, often combined with an iron catalyst and high pressure.

Atmosphere < biosphere < hydrosphere (oceans) < lithosphere (rocks/fossil fuels).

$6\text{CO}_2 + 6\text{H}_2\text{O} \to \text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2$.

$\text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2 \to 6\text{CO}_2 + 6\text{H}_2\text{O}$.

Photosynthesis; ocean dissolution (into phytoplankton).

Respiration; decomposition; combustion.

Fossilisation (dead organisms buried and compressed over millions of years); sedimentation of shells into limestone.

It is the smallest reservoir, so small flux imbalances produce large percentage changes; it also controls the greenhouse effect directly.

Dissolved CO$_2$, carbonic acid (H$_2$CO$_3$), bicarbonate ion (HCO$_3^-$), and carbonate ion (CO$_3^{2-}$).

As calcium carbonate, CaCO$_3$, formed from the shells and skeletons of marine organisms.

Coal (from compressed plant matter in ancient swamps); oil (from compressed marine plankton and algae); natural gas (similar origin, deeper/hotter conditions favour methane).

A reservoir is a store of carbon; a flux is a flow of carbon per unit time between reservoirs.

Carbon stored in coal (lithosphere) is burned, producing CO$_2$ that enters the atmosphere. A flux from lithosphere to atmosphere.

Burning trees releases their stored carbon as CO$_2$; the cleared land stops absorbing CO$_2$ through photosynthesis, so the atmospheric balance shifts upward.

Cement production releases CO$_2$ both from burning fuel in the kiln and directly from the decomposition of limestone -- even with clean energy, CaCO$_3$ $\to$ CaO + CO$_2$ is unavoidable.

(a) Growing trees lock carbon into wood and soils. (b) Mature trees reach a steady state; if the forest burns or is cleared, carbon returns to the atmosphere. Reforestation buys time but does not remove carbon permanently.

CH$_4$ is $\sim 25$ times more potent per molecule than CO$_2$ at trapping heat over a century; large ongoing emissions keep concentrations high even though each molecule is short-lived.

Fuel used: $12\,000 \times \dfrac{8}{100} = 960$ L. (a) Cost: $960 \times 1.85 = 1\,776$ dollars. (b) CO$_2$: $960 \times 2.3 = 2\,208$ kg.

$5$ Gt C/year; over a decade, $\sim 50$ Gt C added.

$\dfrac{420 - 280}{280} \times 100 = 50\%$.

$[\text{H}^+]$ ratio $= 10^{(8.2 - 8.05)} = 10^{0.15} \approx 1.41$. So about a $41\%$ increase.

$\dfrac{3\,500}{20} = 175$ trees per car.

Human emissions continually push the atmosphere away from equilibrium. Sinks (ocean, land) absorb a fraction but cannot keep pace because absorption depends on the difference from equilibrium -- even as that gap widens, the remaining $\sim 50\%$ of emissions accumulates, further shifting equilibrium upward.

Negative: silicate weathering increases with temperature and removes CO$_2$; more CO$_2$ enhances plant growth which absorbs CO$_2$ (limited by water/nutrients). Positive: warming melts permafrost, releasing methane; warmer oceans hold less dissolved CO$_2$. On human timescales (decades), the positive feedbacks act faster than silicate weathering (millennia), making them more urgent.

Scale -- algae biomass would need to exceed current ocean phytoplankton many times over. Nutrients -- huge nitrogen and iron inputs would be required. Permanence -- dead algae decompose, returning CO$_2$; only if they sink and are buried does the carbon leave the fast cycle.

Fossil fuels accumulated over tens of millions of years; burning them in ~200 years releases that carbon ~$10^5$ times faster than it was captured. Natural sinks have no capacity to absorb at that rate, which is why atmospheric CO$_2$ keeps rising.

No atmospheric blurring or absorption, so sharper images and access to wavelengths (X-ray, UV, infrared) that ground telescopes cannot detect.

