Practice

Gamete: a haploid sex cell (sperm or egg). Zygote: the diploid cell formed when two gametes fuse. Haploid ($n$): one set of chromosomes. Diploid ($2n$): two sets.

E.g. (i) binary fission in E. coli; (ii) budding in hydra or yeast; (iii) vegetative runners in strawberry plants; (iv) spore formation in fungi.

(a) 46 (diploid), (b) 23 (haploid), (c) 46 (diploid).

Male: stamen (anther + filament). Female: carpel or pistil (stigma + style + ovary).

Meiosis produces gametes. Mitosis produces body cells for growth and repair.

Advantages: fast, no mate needed, energy-efficient. Disadvantages: no genetic variation, vulnerable to disease and environmental change.

Fungal spores are produced by meiosis in the sexual stage of many fungi (sexual), but many fungi also release asexual spores formed by mitosis. Without more detail both answers are possible; most school contexts treat mushroom spores as products of sexual reproduction because meiosis forms them.

Each parent contributes half of the chromosomes; meiosis shuffles alleles via crossing over and random assortment, and fertilisation randomly pairs one sperm with one egg. The result is a unique combination.

Grafting keeps the desired characteristics (flavour, size, disease resistance) because the offspring are clones of the parent tree. Seed offspring would vary unpredictably.

The variable population -- genetic variation means some frogs are likely to have alleles that give resistance to the new bacterium; clones all have the same susceptibility.

Meiosis halves the chromosome number (2n -> n) when gametes form; fertilisation restores the diploid number (n + n -> 2n). Together they keep the species' chromosome number constant.

Number of divisions: 4 h / 0.5 h = 8. Population: $2^8 = 256$ cells.

Stable conditions favour fast asexual reproduction (exploit resources quickly). In droughts, variation from sexual reproduction increases the chance some offspring tolerate the stress.

Only one sperm fertilises the egg; sperm must compete and most are lost, so large numbers raise the chance of fertilisation. Eggs carry the resources for early development, which is costly, so fewer are made.

Pollination transfers pollen (male gametes) from one variety's anther to the other's stigma. Fertilisation occurs when the pollen tube delivers a sperm nucleus to an egg inside the ovule, forming a zygote. The ovule develops into a seed that combines the parents' genes.

In good conditions, asexual reproduction rapidly increases population size. When conditions worsen (cold, food shortage), a switch to sexual reproduction produces varied offspring (often resting eggs) more likely to survive the challenge. This bet-hedging balances growth with resilience.

Female workers come from fertilised eggs with two sets of chromosomes (sexual). Males come from unfertilised eggs that develop by parthenogenesis -- a form of asexual reproduction -- so drones have only the queen's genes.

(i) No genetic variation, so the population is vulnerable to novel disease or environmental change. (ii) Accumulation of genetic errors cannot be masked by a second allele. Also early ageing issues (as observed in Dolly) and low genetic diversity reducing adaptability.

Self-pollination still involves meiosis (producing pollen and eggs) and fertilisation (pollen + ovule), so offspring receive gametes from two gamete-producing events even if they come from the same plant. Variation is limited but genetic recombination still occurs.

Dendrites: receive signals from other neurons. Cell body: contains the nucleus; integrates incoming signals. Axon: carries the nerve impulse away to the next cell (often insulated by myelin for speed).

A synapse is the gap between two neurons. When an impulse arrives, neurotransmitters are released from vesicles, cross the gap, and bind to receptors on the next neuron, triggering a new impulse.

E.g. pancreas - insulin (lowers blood glucose); thyroid - thyroxine (raises metabolic rate); adrenal - adrenaline (fight-or-flight); pituitary - growth hormone.

Homeostasis is the maintenance of a stable internal environment. Examples: body temperature, blood glucose, blood pH, water/salt balance.

Stimulus, receptor, control centre, effector (with response).

Nervous: fast (milliseconds), short-acting, electrical impulses along neurons. Endocrine: slow (seconds to days), long-acting, chemical hormones via blood.

Reflexes bypass the brain via the spinal cord, saving time. This minimises tissue damage in dangerous situations (hot surfaces, sharp objects).

