Gunma Entrance Science cheat sheet

Average speed = distance ÷ time; average velocity = displacement ÷ time, with direction included.

Acceleration = change in velocity ÷ time taken (a = (v − u)/t); SI unit m/s².

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

Newton's first law: a body keeps constant velocity unless a net external force acts on it.

Newton's second law: F = ma, where F is the resultant (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 = mg (g ≈ 9.8 N/kg on Earth); mass in kg is unchanged by location, weight is not.

Friction opposes relative sliding; on a horizontal surface the normal force N = mg and friction ≤ μN.

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

Work = force × displacement along the force (W = Fs); unit joule, J = N·m.

Kinetic energy = ½mv²; gravitational potential energy = mgh near Earth's surface.

Conservation of energy: energy changes form but total energy in a closed system stays constant; lost mechanical energy usually becomes heat.

Power = work ÷ time = energy transferred ÷ time; unit watt, 1 W = 1 J/s.

Ohm's law: V = IR, valid for ohmic resistors at constant temperature.

Series circuit: current is the same everywhere, R_total = R₁ + R₂ + …, voltage divides in ratio to resistance.

Parallel circuit: voltage is the same across each branch, 1/R_total = 1/R₁ + 1/R₂ + …, current divides.

Electrical power: P = VI = I²R = V²/R; energy used = power × time (1 kWh = 3.6 × 10⁶ J).

Efficiency = useful energy output ÷ total energy input × 100%; always below 100% because some energy spreads as heat.

Pure substances have fixed melting and boiling points; mixtures melt and boil over a range.

Elements contain one kind of atom; compounds contain two or more elements chemically combined in fixed ratios.

Physical change alters state or form without new substances; chemical change forms new substances with different properties.

Signs of chemical change: gas evolution, precipitate, colour change, temperature change, light.

Density = mass ÷ volume; used to identify substances and to predict floating (density less than water ≈ 1 g/cm³ floats).

Separation: filtration for insoluble solids, distillation for dissolved solids or liquids with different boiling points, chromatography for dissolved colours.

Mixtures can be separated by physical means; compounds need chemical reactions to break apart.

Gas tests: oxygen relights a glowing splint, hydrogen burns with a pop, carbon dioxide turns limewater milky.

Conservation of mass applies to chemical reactions in closed systems; mass loss in open systems is escaping gas.

Ions form when atoms gain or lose electrons: metals lose electrons to form cations, non-metals gain electrons to form anions.

Monatomic ion charges: group 1 = +1, group 2 = +2, Al³⁺; halides = −1, oxide and sulfide = −2, nitride = −3.

Polyatomic ions: NH₄⁺, OH⁻, NO₃⁻, SO₄²⁻, CO₃²⁻, HCO₃⁻; ionic formulas balance total positive and negative charge to zero.

Acid + base → salt + water (neutralisation); acid + metal → salt + hydrogen; acid + carbonate → salt + water + carbon dioxide.

pH below 7 is acidic, 7 neutral, above 7 alkaline; pH 1 is ten times more acidic than pH 2 (each unit is ×10 in H⁺ concentration).

Active metals displace less active metals from salt solutions; reactivity series: K, Na, Ca, Mg, Al, Zn, Fe, Cu, Ag, Au.

Precipitation occurs when two soluble salts mix and an insoluble combination forms, e.g. Ag⁺ + Cl⁻ → AgCl.

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

Balanced equations must have equal numbers of each type of atom on both sides, and charge balance for ionic equations.

Producers make organic matter by photosynthesis; consumers eat other organisms; decomposers break down dead matter and recycle nutrients.

A food chain arrow points from the organism being eaten to the eater, showing the direction of energy flow.

Energy is lost at each trophic level (respiration, heat, excretion); roughly 10% passes to the next level.

Population size is limited by food, water, space, disease, predation, and abiotic factors such as temperature and light.

Competition occurs when organisms need the same limited resource; it can be intraspecific (same species) or interspecific.

Symbiosis: mutualism benefits both, parasitism benefits one and harms the host, commensalism benefits one with little effect on the other.

Decomposers such as fungi and bacteria return carbon and nitrogen to the soil, keeping materials cycling.

Adaptations are inherited features improving survival in a habitat; they can be structural, behavioural, or physiological.

Removing one species affects the whole web: a rise in predators lowers prey numbers, which can then reduce predator numbers again.

Cell structures: nucleus holds DNA, mitochondria release energy by respiration, chloroplasts carry out photosynthesis, ribosomes build proteins.

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

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

Human body cells are diploid (46 chromosomes); gametes are haploid (23), so fertilisation restores 46.

