x = a sinθ n₁ sinθ₁ = n₂ sinθ₂ e^x = Σ xⁿ/n! c = λf log_b a = ln a/ln b Q = It m = (y₂ - y₁)/(x₂ - x₁) cos 2θ = cos²θ - sin²θ e = (v₂ - v₁)/(u₁ - u₂) a_c = v²/r s = ut + ½at² d/dx(cos x) = -sin x pK_a = -log K_a s = (a+b+c)/2, A = √(s(s-a)(s-b)(s-c)) d = |Ax₀ + By₀ + C|/√(A²+B²) f''(x) Normality = Molarity × n K_c = ([C]^c[D]^d)/([A]^a[B]^b) d/dx(e^x) = e^x lim_x→a f(x)/g(x) = lim_x→a f'(x)/g'(x) ∫ u dv = uv - ∫ v du sin²(θ/2) = (1 - cosθ)/2 λ = h/p A = πab S_n = a(1 - rⁿ)/(1 - r)

P = IV 2 sin A cos B = sin(A+B) + sin(A-B) Percent Purity = (mass of pure substance/mass of sample) × 100 f'(a) = lim_h→0 (f(a+h)-f(a))/h A = ½ab sin C I = ½ Σ c_i z_i² Rate = k[A]^m[B]ⁿ n = c/v A = ab sinθ p = mv C(n, r) = n!/(r!(n-r)!) U = mgh V = IR (f(g(x)))' = f'(g(x))⋅g'(x) cos²(θ/2) = (1 + cosθ)/2 W = Fd cosθ Φ = BA cosθ E = E° - (0.0591/n) log Q M = moles/volume E = VIt (x-h)² + (y-k)² = r² α + β = -b/a Equivalent Weight = Molecular Weight/n x = [-b ± √(b² - 4ac)]/(2a) m = f'(x)

sin A + sin B = 2 sin((A+B)/2) cos((A-B)/2) F = ma f(x) = Σ_n=0∞ (f⁽ⁿ⁾(0)/n!)xⁿ K.E. = ½mv² pH = -log[H⁺] ΔT_f = iK_fm V = L(dI/dt) a_n = ar^{n - 1} v² = u² + 2as F_x + F_y(dy/dx) = 0 T = 2π√(L/g) A = Pe^rt cos x = Σ (-1)ⁿ x⁽²ⁿ⁾/(2n)! ε = -dΦ/dt αβ = c/a ∫(dx/x) = ln|x| + C a_n = a + (n - 1)d π = MRT n = mass/M ΔT_b = iK_bm V = (4/3)πr³ A = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)| (a+b)ⁿ = Σ_k=0ⁿ (nCk)a^n-kb^k P(n, r) = n!/(n-r)! (Σ a_i²)(Σ b_i²) ≥ (Σ a_ib_i)²

E = hf A = ∫_a^b f(x) dx (1+x)ⁿ = Σ ⁿ C _k.x^k P_solution = X_solvent × P^°_solvent ΔG = ΔH - TΔS 1/f = 1/v + 1/u P = W/t F_c = mv²/r F = k( q₁q₂ )/r² S = a/(1 - r) d/dx(ln x) = 1/x sin 2θ = 2 sinθ cosθ y - y₁ = m(x - x₁) d/dx(sin x) = cos x S_n = (n/2)[2a + (n - 1)d] ln(P₂/P₁) = -ΔH_vap/R (1/T₂ - 1/T₁) sin²θ + cos²θ = 1 F = q(E + v × B) f(x) = Σ_n=0∞ (f⁽ⁿ⁾(a)/n!)(x-a)ⁿ d = √((x₂-x₁)²+(y₂-y₁)²) v = u + at sin x = Σ (-1)ⁿ x⁽²ⁿ⁺¹⁾/(2n+1)!