NYSTCE Earth Science (162) cheat sheet

Hypothesis: a testable, falsifiable prediction; a theory is a broad explanation supported by many independent lines of evidence, and a law describes a consistent relationship (often mathematical) without explaining why.

Independent variable is manipulated by the researcher; dependent variable is measured; controlled variables are held constant; a control group receives no treatment or a placebo for comparison.

Validity = the investigation measures what it claims to measure; reliability = repeated trials yield consistent results. Increasing sample size and trials improves reliability, not necessarily validity.

Percent error = |measured − accepted| ÷ accepted × 100. Percent deviation (difference) between two measurements = |a − b| ÷ average × 100.

Density = mass ÷ volume (g/cm³ for solids, g/mL for liquids). Water's density is 1.0 g/mL at 4 °C; objects denser than the fluid sink, less dense float.

Metric conversions: kilo (10³), centi (10⁻²), milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹). 1 km = 1000 m; 1 mL = 1 cm³.

Scientific notation: move the decimal so one nonzero digit precedes it; positive exponent for numbers ≥ 1, negative for numbers < 1 (e.g., 0.0042 = 4.2 × 10⁻³).

Rate of change = change in value ÷ change in time (slope of a graph). A steeper slope on a distance–time graph indicates greater speed; horizontal line = no change.

Measurement precision is limited by the instrument: record all certain digits plus one estimated digit; graduated cylinders are read at the bottom of the meniscus.

Earth's rotation on its axis (west to east, ~24 h) causes day/night and the apparent daily motion of the Sun and stars; revolution around the Sun (~365.25 days) with 23.5° axial tilt causes seasons.

Solstices: around June 21 the Northern Hemisphere has its longest day (Sun directly over the Tropic of Cancer, 23.5° N); around December 21 the shortest. Equinoxes (~March 21, ~September 22) have ~12 h day and night everywhere.

Moon phases result from the changing angle between Earth, Moon, and Sun: new → waxing crescent → first quarter → waxing gibbous → full → waning gibbous → third quarter → waning crescent.

Spring (highest) tides occur at new and full moon when Sun and Moon align (syzygy); neap (lowest) tides occur at quarter moons when they are at right angles.

Solar eclipse: Moon between Earth and Sun, only at new moon. Lunar eclipse: Earth between Sun and Moon, only at full moon. Eclipses are rare because the Moon's orbit is tilted ~5° to the ecliptic.

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

Solar system order: Mercury, Venus, Earth, Mars (terrestrial/rocky), asteroid belt, Jupiter, Saturn, Uranus, Neptune (gas/ice giants). Inner planets are small, dense, and rocky; outer planets large, low-density, with rings and many moons.

Hertzsprung–Russell diagram: stars plot luminosity vs. temperature (OBAFGKM, hot blue to cool red). Main sequence fuses hydrogen; red giants and supergiants are cool but luminous; white dwarfs are hot but dim.

Evidence for the Big Bang: cosmic microwave background radiation, redshift of distant galaxies (Hubble's law, v = H₀d), and abundance of light elements. Light-year = distance light travels in one year (~9.46 × 10¹² km).

Earth's interior layers by composition: crust (thin, silicate), mantle (silicate rock, ~2,900 km thick), core (iron-nickel). By physical properties: lithosphere (rigid), asthenosphere (plastic, flows), mesosphere, outer core (liquid), inner core (solid).

Plate boundaries: divergent (plates move apart - mid-ocean ridges, rift valleys, seafloor spreading), convergent (collision - subduction zones, trenches, volcanic arcs, mountains), transform (plates slide past - strike-slip faults, earthquakes).

Evidence for plate tectonics: matching continental coastlines and fossils, paleomagnetic striping on the seafloor, age of ocean floor increasing away from ridges, earthquake and volcano distribution.

Earthquake waves: P waves (primary, compressional, fastest, travel through solids and liquids), S waves (secondary, shear, slower, only solids), surface waves (slowest, most destructive). Epicenter located by triangulating arrival-time differences from three stations.

Rock cycle: igneous (from cooling magma/lava; intrusive = coarse-grained, extrusive = fine-grained), sedimentary (compaction/cementation of sediments; often layered, may contain fossils), metamorphic (heat and pressure; foliated or nonfoliated).

