Fukui Entrance Science cheat sheet

Newton's second law: F = ma; net force in newtons equals mass in kilograms times acceleration in m/s².

Equations of motion at constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as.

Weight = mg with g ≈ 9.8 N/kg; mass is constant, weight changes with gravitational field strength.

Work done by a constant force: W = Fs cos θ, measured in joules; work is zero when force is perpendicular to displacement.

Kinetic energy KE = ½mv²; gravitational potential energy PE = mgh; in the absence of friction KE + PE is constant.

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

Momentum p = mv is conserved in collisions; impulse equals change in momentum, FΔt = Δ(mv).

Pressure in a liquid: p = ρgh; a body floats when the upthrust equals its weight (Archimedes' principle).

Lever balance: clockwise moments equal anticlockwise moments about the same pivot; moment = force × perpendicular distance.

Ohm's law: V = IR, valid for a conductor at constant temperature; resistance in ohms equals voltage divided by current.

Series circuit: same current through each component, voltages add, total resistance R = R₁ + R₂ + …

Parallel circuit: same voltage across each branch, currents add, 1/R = 1/R₁ + 1/R₂ + …

Electrical power: P = VI = I²R = V²/R; energy used = power × time, in joules or kilowatt-hours.

Charge flow: Q = It, in coulombs; 1 C is the charge carried by 1 A for 1 s.

A magnetic field surrounds a current-carrying wire; reversing the current reverses the field direction (right-hand grip rule).

Force on a current-carrying wire in a magnetic field: F = BIl sin θ; direction given by Fleming's left-hand rule.

Electromagnetic induction: a changing magnetic flux through a coil induces an emf; the induced current opposes the change (Lenz's law).

Step-up transformers have more turns on the secondary coil; for an ideal transformer V₁/V₂ = N₁/N₂.

Wave equation: v = fλ; frequency in hertz, wavelength in metres, speed in m/s.

Transverse waves oscillate perpendicular to travel (light); longitudinal waves oscillate along travel (sound).

Sound needs a medium, travels about 340 m/s in air at room temperature, and cannot pass through a vacuum.

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

Refraction: light bends toward the normal entering a denser medium; Snell's law n₁ sin θ₁ = n₂ sin θ₂.

Total internal reflection occurs when light travels from denser to less dense medium and the angle exceeds the critical angle.

Convex lens: parallel rays converge at the focal point; 1/f = 1/u + 1/v, with real images inverted.

Frequency determines pitch and wavelength in a medium; amplitude determines loudness or brightness.

Resonance occurs when a driving frequency matches an object's natural frequency, increasing amplitude.

Three states: solid (fixed shape and volume), liquid (fixed volume, variable shape), gas (fills its container).

Particle model: in solids particles vibrate in fixed positions; in liquids they slide past each other; in gases they move rapidly and far apart.

Melting and boiling are endothermic; freezing and condensation are exothermic; temperature stays constant during a change of state.

A mixture can be separated by physical means; a pure substance has a fixed melting and boiling point.

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

Distillation separates liquids by boiling point; fractional distillation separates miscible liquids such as crude oil fractions.

Chromatography separates dissolved substances by differing solubility and attraction to the stationary phase.

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

Law of conservation of mass: atoms are neither created nor destroyed, so equations must be balanced.

Oxidation is loss of electrons (or gain of oxygen); reduction is gain of electrons (or loss of oxygen); OIL RIG.

Acid + base → salt + water (neutralisation); H⁺ + OH⁻ → H₂O.

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

pH below 7 is acidic, 7 neutral, above 7 alkaline; universal indicator and litmus show this.

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

A catalyst speeds up a reaction by lowering activation energy without being used up.

Reaction rate increases with higher temperature, higher concentration, larger surface area, or higher pressure for gases.

In a displacement reaction a more reactive metal displaces a less reactive metal from its compound.

Atom: protons (positive, in nucleus), neutrons (neutral, in nucleus), electrons (negative, in shells).

