TASC Physical Sciences Level 3 cheat sheet

Independent variable is the factor deliberately changed; dependent variable is the measured response; controlled variables are held constant to prevent confounding.

A valid experiment includes a comparison or control group so the effect of the treatment can be isolated from other causes.

Hypothesis must be testable and falsifiable: it predicts a specific, observable relationship between variables.

Accuracy is closeness to the true value; precision is closeness of repeated measurements to each other; random error affects precision, systematic error affects accuracy.

Mean is the sum of values divided by the count; median is the middle value of ordered data; mode is the most frequent value.

Percent error = |measured − accepted| ÷ accepted × 100%; report it to judge accuracy of a measurement.

Correlation does not establish causation; a cause-and-effect claim requires controlled manipulation or strong mechanistic evidence.

Scientific notation: a × 10^n where 1 ≤ a < 10; multiply by adding exponents, divide by subtracting exponents.

Significant figures in a result follow the least precise input for multiplication and division, and the least decimal place for addition and subtraction.

Speed = distance ÷ time (scalar); velocity = displacement ÷ time (vector with direction); acceleration = change in velocity ÷ time.

Newton's second law: F_net = m·a; weight is W = m·g with g ≈ 9.8 m/s² near Earth's surface.

Newton's third law: forces occur in equal-and-opposite pairs acting on different objects, so they never cancel on a single object.

Friction opposes relative motion; static friction adjusts up to a maximum, kinetic friction is roughly constant.

Work = force × distance moved in the force direction (W = F·d·cos θ); power = work ÷ time, measured in watts.

Kinetic energy KE = ½mv²; gravitational potential energy PE = mgh; in a closed system mechanical energy is conserved absent friction.

Momentum p = m·v; in collisions total momentum is conserved, while kinetic energy is conserved only in elastic collisions.

Waves: v = f·λ; frequency is set by the source and does not change when a wave enters a new medium, but speed and wavelength do.

Electric current I = V ÷ R (Ohm's law); power P = V·I; energy is conserved and transfers between kinetic, potential, thermal, and electrical forms.

Atomic number Z = number of protons, which defines the element; mass number A = protons + neutrons; isotopes differ only in neutrons.

Electron configuration fills lowest energy levels first; valence electrons (outer shell) determine bonding and reactivity.

Ionic bonds form by electron transfer between metal and nonmetal, creating charged ions held by electrostatic attraction.

Covalent bonds form by electron sharing between nonmetals; polar covalent bonds arise from electronegativity differences.

Law of conservation of mass: atoms are rearranged, not created or destroyed, so a balanced equation has equal atoms of each element on both sides.

Balancing procedure: change coefficients only, never subscripts; check each element and use the smallest whole-number ratio.

Synthesis A + B → AB; decomposition AB → A + B; single replacement A + BC → AC + B; double replacement AB + CD → AD + CB.

Acids donate H⁺ and have pH below 7; bases accept H⁺ and have pH above 7; neutralization produces salt plus water.

Exothermic reactions release energy (products lower in energy); endothermic reactions absorb energy; a catalyst lowers activation energy without being consumed.

Earth's interior layers by composition: crust (silicate rock), mantle (silicate, slowly flowing), core (iron-nickel); the outer core is liquid and generates the magnetic field.

Plate tectonics: divergent boundaries create new crust (mid-ocean ridges), convergent boundaries produce subduction, mountains, and volcanoes, transform boundaries cause earthquakes.

Rock cycle links igneous (cooled magma), sedimentary (compacted deposited grains), and metamorphic (heat and pressure) rocks.

Water cycle processes: evaporation, transpiration, condensation, precipitation, infiltration, and runoff; energy from the Sun drives the cycle.

Earth's rotation on its axis (~24 h) causes day and night; revolution around the Sun (~365.25 days) with a tilted axis causes seasons.

Moon phases result from the changing angle between Earth, Moon, and Sun; a lunar eclipse occurs at full moon, a solar eclipse at new moon.

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

Gravity governs orbits: stronger gravity with greater mass and shorter distance; orbital speed depends on the central body's mass and orbital radius.

Interdisciplinary application: energy and matter cycle through Earth systems, so human carbon emissions alter atmospheric composition and global temperature.