Praxis General Science cheat sheet

A hypothesis is a testable, falsifiable prediction; a theory is a broad explanation supported by many independent lines of evidence; a law describes a consistent observed pattern (often mathematically). Theories do not 'graduate' into laws.

Experimental design: the independent variable is deliberately manipulated, the dependent variable is measured, controlled variables are held constant, and a control group provides the baseline comparison.

Validity means the procedure measures what it claims to measure; reliability means repeated trials give consistent results. Precise but inaccurate data are reliable yet invalid.

Bias-reduction tools: random assignment, random sampling, placebo controls, single- and double-blind procedures, and adequate sample size. Correlation alone does not establish causation.

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

Useful conversions and formulas: 1 km = 1000 m, 1 mL = 1 cm^3, 1 kg = 1000 g; percent error = |measured - accepted| / accepted x 100%; density = mass / volume.

Engineering design cycle: define the problem, identify criteria and constraints, brainstorm and prototype solutions, test and collect data, then iterate. Optimization always involves trade-offs (cost, safety, durability, environmental impact).

Risk assessment compares the probability and severity of harm against benefits; decisions may involve cost-benefit analysis, and technologies often produce unintended consequences alongside intended ones.

Scientific claims gain standing through peer review and independent replication; anecdotal evidence and appeals to authority are not substitutes for controlled data.

Kinematics (constant acceleration): v = v0 + at; d = v0t + (1/2)at^2; v^2 = v0^2 + 2ad. Near Earth's surface g is about 9.8 m/s^2 downward for free-falling objects.

Newton's laws: (1) an object stays at rest or in uniform motion unless a net force acts; (2) F_net = ma; (3) every action has an equal and opposite reaction on a different object. Weight = mg.

Energy and work: KE = (1/2)mv^2, gravitational PE = mgh; total mechanical energy is conserved without friction; work = Fd cos(theta); power = work / time. Momentum p = mv is conserved when no external net force acts.

Electricity: Ohm's law V = IR; power P = IV = I^2R; series resistances add and current is shared equally, while parallel branches share the same voltage and add as 1/R_total = 1/R1 + 1/R2.

Waves: v = f x wavelength; frequency is set by the source and speed by the medium; sound requires a medium, light does not (c is about 3 x 10^8 m/s). Refraction occurs when wave speed changes at a boundary.

Atomic structure: atomic number = protons (defines the element); mass number = protons + neutrons; isotopes differ in neutrons; ions differ in electrons. Group number for main-group elements equals valence electrons.

Mole concept: 1 mol = 6.02 x 10^23 particles; molar mass in g/mol converts mass to moles; molarity = moles of solute / liters of solution; a balanced equation gives mole ratios for stoichiometry.

Acids and bases: pH = -log[H+], so each unit is a tenfold change; pH < 7 acidic, 7 neutral, > 7 basic; acid + base neutralizes to salt and water. Strong acids and bases dissociate completely.

Thermal and matter formulas: q = mc(delta T) for heat change, density = m/V, and during a phase change temperature stays constant while latent heat is absorbed or released.

Cell theory: all organisms are composed of one or more cells, the cell is the basic unit of life, and all cells come from preexisting cells. Prokaryotes lack a nucleus; eukaryotes have membrane-bound organelles.

Organelle roles: nucleus stores DNA, ribosomes build proteins, mitochondria release ATP, chloroplasts carry out photosynthesis, and the cell membrane regulates transport via diffusion, osmosis, and active transport.

Macromolecules: carbohydrates (quick energy, structural sugars), lipids (energy storage, membranes, hormones), proteins (amino acids; enzymes and structure), nucleic acids (DNA and RNA; information).

Central dogma: DNA replication is semi-conservative (A pairs with T, G with C); transcription makes mRNA in the nucleus; translation at the ribosome reads three-base codons into amino acids.

Photosynthesis: 6CO2 + 6H2O + light energy gives C6H12O6 + 6O2. Aerobic respiration reverses this to release ATP (about 36-38 ATP per glucose) versus about 2 ATP anaerobically.

Mitosis yields two genetically identical diploid cells for growth and repair; meiosis involves two divisions and yields four haploid, genetically varied gametes, with crossing over in prophase I.

Mendelian genetics: dominant alleles mask recessive ones in heterozygotes; a monohybrid cross of two heterozygotes gives a 3:1 phenotype ratio and 1:2:1 genotype ratio; a testcross reveals an unknown genotype.

Evolution by natural selection requires heritable variation, differential reproductive success, and environmental pressure; mutation, gene flow, and genetic drift also change allele frequencies.

Ecology and regulation: energy pyramids transfer roughly 10% per trophic level; populations are limited by carrying capacity; homeostasis is maintained mainly by negative feedback, and enzymes are substrate-specific and denature at extreme heat or pH.

Earth's interior layers: crust, mantle, liquid outer core, solid inner core. S-waves cannot travel through liquids, which is key evidence that the outer core is liquid.

Plate boundaries: divergent (new crust forms at mid-ocean ridges), convergent (subduction, trenches, mountains, volcanoes), transform (lateral sliding, as at the San Andreas Fault). Most earthquakes and volcanoes occur at boundaries.

Rock types: igneous forms from cooling magma or lava, sedimentary from compaction and cementation of sediments (the only type that commonly preserves fossils), and metamorphic from heat and pressure. The rock cycle links all three.

Surface processes: weathering breaks rock in place, erosion transports the material, and deposition lays it down. The water cycle moves water via evaporation, transpiration, condensation, precipitation, and runoff.

Seasons are caused by Earth's 23.5-degree axial tilt changing sun angle and day length, not by distance from the Sun. Solstices mark maximum tilt toward or away from the Sun; equinoxes have roughly equal day and night.

Moon phases result from the Moon's orbital position relative to Earth and Sun; tides are produced mainly by the Moon's gravity with a secondary solar contribution, giving spring and neap tides.

Solar system: four inner terrestrial planets, an asteroid belt, then gas giants and ice giants. Kepler's laws state that orbits are ellipses, equal areas are swept in equal times, and T^2 is proportional to a^3.

Stars: plotted on the H-R diagram by luminosity versus temperature; main-sequence stars fuse hydrogen into helium. The solar system formed by the nebular hypothesis from a collapsing, rotating cloud of gas and dust.

Cosmology and time: Big Bang evidence includes cosmic microwave background radiation, galactic redshift, and Hubble's law; a light-year is a distance. Geologic time uses relative dating (superposition) and absolute radiometric dating with half-lives.