Praxis Physical Science 5485 cheat sheet

Controlled experiment: manipulate the independent variable, measure the dependent variable, and hold extraneous variables constant; a control group receives no treatment or a placebo for comparison.

Accuracy is closeness to the accepted value; precision is closeness of repeated measurements to one another. Random error affects precision, while systematic error shifts accuracy.

Percent error = |(measured − accepted) / accepted| × 100%; percent difference compares two measured values when neither is an established accepted value.

Significant figures: all nonzero digits count; zeros between nonzero digits count; leading zeros do not count; trailing zeros count only when a decimal point is present.

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

Engineering design cycle: define the problem, research constraints, brainstorm solutions, build a prototype, test, analyze data, iterate, and communicate results.

Correlation does not establish causation; evaluate sample size, random selection, control groups, peer review, and reproducibility before accepting a causal claim.

Graph choice: line graph for continuous change, bar graph for categorical comparisons, scatter plot for relationships between two quantitative variables, and histogram for distributions.

Lab safety: wear goggles and gloves, waft vapors toward the nose, add acid to water rather than water to acid, and consult Safety Data Sheets before handling chemicals.

Kinematics: v = v₀ + at; Δx = v₀t + ½at²; v² = v₀² + 2aΔx; average velocity = displacement divided by time.

Newton's second law: net force = mass × acceleration (F = ma); weight = mg; friction force = μN and opposes motion.

Work = force × displacement × cos θ; kinetic energy = ½mv²; gravitational potential energy = mgh; power = work/time = Fv.

Conservation of energy: energy is neither created nor destroyed; mechanical energy is conserved when only conservative forces act.

Impulse = FΔt = change in momentum; in an isolated system, total momentum before a collision equals total momentum after the collision.

Wave equation: v = fλ; period T = 1/f; sound speed depends on medium and temperature; light in vacuum travels at c = 3.00 × 10⁸ m/s.

Ohm's law: V = IR; electric power P = IV = I²R = V²/R; series resistors add, while parallel resistors follow 1/R_eq = 1/R₁ + 1/R₂ + ...

Magnetic force on a moving charge: F = qvB sin θ; force on a current-carrying wire: F = BIL sin θ; Faraday's law: induced emf equals the negative rate of change of magnetic flux.

Heat transfer: conduction requires contact, convection moves fluid, and radiation travels by electromagnetic waves; Q = mcΔT and Q = mL for phase changes.

Refraction: Snell's law n₁ sin θ₁ = n₂ sin θ₂; total internal reflection occurs above the critical angle when light moves from a higher to a lower refractive index.

Atomic number Z equals the number of protons; mass number A equals protons plus neutrons; a neutral atom has electrons equal to Z, while ions differ by gained or lost electrons.

Isotopes have the same atomic number but different mass numbers; average atomic mass = Σ(fractional abundance × isotope mass).

Periodic trends: atomic radius increases down and to the left; ionization energy and electronegativity increase up and to the right; metals tend to lose electrons and nonmetals tend to gain them.

Ionic bonds transfer electrons between a metal and a nonmetal; covalent bonds share electrons between nonmetals; polar covalent bonds involve unequal electron sharing.

Mole: 1 mol = 6.022 × 10²³ particles; molar mass in g/mol is numerically equal to formula mass in amu.

Stoichiometry uses mole ratios from a balanced equation; the limiting reactant is consumed first; theoretical yield comes from the limiting reactant; percent yield = actual/theoretical × 100%.

Balancing equations conserves atoms; reaction types include synthesis, decomposition, single replacement, double replacement, combustion, and acid-base neutralization.

Ideal gas law: PV = nRT, with R = 0.0821 L·atm/(mol·K); at STP, molar volume is 22.4 L/mol at 0 °C and 1 atm.

pH = −log[H₃O⁺]; pH < 7 is acidic, pH = 7 is neutral, and pH > 7 is basic; acid + base → salt + water; dilution follows M₁V₁ = M₂V₂.