Nara Public High School Entrance Examination - Science cheat sheet

Speed = distance ÷ time (m/s); velocity adds direction, so a round trip has average velocity 0 even though average speed is not 0.

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

Newton's first law: an object at rest or moving at constant velocity keeps that state unless a net (unbalanced) force acts on it.

Newton's second law: F = ma; the same force gives smaller acceleration to a larger mass, and acceleration is always in the direction of the net force.

Newton's third law: forces act in equal-and-opposite pairs on two different objects, so the pair never cancels on a single object.

Weight = mass × gravitational acceleration (about 9.8 N/kg on Earth); mass in kg is unchanged on the Moon but weight is about one-sixth.

Friction and air resistance oppose relative motion; a falling object reaches terminal velocity when air resistance equals weight and net force becomes zero.

Pressure = force ÷ area (Pa = N/m²); the same force pressed through a smaller area gives larger pressure.

Work = force × distance moved in the direction of the force (J); power = work ÷ time (W = J/s).

Conservation of energy: energy changes form (kinetic, potential, thermal, electrical, light, sound) but total energy in an isolated system stays constant.

Gravitational potential energy = mgh and kinetic energy = ½mv²; in a frictionless fall, mgh is converted completely into ½mv².

Wave speed = frequency × wavelength (v = fλ); frequency is set by the source and wavelength changes if speed changes.

Transverse waves (light, water surface) vibrate perpendicular to travel; longitudinal waves (sound) vibrate parallel and need a medium.

Sound travels faster in solids than in gases and cannot pass through a vacuum; light travels fastest in a vacuum and refracts when entering a denser medium.

Ohm's law: V = IR; resistance rises with length and temperature and falls with larger cross-sectional area.

Series circuits: current is the same everywhere, voltages add, total resistance = R₁ + R₂ + …; parallel circuits: voltage is the same, currents add.

Electrical power P = VI = I²R = V²/R; energy used = power × time, and a fuse or breaker protects a circuit from excessive current.

A pure substance has a fixed melting and boiling point; a mixture melts over a range and can be separated by filtration, distillation, or chromatography.

Physical changes (melting, dissolving, evaporation) do not create new substances; chemical changes form new substances with different properties.

Signs of a chemical change: gas evolution, precipitate formation, colour change, temperature change, or light emission.

Density = mass ÷ volume (g/cm³); a solid that sinks in water has density greater than 1.0 g/cm³.

Distillation separates liquids by boiling point; filtration separates an insoluble solid from a liquid; chromatography separates dissolved pigments by solubility.

Combustion of a hydrocarbon needs oxygen and yields carbon dioxide and water; incomplete combustion also yields carbon monoxide and soot.

Metals conduct electricity and heat, are malleable and shiny; non-metals are usually poor conductors and brittle when solid.

Acids turn blue litmus red and react with metals to release hydrogen; alkalis turn red litmus blue and neutralise acids to give salt plus water.

An atom has a positive nucleus (protons + neutrons) surrounded by electrons; atomic number = number of protons and determines the element.

Isotopes are atoms of the same element with different numbers of neutrons; mass number = protons + neutrons.

Ions form when atoms gain or lose electrons: metals lose electrons to form positive ions (Na⁺, Mg²⁺); non-metals gain electrons to form negative ions (Cl⁻, O²⁻).

Ionic compounds are held by electrostatic attraction between oppositely charged ions and conduct electricity when molten or dissolved but not when solid.

A chemical equation must be balanced: atoms of each element are equal on both sides, and only coefficients may be changed, never subscripts.

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

Relative masses from an equation give reacting ratios; e.g. 2H₂ + O₂ → 2H₂O means 4 g H₂ reacts with 32 g O₂ to give 36 g H₂O.

Exothermic reactions release heat to the surroundings (combustion, neutralisation); endothermic reactions absorb heat (thermal decomposition, dissolving ammonium salts).

Producers (plants) convert light energy to chemical energy; consumers eat other organisms; decomposers break down dead matter and recycle nutrients.

A food chain shows one-way energy flow; arrows point from the eaten to the eater, and only about 10% of energy passes to the next trophic level.

Population size is affected by birth rate, death rate, immigration, and emigration; carrying capacity is limited by food, space, and predators.

Symbiosis: mutualism benefits both species, commensalism benefits one with no effect on the other, parasitism benefits one and harms the host.

Competition occurs when organisms need the same limited resource; the better-adapted competitor may exclude the other.

Decomposers such as fungi and bacteria return carbon and nitrogen to soil, keeping material cycling while energy flows one way.

Environmental change (temperature, pollution, invasive species) can reduce biodiversity and cause local extinction of poorly adapted species.

Photosynthesis: carbon dioxide + water + light energy → glucose + oxygen, occurring in chloroplasts and requiring chlorophyll.

Respiration: glucose + oxygen → carbon dioxide + water + energy; it occurs in mitochondria in all living cells, day and night.

