Shizuoka Public High School Entrance Examination - Science cheat sheet

Average speed = distance ÷ time; average velocity = displacement ÷ time. Velocity includes direction, so a round trip has zero average velocity but nonzero average speed.

Acceleration = change in velocity ÷ time (m/s²). On a velocity–time graph, slope = acceleration and area under the line = displacement.

Newton's first law: with no net force, an object at rest stays at rest and a moving object continues at constant velocity. Friction is what usually stops it.

Newton's second law: F = ma (net force in N, mass in kg, acceleration in m/s²). Doubling mass under the same force halves acceleration.

Newton's third law: forces act in equal-and-opposite pairs on two different objects; the pair does not cancel because each force acts on a different body.

Weight = mg, with g ≈ 9.8 N/kg in Japan's curriculum. Mass is constant everywhere; weight changes with gravitational field strength.

Work W = F × d only when force and displacement are parallel (unit: joule). Holding a load still does zero work because displacement is zero.

Kinetic energy = ½mv²; gravitational potential energy = mgh. With friction ignored, mechanical energy is conserved: ½mv² + mgh = constant.

Pressure = force ÷ area (N/m² = Pa). A smaller contact area gives larger pressure, which is why a drawing pin has a sharp point.

Current I = charge ÷ time (1 A = 1 C/s). Conventional current flows from + to − outside the source; electrons actually drift the opposite way.

Ohm's law: V = RI. For a fixed resistor, current is proportional to voltage; a filament lamp's resistance rises as it heats, so its V–I graph curves.

Series circuit: current is the same everywhere; resistances add (R = R₁ + R₂); voltages split in proportion to resistance.

Parallel circuit: voltage is the same across each branch; currents add; total resistance is smaller than the smallest branch resistance (1/R = 1/R₁ + 1/R₂).

Electric power P = VI = I²R = V²/R (watt). Energy used = power × time, and 1 kWh = 3.6 × 10⁶ J.

Magnetic field lines run from the N pole to the S pole outside a magnet; closer lines mean a stronger field. Like poles repel, unlike poles attract.

A current-carrying wire in a magnetic field experiences a force (Fleming's left-hand rule); a coil in a magnetic field rotates, which is the motor principle.

Electromagnetic induction: moving a magnet into or out of a coil induces a voltage; the induced current's field opposes the change (Lenz's law), the basis of generators.

Adding a resistor in series with a lamp reduces the current and the voltage across the lamp; adding one in parallel leaves the lamp's voltage nearly unchanged.

Wave speed v = fλ. Frequency is set by the source; when a wave enters a new medium, frequency stays the same while speed and wavelength change.

Transverse waves (light, waves on a string) oscillate perpendicular to travel; longitudinal waves (sound) oscillate parallel to travel, forming compressions and rarefactions.

Sound needs a medium, travels about 340 m/s in air at room temperature, and travels faster in water and solids. It cannot travel through a vacuum.

Higher pitch = higher frequency; larger amplitude = louder sound. Audible range for humans is roughly 20 Hz to 20 kHz.

Law of reflection: angle of incidence = angle of reflection, both measured from the normal. A plane mirror forms a virtual, laterally inverted image of equal size.

Refraction: light bends toward the normal entering a denser medium (air → glass) and away from the normal leaving it. This explains why a straw appears bent in water.

Convex (converging) lens: parallel rays meet at the focal point. Object beyond 2f → real, inverted, diminished image; between f and 2f → real, inverted, magnified; inside f → virtual, upright, magnified.

Total internal reflection occurs when light travels from a denser to a less dense medium beyond the critical angle; this is how optical fibres carry light.

Pure substances have fixed melting and boiling points; mixtures melt and boil over a range and can be separated by physical methods.

Distillation separates a liquid from dissolved solids or two liquids with different boiling points; fractional distillation exploits closer boiling points.

Filtration separates an insoluble solid from a liquid; evaporation or crystallisation recovers a dissolved solid; chromatography separates dissolved coloured substances by differing solubility and adsorption.

Density = mass ÷ volume (g/cm³). It identifies a substance and explains floating: an object floats if its density is less than the liquid's.

