Nagano Entrance Science cheat sheet

Newton's first law: if the net force on an object is zero, it remains at rest or moves at constant velocity in a straight line.

Newton's second law: net force equals mass times acceleration, F = ma; acceleration is in the direction of the net force.

Weight is the force of gravity on a mass: W = mg, where g is about 9.8 N/kg near Earth's surface.

Speed = distance ÷ time. Velocity is speed with direction. Acceleration = change in velocity ÷ time taken.

On a distance-time graph, slope equals speed. On a velocity-time graph, slope equals acceleration and area under the line equals displacement.

Friction acts opposite relative motion; static friction can vary up to a maximum but kinetic friction is roughly constant.

Balanced forces produce no acceleration; unbalanced forces produce acceleration in the direction of the resultant force.

Newton's third law: forces occur in equal and opposite pairs acting on different objects, so they do not cancel on one object.

Kinetic energy: KE = ½mv²; gravitational potential energy near Earth: PE = mgh.

Work done by a constant force: W = Fd when force and displacement are in the same direction; the unit is the joule (J).

Power is the rate of doing work or transferring energy: P = W ÷ t; the unit is the watt (W), equal to one joule per second.

Law of conservation of energy: energy is never created or destroyed, only transferred or transformed.

In a closed system without friction, mechanical energy (KE + PE) stays constant; friction converts mechanical energy to thermal energy.

Efficiency = useful energy output ÷ total energy input × 100%; no real device is 100% efficient.

Heat transfers by conduction (particle collisions), convection (fluid currents), and radiation (electromagnetic waves).

One calorie is about 4.2 joules; energy resources are renewable or non-renewable, but all energy transformations conserve total energy.

Ohm's law: V = IR, where V is voltage in volts, I is current in amperes, and R is resistance in ohms.

In a series circuit, current is the same at all points; total resistance is R1 + R2 + ... and voltage divides among components.

In a parallel circuit, voltage is the same across branches; total current is the sum of branch currents and 1/Rtotal = 1/R1 + 1/R2 + ...

Electrical power: P = VI = I²R = V²/R; energy used = power × time.

Like electric charges repel and opposite charges attract; current is the flow of charge, conventionally from positive to negative.

A current-carrying wire creates a magnetic field; reversing current reverses the field, and a coil with an iron core makes an electromagnet.

Electric motor effect: a current-carrying conductor in a magnetic field experiences a force. Generator effect: moving a conductor in a magnetic field induces a current.

Fuses and circuit breakers break a circuit when current is too high; earth wires provide a low-resistance path for fault current.

Wave speed: v = fλ; frequency f is in hertz, wavelength λ in metres, and speed v in metres per second. Period T = 1/f.

Transverse waves oscillate perpendicular to energy transfer; longitudinal waves oscillate parallel to it. Sound is longitudinal.

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

Frequency determines pitch; amplitude determines loudness; a higher frequency means a higher pitch.

Echo distance: total distance = speed of sound × time; distance to reflector = (v × t) ÷ 2.

Waves reflect, refract, and diffract; refraction occurs when wave speed changes at a boundary, bending the wave.

Light is an electromagnetic wave; in a vacuum its speed is about 3.0 × 10^8 m/s, and it can travel without a medium.

Resonance occurs when a system is driven at its natural frequency, producing a large amplitude vibration.

Density: ρ = m/V; mass in kg, volume in m³, density in kg/m³. An object floats if its average density is less than the fluid's.

Three states: solids have fixed shape and volume; liquids have fixed volume but take container shape; gases fill their container.

Particles in solids vibrate about fixed positions; in liquids they slide past each other; in gases they move rapidly and far apart.

Melting and boiling occur at fixed temperatures for pure substances; mixtures usually melt or boil over a range.

Mass is the amount of matter (kg) and is constant; weight is the gravitational force (N) and changes with gravity.

Diffusion is net movement of particles from high to low concentration; it is faster at higher temperature and for lighter particles.

Most substances expand when heated and contract when cooled because particle vibration increases; water is an important exception near 4 °C.

In a solution, the solute dissolves in the solvent; solubility often increases with temperature for solids but decreases for gases.

A chemical change produces new substances with different properties; signs include gas, precipitate, colour change, and heat or light release.