Stomata in leaves open for gas exchange and close to limit water loss; xylem carries water upward, phloem carries sugars.

Blood transports oxygen, nutrients, and wastes; arteries carry blood away from the heart, veins return it, and capillaries allow exchange.

Mitosis produces genetically identical body cells for growth and repair; meiosis produces gametes with half the chromosome number.

Sexual reproduction combines gametes and increases genetic variation; asexual reproduction (runners, bulbs, budding) makes clones quickly.

Hormones and the nervous system coordinate responses; insulin lowers blood glucose, and reflex actions protect the body without conscious delay.

Fertilisation restores the diploid chromosome number; genes on chromosomes determine inherited traits, and dominant alleles mask recessive ones.

Earth's interior is layered: crust, mantle, outer core (liquid), inner core (solid); seismic wave behaviour reveals these layers.

Plate tectonics: plates move on the mantle; divergent boundaries create ridges, convergent boundaries create mountains, trenches, and volcanoes, and transform boundaries cause earthquakes.

Igneous rock forms from cooling magma or lava, sedimentary rock from compacted deposits, and metamorphic rock from heat and pressure.

Weathering and erosion break down and transport rock; deposition and lithification turn sediments into sedimentary rock.

Weather fronts: a cold front brings short heavy rain and a temperature drop; a warm front brings long gentle rain and gradual warming.

Air moves from high to low pressure; wind is stronger where the pressure gradient is steeper, and sea breezes blow onshore by day.

The Moon's phases depend on the Sun–Earth–Moon angle; a solar eclipse needs the Moon between Earth and Sun at new moon.

Seasons come from Earth's axial tilt (about 23.4°), not from distance to the Sun; solstices have the longest and shortest days.

A controlled experiment changes one independent variable at a time while keeping all other conditions constant to isolate cause and effect.

A hypothesis is a testable prediction; a control group gives a baseline for comparison with the experimental group.

Repeat measurements and average them to reduce random error; identify and correct systematic error such as a zero-point offset in an instrument.

Read instruments to the smallest scale division plus one estimated digit, and always state the unit with the value.

Graphs: plot the independent variable on the x-axis and the dependent variable on the y-axis; a straight line indicates a proportional relationship.

Correlation does not prove causation; a cause must be supported by controlled trials, not only by observed association.

Report data in tables with clear headings and units; describe outliers and anomalies rather than silently discarding them.

Evaluate reliability (repeatability) and validity (whether the method measures what it claims) when judging an experiment.

Speed = distance ÷ time (m/s); velocity adds direction, so a round trip has average velocity 0 even though average speed is not 0.

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

Newton's first law: an object at rest or moving at constant velocity keeps that state unless a net (unbalanced) force acts on it.

Newton's second law: F = ma; the same force gives smaller acceleration to a larger mass, and acceleration is always in the direction of the net force.

Newton's third law: forces act in equal-and-opposite pairs on two different objects, so the pair never cancels on a single object.

Weight = mass × gravitational acceleration (about 9.8 N/kg on Earth); mass in kg is unchanged on the Moon but weight is about one-sixth.

Friction and air resistance oppose relative motion; a falling object reaches terminal velocity when air resistance equals weight and net force becomes zero.

Pressure = force ÷ area (Pa = N/m²); the same force pressed through a smaller area gives larger pressure.

Work = force × distance moved in the direction of the force (J); power = work ÷ time (W = J/s).

Conservation of energy: energy changes form (kinetic, potential, thermal, electrical, light, sound) but total energy in an isolated system stays constant.

Gravitational potential energy = mgh and kinetic energy = ½mv²; in a frictionless fall, mgh is converted completely into ½mv².

Wave speed = frequency × wavelength (v = fλ); frequency is set by the source and wavelength changes if speed changes.

Transverse waves (light, water surface) vibrate perpendicular to travel; longitudinal waves (sound) vibrate parallel and need a medium.

Sound travels faster in solids than in gases and cannot pass through a vacuum; light travels fastest in a vacuum and refracts when entering a denser medium.

Ohm's law: V = IR; resistance rises with length and temperature and falls with larger cross-sectional area.

Series circuits: current is the same everywhere, voltages add, total resistance = R₁ + R₂ + …; parallel circuits: voltage is the same, currents add.

Electrical power P = VI = I²R = V²/R; energy used = power × time, and a fuse or breaker protects a circuit from excessive current.

A pure substance has a fixed melting and boiling point; a mixture melts over a range and can be separated by filtration, distillation, or chromatography.

Physical changes (melting, dissolving, evaporation) do not create new substances; chemical changes form new substances with different properties.

Signs of a chemical change: gas evolution, precipitate formation, colour change, temperature change, or light emission.

Density = mass ÷ volume (g/cm³); a solid that sinks in water has density greater than 1.0 g/cm³.

Distillation separates liquids by boiling point; filtration separates an insoluble solid from a liquid; chromatography separates dissolved pigments by solubility.