Earth's atmosphere absorbs X-rays completely; they must be observed above it.

Infrared.

Pulsars, radio galaxies, cool dust clouds that hide star formation, and distant quasars. Radio also penetrates dust.

Hubble Deep Field (distant galaxies); cosmic microwave background by WMAP and Planck; exoplanet atmospheres by Kepler and James Webb. (Any reasonable answer.)

For every action there is an equal and opposite reaction. A rocket pushes hot exhaust gases backwards; the gases push the rocket forwards.

$\sim 7.8$ km/s (about $28\,000$ km/h).

An orbit with a $24$-hour period so the satellite appears fixed above one spot on the equator; altitude is fixed by the requirement that orbital period equals one Earth day.

Both the station and the astronauts are in continuous free-fall; no surface pushes up on the astronaut, so they feel weightless.

Escape velocity is the minimum speed needed to leave Earth's gravity altogether ($\sim 11.2$ km/s). Orbital velocity only needs to keep an object in free-fall around Earth.

Yuri Gagarin, 1961.

1960s to early 1970s (1969 - 1972).

2000.

Weather: GOES, Himawari (any). Navigation: GPS (US), Galileo (Europe), GLONASS (Russia), BeiDou (China).

USA (NASA, SpaceX), Russia (Roscosmos), China (CNSA). (Any two.)

Reaching orbital speed (~$7.8$ km/s) requires so much $\Delta v$ that most of the launch mass must be propellant; additionally, the fuel itself must be lifted up through the lower atmosphere, requiring yet more fuel.

There is no air in space, so the engine must carry its own oxygen (or equivalent oxidiser) to burn the fuel.

Each satellite gives only a sphere of possible positions. Three satellites intersect to two points; a fourth resolves ambiguity and corrects the receiver's clock.

Human radio transmissions (mobile phones, Wi-Fi, TV) are radio noise that swamps faint astronomical sources. Remote sites minimise interference.

Mars: longer duration (~2-3 years), cosmic radiation outside Earth's magnetic field, much bigger distance, communication delay of $\sim 20$ minutes each way, no rescue possible. Far greater risks than a few-day Moon mission.

Distance from Earth's centre: $6\,400 + 20\,200 = 26\,600$ km. Signal time $= \dfrac{20\,200}{3.0 \times 10^5} \approx 0.067$ s (from satellite to ground, approximate).

Time $= \dfrac{384\,000}{5\,500} \approx 69.8$ h $\approx 2.9$ days. (Real Apollo missions took about 3 days.)

$d = ct = 3.0 \times 10^5 \times 0.12 = 36\,000$ km. Matches the geostationary altitude.

Mars and Earth move on different orbits; a minimum-energy (Hohmann) transfer is only possible when the two planets are in the right relative positions, which happens every $\sim 26$ months.

$\Delta v$: required velocity change; $v_e$: exhaust velocity; $m_0$: initial mass (with fuel); $m_f$: final mass (after fuel burn). The ratio $m_0/m_f$ grows exponentially with $\Delta v$, so a modest increase in required $\Delta v$ multiplies the fuel (and initial mass) needed.

Each stage can be optimised for its task and discarded when empty, reducing the mass that subsequent stages must accelerate. Monolithic designs carry the mass of empty tanks all the way, wasting fuel.

Scientific: humans can adapt, improvise, and collect diverse samples faster than robots. Economic: robots cost orders of magnitude less and need no life support. Ethical: subjecting humans to unknown radiation and travel risks raises serious responsibility questions; arguments exist on both sides. (Any reasoned answer.)

A kinetic impactor or gravity tractor could be sent to nudge the asteroid's trajectory. Over many orbits, a tiny $\Delta v$ translates to a large miss distance; $20$ years of warning makes this feasible. Short warning would require much more energy and may be impossible.

Moon $<$ planet $<$ star $<$ solar system $<$ galaxy $<$ galaxy cluster.

