Physics
Right-Hand Palm Rule (Motor/Force) — Fingers point in current direction, field lines enter palm, thumb shows force direction. For Fleming's Left Hand Rule: thuMb=Motion, First finger=Field, seCond=Current (FBI → Force-B-I).
VIBGYOR Wavelength Order — Violet shortest (400 nm), Red longest (700 nm). Energy inverse: Violet highest energy. Remember "Very Intelligent Boys Generally Read Only Verses" for increasing wavelength.
Lens/Mirror Sign Convention — Real is Positive (RiP): distances measured against incident light are negative, with light are positive. For lenses: real images have positive v, virtual have negative v.
Resistor Color Code — Black=0, Brown=1, Red=2, Orange=3, Yellow=4, Green=5, Blue=6, Violet=7, Grey=8, White=9. Mnemonic: "BB ROY Great Britain Very Good Wife" or "Bye Bye Rosie Off You Go Birmingham Via Great Western".
Capacitor Series/Parallel Flip — Capacitors behave opposite to resistors: series capacitance uses reciprocal sum (like parallel resistors), parallel adds directly (like series resistors). "Capacitors are Contrary".
Escape Velocity Quick Value — √2 × orbital velocity. Earth: 11.2 km/s ≈ √2 × 7.9 km/s. Also √(2GM/R), remember factor 2 distinguishes it from orbital's √(GM/R).
SHM Energy Split — At amplitude A: 100% PE. At mean position: 100% KE. At A/2 displacement: 25% PE, 75% KE (energy ∝ displacement²).
Photoelectric Effect Quick Check — Einstein equation: KEmax = hν - φ. If frequency below threshold, ZERO emission (not low energy). Intensity affects number of electrons, NOT their maximum energy.
Doppler Shift Sign Rule — Source/observer approaching: frequency increases (blue shift), use f' = f(v+v₀)/(v-vₛ). Remember: "A"pproaching = "A"dd in numerator for observer, subtract in denominator for source.
Mathematics
nCr = nCn-r Symmetry — Choosing r items = rejecting (n-r) items. Quick compute: always use smaller number. Example: ₅₀C₄₈ = ₅₀C₂ = 1225, much faster.
Determinant Zero Conditions — Two rows/columns identical OR proportional → det = 0. One row/column all zeros → det = 0. Rows/columns linearly dependent → det = 0.
Binomial Middle Term Trick — For (x+y)ⁿ: if n even, one middle term at position (n/2 + 1); if n odd, two middle terms at positions (n+1)/2 and (n+3)/2. Largest coefficient always at middle.
Quadratic Sign Analysis — For ax²+bx+c: if a>0, parabola opens up (smiles); if a<0, opens down (frowns). Discriminant b²-4ac: positive=2 real roots, zero=1 repeated root, negative=no real roots.
Permutation vs Combination — Arrangement matters = Permutation (nPr). Selection only = Combination (nCr). Remember: "Combination for Committee (selection), Permutation for Password (arrangement matters)".
Probability Complement Shortcut — P(at least one) = 1 - P(none). Far easier than adding multiple cases. Example: probability of at least one head in 3 tosses = 1 - (1/8) = 7/8.
Elementary Astronomy
Planet Order Mnemonic — My Very Educated Mother Just Served Us Nachos: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune. Sun at center, increasing distance outward.
Lunar Phase Cycle — New → Waxing Crescent → First Quarter → Waxing Gibbous → Full → Waning Gibbous → Last Quarter → Waning Crescent. "Wax"ing = growing (right side lit in NH), "Wane"ing = shrinking.
Kepler's Laws Quick Recall — K1: Ellipses (sun at focus). K2: Equal areas in equal times (faster when closer). K3: T²∝a³ (period squared ∝ semi-major axis cubed). "Ellipse-Area-Time" = EAT Kepler's laws.
Celestial Coordinate Systems — Altitude-Azimuth (Horizon): observer-dependent, changes with time. RA-Dec (Equatorial): like lat-long on sky, fixed for stars. Ecliptic: sun's path, 23.5° tilted to equator.
Solar Eclipse Types — Total: Moon closer, umbra reaches Earth. Annular: Moon farther, "ring of fire". Remember: "Annular = Annual ring" (tree rings). Partial always surrounds total/annular path.
Zodiac Constellations Count — 12 traditional signs, but sun passes through 13 constellations (add Ophiuchus between Scorpius and Sagittarius). IAU recognizes 88 total constellations covering entire sky.