Gifu Entrance Science cheat sheet

Uniform acceleration: v = v₀ + at, x = v₀t + ½at², v² = v₀² + 2ax; these three apply only when acceleration is constant.

Newton's second law in vector form: ΣF = ma; on an incline of angle θ, the downslope component of gravity is mg sin θ and the normal force is mg cos θ.

Static friction satisfies f ≤ μsN and adjusts to the applied force; kinetic friction equals μkN and opposes relative sliding.

Work–energy theorem: W_net = ΔKE = ½mv² − ½mv₀²; for a spring, elastic potential energy is ½kx².

Conservation of mechanical energy holds only when non-conservative forces do zero work; otherwise ΔE_mech = W_friction.

Momentum p = mv is conserved in any collision; kinetic energy is conserved only in elastic collisions, and perfectly inelastic collisions share a common final velocity.

Impulse J = FΔt = Δp, so a longer collision time reduces the average force for the same momentum change.

Centripetal acceleration a = v²/r points toward the center; the centripetal force is the net inward force, not an extra force.

Wave speed v = fλ; for a stretched string v = √(T/μ), and for sound in air v depends mainly on temperature, not on frequency.

Snell's law: n₁ sin θ₁ = n₂ sin θ₂, with n = c/v; total internal reflection occurs only when light travels from a denser to a less dense medium beyond the critical angle.

Ohm's law V = IR holds for ohmic resistors at constant temperature; power dissipated is P = VI = I²R = V²/R.

Series: R_total = ΣR and current is the same everywhere. Parallel: 1/R_total = Σ(1/R) and voltage is the same across each branch.

Kirchhoff's rules: junction rule (charge conservation) and loop rule (energy conservation per closed loop).

A straight current-carrying wire produces a magnetic field B = μ₀I/(2πr); a charge moving parallel to B experiences zero magnetic force (F = qvB sin θ).

First law of thermodynamics: ΔU = Q − W, where W is work done by the gas; for an ideal gas U depends only on temperature.

Isothermal work of an ideal gas is W = nRT ln(V₂/V₁); adiabatic processes have Q = 0, so ΔU = −W.

Carnot efficiency η = 1 − T_cold/T_hot with absolute temperatures; no engine operating between two reservoirs can exceed it.

An element's position follows its electron configuration: period = highest principal quantum number, group = valence electron count for main-group elements.

Ionic bonds form between metals and nonmetals by electron transfer; lattice energy increases with higher ionic charge and smaller ionic radius.

Covalent bonds share electron pairs; electronegativity difference roughly < 0.4 is nonpolar, 0.4–1.7 polar covalent, > 1.7 largely ionic.

VSEPR: electron pairs repel and adopt arrangements minimizing repulsion; lone pairs repel more strongly than bonding pairs, compressing bond angles.

Molecular polarity requires polar bonds plus an asymmetric geometry; CO₂ is nonpolar while H₂O is polar despite both having polar bonds.

Intermolecular forces rank roughly H-bonding > dipole–dipole > London dispersion; dispersion grows with electron count and surface area.

Ideal gas law PV = nRT; at STP (0 °C, 1 atm) one mole of ideal gas occupies about 22.4 L.

Le Chatelier's principle: a system at equilibrium shifts to partially offset a change in concentration, pressure, or temperature; catalysts change rate, not position.

Balancing conserves atoms and charge; in redox, oxidation number increases on oxidation and decreases on reduction.

Mole relationships come from balanced coefficients: n = m/M, and concentration c = n/V in mol/L.

Equilibrium constant K depends only on temperature; Q < K favors the forward reaction, Q > K favors the reverse.

For acids and bases, pH = −log[H⁺]; strong acids ionize completely while weak acids obey Ka = [H⁺][A⁻]/[HA].

Neutralization of a strong acid with a strong base gives pH 7 at the equivalence point; weak acid–strong base titrations end basic.