About $200$ billion.

Andromeda (M31).

The distance that light travels in one year, about $9.5$ trillion km.

A region of space where gravity is so strong that nothing, not even light, can escape.

Redshift (Hubble's law); cosmic microwave background; abundance of light elements (H and He).

The recession speed of a galaxy is proportional to its distance: $v = H_0 d$.

The faint thermal radiation from when the universe first became transparent ($\sim 380\,000$ years after the Big Bang). It is direct evidence of the hot, dense early universe.

About $75\%$ hydrogen, $25\%$ helium by mass (of ordinary matter).

About $13.8$ billion years.

Nuclear fusion of hydrogen into helium (and later heavier elements).

A star that is steadily fusing hydrogen to helium in its core -- the longest, most stable life stage.

Red giant, planetary nebula, white dwarf.

Supernova followed by a neutron star or black hole.

In supernova explosions and neutron-star mergers.

A passing ambulance's siren is higher pitched as it approaches and lower as it recedes. Similarly, light from receding galaxies is stretched to longer (redder) wavelengths. Galaxies all showing redshift indicates the universe is expanding.

If all galaxies are moving apart, running the film backwards shows they were all together at one point in the past. Extrapolating gives a starting time about $13.8$ Gyr ago.

Before recombination, the universe was so dense it behaved like a uniform plasma; all regions had the same temperature. Inflation ironed out any variations, so the CMB is almost perfectly uniform except for tiny fluctuations.

Light takes time to travel. The further away we look, the longer the light has been in transit, so we see objects as they were in the past.

Massive stars burn their fuel much faster to counteract their stronger gravity; higher temperatures and pressures consume hydrogen in $\sim 10$ Myr vs the Sun's $\sim 10$ Gyr.

$d = \dfrac{21\,000}{70} = 300$ Mpc $\approx 978$ million ly.

$\sim 2.5$ million years. You are seeing Andromeda as it was $2.5$ Myr ago.

$5 \times 10^9 \text{ yr} \times 3.156 \times 10^7 \text{ s/yr} \approx 1.58 \times 10^{17}$ s.

A supernova releases in seconds roughly the same energy the Sun emits over its entire $10^{10}$-year lifetime. Supernovae are extraordinarily energetic, visible across the universe.

As the universe expands, photon wavelengths are stretched by the same factor. Going from $\sim 3\,000$ K (emission) to $2.73$ K (today) corresponds to a $\sim 1\,100$-fold stretch -- the universe is now $1\,100$ times larger than at the epoch of recombination.

$z = 1.0$ means observed wavelength is twice emitted. Wavelength has been stretched by a factor $1 + z = 2$, meaning space itself has doubled in scale since the light was emitted. So the universe was half its current size.

The two methods probe different epochs (early universe vs nearby universe). If both are right, something in between (new physics, dark energy behaviour) may be missing from the standard model of cosmology.

Life requires carbon, oxygen, nitrogen, calcium, iron -- none of which existed in the pristine Big Bang hydrogen/helium mix. Stars had to form, die, and seed the gas clouds with heavy elements before planets and life were possible. This pushes first-life possibilities back only once enough massive stars had exploded -- likely $\sim 1$ - $2$ Gyr after the Big Bang.

An object continues at rest or at constant velocity unless an unbalanced force acts on it.

$F_{\text{net}} = ma$, where $F$ is in newtons (N), $m$ in kilograms (kg), $a$ in m/s$^2$.

Mass is the amount of matter (kg); weight is the gravitational force on that mass (N). Weight depends on $g$; mass does not.

For every action there is an equal and opposite reaction; the forces act on two different objects.

The tendency of an object to resist changes in its motion; it depends on mass.

$a = \dfrac{20}{4} = 5 \text{ m/s}^2$.

$F = 1\,500 \times 2.5 = 3\,750 \text{ N}$.

$m = \dfrac{50}{10} = 5 \text{ kg}$.

