Aichi Entrance Science cheat sheet

Average speed = distance ÷ time; average velocity = displacement ÷ time (a vector with direction).

Acceleration a = (v − u) ÷ t; for uniform acceleration use v = u + at and s = ut + ½at².

Newton's first law: an object keeps its velocity unless a net external force acts; Newton's second law: F = ma (net force in newtons).

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

Weight W = mg with g ≈ 9.8 N/kg; mass is in kilograms and does not change with location.

Friction opposes relative sliding; static friction adjusts up to a maximum, kinetic friction is roughly constant.

Work W = Fs only when force and displacement are parallel; power P = W ÷ t is measured in watts.

Kinetic energy KE = ½mv²; gravitational potential energy PE = mgh; with no friction, KE + PE is constant.

Conservation of momentum: total momentum before a collision equals total momentum after, in an isolated system.

Current I = Q ÷ t (amperes); in a series circuit current is the same everywhere, in parallel the currents split.

Ohm's law V = IR holds for a resistor at constant temperature; resistance R = V ÷ I in ohms.

Series: R total = R₁ + R₂ + …; parallel: 1/R total = 1/R₁ + 1/R₂ + …

Electrical power P = VI = I²R = V² ÷ R; energy consumed = power × time (joules or kilowatt-hours).

A current-carrying wire has a magnetic field around it (right-hand grip rule); a changing magnetic field induces a voltage (electromagnetic induction).

Wave speed v = fλ; frequency f is set by the source, and speed depends on the medium.

Sound needs a material medium, travels faster in solids than in gases, and cannot pass through a vacuum.

Reflection: angle of incidence equals angle of reflection; refraction bends a wave toward the normal when it slows down.

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

A pure substance has a fixed melting and boiling point; an impurity lowers the melting point and raises the boiling point.

Filtration separates an insoluble solid from a liquid; evaporation or crystallisation recovers a dissolved solid.

Distillation separates liquids by boiling-point difference; fractional distillation is used for petroleum and liquid air.

Chromatography separates dissolved substances by differing solubilities and travel rates on the paper.

Density = mass ÷ volume; density is a characteristic property independent of sample size.

Particle model: solids vibrate in fixed positions, liquids slide past each other, gases move freely with large spacing.

Changes of state (melting, boiling, condensing, freezing) are physical changes; mass is conserved but volume usually is not.

Diffusion is faster at higher temperature and in gases, because particles have greater average kinetic energy.

Mixtures can be separated by physical methods; compounds require chemical reactions to break their bonds.

Balanced equations conserve atoms of each element; coefficients multiply the whole formula.

A metal plus acid gives a salt plus hydrogen gas; a metal carbonate plus acid gives salt, water and carbon dioxide.

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

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

Acids release H⁺ in water, bases accept H⁺; strong acids ionise almost completely, weak acids only partly.

Precipitation occurs when two soluble salts exchange ions to form an insoluble product (e.g. AgCl, BaSO₄).

Oxidation is loss of electrons (increase in oxidation number); reduction is gain of electrons; both occur together in redox.

An oxidising agent is itself reduced; a reducing agent is itself oxidised.

Exothermic reactions release heat (combustion, neutralisation); endothermic reactions absorb heat (thermal decomposition).

Plant cells have a cellulose cell wall, chloroplasts and a large vacuole; animal cells lack all three.

Mitochondria release energy by respiration; ribosomes build proteins; the nucleus holds DNA.

Mitosis produces two genetically identical diploid cells for growth; meiosis produces four haploid gametes with new gene combinations.

Fertilisation restores the diploid number; in humans the gamete has 23 chromosomes and the zygote 46.

Genotype is the allele pair; phenotype is the visible trait; a dominant allele is expressed when present.

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

Sex-linked traits sit on the X chromosome, so recessive disorders appear more often in males.

Evolution by natural selection requires variation, heritability, and differential survival and reproduction.

Fossils, homologous structures and DNA-sequence similarity are evidence for common ancestry.

Blood flows heart → arteries → capillaries → veins → heart; arteries carry blood away, veins return it.

Alveoli and villi both have thin walls and large surface area for efficient exchange.

Digestion: amylase breaks starch to sugars, protease breaks protein to amino acids, lipase breaks fat to fatty acids and glycerol.

Xylem carries water and minerals upward; phloem transports sugars made in leaves by photosynthesis.

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂, using chlorophyll and light energy.

Stomata, controlled by guard cells, allow gas exchange and transpiration; transpiration pulls water up the stem.

A food chain's arrows show energy flow; only about 10% of energy passes to the next trophic level.

Decomposers return nutrients to the soil; carbon and nitrogen cycle through living and non-living parts.

Bioaccumulation and eutrophication are consequences of pollutants entering ecosystems.

Earth's interior: crust, mantle, outer core (liquid), inner core (solid); seismic S-waves cannot pass the liquid outer core.

Plate boundaries: divergent (ridges), convergent (subduction, mountains), transform (faults); earthquakes and volcanoes cluster at boundaries.

Igneous rock forms from cooling magma; sedimentary from deposited layers; metamorphic from heat and pressure.

The principle of superposition: in undisturbed strata, deeper layers are older.

Weathering and erosion break and transport rock; deposition builds layers; fossils give relative ages.

Weather is driven by uneven solar heating; wind flows from high to low pressure, and warm air holds more water vapour.

Fronts: warm front brings gradual cloud and rain; cold front brings short, heavy rain and a temperature drop.

Seasonal change comes from Earth's 23.4° axial tilt, not from distance to the Sun.

Moon phases arise from the changing angle between Sun, Earth and Moon; a solar eclipse needs the Moon between Earth and Sun.