Kagoshima Entrance Science cheat sheet

Newton's first law: an object at rest or moving at constant velocity stays that way 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: when A exerts a force on B, B exerts an equal-magnitude force on A in the opposite direction; the two forces act on different objects.

Weight is the gravitational force on a mass: W = mg, with g ≈ 9.8 N/kg on Earth; mass stays constant while weight changes with location.

Speed = distance ÷ time; velocity is speed with direction; acceleration = change in velocity ÷ time taken.

On a distance–time graph, the slope gives speed; on a velocity–time graph, the slope gives acceleration and the area under the line gives displacement.

Friction opposes relative motion between surfaces; it acts along the contact surface and converts kinetic energy into thermal energy.

For an object on a slope, the component of weight along the slope is mg·sinθ, while the normal force is mg·cosθ.

Work done = force × distance moved in the direction of the force: W = Fd, measured in joules.

Kinetic energy: KE = ½mv²; doubling the speed quadruples the kinetic energy because of the squared term.

Gravitational potential energy: GPE = mgh, where h is the height gained above a chosen reference level.

Conservation of energy: energy is neither created nor destroyed, only transferred or transformed between stores.

Power = energy transferred ÷ time = work done ÷ time, measured in watts; 1 W = 1 J/s.

Efficiency = useful energy output ÷ total energy input × 100%; the remainder is usually dissipated as heat or sound.

Energy stores include kinetic, gravitational potential, elastic potential, thermal, chemical, and nuclear; energy is transferred by forces, electricity, heating, and waves.

Renewable resources such as solar, wind, hydroelectric, and geothermal are replenished naturally; fossil fuels are finite.

Light travels in straight lines in a uniform medium at about 3.0 × 10⁸ m/s in a vacuum; sound needs a medium and cannot travel through a vacuum.

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

Refraction occurs when light changes speed crossing a boundary; bending toward the normal means the second medium is optically denser.

For a converging lens, 1/f = 1/u + 1/v using the real-is-positive convention; a virtual image forms when the object is inside the focal length.

Sound is a longitudinal wave of compressions and rarefactions; its speed is greatest in solids, less in liquids, least in gases.

Frequency determines pitch and amplitude determines loudness; the audible range for humans is about 20 Hz to 20 kHz.

Speed of a wave: v = fλ, where f is frequency in hertz and λ is wavelength in metres.

White light is dispersed by a prism because each colour refracts by a different amount; red bends least and violet most.

A pure substance has a fixed melting and boiling point; an impure substance melts over a range and at a lower temperature.

Physical changes alter state or form without new substances; chemical changes produce new substances with different properties.

Signs of a chemical reaction include gas evolution, colour change, precipitate formation, and temperature change.

An element contains one kind of atom; a compound contains two or more elements chemically combined in fixed proportions; a mixture is not chemically combined.

Exothermic reactions release energy to the surroundings (temperature rises); endothermic reactions absorb energy (temperature falls).

Conservation of mass: the total mass of reactants equals the total mass of products in a closed system.

Rates of reaction increase with higher temperature, higher concentration, greater surface area, and the presence of a catalyst.

A catalyst speeds up a reaction without being consumed and does not change the position of equilibrium.

A balanced equation has the same number of atoms of each element on both sides; coefficients are adjusted, never subscripts.

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

Combustion of a hydrocarbon: C₃H₈ + 5O₂ → 3CO₂ + 4H₂O is a balanced example.

Decomposition of calcium carbonate by heating: CaCO₃ → CaO + CO₂.

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂, balanced with light energy supplied.

Relative formula mass is the sum of relative atomic masses of atoms in the formula; moles = mass ÷ relative formula mass.

Avogadro's number is 6.02 × 10²³ particles per mole; one mole of any gas occupies about 24 dm³ at room temperature and pressure.

In a balanced equation, mole ratios give reacting masses; for example 2H₂ + O₂ → 2H₂O means 2 mol hydrogen reacts with 1 mol oxygen.

An ion is an atom or group of atoms with a net charge formed by losing or gaining electrons; metals lose electrons to form cations.

Common ions: Na⁺, K⁺, Mg²⁺, Ca²⁺, Al³⁺, Cl⁻, O²⁻, OH⁻, NO₃⁻, SO₄²⁻, CO₃²⁻, NH₄⁺.

Neutralisation: acid + base → salt + water; the ionic equation is H⁺ + OH⁻ → H₂O.

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

pH below 7 is acidic, pH 7 is neutral, and pH above 7 is alkaline; each unit is a tenfold change in hydrogen ion concentration.

A strong acid ionises completely in water; a weak acid ionises only partially.

Indicators such as litmus, methyl orange, and phenolphthalein signal the endpoint of a titration by colour change.

During titration, moles of acid = concentration × volume in dm³, and the equation's mole ratio links acid and alkali amounts.