$W = 90 \times 9.8 = 882 \text{ N}$.

$m = \dfrac{196}{9.8} = 20 \text{ kg}$.

$a = \dfrac{2 - 0}{0.8} = 2.5 \text{ m/s}^2$. $F = 0.4 \times 2.5 = 1 \text{ N}$.

Examples: jumping (legs push on ground; ground pushes back on legs). Bat hits ball (bat on ball; ball on bat).

The water pushes the swimmer forwards with an equal and opposite force.

Friction is needed for the ground to push back on your foot; on frictionless ice, there is no reaction force to accelerate you forward.

$200$ N (Newton's third law).

The forces act on different objects. The horse's forward motion comes from the ground pushing back on the horse's hooves (larger than the cart's pull); that net forward force on the horse-cart system causes motion.

FBD: push $40$ N right, friction $15$ N left, normal up, weight down. $F_{\text{net}} = 40 - 15 = 25 \text{ N}$. $a = \dfrac{25}{10} = 2.5 \text{ m/s}^2$.

At terminal velocity, acceleration is zero, so net force is zero. Air resistance $= W = 80 \times 9.8 = 784 \text{ N}$ (upward).

Tension $T - W = ma$, so $T = m(g + a) = 5(9.8 + 1) = 54 \text{ N}$.

$a = \dfrac{0 - 15}{3} = -5 \text{ m/s}^2$. $F = 2\,000 \times 5 = 10\,000 \text{ N}$ (opposing motion).

$F_{\text{net}} = ma = 1.2 \times 0.5 = 0.6$ N. Friction $= 5 - 0.6 = 4.4$ N.

Weight $= 70 \times 9.8 = 686$ N. Net force $= 686 - 400 = 286$ N downward. $a = \dfrac{286}{70} \approx 4.1 \text{ m/s}^2$ downward.

Net force $= 65 - 50 = 15$ N (in direction of $65$ N push). $a = \dfrac{15}{30} = 0.5 \text{ m/s}^2$.

Weight $= 800 \times 9.8 = 7\,840$ N. $T - W = ma$, so $T = 7\,840 + 800 \times 1.5 = 9\,040$ N.

$a = \dfrac{25}{8} = 3.125 \text{ m/s}^2$. Net force $= 1\,300 \times 3.125 = 4\,062.5$ N. Thrust $= 4\,062.5 + 500 = 4\,562.5$ N.

(a) Moon: $W = 80 \times 1.6 = 128$ N. Earth: $W = 80 \times 9.8 = 784$ N. (b) Equally hard in terms of $F = ma$ -- horizontal acceleration depends on mass, not weight. The Moon's lower gravity only affects vertical forces like weight.

(a) $a = \dfrac{30}{0.1} = 300 \text{ m/s}^2$. $F = 75 \times 300 = 22\,500$ N. (b) $a = \dfrac{30}{0.5} = 60 \text{ m/s}^2$. $F = 75 \times 60 = 4\,500$ N -- a fivefold reduction, crucial for survival.

Heavier mass ($5$ kg) accelerates down; lighter ($3$ kg) accelerates up. $a = \dfrac{(5 - 3) \times 9.8}{5 + 3} = \dfrac{19.6}{8} = 2.45 \text{ m/s}^2$. Tension: for lighter mass, $T - mg = ma \Rightarrow T = 3(9.8 + 2.45) = 36.75$ N.

Rocket weight $= 2\,000 \times 9.8 = 19\,600$ N. (a) Thrust ($25\,000$ N) exceeds weight, so yes -- it lifts off with $F_{\text{net}} = 25\,000 - 19\,600 = 5\,400$ N giving $a = 2.7 \text{ m/s}^2$. (b) Thrust $= m(g + a) = 2\,000 \times (9.8 + 3) = 25\,600$ N.

Research $\to$ write-up $\to$ submit to a journal $\to$ peer review $\to$ publication $\to$ replication by other labs $\to$ consensus.