In a solid, particles vibrate about fixed positions; in a liquid they slide past one another; in a gas they move rapidly and far apart, so gases are compressible.

At the melting and boiling points, added heat changes state rather than raising temperature, because energy breaks particle attractions.

Diffusion is the spreading of particles from high to low concentration; it is fastest in gases and slower at low temperature.

A chemical change produces a new substance and is hard to reverse; a physical change (melting, dissolving) changes state or form only.

Heating a hydrate or a carbonate and driving off gas is a decomposition, not a physical change, because the original substance is consumed.

Law of conservation of mass: atoms are neither created nor destroyed, so every equation must be balanced by adjusting coefficients, never subscripts.

Combination (synthesis): A + B → AB, e.g. 2Mg + O₂ → 2MgO. Decomposition: AB → A + B, e.g. 2H₂O → 2H₂ + O₂ by electrolysis.

Oxidation is loss of electrons or gain of oxygen; reduction is gain of electrons or loss of oxygen. In 2CuO + C → 2Cu + CO₂, carbon is oxidised and copper(II) oxide reduced.

Combustion of a hydrocarbon in sufficient oxygen gives CO₂ and H₂O; insufficient oxygen gives CO, a toxic gas.

Exothermic reactions release heat (combustion, neutralisation, respiration); endothermic reactions absorb it (thermal decomposition, photosynthesis).

Metal reactivity series (high to low): K, Na, Ca, Mg, Al, Zn, Fe, Cu, Ag, Au. A more reactive metal displaces a less reactive one from its salt solution.

A precipitate reaction occurs when two solutions form an insoluble salt, e.g. AgNO₃ + NaCl → AgCl↓ + NaNO₃.

Catalysts speed up a reaction without being consumed; they do not change the amount of product formed.

Acids release H⁺ (protons) in water; bases release OH⁻ or accept H⁺. Strong acids and bases ionise completely; weak ones only partly.

pH scale: pH < 7 acidic, pH = 7 neutral, pH > 7 basic. A change of one pH unit means a tenfold change in H⁺ concentration.

Neutralisation: acid + base → salt + water, e.g. HCl + NaOH → NaCl + H₂O. The ionic equation is H⁺ + OH⁻ → H₂O.

Acid + metal → salt + hydrogen gas (test: burns with a pop). Acid + metal carbonate → salt + water + CO₂ (test: turns limewater milky).

Indicators: litmus turns red in acid and blue in base; phenolphthalein is colourless in acid and pink in base; methyl orange is red in acid and yellow in base.

Salts are named from the metal (or ammonium) plus the acid anion: chloride from HCl, sulfate from H₂SO₄, nitrate from HNO₃, carbonate from H₂CO₃.

Every salt is a compound of a positive ion (metal or NH₄⁺) and a negative ion; ionic compounds conduct when molten or dissolved because ions become mobile.

Neutralisation is exothermic; the heat released per mole of water formed is roughly constant for strong acid–strong base reactions.

Plant cells have a cell wall, chloroplasts, and a large vacuole; animal cells lack these but both have a nucleus, cytoplasm, and a cell membrane.

Mitochondria release energy by respiration; ribosomes build proteins; the nucleus holds DNA and controls the cell.

Mitosis produces two genetically identical diploid cells for growth and repair; meiosis produces four genetically varied haploid gametes.

Fertilisation restores the diploid number: in humans, 23 + 23 = 46 chromosomes.

Genes occur in pairs; a dominant allele is expressed even with one copy, while a recessive allele is expressed only when both copies are recessive.

Punnett square for Aa × Aa gives 3:1 dominant to recessive phenotype and 1 AA : 2 Aa : 1 aa genotype.

Sex in humans: XX is female, XY male; the father's sperm determines the child's sex, giving a 1:1 ratio.

Asexual reproduction (runners, bulbs, cuttings) yields clones; sexual reproduction creates variation that helps a population survive environmental change.

Digestion: starch → glucose by amylase (mouth, pancreas), protein → amino acids by pepsin (stomach) and trypsin, fat → fatty acids and glycerol by lipase, with bile emulsifying fat.

