SITEEE cheat sheet

Constant-acceleration kinematics: v = u + at, s = ut + ½at², v² = u² + 2as; these apply only when acceleration is constant.

Projectile motion on level ground: T = 2u sinθ/g, H = u² sin²θ/(2g), R = u² sin 2θ/g; range is maximum at θ = 45° in vacuum.

Newton's laws: F_net = ma in an inertial frame; friction satisfies f_s ≤ μ_sN and f_k = μ_kN; centripetal acceleration is v²/r toward the center.

Work-energy theorem: W_net = ΔKE; for a conservative force, F = −dU/dx and mechanical energy is conserved if only conservative forces do work.

Gravitation: surface gravity g = GM/R²; circular orbital speed v = √(GM/r); escape speed v_esc = √(2GM/R) from the surface.

SHM: T = 2π√(m/k) for a mass-spring system and T = 2π√(L/g) for a small-angle pendulum; velocity is v = ±ω√(A² − x²).

Waves: v = fλ; for a stretched string v = √(T/μ); sound travels faster in solids than gases; beats frequency = |f1 − f2|.

Optics: use 1/f = 1/v + 1/u for mirrors and 1/f = 1/v − 1/u for lenses under the Cartesian sign convention; Snell's law is n1 sinθ1 = n2 sinθ2.

Current electricity: V = IR; series resistances add, parallel conductances add; power P = I²R = V²/R; Coulomb force F = kq1q2/r².

Mole relations: n = m/M = N/N_A; at 273 K and 1 atm, one mole of ideal gas occupies 22.4 L; molarity = moles solute per litre of solution.

Ideal gas: PV = nRT; Dalton's law P_total = ΣP_i; Graham's law compares diffusion rates as rate1/rate2 = √(M2/M1).

Atomic structure: orbitals are labelled by n, l, m_l, m_s; Pauli exclusion allows at most two electrons per orbital; Aufbau and Hund rules set ground-state configurations.

Periodic trends across a period: atomic radius decreases while ionization energy, electron affinity, and electronegativity generally increase; down a group the reverse trends dominate.

Equilibrium: Kp = Kc(RT)^Δn for gas reactions; Le Chatelier shifts oppose imposed changes; ΔG° = −RT ln K and spontaneity requires ΔG < 0 at constant T and P.

Acids and bases: pH = −log[H⁺]; at 25°C Kw = 1.0×10⁻¹⁴ so pH + pOH = 14; Henderson–Hasselbalch gives pH = pKa + log([base]/[acid]) for buffers.

Thermochemistry: ΔH = ΔU + Δn_gRT; Hess's law sums step enthalpies; ΔG = ΔH − TΔS; bond breaking absorbs energy and bond formation releases energy.

Organic reactions: Markovnikov addition gives the more substituted carbocation product; SN1 proceeds via carbocation and racemization, while SN2 is concerted with inversion.

Electrochemistry: E°cell = E°cathode − E°anode using reduction potentials; Nernst at 25°C is E = E° − (0.0592/n) log Q; one faraday deposits one mole of electrons per equivalent.

Quadratic equation ax² + bx + c = 0: roots satisfy α + β = −b/a and αβ = c/a; discriminant D = b² − 4ac; D > 0 real distinct, D = 0 equal, D < 0 complex conjugates.

AP: a_n = a + (n−1)d and S_n = n/2[2a + (n−1)d]; GP: a_n = ar^(n−1), S_n = a(r^n−1)/(r−1) for r ≠ 1, S∞ = a/(1−r) for |r| < 1.

Binomial expansion: (a+b)^n = Σ C(n,r) a^(n−r)b^r; general term T_(r+1) = C(n,r)a^(n−r)b^r; middle term depends on whether n is even or odd.

Trigonometry: sin²θ + cos²θ = 1; sine rule a/sinA = b/sinB = c/sinC; cosine rule a² = b² + c² − 2bc cosA; general solution of sinθ = sinα is θ = nπ + (−1)^n α.

Limits and derivatives: d/dx(x^n)=nx^(n−1), d/dx(sin x)=cos x, d/dx(e^x)=e^x, d/dx(ln x)=1/x; apply product, quotient, and chain rules; L'Hôpital requires 0/0 or ∞/∞.

Integration: ∫x^n dx = x^(n+1)/(n+1)+C for n ≠ −1; ∫u dv = uv − ∫v du; definite integral properties include reversing limits changing sign and splitting at an interior point.

Coordinate geometry: distance = √((x2−x1)²+(y2−y1)²); line slope m = (y2−y1)/(x2−x1); circle (x−h)²+(y−k)²=r²; conic eccentricity e < 1 ellipse, e = 1 parabola, e > 1 hyperbola.

Probability: P(A∪B)=P(A)+P(B)−P(A∩B); conditional P(A|B)=P(A∩B)/P(B); Bayes updates priors; binomial mean = np and variance = np(1−p).

Matrices and vectors: (AB)^T = B^T A^T; inverse exists only if det A ≠ 0; dot product a·b = |a||b|cosθ; cross product magnitude |a||b|sinθ gives area of parallelogram.

Cell types: prokaryotes lack a membrane-bound nucleus and organelles, while eukaryotes have a nucleus, mitochondria, and endoplasmic reticulum; ribosomes occur in both.

Membrane structure: the fluid mosaic model describes a phospholipid bilayer with integral and peripheral proteins, cholesterol, and glycoproteins; small nonpolar molecules diffuse most freely.

Biomolecules: amino acids join by peptide bonds; enzymes lower activation energy and are usually proteins; DNA stores genetic information, while RNA participates in protein synthesis.

Mendelian genetics: segregation separates alleles during gamete formation; independent assortment applies to unlinked genes; monohybrid F2 ratio is 3:1 and dihybrid F2 ratio is 9:3:3:1.

Molecular central dogma: DNA replication is semiconservative; transcription makes RNA from DNA; translation at ribosomes uses mRNA codons and tRNA anticodons to assemble amino acids.

Cellular respiration: glycolysis yields net 2 ATP and 2 NADH per glucose; the Krebs cycle yields 2 ATP, 6 NADH, and 2 FADH2 per glucose; oxidative phosphorylation produces most ATP.

Photosynthesis: light reactions in thylakoids split water, release O2, and produce ATP and NADPH; the Calvin cycle in the stroma fixes CO2 using rubisco and regenerates RuBP.

Human physiology: nephrons filter, reabsorb, and secrete to form urine; alveoli exchange gases by diffusion; the heart's left ventricle pumps oxygenated blood to the systemic circulation.

Ecology and classification: binomial names italicize genus and species; five-kingdom classification includes Monera, Protista, Fungi, Plantae, Animalia; energy transfer between trophic levels averages about 10%.