Independent experts evaluate a manuscript for methodology, statistical rigour, novelty and conclusions before publication. Reviewers are usually researchers in the same field.

Replication guards against chance findings, flukes, fraud, and mistakes. A result that can't be reproduced is treated as unreliable.

Examples: stomach ulcers (stress $\to$ H. pylori); plate tectonics (static Earth $\to$ moving plates); the "four humours" theory of disease; Newtonian absolute space (modified by relativity).

The shared, evidence-based position of most experts in a field, arrived at through repeated testing and peer review.

Electron microscope $\to$ cellular ultrastructure; particle accelerators $\to$ discovery of sub-atomic particles; space telescopes $\to$ exoplanets. (Any reasonable example.)

Understanding of electromagnetism $\to$ electric motors and generators; semiconductor physics $\to$ computers; DNA structure $\to$ genetic engineering. (Any reasonable example.)

The virus genome was sequenced in days and shared online. Scientists could design candidate vaccine mRNA without isolating the virus in every lab.

PCR, DNA sequencers (especially next-generation), CRISPR, cryo-EM, high-throughput screening. (Any one.)

Hubble, James Webb, Kepler, adaptive optics, radio interferometers like ALMA. (Any one.)

Media attention, social amplification, and confirmation bias make a striking claim stick. Retractions receive far less coverage than the original claim, so the false idea persists.

The phrasing falsely suggests scientific uncertainty where there is overwhelming consensus on the physics. Genuine debate exists on policy and on details (like the exact rate of ice-sheet melt), not on the core claim.

A minority scientific opinion is held by credentialed researchers presenting evidence through peer review. A contested public claim may not have scientific support at all; the "controversy" may be manufactured by groups with non-scientific interests.

Check the source of the video, what "toxins" are specified (all vaccines contain some chemical ingredients, many in tiny doses); compare to authoritative sources (WHO, NHMRC, peer-reviewed studies); check whether the video's author is a qualified expert and cites evidence.

Consensus emerges from many independent researchers each examining the evidence. It is a measure of how well a claim holds up under repeated challenge, not a vote on preferred conclusions.

For: could buy time to reduce emissions; effective in preliminary models; cheap compared to mitigation. Against: unknown side effects on rainfall and ecosystems; governance -- who decides?; may discourage emission reduction (moral hazard). (Any two each.)

Bias in training data (may underperform on under-represented skin types); liability if AI errs; transparency of decisions; consent and patient trust; deskilling of dermatologists; privacy of medical data. (Any three.)

Cultural bias, lack of formal recording in Western-science formats, and historical exclusion. Change requires genuine partnerships, funding for Indigenous-led research, and recognising oral knowledge as valid evidence when supported by outcomes.

Bias: companies may suppress negative-result studies and fund research likely to show their drug favourably. Mitigations: mandatory pre-registration of clinical trials, open-data requirements, independent replication, disclosure of funding sources.

It corrupts the collective record; other scientists may waste years building on false results; the public loses trust in the field. Science depends on honesty because no one can personally check every result.

Sample size? Was it peer-reviewed? Was it randomised and controlled? Who funded it? Were effects small or large? Were other variables controlled (diet, exercise)? Have other studies confirmed it? What population was studied? (Any five.)

Nutrition science relies on observational studies of large populations, which can produce varying results. Media often reports each new study as if it overturns the previous one; in reality, the body of evidence evolves slowly. What is missed: mainstream dietary advice has been stable for decades (vegetables good, processed foods bad). Individual studies are snapshots; consensus is the long-run trend.

Answers will vary; reasonable answers note the scientific consensus, the distinction between scientific and policy disagreements, and a considered view linking evidence to action.

Research follows money; profit-driven funding favours issues affecting wealthy markets. Neglected-disease burden is high but paying capacity is low. Society-level correction (e.g. public funding of neglected-disease research, prize funds) is defensible on equity grounds.