Yamaguchi Prefectural Public High School Entrance Examination - Science cheat sheet

Average speed = distance ÷ time; velocity adds direction, so a round trip has average velocity 0 but nonzero average speed.

Acceleration = change in velocity ÷ time (m/s²); on a v–t graph, slope = acceleration and area under the line = distance travelled.

Newton's first law: with zero net force, an object at rest stays at rest and a moving object continues at constant velocity.

Newton's second law: F = ma; the same force gives half the acceleration to twice the mass.

Newton's third law: forces act in equal-and-opposite pairs on two different objects, so they never cancel on one object.

Weight = mg (g ≈ 9.8 N/kg); mass is constant, weight changes with gravitational field strength.

Friction opposes relative sliding and depends on the surfaces and the normal force, not on contact area.

For a falling object, air resistance grows with speed until it equals weight; then net force is zero and speed stays constant (terminal velocity).

Work done against gravity = weight × vertical height; a horizontal carry at constant speed does no work against gravity.

Work (J) = force (N) × displacement in the direction of the force (m); no displacement means no work.

Power (W) = work ÷ time = energy transferred per second.

Kinetic energy = ½mv²; gravitational potential energy = mgh; in a vacuum, mgh converts fully to ½mv² during a fall.

Conservation of energy: energy changes form but total energy is constant; a machine's efficiency = useful output ÷ total input × 100%.

Ohm's law: V = IR; resistance R = V/I in ohms, and for a fixed resistor V–I is a straight line through the origin.

Series circuit: current is the same everywhere, total R = R₁ + R₂ + …, and the supply voltage splits in proportion to resistance.

Parallel circuit: voltage is the same across each branch, and total current equals the sum of branch currents.

Electrical power: P = VI = I²R = V²/R; energy used (J) = power (W) × time (s), and 1 kWh = 3.6 × 10⁶ J.

Joule heating in a resistor: heat produced = I²Rt, so doubling current quadruples the heating for the same resistance and time.

Physical change alters state, shape, or size with no new substance; chemical change forms new substances with different properties.

Signs of chemical change: gas evolution, precipitate formation, colour change, heat or light release, and irreversibility.

Pure substances melt and boil at fixed temperatures; impurities lower the melting point and raise the boiling point.

Mixtures are separated physically: filtration for insoluble solids, distillation for dissolved solids or liquids of different boiling points, chromatography for dyes.

Density = mass ÷ volume (g/cm³); an object floats in a liquid if its density is lower than the liquid's.

Acids turn blue litmus red and give H⁺ in water; alkalis turn red litmus blue and give OH⁻; neutralisation gives salt plus water.

pH below 7 is acidic, 7 neutral, above 7 alkaline; each step of 1 is a tenfold change in hydrogen-ion concentration.

Combustion of a hydrocarbon in sufficient oxygen gives CO₂ and H₂O; insufficient oxygen gives CO, soot, and less heat.

Metals react with oxygen to form basic oxides, non-metals form acidic oxides; a more reactive metal displaces a less reactive one from its salt solution.

An atom has a positive nucleus (protons plus neutrons) surrounded by electrons; proton number defines the element.

Mass number = protons + neutrons; ions form when atoms gain or lose electrons, so the proton number stays the same.

A molecule is two or more atoms bonded together; a compound contains different elements chemically combined in a fixed ratio.

Chemical equations must be balanced because atoms are conserved; coefficients change, subscripts never do.

Mole concept: 1 mol contains 6.0 × 10²³ particles; molar mass in g/mol equals the sum of atomic masses.

For a gas at standard conditions, 1 mol occupies about 22.4 L; mass = moles × molar mass.

Percentage by mass of an element = (total mass of that element in the formula ÷ formula mass) × 100.

Reaction stoichiometry: use the balanced equation's coefficients to convert moles of one substance to moles of another.

Exothermic reactions release heat (temperature rises); endothermic reactions absorb heat (temperature falls).

Producers make organic matter by photosynthesis; consumers eat other organisms; decomposers break down dead matter and return nutrients to soil.

A food chain's arrows point in the direction of energy flow; a food web links several chains in one community.

Energy is lost as heat at each trophic level (roughly 10% passed on), so food chains rarely exceed four or five links.

Population size is limited by food, water, space, disease, and predators; competition occurs when resources are shared.