Genotype is the allele pair; phenotype is the visible trait. Dominant alleles show with one copy, recessive only with two.

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

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

DNA carries the genetic code in bases A, T, G, C; genes are sections of DNA coding for proteins.

Asexual reproduction produces genetically identical offspring from one parent; sexual reproduction mixes parental genes and increases variation.

Earth's layers: crust (thin, silicate rock), mantle (solid but slowly flowing), outer core (liquid iron), inner core (solid iron–nickel).

Igneous rock forms from cooling magma or lava; sedimentary rock forms from compacted deposits in layers; metamorphic rock forms under heat and pressure.

Sedimentary layers are deposited oldest at the bottom (superposition) unless later folding or faulting has overturned them.

Fossils in sedimentary rock show past life; index fossils identify geological periods because they had wide range and short duration.

Plate tectonics: plates move on the mantle; divergent boundaries create ridges, convergent boundaries create mountains, trenches, and volcanoes.

Earthquakes occur where stress in rock is released along a fault; the focus is underground, the epicentre is directly above on the surface.

Weathering breaks rock in place; erosion transports the fragments; deposition lays them down; these are distinct processes.

Folding and faulting show that rock layers were once horizontal and later deformed by tectonic forces.

Soil forms from weathered rock plus humus; its profile has layers (horizons) and develops slowly over long times.

Air pressure decreases with altitude; air moves from high to low pressure, creating wind.

Warm air is less dense and rises; rising air cools, water vapour condenses into clouds and rain.

Relative humidity is the actual water vapour in air compared with the maximum the air can hold at that temperature.

A warm front brings prolonged gentle rain; a cold front brings short heavy rain and a sharp temperature drop.

Seasons result from Earth's axial tilt (about 23.4°), not from changing distance from the Sun.

Day and night come from Earth's rotation (about 24 hours); the year comes from revolution around the Sun (about 365.25 days).

Moon phases arise from the changing angle between Sun, Earth, and Moon; a full cycle takes about 29.5 days.

Solar eclipse: Moon between Sun and Earth (new moon). Lunar eclipse: Earth between Sun and Moon (full moon).

Solar system order: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune; inner planets are rocky, outer are gas/ice giants.

A hypothesis is a testable prediction; an experiment must have one independent variable, a dependent variable, and controlled variables.

A control group receives no treatment or a standard treatment, allowing comparison with the experimental group.

Repeat measurements and average them to reduce the effect of random error; anomalous points are excluded and reported.

Accuracy is closeness to the true value; precision is closeness of repeated readings to each other.

A line graph suits continuous data; a bar chart suits categories; a scatter graph shows correlation between two variables.

Read scales by estimating one digit beyond the smallest marked division, and include units with every value.

Correlation does not prove causation; a third variable or chance may explain an observed association.

A valid conclusion must be supported by the data collected and must not claim more than the evidence allows.

A fair test changes only the independent variable; changing several at once makes results uninterpretable.

Density formula: density = mass ÷ volume, in g/cm³ or kg/m³.

Speed conversion: 1 m/s = 3.6 km/h.

Force unit: newton (N); 1 N accelerates 1 kg at 1 m/s².

Moment of a force = force × perpendicular distance from pivot; equilibrium when clockwise moments equal anticlockwise moments.

Pressure = force ÷ area (Pa = N/m²); reducing area increases pressure for the same force.

In liquids, pressure increases with depth and depends on density and depth, not on the container's shape.

A body floats when the upthrust equals its weight, i.e. when its average density is less than the fluid's.

Energy stores: kinetic, gravitational potential, elastic potential, thermal, chemical, nuclear; transfer by heating, waves, or work.

Hooke's law: F = kx for a spring, with elastic potential energy = ½kx².

Charge Q = It (coulombs = amperes × seconds).

Voltage is energy transferred per unit charge: V = W/Q (1 V = 1 J/C).

Resistance = voltage ÷ current (R = V/I); unit ohm, Ω.

Current is the rate of charge flow; conventional current flows from + to − outside the source.

A fuse and an earth wire protect appliances by providing a low-resistance path and breaking the circuit on overload.

States: solid has fixed shape and volume, liquid fixed volume but flowing shape, gas fills its container.

Changes of state (melting, boiling, condensing, freezing) are physical changes and reversible.

Solubility rises with temperature for most solids but falls for gases as temperature rises.

A solution = solute + solvent; concentration = mass of solute ÷ volume of solution.

Alloys are mixtures of a metal with other elements and are usually harder than the pure metal.