Insulin is a protein. Digestive enzymes in the stomach and small intestine would break it down before it could act. Injection bypasses the digestive system and delivers insulin directly to the blood.

Possible effects: weight loss, rapid heart rate, feeling hot, anxiety, increased appetite, tremor -- all from elevated metabolism.

Adrenaline, released by the adrenal glands (above the kidneys).

Rising glucose is detected by the pancreas; beta cells release insulin; liver and muscle cells take up glucose (stored as glycogen/fat); blood glucose returns to the set point.

Stimulus: body temperature rises above $37^{\circ}\text{C}$. Receptor: thermoreceptors in skin/hypothalamus. Control centre: hypothalamus. Effectors: skin blood vessels (vasodilate), sweat glands (sweat), behaviour (seek shade). Response: heat lost by radiation and evaporation; temperature returns to set point.

Blood glucose rises and stays high (hyperglycaemia) because cells cannot take up glucose without insulin. Injected insulin replaces the missing hormone, allowing uptake and restoring normal levels.

Stimulus: core temperature falls below set point. Receptors and hypothalamus detect the fall. Effector: skeletal muscles contract rapidly (shivering), generating heat through respiration. Response: temperature rises back to set point.

Catching a ball $\approx 0.3$ s; puberty $\approx 2$-$4$ years $\approx 10^{8}$ s. About 8-9 orders of magnitude apart.

Positive feedback -- the response amplifies the stimulus. It stops when the baby is delivered, which removes the pressure on the cervix that triggered oxytocin release.

The adrenal glands sit on top of the kidneys, so adrenaline enters a major blood vessel near the heart and is pumped rapidly throughout the body. It also acts on receptors already present on many cell types, giving rapid widespread effects.

Stimulus: blood becomes too dilute (low solute concentration). Receptors: osmoreceptors in hypothalamus. Effector: pituitary reduces ADH release; kidneys reabsorb less water. Response: more dilute urine is produced, restoring normal blood water content.

Acetylcholine builds up in synapses, causing continued muscle stimulation -- twitching, cramping, weakness. Overdose can cause paralysis of respiratory muscles and death. (This is how some nerve agents and pesticides kill.)

Infectious: caused by a pathogen and can spread (e.g. influenza). Non-infectious: not caused by a pathogen, cannot spread (e.g. type 2 diabetes).

Bacteria (tuberculosis), viruses (flu), fungi (tinea), protists (malaria), prions (CJD).

Antibiotics target bacterial structures (cell walls, ribosomes) that viruses lack. Viruses replicate inside host cells using host machinery.

Physical: skin, mucous membranes, cilia in airways, tears washing eyes. Chemical: stomach acid, lysozyme in tears/saliva, antimicrobial peptides.

An antigen is a molecule (often on a pathogen surface) that the immune system recognises as foreign. An antibody is a Y-shaped protein produced by B-cells that binds to a specific antigen.

A memory cell is a long-lived lymphocyte formed after an infection or vaccination. If the same pathogen returns, memory cells mount a fast, strong response before illness develops.

Any three of: isolate the sick student; vaccinate those at risk; encourage hand washing; cover coughs and sneezes; wipe surfaces; keep non-immune students home.

Vaccination gives immunity without the illness, avoiding the risks of severe disease, complications (pneumonia, encephalitis), and death. It also protects others via herd immunity.

Salmonella is a food-borne pathogen; contamination is expected in food preparation areas, not living quarters. Inspection targets the transmission route.

Stopping early leaves the hardiest bacteria alive; they can multiply and pass on resistance. Finishing the course kills remaining bacteria and reduces the chance of resistance.

Smoking damages lung cell DNA, triggering cancer (uncontrolled division). It also paralyses cilia and irritates airways, making bacterial/viral lung infection more likely.

Expected number who still get sick: $5\% \times 10\,000 = 500$. Herd immunity relies on the other 9500 being protected, which blocks most transmission chains and indirectly protects the 500 plus anyone who cannot be vaccinated.