Activity series predicts single-displacement reactions: a metal displaces ions of metals below it in the series.

Organic functional groups: alcohols (−OH), aldehydes (−CHO), ketones (C=O between carbons), carboxylic acids (−COOH), esters (−COO−).

Addition reactions saturate alkenes; substitution is typical of alkanes and of benzene rings; esters form from carboxylic acid plus alcohol with water eliminated.

Prokaryotes lack a membrane-bound nucleus and organelles; eukaryotes have a nucleus, mitochondria, and (in plants) chloroplasts and a cell wall.

Mitochondria carry out aerobic respiration and chloroplasts photosynthesis; both contain their own DNA and ribosomes.

Mitosis produces two genetically identical diploid cells; meiosis produces four haploid cells with crossing over in prophase I.

DNA replication is semiconservative; base pairing is A–T and G–C, and transcription copies DNA into mRNA for translation at ribosomes.

Mendel's law of segregation: alleles separate during gamete formation; independent assortment applies to genes on different chromosomes.

A monohybrid cross of heterozygotes gives a 3:1 phenotype ratio; a testcross with a homozygous recessive reveals an unknown genotype.

Sex-linked traits on the X chromosome appear more often in males, who have only one X and therefore express a single recessive allele.

Codominance and incomplete dominance produce intermediate or dual phenotypes rather than simple dominance ratios.

Negative feedback opposes a deviation and stabilizes internal conditions; positive feedback amplifies a change, as in childbirth contractions.

Human body temperature is regulated near 37 °C by hypothalamic control of sweating, shivering, and blood flow to the skin.

Insulin lowers blood glucose and glucagon raises it; blood glucose is also regulated by kidney reabsorption and liver glycogen stores.

Energy flows one way through trophic levels, while matter cycles; roughly 10 % of energy transfers to the next trophic level.

Population growth is exponential when resources are unlimited and logistic when a carrying capacity applies.

Natural selection requires heritable variation, differential reproductive success, and change across generations.

Homologous structures indicate common ancestry, analogous structures indicate convergent evolution, and the fossil record plus molecular data support phylogenies.

Genetic drift and gene flow change allele frequencies independently of natural selection; small populations are most affected by drift.

Earth's interior is layered: crust, mantle, outer core (liquid), and inner core (solid); seismic S-waves do not travel through liquids, revealing the liquid outer core.

Plate boundaries: divergent (new crust, mid-ocean ridges), convergent (subduction or mountain building), transform (lateral sliding, earthquakes).

Relative dating uses superposition and cross-cutting relationships; radiometric dating gives absolute ages from parent–daughter isotope ratios.

Weathering breaks rock in place, erosion transports it, and deposition builds sedimentary layers; metamorphism alters rock under heat and pressure.

Air pressure decreases with altitude; wind flows from high to low pressure, deflected by the Coriolis effect (right in the Northern Hemisphere).

Clouds form when rising air cools to the dew point; relative humidity reaches 100 % at saturation, and condensation needs condensation nuclei.

Kepler's third law: T² ∝ a³, so distant planets have longer orbital periods; gravity provides the centripetal force for orbits.

Moon phases arise from the changing Sun–Earth–Moon angle; solar eclipses occur at new moon, lunar eclipses at full moon.

Independent variable is manipulated by the experimenter; dependent variable is measured; controlled variables are held constant.

A control group receives no treatment or a placebo so the effect of the treatment can be isolated.

Accuracy is closeness to the true value; precision is repeatability of measurements; random errors scatter, systematic errors shift all readings.

Significant figures in a result follow the least precise measurement; addition uses decimal places, multiplication uses total significant figures.

A hypothesis must be testable and falsifiable; a single experiment supports or refutes but does not prove it.

Correlation does not establish causation; confounding variables can create apparent relationships.

When interpreting a graph, read slope as rate of change and area under the curve as accumulated quantity; label axes and units before drawing conclusions.

Sample size and repetition reduce the influence of random variation; large differences with small samples warrant caution.

