CLEP Natural Sciences cheat sheet

Chemical evolution: reducing early atmosphere (CH4, NH3, H2, H2O vapor) plus UV/lightning energy forms amino acids; Miller-Urey demonstrated abiotic synthesis of organic monomers.

Oparin-Haldin hypothesis: organic monomers concentrate in primordial soup, polymerize, and form coacervate droplets bounded by membranes - a protocell model.

Endosymbiotic theory: mitochondria and chloroplasts derive from engulfed bacteria; evidence = double membrane, own circular DNA, 70S ribosomes, binary fission.

Evidence for evolution: fossil stratigraphy, homologous structures (divergent), analogous structures (convergent), vestigial organs, biogeography, molecular homology (cytochrome c, rRNA).

Natural selection requires heritable variation, differential reproductive success, and overproduction of offspring; allele frequencies shift if selection, drift, mutation, or migration act.

Speciation: allopatric via geographic isolation, sympatric via polyploidy or behavioral/habitat isolation; reproductive isolation defines species boundaries (biological species concept).

Hardy-Weinberg equilibrium: p + q = 1 and p² + 2pq + q² = 1; null model holds only without selection, drift, mutation, migration, and with random mating.

Three-domain system (Woese): Bacteria, Archaea, Eukarya based on rRNA; five-kingdom alternative = Monera, Protista, Fungi, Plantae, Animalia.

Binomial nomenclature: genus capitalized, species lowercase, italicized (Homo sapiens); taxonomic hierarchy Domain → Kingdom → Phylum → Class → Order → Family → Genus → Species.

Prokaryote vs eukaryote: prokaryotes lack membrane-bound nucleus and organelles, have 70S ribosomes, circular DNA, and 1–10 µm size; eukaryotes have nucleus, 80S ribosomes, linear chromosomes.

Organelles: mitochondria (ATP via oxidative phosphorylation), chloroplasts (photosynthesis), rough ER (protein synthesis), smooth ER (lipid synthesis), Golgi (sorting/modification), lysosome (hydrolysis), ribosome (translation).

Mitosis stages: prophase (chromosomes condense, spindle forms), metaphase (align at plate), anaphase (sister chromatids separate), telophase (nuclear envelope reforms); cytokinesis divides cytoplasm.

Meiosis: two divisions produce four haploid cells; crossing over in prophase I and independent assortment in metaphase I generate genetic variation.

DNA structure: double helix, antiparallel strands, adenine-thymine (2 H bonds), guanine-cytosine (3 H bonds), sugar-phosphate backbone; replication is semiconservative.

Central dogma: DNA → RNA (transcription) → protein (translation); codon = 3 bases, 64 codons, 20 amino acids, start AUG (methionine), stops UAA/UAG/UGA.

Glycolysis: glucose → 2 pyruvate + 2 ATP + 2 NADH in cytosol; Krebs cycle and electron transport chain in mitochondria yield roughly 30–32 ATP total with O2 as final acceptor.

Photosynthesis: light reactions in thylakoid (split water, produce ATP/NADPH and O2), Calvin cycle in stroma fixes CO2 via rubisco to make G3P.

Enzyme kinetics: catalysts lower activation energy, are not consumed, are specific to substrate; Michaelis-Menten v = Vmax[S]/(Km+[S]); competitive inhibitors raise Km, noncompetitive lower Vmax.

Mendel's laws: segregation (alleles separate in meiosis) and independent assortment (genes on different chromosomes assort randomly); monohybrid 3:1, dihybrid 9:3:3:1 phenotypic ratio.

Testcross identifies unknown genotype by crossing with homozygous recessive; incomplete dominance gives blended phenotype, codominance expresses both alleles, multiple alleles (ABO) give >2 variants.

Sex-linked traits: X-linked recessive disorders (hemophilia, red-green color blindness) appear more in males; fathers pass X-linked alleles only to daughters.

Non-Mendelian: polygenic traits show continuous variation, pleiotropy = one gene affects many traits, epistasis = one gene masks another.

Human genetics: autosomal recessive (cystic fibrosis, PKU, sickle cell), autosomal dominant (Huntington, achondroplasia), chromosomal (Down syndrome = trisomy 21).

Homeostasis: negative feedback (insulin/glucagon, thermoregulation, osmoregulation) opposes change; positive feedback (oxytocin in labor) amplifies change.

Animal tissues: epithelial (covering), connective (bone, blood, cartilage), muscle (skeletal, cardiac, smooth), nervous (neurons, glia).

Plant structure: xylem transports water and minerals upward (dead cells, transpiration pull), phloem transports sugars (living sieve tubes, pressure flow); stomata regulate gas exchange.

Development: cleavage → blastula → gastrula (three germ layers: ectoderm, mesoderm, endoderm); morphogens and homeotic (Hox) genes pattern body axes.

Exponential growth: dN/dt = rN (unlimited resources); logistic growth: dN/dt = rN(K−N)/K with carrying capacity K and S-shaped curve.

