Fukuoka Entrance Science cheat sheet

Newton's first law: an object stays at rest or moves at constant velocity unless a net external force acts on it.

Newton's second law: F = ma, where F is the net force in newtons, m is mass in kilograms, and a is acceleration in m/s².

Newton's third law: every action force has an equal-magnitude, opposite-direction reaction force acting on a different object.

Weight is the gravitational force W = mg; on Earth g ≈ 9.8 N/kg, so mass 1 kg weighs about 9.8 N.

Speed = distance ÷ time (m/s); velocity adds direction; acceleration = change in velocity ÷ time.

Constant-velocity motion means zero net force, not zero forces: friction and applied force can balance.

Friction opposes relative motion between surfaces and depends on surface type and normal force, not on contact area.

Momentum p = mv; in a closed system total momentum before a collision equals total momentum after.

Kinetic energy KE = ½mv²; doubling speed quadruples kinetic energy.

Gravitational potential energy PE = mgh, with h measured from a chosen reference level.

Work done by a constant force equals force × displacement in the direction of the force (W = Fd, joules).

Conservation of energy: energy changes form but total energy in an isolated system stays constant.

Power = energy transferred ÷ time, measured in watts (1 W = 1 J/s).

Mechanical energy (KE + PE) is conserved when only gravity acts and friction/air resistance are negligible.

Efficiency = useful output energy ÷ total input energy × 100%; it is always below 100% in real machines.

Heat flows spontaneously from higher to lower temperature; it is not the same quantity as temperature.

Ohm's law: V = IR, where V is volts, I is amperes, and R is ohms, for a conductor at constant temperature.

Series circuit: current is the same everywhere; total resistance R = R₁ + R₂ + …; voltage divides among components.

Parallel circuit: voltage is the same across branches; total current is the sum of branch currents; resistance is less than any branch.

Electric power P = VI = I²R = V²/R; energy used = power × time (kilowatt-hours for household bills).

Current flows only in a closed circuit; conventional current is modeled as positive charge moving from + to −.

Like magnetic poles repel, unlike poles attract; a current-carrying wire creates a magnetic field around it.

Electromagnetic induction: a changing magnetic field through a coil induces a voltage (Faraday's law).

Static electricity: rubbing transfers electrons; objects gaining electrons become negative and repel other negative objects.

Wave speed v = frequency f × wavelength λ; frequency is set by the source and does not change with medium.

Transverse waves oscillate perpendicular to travel (light, water surface); longitudinal waves oscillate parallel (sound).

Sound needs a medium; it travels fastest in solids, slower in liquids, slowest in gases, and not at all in vacuum.

Sound speed in air at room temperature is about 340 m/s; pitch corresponds to frequency, loudness to amplitude.

Reflection, refraction, and diffraction apply to sound and light; diffraction is pronounced when wavelength is comparable to obstacle size.

Resonance occurs when a driving frequency matches a natural frequency, producing large amplitude.

The audible range for humans is roughly 20 Hz to 20,000 Hz; ultrasound is above this range.

Period T = 1/f; a wave with frequency 5 Hz has period 0.2 s.

Light travels in straight lines in a uniform medium at about 3.0 × 10⁸ m/s in vacuum.

Law of reflection: angle of incidence equals angle of reflection, both measured from the normal.

Refraction bends light toward the normal when entering a denser medium (slower speed) and away when leaving it.

Total internal reflection occurs when light in a dense medium hits a boundary beyond the critical angle.

A convex (converging) lens forms real images for objects beyond the focal point; a concave lens forms virtual, upright, reduced images.

White light separates into colors by a prism because refractive index varies with wavelength (dispersion).

Primary colors of light are red, green, blue; mixing all three additively gives white.

Magnification = image height ÷ object height = image distance ÷ object distance (for a simple lens).

A pure substance has fixed composition (element or compound); a mixture contains two or more substances not chemically bonded.

Homogeneous mixtures (salt water, air) have uniform composition; heterogeneous mixtures (sand and iron filings) do not.

Elements cannot be broken down chemically; compounds can be decomposed into simpler substances by chemical reactions.

Filtration separates insoluble solid from liquid; distillation separates liquids by boiling point; chromatography separates dissolved dyes.

A solution has a solvent (usually larger amount) and one or more solutes.

Solubility of most solids in water increases with temperature; gases are less soluble in warm water.

Physical changes (melting, dissolving) do not create new substances; chemical changes do.

