Fukushima Entrance Science cheat sheet

Newton's second law: net force equals mass times acceleration (F = ma); acceleration is always in the direction of the net force.

Kinetic energy is ½mv²; gravitational potential energy near Earth's surface is mgh; total mechanical energy is conserved when only gravity does work.

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

Momentum p = mv is conserved in any collision with no external net force; kinetic energy is conserved only in elastic collisions.

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

For resistors in series, current is the same and resistances add; in parallel, voltage is the same and reciprocals of resistance add.

Wave relation v = fλ: frequency is fixed by the source, and speed changes with the medium, so wavelength changes when speed changes.

Snell's law n₁sinθ₁ = n₂sinθ₂; light bending toward the normal means it entered a medium with a larger refractive index.

Mole relation: n = m/M, where m is mass in grams and M is molar mass in g/mol; one mole contains 6.02 × 10²³ particles.

Molarity M = moles of solute / liters of solution; dilution follows M₁V₁ = M₂V₂ because solute moles stay constant.

Ideal gas law PV = nRT with R = 8.31 J/(mol·K); at constant T and n, pressure and volume are inversely proportional.

pH = −log[H⁺]; a change of one pH unit means a tenfold change in hydrogen ion concentration.

Oxidation is loss of electrons and increase in oxidation number; reduction is gain of electrons and decrease in oxidation number.

Le Chatelier's principle: raising temperature favors the endothermic direction, raising pressure favors the side with fewer gas moles.

Strong acids and bases ionize essentially completely; weak ones ionize partially, so equal concentrations give different pH values.

Balancing equations conserves atoms of each element; ionic charge must also balance in half-reactions and net ionic equations.

Cell theory: all living things are made of cells, the cell is the basic unit of life, and new cells arise from existing cells.

Mitochondria carry out aerobic respiration producing ATP; chloroplasts carry out photosynthesis; neither is present in prokaryotic cells.

DNA replication is semiconservative; transcription makes mRNA from a DNA template, and translation at ribosomes builds protein from codons.

In Mendelian crosses, a monohybrid cross of two heterozygotes gives a 3:1 phenotype ratio and a 1:2:1 genotype ratio.

Enzymes lower activation energy and are not consumed; activity peaks near an optimum temperature and pH and falls when the enzyme denatures.

Photosynthesis: 6CO₂ + 6H₂O + light energy → C₆H₁₂O₆ + 6O₂, with light reactions in the thylakoid membrane and the Calvin cycle in the stroma.

Diffusion moves particles down a concentration gradient without energy input; active transport moves them against the gradient and requires ATP.

In meiosis, homologous chromosomes separate in meiosis I and sister chromatids separate in meiosis II, producing four haploid cells.

Earth's internal layers are crust, mantle, and core; the outer core is liquid, which is why it generates the magnetic field by dynamo action.

Plate tectonics: divergent boundaries create new crust at mid-ocean ridges, convergent boundaries produce subduction and volcanoes, transform boundaries cause earthquakes.

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

Kepler's third law: the square of orbital period is proportional to the cube of the semimajor axis (T² ∝ a³) when T is in years and a in AU.

Earth's seasons are caused by the 23.4° axial tilt, not by changing distance from the Sun.

The Moon's phases result from the changing angle between Earth, Moon, and Sun; a solar eclipse requires the Moon at new phase near a node.

Rock types: igneous forms from cooling magma or lava, sedimentary from compaction of deposits, metamorphic from heat and pressure on existing rock.

Relative dating uses superposition (older layers below) and cross-cutting relationships (a fault is younger than the rock it cuts).