Weathering vs. erosion: weathering breaks rock in place (physical: frost wedging, abrasion; chemical: oxidation, dissolution, hydrolysis); erosion transports material by water, wind, ice, or gravity.

Atmospheric layers: troposphere (weather, temperature decreases with altitude), stratosphere (ozone layer, temperature increases), mesosphere, thermosphere, exosphere. Air is ~78% N₂, 21% O₂.

Clouds and weather: cumulus (fair weather), cumulonimbus (thunderstorms), stratus (layered, overcast), cirrus (high, thin, ice). High pressure brings clear, fair weather; low pressure brings clouds and precipitation.

Water cycle and watersheds: evaporation, transpiration, condensation, precipitation, infiltration, runoff. Porosity = pore space; permeability = ability to transmit water; groundwater flows from high to low water table.

Relative dating principles: superposition (younger rocks on top in undisturbed sequences), original horizontality, lateral continuity, cross-cutting relationships (faults/intrusions younger than the rocks they cut), and inclusions (included fragments older than the host rock).

Unconformities represent missing time: angular unconformity (tilted layers eroded and overlain by flat layers), disconformity (erosion surface between parallel layers), nonconformity (sedimentary rock over igneous or metamorphic rock).

Absolute dating uses radioactive decay: parent isotope decays to daughter at a constant rate. Half-life = time for half the parent to decay. After n half-lives, fraction remaining = (1/2)ⁿ.

Carbon-14 (half-life ~5,730 years) dates organic material up to ~50,000 years. Uranium-238 (half-life ~4.5 billion years) and potassium-40 date ancient rocks and minerals.

Geologic time scale (largest to smallest): eon, era, period, epoch. Precambrian covers ~88% of Earth's history; Phanerozoic includes Paleozoic, Mesozoic, and Cenozoic eras.

Major events: first life (prokaryotes) in Archean; Cambrian explosion (~541 Ma); Permian–Triassic extinction (~252 Ma, largest); dinosaurs extinct at K–Pg boundary (~66 Ma); first hominins in late Cenozoic.

Fossils: preserved remains or traces. Index fossils are widespread, short-lived species used to correlate rock layers. Fossil succession in layered rock shows evolutionary change over time.

Ice cores and tree rings provide proxy climate records; layers (varves) in lake sediments record annual cycles. Radiometric ages plus stratigraphy establish the ~4.6-billion-year age of Earth.

Uniformitarianism (Hutton, Lyell): present-day geologic processes operating over long time explain past events. Catastrophism attributes some changes to sudden events such as impacts and floods.

Relative dating principles: superposition (younger rocks on top in undisturbed sequences), original horizontality, lateral continuity, cross-cutting relationships (faults/intrusions younger than the rocks they cut), and inclusions (included fragments older than the host rock).

Unconformities represent missing time: angular unconformity (tilted layers eroded and overlain by flat layers), disconformity (erosion surface between parallel layers), nonconformity (sedimentary rock over igneous or metamorphic rock).

Absolute dating uses radioactive decay: parent isotope decays to daughter at a constant rate. Half-life = time for half the parent to decay. After n half-lives, fraction remaining = (1/2)ⁿ.

Carbon-14 (half-life ~5,730 years) dates organic material up to ~50,000 years. Uranium-238 (half-life ~4.5 billion years) and potassium-40 date ancient rocks and minerals.

Geologic time scale (largest to smallest): eon, era, period, epoch. Precambrian covers ~88% of Earth's history; Phanerozoic includes Paleozoic, Mesozoic, and Cenozoic eras.

Major events: first life (prokaryotes) in Archean; Cambrian explosion (~541 Ma); Permian–Triassic extinction (~252 Ma, largest); dinosaurs extinct at K–Pg boundary (~66 Ma); first hominins in late Cenozoic.

Fossils: preserved remains or traces. Index fossils are widespread, short-lived species used to correlate rock layers. Fossil succession in layered rock shows evolutionary change over time.

Ice cores and tree rings provide proxy climate records; layers (varves) in lake sediments record annual cycles. Radiometric ages plus stratigraphy establish the ~4.6-billion-year age of Earth.

Uniformitarianism (Hutton, Lyell): present-day geologic processes operating over long time explain past events. Catastrophism attributes some changes to sudden events such as impacts and floods.