Draining water: removes mosquito breeding sites (prevents vector population). Bed nets: prevent biting during peak mosquito activity (breaks transmission to human). Insecticide spraying: kills adult mosquitoes (reduces vector numbers and biting).

E.g.: lose weight through diet changes and portion control; increase physical activity to at least 150 min/week; reduce refined-sugar intake; regular blood-glucose monitoring with a doctor.

Quarantine interrupts person-to-person transmission, which infectious diseases need. Non-infectious diseases arise within an individual and do not spread, so isolation has no effect.

Selection pressure: every antibiotic course kills susceptible bacteria but allows resistant mutants to reproduce. Frequent, unnecessary use (viral infections, livestock growth promotion) intensifies selection, so resistance genes spread. Controls: prescribe antibiotics only when needed; finish full courses; restrict non-therapeutic use in animals.

Flu's surface antigens (haemagglutinin, neuraminidase) mutate quickly, so memory cells from last year may not recognise this year's strain -- a new vaccine formulation is needed. Measles antigens barely change, so one vaccine gives decades of protection.

HIV destroys T-helper cells, which coordinate both B-cell and cytotoxic T-cell responses. Without them, adaptive immunity collapses, leaving the patient vulnerable to opportunistic infections (Pneumocystis pneumonia, Kaposi's sarcoma) that a healthy immune system normally suppresses.

Primary response: slow (days to peak), low antibody level, mostly IgM. Secondary response: fast (hours to days), much higher antibody level, mostly IgG, due to memory cells. Sketch: low bump after first exposure; much higher, faster peak after second exposure.

Dalton (solid sphere) -> Thomson (plum pudding) -> Rutherford (nuclear) -> Bohr (shells) -> Schrodinger/quantum (orbitals).

Alpha particles were fired at a thin gold foil. Most passed straight through, a few were deflected, and a very small fraction bounced back. Conclusion: the atom is mostly empty space with a tiny, dense, positively charged nucleus at its centre.

Protons 17, neutrons $35 - 17 = 18$, electrons 17.

Isotopes are atoms of the same element (same number of protons) with different numbers of neutrons. Example: carbon-12 and carbon-14.

Chemistry depends on electrons (and their arrangement). Isotopes have the same electron configuration because they have the same number of protons and electrons.

(a) $^{13}_{6}\text{C}$ (carbon-13), (b) $^{42}_{20}\text{Ca}$ (calcium-42).

$^{226}_{88}\text{Ra} \to \,^{222}_{86}\text{Rn} + \,^{4}_{2}\alpha$.

$^{90}_{38}\text{Sr} \to \,^{90}_{39}\text{Y} + \,^{0}_{-1}\beta$.

$^{241}_{95}\text{Am} \to \,^{237}_{93}\text{Np} + \,^{4}_{2}\alpha$. Daughter: neptunium-237.

(a) alpha, (b) beta-minus (an electron emitted from the nucleus), (c) gamma (high-energy photon).

Two alpha: $A$ drops by 8, $Z$ drops by 4. One beta: $Z$ rises by 1, $A$ unchanged. Overall: $\Delta A = -8$, $\Delta Z = -3$.

$1600 \times (1/2)^3 = 1600 / 8 = 200$ atoms.

Half-lives in 24 h: $24/6 = 4$. Remaining: $80 \times (1/2)^4 = 80/16 = 5$ mg.

$(1/2)^n = 1/16 = (1/2)^4$, so 4 half-lives.

$10.54 / 5.27 = 2$ half-lives. Remaining: $100 \times (1/2)^2 = 25$ g.

$6/2 = 3$ half-lives. Remaining activity: $40 \times (1/2)^3 = 5$ MBq.

Long half-lives work for dating because activity changes measurably over thousands/millions of years. For medical imaging the source should decay quickly after the scan so the patient is not exposed to radiation for long -- a short half-life (hours) is better.

$1/8 = (1/2)^3$, so 3 half-lives. Age $= 3 \times 5730 = 17\,190$ years.

Gamma rays penetrate tissue to reach tumours and can be aimed precisely. Alpha particles have very short range in tissue, so external alpha cannot reach tumours; their high ionising power also makes them dangerous inside the body but ineffective from outside.

