Physics
Right-Hand Palm Rule — For force on current-carrying conductor: fingers in B direction, thumb in I direction, palm push shows F direction. For motor effect, remember FBI order.
VIBGYOR for EM Spectrum — Violet–Indigo–Blue–Green–Yellow–Orange–Red for visible light. Extended: Radio–Microwave–IR–Visible–UV–X-ray–Gamma for increasing frequency/energy.
SHM Spring constant trick — Series springs: 1/k_eq = 1/k₁ + 1/k₂ (like resistors in parallel). Parallel springs: k_eq = k₁ + k₂ (like resistors in series). Opposite to intuition!
Lenz Law Memory — "Nature opposes change." Induced current creates magnetic field opposing the flux change. Right palm curl shows induced field direction when thumb points to induced current.
Escape Velocity = √2 × Orbital — v_escape = √2 × v_orbital always. At Earth surface: 11.2 km/s = √2 × 7.9 km/s. Quick check for calculation errors.
Kirchhoff Loop Rule sign — Going with EMF source (+ve terminal to -ve): add voltage. Going against current through resistor: add IR. Opposite directions: subtract.
Photoelectric Threshold Check — If λ > λ₀ (wavelength exceeds threshold), no emission regardless of intensity. If λ < λ₀, then K.E. = hc/λ - φ. Wave theory fails here.
Bohr Radius Scaling — r_n = n² × 0.529 Å for hydrogen. For He⁺, Li²⁺: divide by Z. Energy scales as -13.6Z²/n² eV. Quick calculation for isoelectronic species.
Chemistry
HONC 1234 Rule — Hydrogen forms 1 bond, Oxygen 2, Nitrogen 3, Carbon 4 (normal valency). Helps quickly draw organic structures and spot errors in formulae.
Aufbau: n+l Rule — Fill orbitals by increasing n+l value; if equal, lower n first. Example: 4s (n+l=4) fills before 3d (n+l=5). Then 3d before 4p (both 5, but 3<4).
Strong Acid Six — HCl, HBr, HI, HNO₃, H₂SO₄, HClO₄. Memorize these; all others are weak acids. Completely dissociate in water. Critical for pH and buffer problems.
VSEPR: Lone Pairs Repel More — Repulsion order: lp-lp > lp-bp > bp-bp. NH₃ has 107° (lp present), CH₄ has 109.5° (no lp). Explains bent water, pyramidal ammonia.
Markovnikov's Rule Shortcut — "Rich get richer": H adds to carbon with more H already; halide/OH to carbon with fewer H. Anti-Markovnikov with peroxide (HBr only).
SN1 vs SN2 Quick Check — SN1: 3° > 2° > 1° (carbocation stable), racemic. SN2: 1° > 2° > 3° (steric factor), inversion. Protic solvent favors SN1, aprotic favors SN2.
d-Block +2/+3 Oxidation — First half: +2 common (Mn²⁺, Fe²⁺). Second half: +3 less stable. Exception: Cu²⁺ more stable than Cu⁺. Zn always +2 (d¹⁰ stable).
Buffer pH = pKa — Henderson-Hasselbalch: pH = pKa + log([A⁻]/[HA]). When acid = conjugate base (1:1 ratio), pH exactly equals pKa. Maximum buffer capacity here.
Aldol vs Cannizzaro — Aldol needs α-hydrogen for enolate formation. Cannizzaro: no α-H (benzaldehyde, formaldehyde), requires strong base, gives alcohol + acid (disproportionation).
Mathematics
ASTC Circle for Signs — All positive (1st quadrant), Sine only (2nd), Tangent only (3rd), Cosine only (4th). Going anticlockwise: "Add Sugar To Coffee."
Binomial Middle Term — For (a+b)ⁿ: if n even, middle term is (n/2 + 1)th term. If n odd, two middle terms: (n+1)/2 and (n+3)/2. Greatest coefficient here.
Quadratic Root Shortcut — Sum of roots = -b/a, product = c/a. If α, β are roots, then α² + β² = (α+β)² - 2αβ = b²/a² - 2c/a. Saves time.
Conic Eccentricity Memory — Circle: e=0, Ellipse: 0<e<1, Parabola: e=1, Hyperbola: e>1. CEPH order. For ellipse: b² = a²(1-e²); hyperbola: b² = a²(e²-1).
L'Hospital Trap Check — Only for 0/0 or ∞/∞ forms. Not valid for 0×∞, 1^∞, ∞-∞. Convert these first: 0×∞ = 0/(1/∞) to get 0/0 form.
Integration by Parts: ILATE — Choose u in order: Inverse trig, Logarithm, Algebraic, Trig, Exponential. First in order becomes u, rest becomes dv. ∫u dv = uv - ∫v du.
Determinant Row/Column Trick — If two rows/columns identical: determinant = 0. If row/column all zeros: determinant = 0. If one row is k×(another row): determinant = 0. Instant answers.
Differential Equation Order — Order = highest derivative present. Degree = power of highest derivative (after removing fractions/radicals). Linear if degree of all terms = 1.