MTEL General Science (64) cheat sheet

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

Valid experiment requires a control group or baseline condition, a testable hypothesis, and repetition or adequate sample size to reduce random error.

Accuracy is closeness to the true value; precision is closeness of repeated measurements to one another. Systematic error shifts accuracy; random error limits precision.

Mean = sum of values divided by n. Median is the middle value of ordered data; resistant to outliers. Mode is the most frequent value.

SI base units: meter (length), kilogram (mass), second (time), ampere (current), kelvin (temperature), mole (amount), candela (luminous intensity).

Density = mass/volume (kg/m³). Percent error = |measured − accepted| / accepted × 100. Percent yield = actual/theoretical × 100.

Significant figures: all nonzero digits count; zeros between nonzero digits count; leading zeros do not; trailing zeros count only with a decimal point. Addition keeps least decimal places; multiplication keeps least sig figs.

Scientific method sequence: observation, question, hypothesis, prediction, experiment, analysis, conclusion, communication. A hypothesis must be falsifiable.

Metric prefixes: kilo (10³), centi (10⁻²), milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹), pico (10⁻¹²).

Atomic number = protons; mass number = protons + neutrons. Isotopes share atomic number but differ in neutron count; ions differ in electron count.

Electron configuration fills aufbau order (1s 2s 2p 3s 3p 4s 3d...); valence electrons determine group chemistry and periodic trends.

Periodic trends: atomic radius decreases left-to-right and increases top-to-bottom; ionization energy and electronegativity increase left-to-right and up a group.

Three main bond types: ionic (metal + nonmetal, electron transfer), covalent (nonmetals, sharing), metallic (delocalized electron sea).

Conservation of mass in chemical equations; balance by adjusting coefficients, never subscripts.

Mole concept: 1 mol = 6.022 × 10²³ particles = molar mass in grams. Molarity = moles solute / liters solution.

pH = −log[H⁺]; pH < 7 acidic, 7 neutral, > 7 basic. Strong acid + strong base neutralizes to salt and water.

Phase changes: melting, freezing, vaporization, condensation, sublimation, deposition. Energy absorbed on melting and vaporization; released on freezing and condensation.

Newton's laws: (1) inertia - object stays at rest or constant velocity unless net force acts; (2) F = ma; (3) every action has an equal and opposite reaction.

Kinematics: v = v₀ + at; d = v₀t + ½at²; v² = v₀² + 2ad. Acceleration due to gravity near Earth's surface ≈ 9.8 m/s².

Work = force × distance × cos θ; power = work/time. Kinetic energy = ½mv²; gravitational potential energy = mgh.

Conservation of energy: energy transforms between forms but total energy is constant in a closed system; friction dissipates mechanical energy as heat.

Momentum p = mv; in an isolated system total momentum is conserved in collisions (elastic: kinetic energy conserved; inelastic: not).

Circular motion requires centripetal force directed toward center; F = mv²/r.

Simple machines (lever, pulley, inclined plane, wedge, screw, wheel and axle) trade force for distance; ideal mechanical advantage = effort distance / resistance distance.

Electric current I = V/R (Ohm's law); power P = IV. Series circuits share current; parallel circuits share voltage.

Wave equation: v = fλ. Frequency is set by the source; speed is set by the medium.

Transverse waves oscillate perpendicular to propagation (light); longitudinal waves oscillate parallel (sound).

Sound requires a medium; speed is highest in solids, lowest in gases. Pitch corresponds to frequency; loudness to amplitude.

Reflection angle equals incidence angle. Refraction occurs when waves change speed at a boundary; Snell's law: n₁ sin θ₁ = n₂ sin θ₂.

Electromagnetic spectrum in order of increasing frequency: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.

Visible light order by increasing frequency: red, orange, yellow, green, blue, indigo, violet. Red has longest wavelength.

Convex lens converges light (real or virtual image); concave lens diverges. Real images are inverted and can be projected.

Static electricity: like charges repel, opposite attract; charging by friction, conduction, or induction. Electric field lines point away from positive charge.

Earth's layers: crust, mantle, outer core (liquid), inner core (solid). Plate tectonics driven by mantle convection; boundaries are divergent, convergent, transform.

Rock types: igneous (cooled magma/lava), sedimentary (compacted deposited material), metamorphic (heat and pressure altered). Rock cycle links all three.

Earth's rotation (≈24 h) causes day/night; revolution (≈365.25 days) with 23.5° axial tilt causes seasons.

Moon phases result from changing Sun-Earth-Moon geometry; cycle ≈29.5 days. Solar eclipse at new moon; lunar eclipse at full moon.

Water cycle: evaporation, transpiration, condensation, precipitation, runoff, infiltration, groundwater.

Weathering breaks rock (physical/chemical); erosion transports sediment; deposition builds landforms.

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

Relative dating uses superposition (oldest layers at bottom) and cross-cutting relationships; radiometric dating gives absolute ages.

Cell theory: all living things are made of cells; cells arise from existing cells; the cell is the basic unit of life. Prokaryotes lack a nucleus; eukaryotes have membrane-bound organelles.

Mitochondria produce ATP via cellular respiration; chloroplasts perform photosynthesis (6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂).

DNA structure: double helix of nucleotides (A-T, C-G). Replication is semiconservative; transcription makes mRNA; translation at ribosomes builds protein.

Mendelian genetics: dominant and recessive alleles; Punnett squares predict genotype and phenotype ratios (e.g., 3:1 phenotype for monohybrid cross).

Natural selection requires variation, heritability, and differential reproductive success; leads to adaptation over generations.

Ecosystem trophic levels: producers, primary consumers, secondary consumers, decomposers. Energy decreases ~90% per level (10% rule).

Homeostasis maintains stable internal conditions via feedback loops (e.g., negative feedback in body temperature and blood glucose).

Photosynthesis occurs in chloroplasts; cellular respiration in mitochondria. Both involve energy conversion and electron transport.

Classification hierarchy: domain, kingdom, phylum, class, order, family, genus, species. Binomial nomenclature uses genus and species.

Crosscutting concepts: patterns, cause and effect, scale/proportion, systems, energy and matter flows, structure and function, stability and change.

Science and engineering practices include asking questions, developing models, planning investigations, analyzing data, using math, constructing explanations, arguing from evidence, and communicating.

Graph interpretation: slope of a distance-time graph = speed; slope of a velocity-time graph = acceleration; area under velocity-time graph = displacement.

Data tables and graphs should label axes with units, use appropriate scales, and select graph type by data (bar for categories, line for trends, scatter for correlation).

Scientific models are simplifications; they have limits and are revised as evidence accumulates.

Correlation does not imply causation; controlled experiments or longitudinal studies help establish causal claims.

Engineering design cycle: define problem, research, prototype, test, iterate. Constraints include cost, safety, and materials.

Interpreting claims: evaluate sample size, control groups, peer review, replication, and potential bias before accepting conclusions.