Bohr's model assumed fixed circular orbits and a single electron. In multi-electron atoms, electron-electron repulsion and subshell structure (s, p, d) affect spectra in ways Bohr could not predict. The quantum model with orbitals handles these correctly.

If atoms were uniform positive "puddings", alpha particles (positive, fast) should have deflected only slightly. The back-scattering of a few shows there is a concentrated positive mass inside -- the nucleus. Most passing straight through shows the atom is mostly empty space. This contradicts the plum pudding and supports Rutherford's nuclear model.

Each alpha: $\Delta A = -4$, $\Delta Z = -2$. Each beta: $\Delta A = 0$, $\Delta Z = +1$. Let $a$ alphas and $b$ betas. Then $4a = 32 \Rightarrow a = 8$, and $-2a + b = -10 \Rightarrow -16 + b = -10 \Rightarrow b = 6$. So 8 alpha and 6 beta-minus decays.

$16/4 = 4$ half-lives. Remaining: $800 \times (1/2)^4 = 50$ MBq. Tc-99m has a short half-life (about 6 hours physically, shorter effectively), giving enough time for imaging but minimal radiation dose afterwards; it also emits gamma rays detectable outside the body.

$N/N_0 = (1/2)^{t/t_{1/2}} \Rightarrow t = t_{1/2} \cdot \dfrac{\log(N/N_0)}{\log(1/2)}$. For $N/N_0 = 0.3$ and $t_{1/2} = 1.3 \times 10^9$ y: $t = 1.3 \times 10^9 \times \dfrac{\log 0.3}{\log 0.5} = 1.3 \times 10^9 \times 1.737 \approx 2.26 \times 10^9$ years.

(i) Sunlight reaches Earth's surface. (ii) The warm surface emits infrared radiation. (iii) Greenhouse gas molecules absorb some of this infrared. (iv) They re-emit it in all directions, including back down, warming the lower atmosphere and surface.

E.g. CO$_2$ - burning fossil fuels; CH$_4$ - livestock, gas leaks, rice paddies; N$_2$O - fertiliser use; water vapour - evaporation; CFC/HFC - refrigeration/industrial.

The natural effect keeps Earth habitable ($\sim 15^{\circ}\text{C}$ average). The enhanced effect is the extra warming caused by human-added greenhouse gases raising their atmospheric concentrations.

Any four of: rising global temperature; ice core CO$_2$ and temperature records; shrinking glaciers and sea ice; rising sea level; ocean acidification; shifts in species ranges and flowering times.

"ppm" means parts per million, so 420 ppm means 420 molecules of CO$_2$ in every million air molecules. Current level about 420 ppm.

Warming melts ice/snow; darker exposed ocean or land absorbs more sunlight, causing further warming (positive feedback).

Without greenhouse gases, more of the infrared Earth emits would escape directly to space. The balance between absorbed solar energy and emitted infrared would then sit at a much colder surface temperature (around $-18^{\circ}\text{C}$).

Water vapour concentration is controlled by temperature (warmer air holds more); it cannot be directly managed. It acts as a feedback, amplifying warming triggered by CO$_2$ and other long-lived gases, which we can manage.

Weak argument. Small concentrations can still absorb strongly at specific infrared wavelengths. CO$_2$'s greenhouse effect is well measured in lab and field; doubling CO$_2$ roughly doubles the added radiative forcing.

Snowfall traps tiny air bubbles as it is buried and compressed into ice. Drilling cores and analysing the bubbles reveals CO$_2$, methane, and isotope records going back hundreds of thousands of years.

Mitigation reduces the cause (e.g. switch to renewables). Adaptation adjusts to the impacts (e.g. build sea defences).

$3.5 \times 100 = 350$ mm $= 0.35$ m over 100 years. For a suburb at 1 m, a third of that elevation is lost, and storm surges plus high tides would already flood much of the area -- plus feedback from rapid ice-sheet loss could make the rise larger.

