Ehime Entrance Science cheat sheet

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

Newton's second law: F = ma; net force and acceleration share direction. Weight W = mg with g ≈ 9.8 m/s².

Work and energy: W = Fd cosθ, kinetic energy ½mv², gravitational potential energy mgh; mechanical energy conserved without friction.

Momentum p = mv is conserved in collisions; perfectly inelastic collisions merge masses, elastic collisions conserve kinetic energy.

Waves: v = fλ; for a string or pipe, boundary conditions fix allowed wavelengths (open pipe λ = 2L/n, closed pipe λ = 4L/(2n−1)).

Ohm's law V = IR; series resistances add, parallel conductances add (1/R = 1/R₁ + 1/R₂); power P = VI = I²R.

Refraction obeys Snell's law n₁sinθ₁ = n₂sinθ₂; total internal reflection occurs beyond the critical angle sinθc = n₂/n₁.

Heat: Q = mcΔT for temperature change, Q = mL at phase change; ideal gas PV = nRT with T in kelvin.

Amount of substance: n = m/M = N/N_A = V/22.4 L at STP for gases; molarity c = n/V(L).

Balanced equations give mole ratios; limiting reagent is the reactant producing the least product.

Acid-base: pH = −log[H⁺]; strong acid/base fully dissociates, weak ones use Ka or Kb; neutralization H⁺ + OH⁻ → H₂O.

Redox: oxidation is loss of electrons (increase in oxidation number); assign oxidation numbers by electronegativity and sum rules.

Periodic trends: atomic radius decreases across a period and increases down a group; ionization energy and electronegativity show the reverse.

Bonding: ionic between metal and nonmetal, covalent between nonmetals, metallic in metals; polarity depends on electronegativity difference and geometry.

Le Chatelier's principle: raising concentration of a reactant, raising pressure for gas reactions, or shifting temperature favors the endothermic direction when heated.

Organic functional groups: alcohols –OH, aldehydes –CHO, carboxylic acids –COOH, esters –COO–; combustion of hydrocarbons gives CO₂ and H₂O.

Cell theory: all organisms are made of cells, cells arise from existing cells; prokaryotes lack a nucleus, eukaryotes have membrane-bound organelles.

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ in chloroplasts; light reactions make ATP and NADPH, the Calvin cycle fixes CO₂.

Cellular respiration: glycolysis in cytoplasm, then Krebs cycle and electron transport in mitochondria; net ATP yield is far higher with oxygen.

DNA replication is semiconservative; transcription makes mRNA from DNA, translation at ribosomes uses codons paired with tRNA anticodons.

Mendel's laws: segregation of alleles and independent assortment; test cross reveals genotype, and dominance determines phenotype ratios.

Homeostasis uses negative feedback: sensors detect deviation, effectors restore the set point (e.g., insulin lowers blood glucose).

Natural selection requires heritable variation and differential reproductive success; it acts on phenotypes, changing allele frequencies.

Ecosystem energy flow: producers capture light, about 10% transfers between trophic levels; decomposers recycle nutrients.

Earth's interior: crust, mantle, outer core (liquid, generates the magnetic field by dynamo action), inner core (solid iron-nickel).

Plate tectonics: divergent boundaries create ocean ridges, convergent boundaries produce subduction and volcanoes, transform boundaries cause earthquakes.

Seismic waves: P waves are longitudinal and travel through solids and liquids; S waves are transverse and cannot pass through liquids.

Rock types: igneous from cooling magma, sedimentary from deposition and lithification, metamorphic from heat and pressure; the rock cycle links them.

Weathering and erosion: mechanical (frost, roots) and chemical (dissolution, oxidation) break rock; transport moves sediment.

Earth's rotation causes day/night and apparent star motion; revolution plus 23.4° axial tilt causes seasons.

Moon phases follow the synodic month (~29.5 days); solar eclipses occur at new moon, lunar eclipses at full moon.

Atmosphere: temperature falls with altitude in the troposphere, rises in the stratosphere where ozone absorbs ultraviolet; winds flow from high to low pressure.