Particle model: in gases particles are far apart and move fast; in solids they vibrate about fixed positions.

Distillation separates liquids by boiling point; the liquid with the lower boiling point distils first.

Word equation order: reactants → products; state symbols (s), (l), (g), (aq) show physical state.

Combustion of a hydrocarbon: hydrocarbon + oxygen → carbon dioxide + water.

Thermal decomposition of calcium carbonate: CaCO₃ → CaO + CO₂ on heating.

Rusting needs both oxygen and water; salt accelerates it; coating or galvanising prevents contact with these.

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

Oxidation is loss of electrons, reduction is gain (OIL RIG); redox reactions involve both together.

Catalysts speed up a reaction without being used up, lowering the activation energy.

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

Respiration releases energy from glucose; aerobic: glucose + oxygen → carbon dioxide + water.

Carbon cycle: photosynthesis removes CO₂; respiration, combustion, and decomposition return it.

Nitrogen-fixing bacteria and lightning convert N₂ into usable compounds; decomposers release nitrogen back to soil.

A pyramid of numbers can be inverted (one tree, many insects); a pyramid of energy is never inverted.

Indicator species reveal pollution: lichens indicate clean air; mayfly larvae indicate clean, oxygen-rich water.

Biodiversity is highest in stable habitats with many niches; it improves ecosystem resistance to change.

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

Homozygous = two identical alleles; heterozygous = two different alleles.

Punnett squares predict offspring ratios from parental gametes.

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

Pollen transfer (pollination) precedes fertilisation in flowers; seeds form in the ovary, fruit from the ovary wall.

Cell division for growth is mitosis; gamete formation is meiosis, which halves the chromosome number.

Selective breeding and genetic modification both change inherited traits, but only genetic modification moves genes between species.

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

Magma is molten rock below the surface; lava is molten rock that has reached the surface.

Volcanic eruptions are more explosive when magma is viscous (high silica) and gas-rich.

Soil erosion is accelerated by removing vegetation; contour ploughing and terracing reduce it.

Fossil fuels (coal, oil, gas) are formed from buried organisms over millions of years.

Groundwater is stored in permeable rock (aquifer); impermeable rock stops water flow.

Earthquake magnitude is a logarithmic scale, so +1 in magnitude means about 10× larger amplitude.

Weather is the short-term state of the atmosphere; climate is the long-term average pattern.

Clouds form when rising air cools to the dew point and water vapour condenses on condensation nuclei.

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

Wind direction names the direction it comes from; a westerly wind blows from the west.

The Sun's apparent daily motion east to west is caused by Earth rotating west to east.

Inner planets have short orbital periods; the farther a planet is from the Sun, the longer its year.

The Moon always shows the same face to Earth because its rotation period equals its orbital period.

Independent variable: what you deliberately change; dependent variable: what you measure in response.

Control variables are kept constant so the effect of the independent variable can be isolated.

Mean = sum of values ÷ number of values; median = middle value when ordered.

Range = largest value − smallest value; a large range indicates high spread.

Percentage change = (new − old) ÷ old × 100%.

Measurement uncertainty is about half the smallest scale division for a simple analogue scale.

A prediction is a stated expected outcome; a conclusion judges whether the hypothesis was supported.

Resultant force of two forces in opposite directions = difference; in the same direction = sum.

Balanced forces give zero acceleration: the object stays still or moves at constant velocity.

Terminal velocity occurs when air resistance equals weight, so acceleration becomes zero.

Mass is the amount of matter (kg); weight is the force of gravity on it (N).

Gradient of a distance–time graph gives speed; a horizontal line means the object is stationary.

For a falling object, gravitational potential energy lost = kinetic energy gained (ignoring air resistance).

Energy cannot be created or destroyed, only transferred between stores.

Useful energy is the energy transferred to the intended store; wasted energy spreads to the surroundings as heat.

In a series circuit, adding resistors increases total resistance and reduces current.

In a parallel circuit, adding branches decreases total resistance and increases total current.

Voltage across components in series sums to the supply voltage; in parallel each branch gets the full supply voltage.

Ammeters are connected in series; voltmeters are connected in parallel across a component.

Static electricity arises from transfer of electrons by friction; like charges repel, unlike attract.

An atom has a nucleus of protons and neutrons, with electrons in shells around it.

Atomic number = number of protons; mass number = protons + neutrons.

Isotopes have the same atomic number but different numbers of neutrons.

The periodic table arranges elements by increasing atomic number; a group is a column, a period is a row.

Group 1 alkali metals are soft and reactive; group 17 halogens are reactive non-metals; group 18 noble gases are unreactive.