Rise: $420 - 317 = 103$ ppm. Percentage: $\dfrac{103}{317} \times 100 \approx 32.5\%$.

Mitigation -- solar electricity replaces fossil-fuel generation, cutting CO$_2$ emissions.

Typical ranking (large to small): EV on renewables and flying less tend to be large; reducing red meat is sizable (methane, land use); LED lights give meaningful but smaller savings. Exact order depends on household baseline, but flying and vehicle fuel usually dominate.

Arctic permafrost contains huge quantities of organic carbon. As air warms, permafrost thaws; microbes decompose the organic matter, releasing CO$_2$ and methane. These gases cause further warming and more thawing -- a positive feedback that could lock in warming even if human emissions were stopped.

Dissolved CO$_2$ + water -> carbonic acid, which lowers ocean pH and reduces carbonate ions needed for shells and coral skeletons. Shell-forming organisms (plankton, molluscs, corals) are weakened, threatening food webs. Called the "other CO$_2$ problem" because acidification is distinct from, but caused by the same CO$_2$ that drives, climate warming.

Volcanoes cause short-term cooling from sulfate aerosols, not warming. Solar output has been roughly flat since 1970. Milankovitch cycles act on tens of thousands of years, not decades. None matches the timing or magnitude of the post-1970 rise, while CO$_2$ forcing does.

Counter-arguments: (i) Australia has high per-capita emissions, so "small" is misleading. (ii) Climate change is a collective action problem -- if every country said "we are small", global emissions never fall. (iii) Australia is particularly exposed to climate impacts (droughts, bushfires, Great Barrier Reef), so mitigation protects self-interest. (iv) Leadership and export economics -- clean-tech and renewables trade will favour early movers.

(a) transverse, (b) longitudinal, (c) mostly transverse (water surface moves up/down), (d) transverse.

Amplitude: max displacement from equilibrium. Frequency: cycles per second (Hz). Wavelength: distance between consecutive crests (m). Period: time for one full cycle (s).

$v = f \lambda$: the speed of a wave equals its frequency multiplied by its wavelength.

Radio -> microwave -> infrared -> visible -> ultraviolet -> X-ray -> gamma.

Conduction (needs matter, best in solids), convection (needs fluid), radiation (no medium needed).

Sound is a mechanical wave needing particles to vibrate. Vacuum has (almost) no particles, so no vibration can propagate.

$v = 50 \times 4 = 200$ m/s.

$\lambda = \dfrac{3 \times 10^{8}}{2.4 \times 10^{9}} = 0.125$ m $= 12.5$ cm.

$f = \dfrac{3 \times 10^{8}}{3} = 1 \times 10^{8}$ Hz = 100 MHz.

$f = v/\lambda = 12/0.4 = 30$ Hz. Period $T = 1/30 \approx 0.033$ s.

$\lambda = 1480/20 = 74$ m.

$f = 3 \times 10^{8} / (650 \times 10^{-9}) \approx 4.6 \times 10^{14}$ Hz.

Low frequency = long wavelength. Diffraction is strongest when wavelength is similar to or larger than the obstacle/gap. Bass has wavelengths of metres, comparable to door widths, so it diffracts around corners. Treble has wavelengths of centimetres and diffracts much less.

Microwaves: mobile phone signals, microwave ovens, radar. Infrared: TV remotes, thermal imaging. X-rays: medical imaging, airport security.

UV photons carry more energy per photon and can ionise atoms or damage DNA directly, causing sunburn and skin cancer. Visible photons have less energy and are mostly absorbed harmlessly.

Speed decreases (light is slower in water); wavelength decreases proportionally; frequency stays the same (set by the source).

Incorrect. Sound travels faster in steel (rigid bonds transmit vibration quickly) than in air; "heavier" is the wrong factor -- stiffness matters more than density.

Distance $= 343 \times 6 \approx 2060$ m or about $2$ km.

$\lambda = 343 / (40\,000) = 0.00858$ m $\approx 8.6$ mm. Short wavelength lets bats resolve small objects (insects) and focus the beam more tightly.

$v = f\lambda = 2 \times 1.5 = 3$ m/s. Time $= 25 / 3 \approx 8.3$ s.