Villi in the small intestine increase surface area for absorption; their thin walls and rich blood supply speed uptake into the blood.

Blood: red cells carry oxygen via haemoglobin, white cells defend against pathogens, platelets clot, plasma transports nutrients, CO₂, and hormones.

Double circulation: right side pumps to the lungs, left side pumps to the body; arteries carry blood away from the heart, veins toward it.

Gas exchange occurs in alveoli, which have thin walls, large total area, and a moist surface; breathing rate rises with exercise to remove CO₂.

Homeostasis keeps internal conditions stable: insulin lowers blood glucose, sweating and vasodilation cool the body, shivering and vasoconstriction warm it.

Reflex arcs bypass conscious thought: receptor → sensory neurone → spinal cord → motor neurone → muscle, allowing rapid protective responses.

Vaccination exposes the body to weakened antigens so memory cells give a faster, stronger response on later infection; antibiotics work on bacteria, not viruses.

Producers (plants) capture light energy by photosynthesis; energy passes to consumers along food chains, and decomposers return nutrients to the soil.

Only about 10% of energy passes to the next trophic level, so food chains rarely exceed four or five links; energy is lost as heat and in waste.

A food web is more stable than a single chain because a predator can switch prey if one species declines.

Population size is limited by food, predators, disease, and space; removal of a top predator can cause a cascade that reduces biodiversity.

Symbiosis: mutualism benefits both species, commensalism benefits one without harming the other, parasitism benefits one at the other's expense.

The carbon cycle moves carbon through photosynthesis, respiration, feeding, decomposition, and combustion; excess CO₂ from fossil fuels strengthens the greenhouse effect.

Eutrophication: nutrient runoff causes algal blooms, which die and are decomposed, depleting oxygen and killing fish.

Biodiversity is highest in tropical forests and coral reefs; habitat loss is the leading cause of species decline.

The principle of superposition: in undisturbed strata, lower layers are older. Cross-cutting faults or intrusions are younger than the layers they cut.

Fossils in strata indicate relative age; index fossils with wide distribution and short time ranges correlate layers across regions.

Earthquakes occur where stress in the crust releases along a fault; the focus is underground, and the epicentre is directly above it.

P-waves are fastest, longitudinal, and travel through solids and liquids; S-waves are slower, transverse, and cannot pass through liquids, so S-wave shadows reveal a liquid outer core.

The time gap between P and S arrivals increases with distance from the epicentre, allowing location by triangulation from three stations.

Magnitude measures energy released (one scale step ≈ 32× more energy); seismic intensity measures local shaking and damage.

Volcanoes form at subduction zones, mid-ocean ridges, and hotspots. Basaltic lava flows easily and erupts gently; viscous, silica-rich magma erupts explosively.

Plate boundaries: divergent (ridges), convergent (trenches, mountains, subduction), transform (strike-slip faults such as the San Andreas). Japan lies where four plates meet, hence frequent earthquakes and volcanoes.

Air pressure decreases with altitude; wind blows from high to low pressure, deflected by the Coriolis force-counterclockwise around lows in the Northern Hemisphere.

Warm air holds more water vapour than cold air; the temperature at which relative humidity reaches 100% is the dew point, where clouds and fog form.

High pressure brings clear, settled weather; low pressure brings cloud, rain, and stronger winds.

A warm front brings steady rain that eases; a cold front brings brief heavy rain and a sharp temperature drop with clearing skies.

Earth's 23.4° axial tilt causes the seasons; the hemisphere tilted toward the Sun has longer days and more direct sunlight.

Moon phases depend on the Sun–Earth–Moon angle: new (between Earth and Sun), full (opposite the Sun), with about 29.5 days between repeats.

Solar eclipse: Moon between Earth and Sun (new moon). Lunar eclipse: Earth between Sun and Moon (full moon).

Kepler's third law: the orbital period squared is proportional to the semi-major axis cubed. Inner planets orbit faster and have shorter years.

The Sun's energy comes from hydrogen fusion in its core; the Sun is a main-sequence star, and stars are classified by spectral type (O B A F G K M) and luminosity.