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

An ion forms when an atom gains or loses electrons: metals lose electrons to form positive ions, non-metals gain electrons.

Groups are vertical columns with the same number of outer electrons and similar chemical properties.

Periods are horizontal rows; the period number equals the number of occupied electron shells.

Group 1 alkali metals become more reactive down the group; Group 7 halogens become less reactive down the group.

Group 0 noble gases have full outer shells and are unreactive.

Ionic compounds form between metals and non-metals, are held by electrostatic attraction, and conduct when molten or dissolved.

Covalent bonds form by sharing electron pairs, usually between non-metals, giving molecules.

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

Nucleus, cytoplasm and cell membrane are common to plant and animal cells; mitochondria are the site of respiration.

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

Fertilisation restores the diploid number, combining one set of chromosomes from each gamete.

Genes occur in pairs; a dominant allele is expressed even when only one copy is present, a recessive allele needs two.

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

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

Sex determination in humans: XX is female, XY is male; the father's sperm determines the sex of the child.

DNA carries the genetic code; chromosomes are made of DNA and protein and are found in the nucleus.

Digestion: carbohydrates → glucose, proteins → amino acids, fats → fatty acids and glycerol.

Enzymes are biological catalysts; amylase acts on starch, protease on protein, lipase on fat; each has an optimum temperature and pH.

Villi in the small intestine increase surface area for absorption of digested food into the blood.

Aerobic respiration: glucose + oxygen → carbon dioxide + water, releasing energy; occurs mainly in mitochondria.

Anaerobic respiration in muscle produces lactic acid; in yeast it produces ethanol and carbon dioxide.

The heart has four chambers; the left ventricle pumps oxygenated blood to the body through the aorta.

Arteries carry blood away from the heart at high pressure; veins return blood and contain valves.

Excretion removes metabolic waste: kidneys filter blood to form urine, removing urea and excess water and salts.

The lungs exchange gases in alveoli, which have thin walls and a large surface area.

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

Limiting factors of photosynthesis include light intensity, carbon dioxide concentration and temperature.

Stomata open and close to control gas exchange and water loss; guard cells regulate them.

Root hair cells absorb water and mineral ions; xylem transports water upward, phloem transports sugars.

Transpiration is water loss as vapour from leaves; it is faster in warm, dry, windy, bright conditions.

Food chain: producer → primary consumer → secondary consumer; arrows show the direction of energy flow.

Only about 10% of energy passes to the next trophic level, so food chains are short.

Decomposers break down dead matter and recycle nutrients such as carbon and nitrogen.

Population size is affected by food, predators, disease and competition; carrying capacity limits growth.

Sedimentary rock forms in layers (strata); the lowest layer is usually the oldest (law of superposition).

Fossils are mainly found in sedimentary rock and are used to date and correlate rock layers.

Index fossils are widespread, short-lived species useful for identifying a geological period.

Igneous rock forms from cooled magma or lava; intrusive igneous rock cools slowly with large crystals.

Metamorphic rock forms when existing rock is changed by heat and pressure.

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

Earth's interior: crust, mantle, outer core (liquid) and inner core (solid); the mantle drives plate movement.

Plate tectonics explains earthquakes, volcanoes and mountain building at plate boundaries.

Weathering and erosion break down and transport rock; deposition and compaction form new sedimentary layers.

Atmospheric composition: about 78% nitrogen, 21% oxygen, and small amounts of argon and carbon dioxide.

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

Warm air rises and expands, cools, and water vapour condenses into clouds and precipitation.

High pressure brings settled, clear weather; low pressure brings cloud and rain.

Weather front: warm front brings steady rain; cold front brings brief heavy rain and cooler air.

Earth rotates on its axis once a day, causing day and night; it orbits the Sun once a year.

The tilt of Earth's axis (about 23.5°) causes the seasons, not the distance from the Sun.

The Moon orbits Earth about every 27 days; phases depend on the angle between Earth, Moon and Sun.

Solar system order: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune; inner planets are rocky.