Tochigi Public High School Entrance Examination - Science cheat sheet

Average speed = distance ÷ time; velocity adds direction. On a distance–time graph, slope = speed; on a velocity–time graph, slope = acceleration and area under the line = distance travelled.

Newton's three laws: no net force means constant velocity (or rest); F = ma; every action force has an equal, opposite reaction force acting on a different object.

Weight = mass × gravitational acceleration (about 9.8 N/kg on Earth); mass is constant, weight changes with gravity. Friction opposes relative motion and converts kinetic energy to thermal energy.

Work = force × distance moved along the force (J); power = work ÷ time (W). Kinetic energy = ½mv²; gravitational potential energy = mgh.

Law of conservation of energy: energy changes form but total amount is constant; a pendulum or roller coaster trades potential and kinetic energy, with losses to heat and sound.

Wave speed = frequency × wavelength. Frequency (Hz) is set by the source; speed is set by the medium. Light refracts when entering a new medium because its speed changes.

Reflection: angle of incidence = angle of reflection, both measured from the normal. Refraction toward the normal occurs when light slows down (e.g., air to water).

Ohm's law V = IR; series circuits share one current and split voltage; parallel circuits share one voltage and split current. Resistance of a wire rises with length and falls with cross-section area.

Electric power P = VI = I²R; energy used = power × time. A magnetic field surrounds a current-carrying wire; reversing current reverses field direction, and a coil in a changing field induces a current (electromagnetic induction).

All matter is made of particles in constant motion; temperature is a measure of average kinetic energy, so heating increases particle speed and spacing.

States of matter: solid (fixed shape and volume, particles in a lattice vibrating in place), liquid (fixed volume, changing shape), gas (fills its container, particles far apart).

Changes of state - melting, boiling, condensation, freezing, sublimation - are physical changes; the substance's identity is unchanged.

Pure substances have fixed melting and boiling points; mixtures do not. Boiling point depends on pressure: lower pressure lowers the boiling point.

Mixtures separate by physical methods: filtration (insoluble solid from liquid), distillation (boiling-point difference), chromatography (different travel rates), recrystallisation.

Density = mass ÷ volume (g/cm³). An object floats if its density is less than the liquid's; it sinks if greater.

Elements are one kind of atom; compounds contain two or more elements chemically bonded in fixed ratio; mixtures contain substances not chemically bonded.

Atoms have a nucleus (protons + neutrons) surrounded by electrons. Atomic number = protons; mass number = protons + neutrons; ions form by gaining or losing electrons.

A chemical change produces new substances with different properties; evidence includes gas evolution, precipitate, colour change, heat or light, and it is generally not easily reversed.

Chemical equations must be balanced: the number of each kind of atom is equal on both sides. Coefficients change amounts; subscripts must never be altered to balance.

Combustion of a hydrocarbon with sufficient oxygen gives CO₂ and H₂O; incomplete combustion gives CO (toxic) and soot.

Acids release H⁺ in water; alkalis release OH⁻. Neutralisation: acid + base → salt + water. Acid + metal → salt + hydrogen gas; acid + carbonate → salt + water + CO₂.

pH below 7 is acidic, 7 neutral, above 7 alkaline. Litmus turns red in acid and blue in alkali; universal indicator gives a colour scale.

Redox: oxidation is loss of electrons (or gain of oxygen), reduction is gain of electrons (or loss of oxygen); they always occur together.

Mole concept: 1 mol contains 6.0 × 10²³ particles and has a mass in grams equal to the molar mass. Amount (mol) = mass ÷ molar mass.

Quantitative reaction: use the balanced equation's mole ratio to convert between amounts of reactants and products; for gases at the same conditions, volume ratio equals mole ratio.

Cell theory: all living things are made of cells, cells come from pre-existing cells, and the cell is the basic unit of structure and function.

Plant cells have a cell wall, chloroplasts and a large vacuole; animal cells lack these but both have a nucleus, cytoplasm, mitochondria and cell membrane.

Organelles: nucleus stores DNA and controls activity; mitochondria release energy by respiration; chloroplasts carry out photosynthesis; ribosomes build proteins.

Photosynthesis: CO₂ + H₂O + light energy → glucose + O₂, occurring in chloroplasts. Respiration: glucose + O₂ → CO₂ + H₂O + energy, occurring in mitochondria.

Unicellular organisms such as Paramecium and Euglena carry out all life processes in one cell; Euglena has chloroplasts and can photosynthesise.

Levels of organisation: cell → tissue → organ → organ system → individual organism.

Microscopy: total magnification = eyepiece × objective. Specimen images are inverted and reversed, so moving the slide left moves the image right in view.

Diffusion moves particles from high to low concentration; osmosis is water movement across a semi-permeable membrane toward higher solute concentration.