Combustion of a hydrocarbon needs oxygen and yields carbon dioxide and water; incomplete combustion also yields carbon monoxide and soot.

Metals conduct electricity and heat, are malleable and shiny; non-metals are usually poor conductors and brittle when solid.

Acids turn blue litmus red and react with metals to release hydrogen; alkalis turn red litmus blue and neutralise acids to give salt plus water.

An atom has a positive nucleus (protons + neutrons) surrounded by electrons; atomic number = number of protons and determines the element.

Isotopes are atoms of the same element with different numbers of neutrons; mass number = protons + neutrons.

Ions form when atoms gain or lose electrons: metals lose electrons to form positive ions (Na⁺, Mg²⁺); non-metals gain electrons to form negative ions (Cl⁻, O²⁻).

Ionic compounds are held by electrostatic attraction between oppositely charged ions and conduct electricity when molten or dissolved but not when solid.

A chemical equation must be balanced: atoms of each element are equal on both sides, and only coefficients may be changed, never subscripts.

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

Relative masses from an equation give reacting ratios; e.g. 2H₂ + O₂ → 2H₂O means 4 g H₂ reacts with 32 g O₂ to give 36 g H₂O.

Exothermic reactions release heat to the surroundings (combustion, neutralisation); endothermic reactions absorb heat (thermal decomposition, dissolving ammonium salts).

Producers (plants) convert light energy to chemical energy; consumers eat other organisms; decomposers break down dead matter and recycle nutrients.

A food chain shows one-way energy flow; arrows point from the eaten to the eater, and only about 10% of energy passes to the next trophic level.

Population size is affected by birth rate, death rate, immigration, and emigration; carrying capacity is limited by food, space, and predators.

Symbiosis: mutualism benefits both species, commensalism benefits one with no effect on the other, parasitism benefits one and harms the host.

Competition occurs when organisms need the same limited resource; the better-adapted competitor may exclude the other.

Decomposers such as fungi and bacteria return carbon and nitrogen to soil, keeping material cycling while energy flows one way.

Environmental change (temperature, pollution, invasive species) can reduce biodiversity and cause local extinction of poorly adapted species.

Photosynthesis: carbon dioxide + water + light energy → glucose + oxygen, occurring in chloroplasts and requiring chlorophyll.

Respiration: glucose + oxygen → carbon dioxide + water + energy; it occurs in mitochondria in all living cells, day and night.

Stomata in leaves open for gas exchange and close to limit water loss; xylem carries water upward, phloem carries sugars.

Blood transports oxygen, nutrients, and wastes; arteries carry blood away from the heart, veins return it, and capillaries allow exchange.

Mitosis produces genetically identical body cells for growth and repair; meiosis produces gametes with half the chromosome number.

Sexual reproduction combines gametes and increases genetic variation; asexual reproduction (runners, bulbs, budding) makes clones quickly.

Hormones and the nervous system coordinate responses; insulin lowers blood glucose, and reflex actions protect the body without conscious delay.

Fertilisation restores the diploid chromosome number; genes on chromosomes determine inherited traits, and dominant alleles mask recessive ones.

Earth's interior is layered: crust, mantle, outer core (liquid), inner core (solid); seismic wave behaviour reveals these layers.

Plate tectonics: plates move on the mantle; divergent boundaries create ridges, convergent boundaries create mountains, trenches, and volcanoes, and transform boundaries cause earthquakes.

Igneous rock forms from cooling magma or lava, sedimentary rock from compacted deposits, and metamorphic rock from heat and pressure.

Weathering and erosion break down and transport rock; deposition and lithification turn sediments into sedimentary rock.

Weather fronts: a cold front brings short heavy rain and a temperature drop; a warm front brings long gentle rain and gradual warming.

Air moves from high to low pressure; wind is stronger where the pressure gradient is steeper, and sea breezes blow onshore by day.

The Moon's phases depend on the Sun–Earth–Moon angle; a solar eclipse needs the Moon between Earth and Sun at new moon.

Seasons come from Earth's axial tilt (about 23.4°), not from distance to the Sun; solstices have the longest and shortest days.

A controlled experiment changes one independent variable at a time while keeping all other conditions constant to isolate cause and effect.

A hypothesis is a testable prediction; a control group gives a baseline for comparison with the experimental group.

Repeat measurements and average them to reduce random error; identify and correct systematic error such as a zero-point offset in an instrument.

Read instruments to the smallest scale division plus one estimated digit, and always state the unit with the value.

Graphs: plot the independent variable on the x-axis and the dependent variable on the y-axis; a straight line indicates a proportional relationship.

Correlation does not prove causation; a cause must be supported by controlled trials, not only by observed association.

Report data in tables with clear headings and units; describe outliers and anomalies rather than silently discarding them.

Evaluate reliability (repeatability) and validity (whether the method measures what it claims) when judging an experiment.