Plant cells have a cellulose cell wall, chloroplasts, and a large permanent vacuole; animal cells do not.

Both plant and animal cells contain a nucleus, cytoplasm, cell membrane, mitochondria, and ribosomes.

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

Asexual reproduction involves one parent and produces genetically identical offspring; sexual reproduction combines gametes from two parents.

In humans, the male gamete is the sperm and the female gamete is the egg, each haploid with 23 chromosomes; the zygote is diploid with 46.

Fertilisation restores the diploid chromosome number; in plants, pollen transfers to the stigma and a pollen tube grows to the ovule.

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

Enzymes are biological catalysts with a specific active site; high temperature or wrong pH denatures them and slows reaction rate.

A gene is a section of DNA coding for a protein; alleles are different versions of a gene at the same locus.

Genotype is the allele combination; phenotype is the observable characteristic.

Dominant alleles are written with a capital letter and mask recessive alleles; recessive phenotypes appear only when both alleles are recessive.

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

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

Co-dominance means both alleles are expressed in the phenotype, as in AB blood type.

A mutation is a change in DNA base sequence; most have no effect, some cause genetic disorders, and occasionally they are beneficial.

Pedigree analysis: a recessive trait can skip generations, while a dominant trait typically appears in every generation.

A food chain shows energy flow: producer → primary consumer → secondary consumer → tertiary consumer.

Arrows in a food chain point in the direction of energy transfer, from the organism eaten to the eater.

Producers are photosynthetic organisms such as plants and algae; they convert light energy into chemical energy.

Only about 10% of energy passes to the next trophic level; the rest is lost as heat, used in movement, or egested.

Decomposers such as bacteria and fungi break down dead matter and return nutrients to the soil.

A food web is interlinked food chains and better reflects real ecosystems than a single chain.

Population size is affected by food availability, predation, disease, and competition; a predator–prey cycle shows lagged peaks.

Bioaccumulation: toxins become more concentrated at higher trophic levels because they are not excreted.

The principle of superposition states that in undisturbed strata, lower layers are older than upper layers.

The principle of cross-cutting relationships: a fault or intrusion is younger than the rock it cuts through.

Sedimentary rock forms in layers (strata) from compacted and cemented sediment; fossils are most common in these rocks.

Igneous rock forms from cooling magma or lava; rapid cooling gives fine crystals, slow cooling gives coarse crystals.

Metamorphic rock forms when existing rock is altered by heat and pressure, often with foliation.

The rock cycle links igneous, sedimentary, and metamorphic rocks through melting, weathering, and heat and pressure.

Fossils are useful for relative dating; index fossils are widespread, abundant, and short-lived in time.

Plate boundaries: divergent boundaries create new crust, convergent boundaries create mountains or subduction zones, and transform boundaries cause earthquakes.

Air pressure decreases with altitude because fewer air molecules lie above the observer.

Warm air is less dense and rises; cool air is denser and sinks, driving convection and low-pressure systems.

Wind blows from high pressure to low pressure; the greater the pressure difference, the stronger the wind.

An air mass gains the temperature and humidity of the region where it forms, such as polar continental or tropical maritime.

A warm front brings slow, steady rain; a cold front brings brief, heavy rain and a sharp temperature drop.

Relative humidity is the actual water vapour content divided by the maximum possible at that temperature, expressed as a percentage.

Condensation occurs when air cools to its dew point, forming clouds, fog, or dew.

Land heats and cools faster than water, producing sea breezes by day (onshore) and land breezes by night (offshore).

Earth rotates west to east on its axis once every 24 hours, making the Sun, Moon, and stars appear to move east to west.

Earth revolves around the Sun once every 365.26 days; the axis tilt of 23.4° causes the seasons.

Solstices occur when a pole is most tilted toward or away from the Sun; equinoxes occur when day and night are nearly equal.

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

Moon phases depend on the angle between the Sun, Earth, and Moon: new moon, first quarter, full moon, third quarter.

Spring tides occur at new and full moon when solar and lunar pulls align; neap tides occur at quarter moons.

Solar eclipses occur at new moon, lunar eclipses at full moon, and both need near alignment of the three bodies.

Apparent motion of stars: circumpolar stars never set, while other stars rise and set due to Earth's rotation.

An independent variable is deliberately changed, the dependent variable is measured, and control variables are kept constant.

A control group receives no treatment or a standard treatment and provides a baseline for comparison.

A hypothesis is a testable prediction that can be supported or refuted by evidence.

Valid conclusions require repeated trials and data from multiple samples; a single trial cannot establish a pattern.

Reliability increases with repeated measurements; accuracy is closeness to the true value, and precision is closeness of repeated readings.

Line graphs suit continuous data, bar charts suit discrete categories, and scatter plots reveal correlation between two variables.

Correlation does not prove causation; a confounding variable may explain an observed association.

Observation describes what is detected with the senses or instruments; a conclusion interprets observations against the hypothesis.