Akita Entrance Science cheat sheet

Uniform acceleration: v = u + at, s = ut + ½at², v² = u² + 2as; these three equations apply only when acceleration is constant.

Newton's second law: F_net = ma; weight is W = mg, and mass (kg) stays constant while weight (N) changes with local g.

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

Work W = Fd cosθ and power P = W/t = Fv; energy converts between kinetic (½mv²) and gravitational potential (mgh) with no loss in ideal systems.

Ohm's law V = IR with series resistances adding (R = R₁ + R₂) and parallel resistances adding reciprocally (1/R = 1/R₁ + 1/R₂).

Wave relation v = fλ; for a wave crossing into a new medium the frequency stays fixed while speed and wavelength change.

Snell's law n₁sinθ₁ = n₂sinθ₂, with refractive index n = c/v; total internal reflection occurs only when light moves from denser to less dense medium.

Pressure in a fluid P = P₀ + ρgh, and Archimedes' principle: buoyant force equals the weight of displaced fluid.

Mole relations: n = m/M, n = N/N_A (N_A = 6.02 × 10²³ mol⁻¹), and at STP one mole of ideal gas occupies about 22.4 L.

Balancing equations conserves atoms; use coefficients to convert between substances via mole ratios, never by direct mass ratio.

pH = −log₁₀[H⁺]; each unit change means a tenfold change in hydrogen-ion concentration, and pH + pOH = 14 at 25 °C.

Strong acids and bases dissociate almost completely; weak ones reach equilibrium described by K_a, where smaller K_a means weaker acid.

Oxidation is loss of electrons (increase in oxidation number); reduction is gain of electrons, and both always occur together.

Ionic bonds form by electron transfer between metal and nonmetal; covalent bonds form by electron sharing, usually between nonmetals.

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

Periodic trends: atomic radius decreases across a period and increases down a group; electronegativity and ionisation energy show the opposite pattern.

Cell theory: all organisms are made of cells, cells arise from existing cells, and the cell is the basic unit of structure and function.

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

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts; cellular respiration reverses this to release ATP.

Enzymes are biological catalysts that lower activation energy; each has an optimum temperature and pH, and denatures when these are exceeded.

DNA replication is semi-conservative; transcription makes mRNA from DNA, and translation at ribosomes assembles amino acids using codons.

Mendelian inheritance: a monohybrid cross of heterozygotes gives a 3:1 phenotype ratio and a 1:2:1 genotype ratio.

Mitosis produces two genetically identical diploid cells for growth; meiosis produces four genetically varied haploid gametes.

Homeostasis uses negative feedback: a deviation from the set point triggers a response that reverses the deviation, as in body-temperature control.

Earth's layered structure: crust, mantle, outer core (liquid), and inner core (solid); seismic S-waves cannot pass through the liquid outer core.

Plate tectonics: divergent boundaries create new crust, convergent boundaries cause subduction and mountain building, and transform boundaries cause earthquakes.

The rock cycle links igneous (cooled magma), sedimentary (compacted deposits), and metamorphic (heat and pressure) rocks.

Earth rotates west to east once in about 24 hours, causing day and night; it orbits the Sun once in about 365.25 days, causing seasons with axial tilt.

The Moon's phases arise from changing angles between Earth, Moon, and Sun; a lunar eclipse requires a full moon and a solar eclipse a new moon.

Kepler's third law: T² ∝ a³, so a planet farther from the Sun has a longer orbital period.

The solar system's order from the Sun is Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, with rocky planets inner and gas giants outer.

Weathering breaks rock in place; erosion transports the debris; deposition lays it down, and each process shapes landforms differently.

The independent variable is deliberately changed, the dependent variable is measured, and controlled variables are held constant.

A valid experiment includes a control group and repeated trials; a single trial cannot establish reliability.

A hypothesis must be testable and falsifiable; a prediction states an expected measurable outcome if the hypothesis is true.

Correlation does not establish causation; a confounding variable may explain an observed association.

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

Random and systematic errors differ: random error scatters results and averages out, systematic error shifts all results in one direction.

A conclusion must be based on the data collected and should state whether results support or refute the hypothesis, not merely restate it.

Graph choice: line graphs show continuous change, bar charts compare categories, and the independent variable goes on the horizontal axis.