Uniform acceleration: v = v₀ + at, x = v₀t + ½at², v² = v₀² + 2ax; these three apply only when acceleration is constant.

Newton's second law in vector form: ΣF = ma; on an incline of angle θ, the downslope component of gravity is mg sin θ and the normal force is mg cos θ.

Static friction satisfies f ≤ μsN and adjusts to the applied force; kinetic friction equals μkN and opposes relative sliding.

Work–energy theorem: W_net = ΔKE = ½mv² − ½mv₀²; for a spring, elastic potential energy is ½kx².

Conservation of mechanical energy holds only when non-conservative forces do zero work; otherwise ΔE_mech = W_friction.

Momentum p = mv is conserved in any collision; kinetic energy is conserved only in elastic collisions, and perfectly inelastic collisions share a common final velocity.

Impulse J = FΔt = Δp, so a longer collision time reduces the average force for the same momentum change.

Centripetal acceleration a = v²/r points toward the center; the centripetal force is the net inward force, not an extra force.

Wave speed v = fλ; for a stretched string v = √(T/μ), and for sound in air v depends mainly on temperature, not on frequency.

Snell's law: n₁ sin θ₁ = n₂ sin θ₂, with n = c/v; total internal reflection occurs only when light travels from a denser to a less dense medium beyond the critical angle.

Ohm's law V = IR holds for ohmic resistors at constant temperature; power dissipated is P = VI = I²R = V²/R.

Series: R_total = ΣR and current is the same everywhere. Parallel: 1/R_total = Σ(1/R) and voltage is the same across each branch.

Kirchhoff's rules: junction rule (charge conservation) and loop rule (energy conservation per closed loop).

A straight current-carrying wire produces a magnetic field B = μ₀I/(2πr); a charge moving parallel to B experiences zero magnetic force (F = qvB sin θ).

First law of thermodynamics: ΔU = Q − W, where W is work done by the gas; for an ideal gas U depends only on temperature.

Isothermal work of an ideal gas is W = nRT ln(V₂/V₁); adiabatic processes have Q = 0, so ΔU = −W.

Carnot efficiency η = 1 − T_cold/T_hot with absolute temperatures; no engine operating between two reservoirs can exceed it.

An element's position follows its electron configuration: period = highest principal quantum number, group = valence electron count for main-group elements.

Ionic bonds form between metals and nonmetals by electron transfer; lattice energy increases with higher ionic charge and smaller ionic radius.

Covalent bonds share electron pairs; electronegativity difference roughly < 0.4 is nonpolar, 0.4–1.7 polar covalent, > 1.7 largely ionic.

VSEPR: electron pairs repel and adopt arrangements minimizing repulsion; lone pairs repel more strongly than bonding pairs, compressing bond angles.

Molecular polarity requires polar bonds plus an asymmetric geometry; CO₂ is nonpolar while H₂O is polar despite both having polar bonds.

Intermolecular forces rank roughly H-bonding > dipole–dipole > London dispersion; dispersion grows with electron count and surface area.

Ideal gas law PV = nRT; at STP (0 °C, 1 atm) one mole of ideal gas occupies about 22.4 L.

Le Chatelier's principle: a system at equilibrium shifts to partially offset a change in concentration, pressure, or temperature; catalysts change rate, not position.

Balancing conserves atoms and charge; in redox, oxidation number increases on oxidation and decreases on reduction.

Mole relationships come from balanced coefficients: n = m/M, and concentration c = n/V in mol/L.

Equilibrium constant K depends only on temperature; Q < K favors the forward reaction, Q > K favors the reverse.

For acids and bases, pH = −log[H⁺]; strong acids ionize completely while weak acids obey Ka = [H⁺][A⁻]/[HA].

Neutralization of a strong acid with a strong base gives pH 7 at the equivalence point; weak acid–strong base titrations end basic.

Activity series predicts single-displacement reactions: a metal displaces ions of metals below it in the series.