Mitosis produces two genetically identical cells for growth and repair; meiosis produces four genetically varied gametes with half the chromosome number.

Fertilisation restores the diploid number. Humans: 46 chromosomes in body cells, 23 in gametes; sex determined by X or Y sperm fertilising the egg.

Genotype versus phenotype: dominant alleles are expressed even when paired with a recessive allele. A cross of two heterozygotes (Aa × Aa) gives 3:1 dominant to recessive phenotype.

Mendel's law of segregation: the two alleles for a gene separate when gametes form, so each gamete carries only one.

Ecosystem components: producers, consumers, decomposers, and non-living factors (light, temperature, water, soil). Food webs show energy flow; arrows point toward the consumer.

Energy is lost at each trophic level (about 10% transferred), so food chains rarely exceed four or five levels; numbers of organisms are limited by this loss.

Evolution by natural selection: individuals vary, more offspring are produced than survive, favourable variations are inherited, and populations change over generations.

Adaptation examples: cactus spines are modified leaves reducing water loss; industrial melanism in moths shows selection changing allele frequencies.

Earth's interior: crust, mantle, outer core (liquid), inner core (solid). P-waves pass through solids and liquids; S-waves cannot pass through liquids, which reveals the liquid outer core.

Igneous rocks form from cooling magma or lava; sedimentary rocks form from deposited layers (may contain fossils); metamorphic rocks form under heat and pressure.

Plate tectonics: earthquakes and volcanoes concentrate at plate boundaries. Divergent boundaries create ridges; convergent boundaries create trenches and mountain ranges.

Weathering breaks rock in place; erosion transports the fragments; deposition lays them down. Running water is the most common agent of erosion.

Weather: air pressure decreases with altitude; wind blows from high to low pressure. Warm air holds more water vapour, so cooling air forms clouds and rain.

Fronts: a cold front brings rapid cooling, heavy rain and clearing; a warm front brings gradual warming and prolonged light rain.

Seasons result from Earth's axial tilt (about 23.4°), not distance from the Sun. Solstices have the longest and shortest days; equinoxes have equal day and night.

Moon phases arise from the changing angle between Earth, Moon and Sun; a solar eclipse occurs at new moon, a lunar eclipse at full moon.

Inner planets (Mercury, Venus, Earth, Mars) are rocky and small; outer planets are gas or ice giants with many moons and rings. The Sun is a star powered by nuclear fusion of hydrogen.

Controlled experiment: change one independent variable, measure one dependent variable, and hold all other conditions (control variables) constant.

Include a control group to show what happens without the treatment; repeat trials and average results to reduce random error.

Accuracy means closeness to the true value; precision means repeated measurements agree with each other. A systematic error shifts all readings in the same direction.

Graph choice: line graph for continuous change over time; bar chart for categories; scatter plot to test correlation between two measured quantities.

Read graphs carefully: identify axes and units, calculate slope from two points, and describe trends as increasing, decreasing, or constant, with specific values.

Hypothesis must be testable and falsifiable. A conclusion must be supported by the data; correlation alone does not prove causation.

Significant figures and units: report the same precision as the measuring instrument; convert units before calculating (e.g., cm to m, g to kg).

Observation versus inference: observation is what is directly sensed or measured; inference is an explanation based on evidence and prior knowledge.

Average speed = distance ÷ time; velocity adds direction. On a distance–time graph, slope = speed; on a velocity–time graph, slope = acceleration and area under the line = distance travelled.

Newton's three laws: no net force means constant velocity (or rest); F = ma; every action force has an equal, opposite reaction force acting on a different object.

Weight = mass × gravitational acceleration (about 9.8 N/kg on Earth); mass is constant, weight changes with gravity. Friction opposes relative motion and converts kinetic energy to thermal energy.

Work = force × distance moved along the force (J); power = work ÷ time (W). Kinetic energy = ½mv²; gravitational potential energy = mgh.

Law of conservation of energy: energy changes form but total amount is constant; a pendulum or roller coaster trades potential and kinetic energy, with losses to heat and sound.

Wave speed = frequency × wavelength. Frequency (Hz) is set by the source; speed is set by the medium. Light refracts when entering a new medium because its speed changes.

Reflection: angle of incidence = angle of reflection, both measured from the normal. Refraction toward the normal occurs when light slows down (e.g., air to water).

Ohm's law V = IR; series circuits share one current and split voltage; parallel circuits share one voltage and split current. Resistance of a wire rises with length and falls with cross-section area.

Electric power P = VI = I²R; energy used = power × time. A magnetic field surrounds a current-carrying wire; reversing current reverses field direction, and a coil in a changing field induces a current (electromagnetic induction).