AM wavelength $= 3 \times 10^{8} / 10^{6} = 300$ m, comparable to hills -- diffracts well. FM wavelength $= 3 \times 10^{8} / 10^{8} = 3$ m, much smaller than hills -- little diffraction, so FM needs line of sight.

Transverse waves cannot propagate through fluids because fluids have no shear rigidity. Observations show a "shadow zone" where S-waves do not arrive, meaning they pass through a liquid layer. P-waves still arrive (longitudinal, slower in liquid). This is evidence that the outer core is liquid.

$\lambda = 1540 / (3 \times 10^{6}) \approx 5.1 \times 10^{-4}$ m $= 0.51$ mm. Smallest resolvable feature is roughly the wavelength, so about $0.5$ mm -- enough to see an unborn baby's bones and organs.

Where waves from the two speakers arrive in phase (crests coincide), amplitudes add -- loud (constructive interference). Where they arrive out of phase (crest meets trough), they cancel -- quiet (destructive interference). The pattern depends on the path-length difference relative to wavelength.

Pulse travels to target and back, total distance $= c \times t = 3 \times 10^{8} \times 1.2 \times 10^{-4} = 3.6 \times 10^{4}$ m. Distance to target $= 1.8 \times 10^{4}$ m $= 18$ km. Ideas used: EM waves travel at $c$; distance = speed times time.

Point the right thumb in the direction of conventional current; the fingers curl in the direction of the magnetic field.

(a) Inside a solenoid: strong, nearly uniform field running along the axis. (b) Outside: weaker field that loops from one end to the other like a bar magnet.

E.g. MRI scanners, scrap-metal cranes, relays, doorbells, loudspeakers, electric motors.

A changing magnetic field through a coil induces a voltage (EMF) in that coil; if the circuit is closed, a current flows.

$50$ Hz.

Coal, natural gas, wind, hydro, nuclear (globally), biomass. Any three.

AC reverses direction (at 50 Hz here), DC does not. AC voltage is easy to change with transformers; DC needs electronic converters. AC is used for transmission and mains; DC is used in batteries and electronics.

AC: mains power, home outlets. DC: battery (torch, phone, car), solar panel.

AC can be stepped up to very high voltage with a transformer, reducing $I^2 R$ transmission losses. Electronics need stable low-voltage DC for logic circuits; wall adaptors rectify AC to DC.

An inverter converts DC from solar panels or batteries into AC at mains voltage and frequency, so it can feed household appliances or be exported to the grid.

The alternator produces AC efficiently via rotation; its output is rectified (by diodes) to DC for battery charging and car electronics.

Labelled diagram: magnet N/S poles either side; rectangular coil with axis horizontal; slip rings on the axle; two brushes in contact with slip rings; leads to external circuit. Arrow on one side of the coil shows induced current direction at the instant drawn.

(a) Coal: chemical (coal) -> heat (combustion) -> kinetic (steam turbine) -> electrical (generator). (b) PV: light energy -> electrical (directly, via semiconductor junction).

Voltage doubles (faster change of flux) and the frequency of the AC also doubles.

An electromagnet can be switched on to pick up iron and switched off to drop it; a permanent magnet could not release the load.

For a fixed power $P = VI$, raising $V$ allows $I$ to be lower. Since $P_{\text{loss}} = I^2 R$ depends on the square of current, halving current cuts losses to one-quarter. That is why transmission uses 275-500 kV, then transformers step voltage down for distribution and use.

Induced voltage roughly doubles from faster rotation (greater rate of change of flux) and doubles again from twice the turns, so $\approx 4$ times greater. (Faraday's law: induced EMF $\propto N \cdot d\Phi/dt$.)

Combustion converts only some chemical energy to useful heat (boiler losses, flue-gas losses). Steam turbine: thermodynamic limit -- a substantial share of heat must be dumped at the cold end (large). Generator: small resistive/mechanical losses. Transmission: $I^2 R$ losses and transformer losses, typically a few percent. Largest losses are in the heat-to-kinetic stage (Carnot limit) and waste heat at the condenser.