Life tables and survivorship curves: Type I (high early survival, humans), Type II (constant mortality, birds), Type III (high early mortality, oysters).

Population regulation: density-dependent factors (competition, disease, predation) vs density-independent (weather, fire); r-selected vs K-selected strategies.

Species interactions: mutualism (+,+), commensalism (+,0), parasitism (+,−), predation (+,−), competition (−,−); competitive exclusion vs resource partitioning.

Trophic levels: producers → primary consumers → secondary consumers → decomposers; only ~10% of energy transfers between levels (energy pyramid); biomass pyramids may invert in aquatic systems.

Biogeochemical cycles: carbon (photosynthesis/respiration/combustion), nitrogen (fixation by Rhizobium, nitrification, denitrification), phosphorus (no gaseous phase, sedimentary).

Succession: primary begins on bare substrate (lichens, mosses) and secondary follows disturbance; climax community is a stable endpoint in that climate.

Biomes: tropical rainforest (high rainfall/diversity), desert (<25 cm rain), tundra (permafrost), taiga (conifers), grassland, temperate deciduous forest.

Human impact: greenhouse gases (CO2, CH4) trap infrared radiation; eutrophication from nutrient runoff causes algal blooms and oxygen depletion; ozone depletion by CFCs.

Atom: protons and neutrons in nucleus, electrons in orbitals; atomic number Z = protons, mass number A = protons + neutrons; isotopes differ in neutron count.

Electron configuration follows Aufbau (lowest energy first), Pauli exclusion (2 electrons per orbital, opposite spin), and Hund's rule (maximum unpaired spins).

Quantum numbers: n (shell), l (subshell s,p,d,f = 0–3), ml (orientation), ms (spin ±1/2); orbital shapes: s spherical, p dumbbell, d cloverleaf.

Radioactive decay: alpha (⁴₂He, Z−2, A−4), beta-minus (neutron → proton, Z+1), beta-plus/positron (proton → neutron, Z−1), gamma (photon, no change in Z or A).

Half-life: N = N0(1/2)^(t/T); after n half-lives fraction remaining = (1/2)^n; carbon-14 half-life ≈ 5,730 years for dating organic remains.

Binding energy: mass defect converted to energy via E = mc²; nuclear binding energy per nucleon peaks near iron-56 (fusion releases energy for light nuclei, fission for heavy).

Fission splits heavy nuclei (U-235 + neutron → Ba + Kr + 2–3 neutrons); fusion joins light nuclei (hydrogen → helium in stars); chain reactions require critical mass.

Standard model: quarks (up, down, charm, strange, top, bottom) and leptons (electron, muon, tau, neutrinos); protons/neutrons are baryons of three quarks; force carriers include photons, gluons, W/Z bosons.

Periodic trends: atomic radius decreases left to right, increases down a group; ionization energy and electronegativity increase across a period and decrease down a group.

Bond types: ionic (metal + nonmetal, electron transfer), covalent (nonmetal + nonmetal, sharing), metallic (delocalized electrons); bond polarity from electronegativity difference.

VSEPR geometry: 2 electron domains linear (180°), 3 trigonal planar (120°), 4 tetrahedral (109.5°), 5 trigonal bipyramidal, 6 octahedral; lone pairs compress angles.

Intermolecular forces: hydrogen bonding (N, O, F with H) > dipole-dipole > London dispersion; explain boiling point and solubility trends.

Stoichiometry: balance equations by conservation of atoms; mole = 6.022×10²³ particles; molarity M = mol solute / L solution; use mole ratios from balanced equations.

Reaction types: synthesis, decomposition, single replacement, double replacement (precipitation), combustion, acid-base neutralization, redox (oxidation number changes).

Acids and bases: Arrhenius vs Brønsted-Lowry (proton donor/acceptor); pH = −log[H⁺]; strong acids fully dissociate; Kw = [H⁺][OH⁻] = 1×10⁻¹⁴ at 25 °C.

Le Chatelier's principle: adding reactant shifts right, increasing pressure shifts toward fewer gas moles, raising temperature favors the endothermic direction; catalyst speeds equilibrium without shifting it.

Gas laws: PV = nRT; Boyle (P↑V↓ at constant T), Charles (V↑T↑ at constant P), Avogadro (V proportional to n); STP = 0 °C and 1 atm, molar volume 22.4 L.

Kinematics: v = v0 + at, x = v0t + ½at², v² = v0² + 2ax; projectile motion separates horizontal (constant v) and vertical (constant a = g) components.

Newton's laws: inertia (ΣF = 0 → constant velocity), F = ma, action-reaction pairs act on different bodies; friction f = µN.

Energy and momentum: KE = ½mv², PE = mgh, work W = Fd cosθ; momentum p = mv conserved in collisions; elastic collisions conserve KE, inelastic do not.

Circular motion: centripetal force Fc = mv²/r directed toward center; angular velocity ω = v/r; torque τ = rF sinθ.

Heat: Q = mcΔT (specific heat), latent heat Q = mL for phase changes; conduction, convection, radiation are the three transfer modes.