Law of conservation of mass: total mass of reactants equals total mass of products in a closed system; balance equations to show this.

Exothermic reactions release energy to surroundings; endothermic reactions absorb energy, often causing a temperature drop.

Combustion of a hydrocarbon needs oxygen and produces carbon dioxide and water; incomplete combustion can produce carbon monoxide and soot.

Rusting of iron requires both oxygen and water; salt accelerates rusting, while painting, greasing, or galvanizing excludes them.

Reaction rate increases with higher temperature, higher concentration, greater surface area, and catalysts; a catalyst speeds a reaction without being used up.

Neutralization: acid + base → salt + water; the reaction is exothermic and reduces acidity or alkalinity.

Oxidation can mean gaining oxygen or losing electrons; reduction is the reverse. Redox reactions involve both together.

An atom has a nucleus of protons and neutrons, surrounded by electrons in energy levels; most atomic mass is in the nucleus.

Atomic number Z = number of protons; mass number A = protons + neutrons; isotopes have the same Z but different A.

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

Chemical formula subscripts show atom counts; relative molecular mass is the sum of relative atomic masses of all atoms in the formula.

Periodic table groups have similar outer-electron configurations; periods are horizontal rows with increasing proton number.

Group 1 alkali metals are soft, reactive, and form +1 ions; Group 17 halogens are reactive nonmetals forming −1 ions; Group 18 noble gases are unreactive.

Ionic bonding transfers electrons from metal to nonmetal; covalent bonding shares electron pairs between nonmetals.

Electron shells fill in order 2, 8, 8 for the first 20 elements; the outer-shell electron count determines group number for main-group elements.

An ion is a charged atom or group of atoms; cations are positive (usually metals) and anions are negative (usually nonmetals).

An ionic formula balances total positive and negative charge; for example, Mg²⁺ and Cl⁻ give MgCl₂.

Acids produce hydrogen ions (H⁺) in water; bases produce hydroxide ions (OH⁻); pH below 7 is acidic, above 7 is basic.

Neutralization: H⁺ + OH⁻ → H₂O; the other ions form a salt, which can be recovered by evaporation.

A precipitation reaction forms an insoluble solid when two solutions are mixed; solubility rules predict whether a precipitate forms.

Displacement occurs when a more reactive metal displaces a less reactive metal from its compound; the reactivity series ranks metals.

Electrolysis uses electric current to decompose an ionic compound; cations go to the cathode and anions to the anode.

Gas tests: CO₂ turns limewater milky; H₂ gives a squeaky pop with a burning splint; O₂ relights a glowing splint; Cl₂ bleaches damp litmus.

Digestion breaks food into small soluble molecules; enzymes are specific, and most absorption occurs in the small intestine through villi.

The heart has four chambers; arteries carry blood away from the heart, veins return blood, and capillaries allow exchange with tissues.

Alveoli in the lungs provide a large, thin, moist surface for gas exchange: oxygen enters blood and carbon dioxide leaves.

The nervous system uses electrical impulses along neurons; a reflex arc bypasses the conscious brain for a rapid response.

Muscles work in antagonistic pairs; one contracts while the other relaxes, and tendons attach muscle to bone across joints.

The kidneys filter blood, removing urea and excess water and salts as urine; this helps maintain homeostasis.

Blood contains red cells with haemoglobin for oxygen transport, white cells for immunity, platelets for clotting, and plasma as transport fluid.

Homeostasis keeps internal conditions such as temperature, blood glucose, and water balance within narrow limits using feedback mechanisms.

Asexual reproduction produces genetically identical offspring from one parent; sexual reproduction combines gametes and creates genetic variation.

Meiosis halves the chromosome number to produce haploid gametes; fertilization restores the diploid number in the zygote.

Genes are DNA sections on chromosomes; alleles are different versions of a gene, and dominant alleles are expressed when present.

Genotype is the allele combination; phenotype is the visible trait. A recessive phenotype requires two recessive alleles.

A Punnett square predicts offspring ratios from parental gametes; a cross of two heterozygotes gives a 3:1 phenotype ratio for a simple dominant trait.

Human sex chromosomes: XX is female and XY is male; the father's sperm determines the offspring's sex.

Mitosis produces identical diploid cells for growth and repair; meiosis produces four genetically different haploid cells.