PV: energy from sunlight; capacity factor roughly 15-25% (depends on weather and latitude); low operating impact but land use and manufacturing footprint. Hydro: energy from gravitational potential in water; high capacity factor (often 40-60%) and dispatchable; big ecological impact from dams, displacement, and habitat change.

Energy cannot be created or destroyed, only transformed from one form to another. In a closed system the total energy stays constant.

Useful energy: output that fulfils the device's purpose. Wasted energy: output in forms we cannot or do not use (usually heat, sometimes sound). Efficiency: the fraction of input energy that becomes useful output.

(a) $\eta = 150/200 \times 100 = 75\%$. (b) Useful $= 400 - 80 = 320$ kJ. $\eta = 320/400 \times 100 = 80\%$.

$\eta = 210/250 \times 100 = 84\%$.

Sankey: input band (say 100 J) splits into useful (70 J heated air flow) and wasted (30 J heat + sound). Widths must add to input width.

Chemical -> electrical: battery. Electrical -> light: LED. Kinetic -> electrical: generator (wind turbine or hydro).

Incandescent: $\eta = 3/60 = 5\%$. LED: $\eta = 6/10 = 60\%$. LED gives twice the light for one-sixth the electricity, so the yearly saving at 4 h/day is about $(60 - 10) \times 4 \times 365 = 73\,000$ Wh $= 73$ kWh per bulb. Across a house that is a large reduction in bill and emissions.

The engine's wasted energy leaves the car mainly as hot exhaust gas and heat carried away by the radiator; these are the largest loss paths, so any calculation of efficiency must include them to be realistic.

Electricity $= 0.40 \times 1000 = 400$ MJ. The rest ($600$ MJ) is mostly waste heat lost at the boiler and cooling towers, plus smaller losses at the turbine and generator.

Each bounce loses some kinetic energy to heat, sound, and air resistance. That energy is not returned, so kinetic energy on the way up is smaller each time, reducing the bounce height. Total energy is still conserved (the lost energy warms the ball, floor, and air).

Kinetic energy -> heat (via friction between skin surfaces). Some sound is also produced.

$\eta = 196\,000 / 1.8 \times 10^{7} \times 100 \approx 1.09\%$. That is low because 5 kWh is a huge amount of energy for a 20 m lift -- probably this is a single lift of many, or most energy is elsewhere. (Or the numbers represent all the runs over an hour, not one.)

$\eta = 180/1000 \times 100 = 18\%$.

The other $200$ W is lost as heat in the motor and casing, and some sound. $\eta = 1800/2000 = 90\%$.

$\eta = (500 - 8)/500 \times 100 = 492/500 \times 100 = 98.4\%$.

Overall $= 0.40 \times 0.92 \times 0.70 = 0.2576$, or about $25.8\%$. Only about a quarter of the coal's chemical energy becomes useful output; most is lost as heat at the power station, with smaller losses in transmission and in the appliance.

A heat pump does not create energy; it moves heat from a colder outside to a warmer inside using electrical work. Total energy into the house = electrical input + heat taken from outside = heat delivered. Conservation holds; COP just describes the ratio of heat delivered to work input.

Counter-points: (i) Electricity is often more expensive per joule than gas heat, so using electric bulbs for heating is wasteful financially. (ii) The light that leaves through windows is not returned; part of the energy leaves the house rather than warming it. (iii) In summer the heat is unwanted and may drive more air-conditioning. (iv) Switching to LEDs + efficient heating saves more energy and emissions overall.

Overall $= 0.40 \times 0.92 \times 0.50 = 0.184$ or $18.4\%$ of the original coal energy becomes visible light. Sankey: coal 100 -> power station (40 to electricity, 60 waste heat) -> transmission (36.8 delivered, 3.2 line losses) -> LED bulb (18.4 light, 18.4 heat).

E.g. "Does increasing water temperature reduce the time for $5$ g of salt to dissolve in $100$ mL of water?"

"If water temperature is increased, then the time for salt to dissolve will decrease, because particles move faster at higher temperature, giving more frequent collisions with the solvent."