Organic functional groups: alcohols (−OH), aldehydes (−CHO), ketones (C=O between carbons), carboxylic acids (−COOH), esters (−COO−).

Addition reactions saturate alkenes; substitution is typical of alkanes and of benzene rings; esters form from carboxylic acid plus alcohol with water eliminated.

Prokaryotes lack a membrane-bound nucleus and organelles; eukaryotes have a nucleus, mitochondria, and (in plants) chloroplasts and a cell wall.

Mitochondria carry out aerobic respiration and chloroplasts photosynthesis; both contain their own DNA and ribosomes.

Mitosis produces two genetically identical diploid cells; meiosis produces four haploid cells with crossing over in prophase I.

DNA replication is semiconservative; base pairing is A–T and G–C, and transcription copies DNA into mRNA for translation at ribosomes.

Mendel's law of segregation: alleles separate during gamete formation; independent assortment applies to genes on different chromosomes.

A monohybrid cross of heterozygotes gives a 3:1 phenotype ratio; a testcross with a homozygous recessive reveals an unknown genotype.

Sex-linked traits on the X chromosome appear more often in males, who have only one X and therefore express a single recessive allele.

Codominance and incomplete dominance produce intermediate or dual phenotypes rather than simple dominance ratios.

Negative feedback opposes a deviation and stabilizes internal conditions; positive feedback amplifies a change, as in childbirth contractions.

Human body temperature is regulated near 37 °C by hypothalamic control of sweating, shivering, and blood flow to the skin.

Insulin lowers blood glucose and glucagon raises it; blood glucose is also regulated by kidney reabsorption and liver glycogen stores.

Energy flows one way through trophic levels, while matter cycles; roughly 10 % of energy transfers to the next trophic level.

Population growth is exponential when resources are unlimited and logistic when a carrying capacity applies.

Natural selection requires heritable variation, differential reproductive success, and change across generations.

Homologous structures indicate common ancestry, analogous structures indicate convergent evolution, and the fossil record plus molecular data support phylogenies.

Genetic drift and gene flow change allele frequencies independently of natural selection; small populations are most affected by drift.

Earth's interior is layered: crust, mantle, outer core (liquid), and inner core (solid); seismic S-waves do not travel through liquids, revealing the liquid outer core.

Plate boundaries: divergent (new crust, mid-ocean ridges), convergent (subduction or mountain building), transform (lateral sliding, earthquakes).

Relative dating uses superposition and cross-cutting relationships; radiometric dating gives absolute ages from parent–daughter isotope ratios.

Weathering breaks rock in place, erosion transports it, and deposition builds sedimentary layers; metamorphism alters rock under heat and pressure.

Air pressure decreases with altitude; wind flows from high to low pressure, deflected by the Coriolis effect (right in the Northern Hemisphere).

Clouds form when rising air cools to the dew point; relative humidity reaches 100 % at saturation, and condensation needs condensation nuclei.

Kepler's third law: T² ∝ a³, so distant planets have longer orbital periods; gravity provides the centripetal force for orbits.

Moon phases arise from the changing Sun–Earth–Moon angle; solar eclipses occur at new moon, lunar eclipses at full moon.

Independent variable is manipulated by the experimenter; dependent variable is measured; controlled variables are held constant.

A control group receives no treatment or a placebo so the effect of the treatment can be isolated.

Accuracy is closeness to the true value; precision is repeatability of measurements; random errors scatter, systematic errors shift all readings.

Significant figures in a result follow the least precise measurement; addition uses decimal places, multiplication uses total significant figures.

A hypothesis must be testable and falsifiable; a single experiment supports or refutes but does not prove it.

Correlation does not establish causation; confounding variables can create apparent relationships.

When interpreting a graph, read slope as rate of change and area under the curve as accumulated quantity; label axes and units before drawing conclusions.

Sample size and repetition reduce the influence of random variation; large differences with small samples warrant caution.