Thermodynamics: first law ΔU = Q − W (energy conserved); second law entropy of an isolated system never decreases; heat flows hot → cold spontaneously.

Ideal gas kinetic theory: pressure from molecular collisions; average KE = (3/2)kT; temperature measures average molecular kinetic energy.

Phase diagram: triple point where solid, liquid, gas coexist; critical point beyond which no distinct liquid/gas phase; sublimation goes solid → gas directly.

Special relativity: c constant for all observers; time dilation t = t0/√(1−v²/c²), length contraction, mass-energy E = mc²; relativistic effects grow as v approaches c.

Coulomb's law: F = kq1q2/r²; electric field E = F/q; electric potential V = kq/r; field lines point from positive to negative charge.

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

Magnetic force: F = qvB sinθ on moving charge, F = BIL sinθ on current-carrying wire; right-hand rule gives force direction; electromagnetic induction (Faraday) produces EMF from changing magnetic flux.

Wave equation v = fλ; period T = 1/f; transverse waves (light, string) oscillate perpendicular to travel, longitudinal waves (sound) parallel.

Sound: needs a medium, speed ≈ 343 m/s in air at 20 °C, faster in solids; pitch = frequency, loudness = amplitude, Doppler shift changes observed frequency with relative motion.

Light: reflection angle equals incidence angle; refraction follows Snell's law n1sinθ1 = n2sinθ2; total internal reflection above the critical angle.

Lenses and mirrors: converging lens/mirror forms real inverted images beyond focal length; 1/f = 1/do + 1/di; magnification m = −di/do.

Electromagnetic spectrum by increasing frequency: radio, microwave, infrared, visible (red→violet), ultraviolet, X-ray, gamma; all travel at c in vacuum.

Interference and diffraction: double slit maxima at d sinθ = mλ; single-slit minima at a sinθ = mλ; polarization demonstrates light's transverse nature.

Big Bang evidence: cosmic microwave background (~2.7 K), Hubble's law (recession velocity proportional to distance, v = H0d), abundance of light elements, and redshift of distant galaxies.

Stellar life cycle: nebula → protostar → main sequence (hydrogen fusion) → red giant/supergiant → white dwarf (low mass) or supernova → neutron star/black hole (high mass).

Hertzsprung-Russell diagram plots luminosity vs temperature (or spectral class OBAFGKM); main sequence runs diagonally, giants upper right, white dwarfs lower left.

Stars generate energy by nuclear fusion; main-sequence lifetime depends strongly on mass - massive stars burn hotter and die younger.

Solar system: four inner terrestrial planets (Mercury, Venus, Earth, Mars), asteroid belt, four outer gas/ice giants (Jupiter, Saturn, Uranus, Neptune); Pluto is a dwarf planet.

Kepler's laws: orbits are ellipses with the Sun at one focus; equal areas in equal times; T² proportional to a³ (period squared ∝ semi-major axis cubed).

Earth-Moon-Sun geometry: solar eclipse at new moon (Moon between), lunar eclipse at full moon (Earth between); seasons arise from 23.5° axial tilt, not distance from the Sun.

Galaxies: spiral, elliptical, irregular; Milky Way is a barred spiral ~100,000 light-years across; dark matter inferred from rotation curves and gravitational lensing.

Nebular hypothesis: solar system formed from a rotating cloud of gas and dust; inner planets are rocky (high condensation temperature), outer planets icy/gaseous.

Earth's interior layers: crust (continental granitic, oceanic basaltic), mantle (solid but slowly flowing), outer core (liquid iron, generates magnetic field), inner core (solid iron-nickel).

Plate tectonics: divergent boundaries (mid-ocean ridges, seafloor spreading), convergent (subduction zones, trenches, volcanic arcs, mountain belts), transform (strike-slip faults).

Rock types: igneous (from magma - intrusive coarse, extrusive fine), sedimentary (layered, fossils, from deposition), metamorphic (heat/pressure altered, foliated or nonfoliated).

Rock cycle links igneous, sedimentary, and metamorphic rocks through melting, weathering, erosion, deposition, and metamorphism.

Atmosphere composition: ~78% N2, 21% O2, ~1% argon and trace CO2; layers troposphere (weather), stratosphere (ozone layer), mesosphere, thermosphere.

Weathering and erosion: mechanical (frost wedging, abrasion) vs chemical (oxidation, hydrolysis, dissolution); rivers, glaciers, wind, and waves transport sediment.

Hydrologic cycle: evaporation, transpiration, condensation, precipitation, runoff, infiltration, groundwater flow; aquifers store groundwater.

Geologic time: Precambrian (~88% of Earth history), Paleozoic, Mesozoic, Cenozoic eras; relative dating uses superposition and cross-cutting relations, absolute dating uses radiometric isotopes.

Seismic waves: P waves (compressional, fastest, travel through solids and liquids), S waves (transverse, only solids), surface waves (most damaging); epicenter located by triangulation of arrival times.