Density = mass ÷ volume; it identifies substances and predicts floating (density less than water, about 1 g/cm³).

Signs of a chemical reaction: gas production, color change, precipitate formation, temperature change, light emission.

Exothermic reactions release heat to the surroundings; endothermic reactions absorb heat.

Combustion of a hydrocarbon with sufficient oxygen yields carbon dioxide and water.

Oxidation is loss of electrons or gain of oxygen; reduction is gain of electrons or loss of oxygen; they occur together.

Catalysts speed up reactions by lowering activation energy without being consumed.

Reaction rate increases with higher temperature, higher concentration, greater surface area, and catalysts.

Decomposition: one compound breaks into simpler substances (e.g., electrolysis of water gives H₂ and O₂).

Neutralization is an acid–base reaction producing salt and water.

An atom has a nucleus (protons + neutrons) surrounded by electrons; protons determine the element.

Atomic number = number of protons; mass number = protons + neutrons; isotopes differ in neutron number.

Electron arrangement fills shells 2, 8, 8…; the outermost shell (valence electrons) governs chemical behavior.

Ions form when atoms gain or lose electrons: metals lose electrons (cations), nonmetals gain electrons (anions).

A molecule is two or more atoms bonded; a compound molecule contains different elements (H₂O, CO₂).

Chemical formulas show atom ratios; the subscript applies only to the element just before it (Ca(OH)₂ has 2 O and 2 H).

Covalent bonds share electrons between nonmetals; ionic bonds transfer electrons between metals and nonmetals.

Relative atomic masses: H ≈ 1, C ≈ 12, O ≈ 16, Na ≈ 23, Cl ≈ 35.5; molar mass in g/mol equals formula mass.

Acids release H⁺ ions in water; bases release OH⁻ ions (or accept H⁺).

pH below 7 is acidic, 7 is neutral, above 7 is basic; each unit is a tenfold change in H⁺ concentration.

Litmus: red in acid, blue in base; phenolphthalein is colorless in acid and pink in base.

Acid + base → salt + water (neutralization); HCl + NaOH → NaCl + H₂O.

Acid + metal → salt + hydrogen gas; acid + carbonate → salt + water + carbon dioxide.

Strong acids (HCl, H₂SO₄) ionize almost completely; weak acids (acetic acid) ionize only partly.

Metal oxides and hydroxides are generally basic; nonmetal oxides (CO₂, SO₂) are generally acidic.

pH can be measured with indicator paper or a pH meter; dilution moves pH toward 7.

A chemical equation must be balanced: the number of each type of atom is equal on both sides.

Coefficients multiply whole formulas; subscripts within a formula must never be changed to balance.

State symbols: (s) solid, (l) liquid, (g) gas, (aq) aqueous solution.

Example: 2H₂ + O₂ → 2H₂O; four H and two O atoms on each side.

Combustion example: CH₄ + 2O₂ → CO₂ + 2H₂O.

Decomposition example: 2H₂O → 2H₂ + O₂ (electrolysis).

Precipitation example: AgNO₃ + NaCl → AgCl↓ + NaNO₃.

The law of conservation of mass: total mass of reactants equals total mass of products in a closed system.

Cell theory: all organisms are made of cells, cells come from pre-existing cells, and the cell is the basic unit of life.

Plant cells have a cell wall, chloroplasts, and a large vacuole; animal cells lack these structures.

Nucleus contains DNA and controls cell activities; mitochondria release energy; ribosomes build proteins.

Mitosis produces two genetically identical diploid cells for growth and repair.

Meiosis produces four haploid gametes with half the chromosome number, creating genetic variation.

Fertilization restores the diploid number: haploid sperm + haploid egg → diploid zygote.

Asexual reproduction (binary fission, budding, runners) produces offspring genetically identical to the parent.

Human body cells have 46 chromosomes (23 pairs); gametes have 23.

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

Respiration: glucose + oxygen → carbon dioxide + water + energy, occurring in mitochondria in both plants and animals.

Stomata on leaves allow gas exchange; guard cells open and close them.

Xylem transports water and minerals upward from roots; phloem transports sugars from leaves.

Transpiration is water loss through leaves, pulling water up the plant; it increases with heat, wind, and light.

Digestion breaks food into absorbable molecules; enzymes act on starch, protein, and fat at specific pH optima.

Blood transports oxygen (via hemoglobin in red cells), nutrients, and wastes; the heart pumps it in a double circulation.

Homeostasis keeps internal conditions (temperature, blood glucose, water) within narrow limits via feedback.

