Physics
Fleming's Left & Right Hand Rules — LEFT for motor (force): thuMb = Motion, First finger = Field, seCond = Current. RIGHT for generator (induced current): thuMb = Motion, First = Field, seCond = induced Current. Remember "motors are sinister (left)."
Lenz's Law Direction — Induced current always opposes the change causing it. Think "nature is lazy"—it resists change. Drop magnet (N-pole down) through coil: induced field creates N-pole upward to repel.
AC Circuit Resonance — At resonance: XL = XC, impedance Z = R (minimum), current maximum, power factor = 1. Mnemonic: "RELAXED Circuit"—Resonance, Equal reactances, Low impedance, Maximum current.
Photoelectric Effect Thresholds — Remember: frequency matters, intensity doesn't (for ejection). "Frequent visits needed to enter (threshold), crowd size (intensity) irrelevant." KEmax = hf - φ; only f above threshold ejects electrons.
Right-Hand Thumb Rule (Current) — Thumb = current direction, curled fingers = magnetic field direction around wire. For solenoid: fingers curl with current flow, thumb points to N-pole.
Electromagnetic Spectrum Order — "Raging Martians Invaded Venus Using X-ray Guns": Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma. Wavelength decreases left to right; frequency/energy increases.
Nuclear Decay Alpha/Beta — Alpha (α): mass ↓4, atomic number ↓2. Beta⁻ (β): mass same, Z ↑1 (neutron → proton). Beta⁺: Z ↓1. "Alpha loses bulk; Beta flips identity."
Capacitor Charge/Voltage Relation — Q = CV (charge = capacitance × voltage). Series: same Q, voltage divides (V ∝ 1/C). Parallel: same V, charge divides (Q ∝ C). "Series shares charge; Parallel shares voltage."
Chemistry
Alcohol Reactivity Order — Primary > Secondary > Tertiary for oxidation/dehydration (E2). Reverse for SN1 reactions: 3° > 2° > 1°. "Poor Students Try; Rich Students Never"—oxidation vs substitution stability.
Lucas Test Timing — Tertiary alcohol: turbidity immediate. Secondary: 5 min. Primary: no reaction at RT. "3-2-1 Countdown"—3° instant, 2° wait, 1° never (without heat).
Aldehyde vs Ketone Tests — Aldehydes: positive Tollen's (silver mirror), Fehling's (red ppt). Ketones: negative. Mnemonic: "Aldehydes Are Generous"—they give positive tests (easily oxidized).
Biomolecule Identification — Carbohydrates: Molisch (violet ring), Benedict's (reducing sugars). Proteins: Biuret (violet, peptide bonds), Ninhydrin (blue/purple, amino acids). Fats: translucent grease spot test.
Electrochemical Series Memory — "Little Kids Caring Nothing About Zesty Interesting Copper Hats Silver Ate Gold Platinum": Li, K, Ca, Na, Al, Zn, Fe, Cu, H, Ag, Au, Pt. Reactivity decreases left to right.
d-Block Oxidation States — Scandium to Zinc: variable oxidation states in middle (Mn shows +2 to +7). "Middle children get more attention"—Cr, Mn, Fe show maximum states.
Haloalkane SN1 vs SN2 — SN1: 3° > 2°, carbocation, racemization, weak nucleophile. SN2: 1° > 2°, backside attack, inversion (Walden), strong nucleophile. "1-step SN2 simple; 2-step SN1 stable."
Rate Law Order Determination — Zero order: [A] vs t is straight line. First: ln[A] vs t linear. Second: 1/[A] vs t linear. Graph linearity reveals order directly.
Mathematics
De Moivre's Theorem Quick — (cos θ + i sin θ)ⁿ = cos nθ + i sin nθ. For roots: divide angle by n, add 2πk/n for k = 0,1,2...(n-1). "Divide angle, multiply roots."
|z₁ + z₂| Triangle Rule — ||z₁| - |z₂|| ≤ |z₁ + z₂| ≤ |z₁| + |z₂|. Minimum when opposite direction (straight line), maximum when same direction. Think actual triangle inequality.
Integration by Parts (ILATE) — Choose u in order: Inverse, Logarithmic, Algebraic, Trigonometric, Exponential. First available becomes u, rest dv. ∫u dv = uv - ∫v du.
King Property Definite Integration — ∫₀ᵃ f(x)dx = ∫₀ᵃ f(a-x)dx. Replace x with (a-x), limits stay same. Helps simplify symmetry: ∫₀^(π/2) sin x/(sin x + cos x) = π/4 instantly.
Determinant Row/Column Tricks — If two rows/columns identical: det = 0. Scalar multiple of k in row: det multiplied by k. Interchange rows: det sign flips. "Identical twins = zero; swap = sign flip."
Permutation nPr vs Combination nCr — ⁿPᵣ = n!/(n-r)! when order matters (arrangement). ⁿCᵣ = n!/[r!(n-r)!] when order doesn't (selection). "Position = Permutation; Choose = Combination."
Probability Complement Rule — P(A') = 1 - P(A). For "at least one" problems, use P(at least 1) = 1 - P(none). Saves time vs. calculating individual cases.
Derivative of Composite Functions — For f(g(x)): chain rule f'(g(x))·g'(x). "Outside derivative × inside derivative." For limits: L'Hôpital when 0/0 or ∞/∞ form—differentiate top and bottom separately.