Ionic compounds have high melting points and conduct electricity when molten or dissolved, not when solid.

Simple molecular substances have low melting points and do not conduct electricity.

Rate of reaction increases with higher temperature, higher concentration, greater surface area, and a catalyst.

Collision theory: particles must collide with enough energy (activation energy) and correct orientation to react.

The law of conservation of mass means the total mass of reactants equals the total mass of products.

Mole concept: 1 mole = 6.02 × 10²³ particles; molar mass in g/mol equals the relative formula mass.

Concentration in mol/dm³ = number of moles ÷ volume in dm³.

A neutral solution has equal H⁺ and OH⁻ concentrations; adding acid increases H⁺ and lowers pH.

Indicators such as litmus and universal indicator show acidity or alkalinity by colour change.

Biotic factors are living influences (predators, disease); abiotic factors are non-living (temperature, light, water, pH).

A habitat is where an organism lives; a niche is its role, including what it eats and when.

A community is all populations in an area; an ecosystem includes the community plus its physical environment.

Population growth is limited by carrying capacity, the maximum the environment can sustain.

Bioaccumulation: pollutants concentrate in organisms at higher trophic levels.

Sampling with quadrats estimates plant abundance; random placement avoids bias.

Conservation measures include protected areas, habitat restoration, and captive breeding programmes.

Prokaryotic cells (bacteria) lack a nucleus; eukaryotic cells (plants, animals, fungi) have one.

Diffusion moves particles from high to low concentration without energy input.

Osmosis is diffusion of water through a partially permeable membrane from dilute to concentrated solution.

Active transport moves substances against a concentration gradient and requires energy from respiration.

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

In humans, the mother contributes an X chromosome and the father an X or Y, so the father determines sex.

Clones are genetically identical; variation in sexual offspring comes from meiosis and random fertilisation.

The atmosphere is about 78% nitrogen, 21% oxygen, with small amounts of argon and carbon dioxide.

Temperature falls with altitude in the troposphere but rises in the stratosphere because of ozone absorption.

Sea breezes blow from sea to land by day because land heats faster than water.

Absolute humidity is the mass of water vapour per unit volume of air.

The greenhouse effect keeps Earth warm by trapping outgoing infrared radiation.

Comets have highly elliptical orbits and tails that point away from the Sun.

Stars produce energy by nuclear fusion of hydrogen into helium in their cores.

A reliable result is reproducible when the experiment is repeated by others.

Sample size should be large enough to reduce the influence of chance variation.

Random sampling avoids selection bias when choosing subjects or sites.

A systematic error shifts all readings the same way (e.g. zero error); random error scatters readings.

Extrapolating a graph beyond the measured range is less reliable than interpolating within it.

Tables should show the independent variable in the first column and units in the headings.

A trend line on a scatter graph summarises the relationship but does not guarantee a mechanism.

Energy transfer by heating occurs from hotter to cooler regions until thermal equilibrium.

Specific heat capacity is the energy needed to raise 1 kg of a substance by 1 °C; energy = mcΔT.

Latent heat is energy absorbed or released during a change of state at constant temperature.

Conduction transfers energy through solids by particle vibration; metals conduct well because of free electrons.

Convection transfers energy in fluids by density differences; radiation needs no medium.

Dark, matte surfaces absorb and emit radiation better than light, shiny ones.

Reducing heat loss uses insulation, double glazing, and draught exclusion.

Acids release H⁺ ions in water; alkalis release OH⁻ ions.

Strong acids ionise completely in water; weak acids ionise only partially.

pH scale runs 0–14; universal indicator gives red in strong acid and purple in strong alkali.

Neutralisation with a carbonate produces a salt, water, and carbon dioxide.

Titration uses a burette and a pipette with an indicator to find the volume needed to neutralise a solution.

Soluble salts can be made by reacting an acid with a metal, a base, or a carbonate, then crystallising.

Insoluble salts are made by precipitation, mixing two solutions and filtering the solid.

Photosynthesis rate rises with light intensity until another factor (CO₂ or temperature) becomes limiting.

Leaves are adapted with a large flat surface, thin shape, stomata, and palisade cells rich in chloroplasts.

Stomata open to let CO₂ in and close to reduce water loss; guard cells control this.

Transpiration is water loss as vapour from leaves and pulls water up the xylem.

Xylem carries water and minerals upward; phloem carries dissolved sugars both ways.

Root hair cells increase surface area for absorbing water and mineral ions.

Respiration rate increases with exercise because muscles need more energy and produce more CO₂.