Symbiosis: mutualism benefits both species, parasitism benefits one and harms the other, commensalism benefits one without affecting the other.

Photosynthesis: CO₂ + H₂O → glucose + O₂ using light and chlorophyll; respiration reverses this, releasing energy from glucose.

Carbon cycles through photosynthesis, respiration, feeding, decomposition, and combustion of fossil fuels.

Adaptation is a heritable trait that raises survival in a habitat; organisms with favourable traits leave more offspring (natural selection).

Environmental change such as habitat loss or water pollution reduces biodiversity and can collapse a food web.

Digestion: starch begins breakdown in the mouth (amylase, slightly alkaline), protein in the stomach (pepsin, acidic), fats mainly in the small intestine with bile and lipase.

Villi in the small intestine increase surface area for absorption of digested nutrients into blood and lymph.

Blood: red cells carry oxygen with haemoglobin, white cells defend, platelets clot, plasma transports nutrients, CO₂, and wastes.

Human circulation is double: pulmonary (heart–lungs–heart) and systemic (heart–body–heart); arteries carry blood away from the heart.

Respiration: the diaphragm contracts and flattens, ribs rise, chest volume increases, pressure drops, air enters; gas exchange occurs in alveoli.

Nephron filtration in the kidneys removes urea and excess salts and water, reabsorbing glucose and most water.

Nervous coordination: stimulus → receptor → sensory neuron → spinal cord or brain → motor neuron → muscle or gland (effector).

Reflexes are rapid involuntary responses that bypass conscious brain control, protecting the body from harm.

Hormones such as insulin lower blood glucose; the liver stores glucose as glycogen and releases it when levels fall.

Earth's rotation on its axis (about 24 h, west to east) causes day and night; revolution around the Sun (about 365 days) with a 23.4° tilt causes seasons.

The Moon's phases repeat about every 29.5 days; solar eclipses occur at new moon, lunar eclipses at full moon.

Solar system order: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune; inner planets are rocky, outer planets gaseous.

Stars shine by nuclear fusion of hydrogen; apparent brightness depends on luminosity and distance, and colour indicates surface temperature (blue hot, red cool).

Seismic P waves travel fastest through solids and liquids; S waves pass only through solids, revealing Earth's liquid outer core.

Plate tectonics: divergent boundaries form ridges, convergent boundaries form trenches and volcanoes, transform boundaries cause earthquakes.

Igneous rock forms from cooled magma, sedimentary from deposited layers, metamorphic from heat and pressure; fossils occur mainly in sedimentary rock.

Folding and faulting of strata record crustal movement; older layers normally lie below younger ones unless overturned.

Air pressure falls with altitude; high pressure brings descending air and fair weather, low pressure brings rising air, clouds, and rain.

Winds blow from high to low pressure; the larger the pressure difference, the stronger the wind.

Warm air holds more water vapour; when air cools to its dew point, condensation forms clouds, fog, or dew.

Cumulonimbus clouds with rapid updraughts produce thunderstorms and heavy showers; stratus clouds produce steady drizzle.

Sea breeze blows from sea to land by day; land breeze blows from land to sea at night, driven by differing heating rates.

A warm front brings gradual cloud thickening and prolonged rain; a cold front brings abrupt cooling and short heavy showers.

Japan's rainy season (tsuyu) comes from the collision of warm moist air and cold air masses; typhoons form over warm tropical seas.

Water cycle: evaporation, transpiration, condensation, precipitation, and runoff; groundwater and rivers return water to the sea.

Global warming from greenhouse gases (CO₂, methane) raises average temperature, melting ice and raising sea level.

Experiment steps: question → hypothesis → controlled experiment → data → analysis → conclusion; a hypothesis must be testable.

Independent variable is changed by the experimenter, the dependent variable is measured, and control variables are held constant.

A control group receives no treatment so the effect of the variable can be compared.

Repeat trials and average results to reduce random error; report mean and range, not a single reading.

Measure at eye level with a graduated cylinder; read the bottom of the meniscus for water.

Use the smallest scale division to judge precision; record one estimated digit beyond the finest marked division.

Plot the independent variable on the x-axis and the dependent on the y-axis; a straight-line graph indicates proportionality.

Distinguish accuracy (closeness to true value) from precision (reproducibility of readings).

Safety: use goggles, tie back hair near flames, heat test tubes at an angle away from people, and never taste or directly smell chemicals.