In flowering plants, pollination transfers pollen to the stigma, fertilization forms seeds, and fruits develop from the ovary.

All living organisms are made of cells; the cell is the basic unit of structure and function, and new cells arise from existing cells.

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

The nucleus contains DNA and controls cell activities; mitochondria carry out aerobic respiration; ribosomes assemble proteins.

Chloroplasts contain chlorophyll and carry out photosynthesis, converting light energy into chemical energy in glucose.

The cell membrane is selectively permeable, controlling movement of substances into and out of the cell.

Diffusion moves particles from high to low concentration; osmosis is water diffusion across a partially permeable membrane.

Mitosis produces genetically identical cells for growth and repair; uncontrolled mitosis can form tumours.

Specialized cells have structures suited to their function, such as root hair cells for absorption and red blood cells for oxygen transport.

A food chain starts with a producer that makes food by photosynthesis; arrows show the direction of energy transfer to consumers.

Only about 10% of energy passes to the next trophic level; the rest is lost as heat through respiration and in waste.

A food web combines interconnected food chains and shows that most consumers eat more than one type of organism.

Decomposers break down dead organisms and waste, recycling nutrients such as nitrogen and minerals to the soil.

Photosynthesis stores energy in glucose; respiration releases that energy in producers and consumers, linking ecosystems to energy flow.

Population size is affected by food, predators, disease, and space; carrying capacity is the maximum a habitat can sustain.

Symbiosis includes mutualism (both benefit), parasitism (one benefits, one is harmed), and commensalism (one benefits, the other is unaffected).

Carbon cycles between organisms and the environment through photosynthesis, respiration, feeding, decomposition, and combustion.

Law of superposition: in undisturbed sedimentary layers, older strata lie below younger strata.

Principle of original horizontality: sedimentary layers are deposited roughly horizontally, so tilted layers indicate later movement.

Cross-cutting relationships: a fault or igneous intrusion is younger than the rock layers it cuts through.

An unconformity is an erosion surface or gap in the rock record, showing that deposition was interrupted.

Fossils are preserved remains or traces, usually found in sedimentary rock; igneous and metamorphic rocks rarely contain fossils.

Index fossils have a short time range and wide distribution, allowing correlation of rock layers across distances.

Relative dating orders events without exact ages; radiometric dating uses decay of isotopes to estimate absolute ages.

Fossil succession: different fossil species appear in a consistent order, so strata can be recognized by their fossil content.

Dry air is about 78% nitrogen, 21% oxygen, 0.9% argon, and 0.04% carbon dioxide, with variable water vapour.

Atmospheric layers from bottom: troposphere (weather), stratosphere (ozone layer), mesosphere, thermosphere, exosphere.

Air pressure decreases with altitude; wind blows from higher pressure to lower pressure and is affected by Earth's rotation.

Weather is short-term atmospheric conditions; climate is the long-term average pattern for a region.

Clouds form when moist air cools and water vapour condenses on tiny particles; precipitation occurs when droplets or ice crystals grow heavy.

A front is a boundary between air masses; warm fronts bring gradual cloud and rain, while cold fronts bring rapid cooling and heavy showers.

The water cycle: evaporation, condensation, precipitation, and runoff; the Sun supplies the energy that drives it.

The greenhouse effect traps infrared radiation, warming Earth; increased greenhouse gases raise average global temperature.

Earth rotates on its axis about once every 24 hours, causing day and night; it revolves around the Sun in about 365.25 days.

Earth's axis is tilted about 23.4°, causing seasons as the hemispheres receive different amounts of direct sunlight during the year.

The Moon orbits Earth in about 27.3 days; its phases repeat about every 29.5 days as the Sun–Earth–Moon angle changes.

A solar eclipse occurs when the Moon passes between Earth and the Sun; a lunar eclipse occurs when Earth's shadow falls on the Moon.

Solar system order from the Sun: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune; inner planets are rocky, outer planets are mostly gas or ice giants.

Gravity provides the centripetal force that keeps planets in orbit; orbital speed decreases with greater distance from the Sun.

A light-year is the distance light travels in one year, about 9.5 × 10^12 km; it measures distance, not time.

Solstices occur when the Sun is highest or lowest at noon; equinoxes occur when day and night are about equal worldwide.