Genes are DNA segments on chromosomes; alleles are alternative forms of a gene.

Dominant alleles mask recessive alleles in heterozygotes; recessive traits appear only in homozygotes.

Genotype is the allele combination (AA, Aa, aa); phenotype is the observable trait.

A cross of two heterozygotes (Aa × Aa) gives a 3:1 phenotype ratio and 1:2:1 genotype ratio.

Sex chromosomes: in humans XX is female and XY is male; the father determines the offspring's sex.

Mutations change DNA sequence and are the source of new alleles for evolution.

Natural selection: individuals with favorable inherited traits survive and reproduce more, increasing those traits in the population.

Evidence for evolution includes fossils, homologous structures, and similarities in DNA and embryo development.

Producers (plants, algae) convert light energy into chemical energy; consumers obtain energy by eating other organisms.

Food chains show energy flow; arrows point from the organism eaten to the eater.

Decomposers (bacteria, fungi) break down dead matter and recycle nutrients back into the soil.

Only about 10% of energy passes to the next trophic level, so food chains rarely exceed four or five links.

A food web is interconnected food chains and better reflects real ecosystem complexity.

Population size is affected by food, predators, disease, and space; carrying capacity is the maximum sustainable size.

Symbiosis includes mutualism (both benefit), commensalism (one benefits), and parasitism (one benefits, one harmed).

Carbon cycles through photosynthesis, respiration, combustion, and decomposition; nitrogen is fixed by bacteria.

Earth's layers: crust (thin, silicate rock), mantle (thick, hot rock), outer core (liquid iron), inner core (solid iron).

Tectonic plates move on the mantle; divergent boundaries create new crust, convergent boundaries cause subduction and mountains.

Earthquakes occur at faults where stress releases suddenly; the focus is underground, the epicenter is above it.

Seismic P waves arrive first and travel through solids and liquids; S waves arrive later and cannot pass through liquids.

The Richter scale is logarithmic: magnitude 6 releases about 32 times the energy of magnitude 5.

Igneous rock forms from cooled magma or lava; sedimentary from compacted deposits; metamorphic from heat and pressure.

The rock cycle converts among the three rock types over geological time.

Fossils in sedimentary layers indicate relative age: deeper layers are generally older (superposition).

Air pressure decreases with altitude; wind blows from high pressure to low pressure.

Warm air is less dense and rises; rising air cools, and water vapor condenses to form clouds and rain.

High pressure generally brings fair weather; low pressure brings clouds and precipitation.

Weather fronts: cold fronts bring short, heavy rain; warm fronts bring gentle, prolonged rain.

Humidity is the amount of water vapor in air; relative humidity compares it to the maximum at that temperature.

Climate is long-term average weather; it is influenced by latitude, altitude, oceans, and prevailing winds.

The greenhouse effect traps outgoing infrared radiation; increased CO₂ and methane strengthen it.

Sea breezes blow from sea to land by day because land heats faster than water.

Order from the Sun: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune.

Inner planets are small, rocky, and dense; outer planets are large, gaseous, and have many moons.

Earth's rotation on its axis (about 24 hours) causes day and night; revolution around the Sun (about 365.25 days) causes seasons.

Seasons result from Earth's axial tilt (about 23.4°), not from distance from the Sun.

The Moon orbits Earth about every 27.3 days; the same side always faces Earth (synchronous rotation).

Solar eclipses occur at new moon when the Moon passes between Earth and Sun; lunar eclipses at full moon.

Gravity keeps planets in orbit; orbital speed decreases with distance from the Sun.

The Sun is a medium-sized star composed mainly of hydrogen and helium, powered by nuclear fusion.

Stars form from collapsing clouds of gas and dust (nebulae) and shine by nuclear fusion of hydrogen into helium.

The Hertzsprung–Russell diagram plots luminosity against temperature; most stars lie on the main sequence.

A star's life path depends on mass: massive stars end as supernovae and may leave neutron stars or black holes.

The Sun will become a red giant and then a white dwarf; it is not massive enough to become a supernova.

Light-year is a distance: about 9.5 × 10¹² km, the distance light travels in one year.

The Milky Way is a spiral galaxy containing hundreds of billions of stars; the Sun is about 26,000 light-years from its center.

The universe is expanding; the redshift of distant galaxies supports the Big Bang theory.

Apparent brightness depends on both luminosity and distance; a nearby dim star can look brighter than a distant bright one.