IV: mass of fertiliser per plant. DV: tomato yield (mass or count of fruit). Controlled: variety of tomato, size of pot, amount of water, light exposure, soil type, duration of experiment.

The IV is the variable the experimenter changes; the DV is what is measured and is expected to respond to changes in the IV.

A control group is a comparison group that does not receive the treatment/change, showing what happens without the IV. Example: placebo group in a drug trial.

Validity: the experiment measures what it claims to measure. Reliability: repeated measurements give consistent results. Accuracy: measurements are close to the true value.

Systematic error -- off by a consistent $+2^{\circ}\text{C}$.

Reliable (very consistent), reasonably accurate if the true time is near $12.40$ s. Validity depends on whether timing actually measures what we want.

E.g. using a cheap bathroom scale that always reads $2$ kg too low -- gives repeatable (reliable) but inaccurate readings; still not valid for a "true weight" study.

Repeating averages out random fluctuations, improving reliability. It does not fix systematic errors, which push every reading the same way.

IV: drop height (e.g. 25, 50, 75, 100, 125 cm). DV: bounce height (cm) from the floor to top of first bounce. Controlled: same ball, same surface, same ball release technique (no push), same temperature, same measurer. Data: measure bounce height 3 times per drop height; average. Analysis: plot bounce height (y) vs drop height (x); look for a linear trend and comment on outliers.

Issues: (i) $n = 1$; no replication; (ii) no control (different plants, different conditions -- uncontrolled confounds); (iii) a single outcome (taller) doesn't prove the fertiliser is responsible; (iv) no randomisation; (v) no measure of variability.

Bias sources: (i) selective reporting of favourable results; (ii) study design choices favouring the sponsor (short duration, specific group). Address by independent replication, pre-registering the study, and full public data access.

Investigate first: were the two outliers from a procedural mistake (e.g. different method)? If yes, exclude and state this. If there's no mistake, keep them but report them -- they may reflect real variation. Use a consistent rule (e.g. outlier test) rather than discarding data to make the result look cleaner.

Correlation does not imply causation. Both ice-cream sales and drownings rise in summer because of higher temperatures and more swimming; the common cause is hot weather, not ice cream.

Reaction time falls from 280 ms (0 mg) to 245 ms (150 mg), showing caffeine shortens reaction time up to a point. At 200 mg it rises again (260 ms), suggesting a "too much" effect (jitteriness, over-arousal). Plausible interpretation: moderate doses improve alertness; high doses may impair.

Claim: LED bulbs are more efficient than incandescents. Evidence: typical LED outputs $\sim 60\%$ of input as visible light vs $\sim 5\%$ for incandescents; LEDs use $10$ W to produce about the same light as a $60$ W incandescent. Reasoning: both convert electrical input into light and heat; LEDs use semiconductor electroluminescence, which diverts little energy to heat, while incandescents rely on a heated filament where most energy becomes heat. Therefore, for the same useful light, LEDs use far less electrical input, which is the definition of higher efficiency.

In a double-blind trial, neither side can consciously or unconsciously influence outcomes. If doctors knew, they might treat the drug group differently (more attentive care, interpret symptoms differently); if patients knew, the placebo effect and reporting would differ. Double-blinding removes both channels of bias.

Study B deserves more weight: much larger $n$ (better reliability), researcher-measured weight (more accurate and valid than self-report), longer duration (captures real effects). Study A's small sample and self-reported DV make both reliability and validity weaker.

"Proof" in everyday use means certainty. In science, no finite set of observations can establish certainty -- there may always be a future experiment that contradicts a theory. Science "supports" hypotheses tentatively and is open to revision. Paradoxically, this is a strength: self-correction is why science advances, while dogma that claims proof cannot be improved.

Claim: higher hours of study are associated with higher test scores. Evidence: positive trend on the graph. Reasoning: more time on content could plausibly improve retention and skill. But correlation is not causation; confounding variables (e.g. motivation, sleep, subject aptitude, prior knowledge) might cause both more study and better scores. A controlled experiment or statistical control is needed to distinguish the effect of study time itself.