Minerals are naturally occurring solids with a definite chemical composition and crystal structure.

Hardness is compared with Mohs' scale; diamond is hardest at 10, talc softest at 1.

Sedimentary rocks such as sandstone, limestone, and shale form from sand, shells, and mud respectively.

Metamorphic examples: limestone → marble, shale → slate, granite → gneiss.

Intrusive igneous rock (granite) cools slowly underground with large crystals; extrusive rock (basalt) cools fast with small crystals.

Relative dating orders events; absolute dating uses radioactive decay half-lives to give ages in years.

Earthquakes and volcanoes cluster at plate boundaries, especially around the Pacific Ring of Fire.

The water cycle: evaporation, condensation, precipitation, and collection, driven by solar energy.

Weather fronts mark boundaries between air masses of different temperature and humidity.

Rain shadows form when moist air rises over mountains and drops rain on the windward side, leaving the leeward side dry.

The Coriolis effect deflects moving air, producing prevailing wind patterns.

Summer solstice gives the longest day in the northern hemisphere; winter solstice the shortest.

The Moon's gravitational pull, mainly, causes tides; spring tides occur at new and full moon.

Light-year is a distance (about 9.5 × 10¹² km), not a time.

A bar chart is used for discrete categories; a histogram for continuous grouped data.

The mode is the most frequent value; it is useful for categorical data.

Standard deviation measures spread around the mean; a small value means values cluster near the mean.

A scatter graph showing points rising to the right indicates positive correlation.

A fair conclusion must specify the conditions of the experiment, since results may not generalise.

Recording raw data before averaging allows errors to be checked and corrected.

Graph axes need labels with units, and the scale must be uniform along each axis.

Newton's second law in words: acceleration is proportional to resultant force and inversely proportional to mass.

Doubling the resultant force doubles acceleration if mass is constant.

Doubling the mass halves acceleration for the same force.

A force perpendicular to motion changes direction, not speed (e.g. circular motion).

Momentum = mass × velocity; in a closed system total momentum is conserved in collisions.

Stopping distance = thinking distance + braking distance; it increases with speed and with wet or icy roads.

Melting and boiling points increase with stronger forces between particles.

Diffusion is faster at higher temperature because particles move faster.

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

Chromatography separates dissolved substances by how far they travel up the paper.

Filtration separates an insoluble solid from a liquid; the solid stays on the filter paper.

Evaporation or crystallisation recovers a dissolved solid from its solution.

Hard water contains dissolved calcium and magnesium ions and forms scum with soap.

A recessive disorder appears only when both alleles are recessive, so carriers show no symptoms.

A dominant allele masks the effect of a recessive allele in a heterozygote.

Genetic diagrams use capital letters for dominant alleles and lowercase for recessive.

Mutations change the DNA base sequence and can create new alleles, sometimes causing disease.

The environment also affects phenotype, e.g. diet and sunlight, alongside genes.

Sexual reproduction in plants: pollen nucleus fuses with egg cell to form a zygote, which becomes the seed.

Cell differentiation makes specialised cells; stem cells remain unspecialised and can become many cell types.

Air pressure is measured with a barometer; temperature with a thermometer; rainfall with a rain gauge.

Isobars close together indicate strong winds; far apart indicate light winds.

An anemometer measures wind speed; a wind vane shows wind direction.

The troposphere contains most of the atmosphere's mass and nearly all its water vapour.

Ozone in the stratosphere absorbs harmful ultraviolet radiation.

Planets orbit the Sun in ellipses, with the Sun at one focus.

Galaxies contain billions of stars; the Milky Way is our galaxy, and the Universe is expanding.

A hypothesis must be falsifiable: an observation must be able to show it wrong.

A controlled experiment compares an experimental group with a control group under identical conditions.

A pilot study checks methods and equipment before the main experiment.

Qualitative data describe qualities (colour, smell); quantitative data are numerical measurements.

A systematic sample follows a pattern (e.g. every tenth item); it can miss periodic variation.

Peer review checks methods and conclusions before publication.

Ethical considerations require informed consent, humane treatment of animals, and safe disposal of chemicals.

Reaction profile diagrams show activation energy as the height from reactants to the peak.

Exothermic profiles have products lower in energy than reactants; endothermic profiles have products higher.

A catalyst lowers the activation energy peak but does not change the overall energy change.

Increasing surface area exposes more particles to collisions, increasing reaction rate.

Increasing concentration or pressure increases the frequency of collisions and the rate.

Bond breaking requires energy; bond forming releases energy.

Reversible reactions reach equilibrium when forward and reverse rates are equal.