Physics
Right-Hand Thumb Rule — Thumb = current direction, curled fingers = magnetic field lines. For force on conductor: First finger = Field, seCond = Current, thuMb = Motion (Fleming's left hand).
VIBGYOR for EM Spectrum — Radio, Micro, Infrared, Visible, Ultra, X-ray, Gamma in increasing frequency/energy order. Remember: "Raging Martians Invaded Venus Using X-ray Guns."
Kirchhoff's Rules Trick — Junction rule: current IN = current OUT (like water pipes). Loop rule: voltage rises (–→+) add positive, drops (+→–) subtract. Battery gives rise, resistor gives drop.
Projectile Range Formula — Maximum range at 45°; complementary angles (30°-60°, 15°-75°) give same range. Formula: R = u²sin(2θ)/g.
Lens/Mirror Sign Convention — Distances measured FROM optical center/pole. LEFT is negative, RIGHT is positive. Upward heights positive, downward negative. Real image has negative v.
Escape Velocity = √2 × Orbital — If orbital velocity is v, escape velocity = v√2. At Earth: orbital ≈7.9 km/s, escape ≈11.2 km/s. Factor of √2 always applies.
Bohr Model: Energy ∝ 1/n² — Ground state n=1 has –13.6 eV. For nth level: E = –13.6/n². First excitation (n=2) = –3.4 eV. Radius ∝ n².
Alternating Current XL vs XC — Inductive reactance XL = 2πfL (increases with frequency). Capacitive XC = 1/(2πfC) (decreases with frequency). At resonance: XL = XC.
Photoelectric Effect Threshold — Einstein equation: KE_max = hf – φ. If frequency < threshold, NO electrons emitted regardless of intensity. Higher intensity = more electrons, NOT more energy per electron.
Nuclear Decay Memory: APE — Alpha decay: A drops by 4, Z drops by 2. Beta⁻ decay: A same, Z increases by 1. Positron/Beta⁺: A same, Z decreases by 1.
Ampere's Law Direction — Curl right-hand fingers in current loop direction; thumb points to magnetic field's North pole. For solenoid: fingers follow coil current, thumb shows N-pole.
Equipotential Surface Rule — Electric field ALWAYS perpendicular to equipotential surfaces. No work done moving charge along equipotential. Surfaces never intersect.
Chemistry
HONC 1234 Rule — Hydrogen forms 1 bond, Oxygen 2, Nitrogen 3, Carbon 4 in organic molecules. Quick check for structure validity in hydrocarbons and functional groups.
Le Chatelier's Principle Shortcut — Stress applied, equilibrium shifts to relieve it. Increase pressure → fewer moles side. Increase temperature → endothermic direction. Add reactant → forward shift.
Hybridization = ½(V+M–C+A) — V = valence electrons of central atom, M = monovalent atoms, C = cationic charge, A = anionic charge. Result: 2=sp, 3=sp², 4=sp³, 5=sp³d, 6=sp³d².
SN1 vs SN2: "One is Slow, Two is Fast" — SN1: 1-step, forms carbocation (slow), 3°>2°>1° order, racemic mixture. SN2: 2-step, backside attack, 1°>2°>3° order, inversion occurs.
Electronegativity: FONCL Br — Decreasing order: F > O > N ≈ Cl > Br. Fluorine most electronegative (4.0), Francium least (0.7). Use to predict bond polarity instantly.
Markovnikov's Rule — "Rich get richer": In HX addition to alkene, H goes to carbon with MORE hydrogens already. Anti-Markovnikov with peroxide (HBr only): free radical mechanism.
pH + pOH = 14 — At 25°C always. If pH = 3, pOH = 11. Quick acid/base strength check. [H⁺][OH⁻] = 10⁻¹⁴. Each pH unit = 10× concentration change.
Hund's Rule: Empty Bus Seats — Electrons fill orbitals singly (parallel spins) before pairing, like passengers preferring empty seats. Maximum spin multiplicity = most stable configuration.
Lucas Test Timing — 3° alcohol: cloudiness immediate (ZnCl₂ turbidity). 2° alcohol: 5 minutes. 1° alcohol: no reaction at room temp. Tests for alcohol class identification.
Aldehyde vs Ketone: H-Test — Aldehyde has H on carbonyl (RCHO), gives Tollen's/Fehling's positive (reducing). Ketone has two R groups (RCOR'), non-reducing. Aldehydes easier to oxidize.
Biomolecule Memory: CAPE — Carbohydrates (polyhydroxy aldehydes/ketones), Amino acids/Proteins (peptide bonds), Phospholipids/fats (ester linkages), Enzymes (biological catalysts with active sites).
Rate Law Trick — Order determined ONLY by experiment, not stoichiometry. Rate = k[A]^m[B]^n. Units of k reveal order: M¹⁻ⁿs⁻¹ where n = total order.
Mathematics
Binomial Coefficient Symmetry — ⁿCᵣ = ⁿCₙ₋ᵣ. Middle term(s): if n even, (n/2 + 1)th term; if odd, two middle terms at positions (n+1)/2 and (n+3)/2.
Complex Number Modulus-Argument — |z₁z₂| = |z₁||z₂|, arg(z₁z₂) = arg(z₁) + arg(z₂). For division: divide moduli, subtract arguments. i² = –1, i³ = –i, i⁴ = 1 (cycle repeats).
Conic Section Eccentricity — Circle e=0, Ellipse 0<e<1, Parabola e=1, Hyperbola e>1. Mnemonic: "CEPH" in alphabetical order matches increasing eccentricity value.
Determinant Row Operations — Swapping rows: multiply by –1. Multiply row by k: multiply determinant by k. Add multiple of one row to another: determinant unchanged. Zero row/column = zero determinant.
Integration by Parts: ILATE — Priority order for choosing 'u': Inverse trig, Logarithmic, Algebraic, Trigonometric, Exponential. Lower priority becomes 'dv'. Formula: ∫u dv = uv – ∫v du.
L'Hôpital's Rule Conditions — Use ONLY for 0/0 or ∞/∞ forms. Differentiate numerator and denominator separately (NOT quotient rule). Repeat if indeterminate form persists.
Matrix Inverse Shortcut (2×2) — For [a b; c d]: determinant = ad–bc. Inverse = (1/det)[d –b; –c a]. Swap diagonals, negate off-diagonals, divide by determinant.
Permutation vs Combination — Arrangement matters? Permutation ⁿPᵣ = n!/(n–r)!. Selection only? Combination ⁿCᵣ = n!/[r!(n–r)!]. Remember: ⁿPᵣ = ⁿCᵣ × r!
Differential Equation Order-Degree — Order = highest derivative