α + β = -b/a αβ = c/a cos 2θ = cos²θ - sin²θ s = ut + ½at² ΔG = ΔH - TΔS V = (4/3)πr³ m = f'(x) E = E° - (0.0591/n) log Q lim_x→a f(x)/g(x) = lim_x→a f'(x)/g'(x) M = moles/volume (f(g(x)))' = f'(g(x))⋅g'(x) 2 sin A cos B = sin(A+B) + sin(A-B) a_n = a + (n - 1)d f'(a) = lim_h→0 (f(a+h)-f(a))/h F = ma d/dx(sin x) = cos x e = (v₂ - v₁)/(u₁ - u₂) ΔT_b = iK_bm x = [-b ± √(b² - 4ac)]/(2a) P = IV sin 2θ = 2 sinθ cosθ v² = u² + 2as Q = It a_c = v²/r S_n = a(1 - rⁿ)/(1 - r)

A = Pe^rt s = (a+b+c)/2, A = √(s(s-a)(s-b)(s-c)) d = |Ax₀ + By₀ + C|/√(A²+B²) A = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)| Rate = k[A]^m[B]ⁿ F_x + F_y(dy/dx) = 0 ε = -dΦ/dt V = IR x = a sinθ Normality = Molarity × n log_b a = ln a/ln b (x-h)² + (y-k)² = r² d/dx(cos x) = -sin x ∫ u dv = uv - ∫ v du A = ab sinθ n = mass/M d = √((x₂-x₁)²+(y₂-y₁)²) (a+b)ⁿ = Σ_k=0ⁿ (nCk)a^n-kb^k n = c/v d/dx(ln x) = 1/x λ = h/p Percent Purity = (mass of pure substance/mass of sample) × 100 (Σ a_i²)(Σ b_i²) ≥ (Σ a_ib_i)² ΔT_f = iK_fm K_c = ([C]^c[D]^d)/([A]^a[B]^b)

I = ½ Σ c_i z_i² P = W/t V = L(dI/dt) sin²θ + cos²θ = 1 F_c = mv²/r p = mv c = λf A = πab m = (y₂ - y₁)/(x₂ - x₁) F = k( q₁q₂ )/r² S_n = (n/2)[2a + (n - 1)d] C(n, r) = n!/(r!(n-r)!) ln(P₂/P₁) = -ΔH_vap/R (1/T₂ - 1/T₁) v = u + at S = a/(1 - r) Φ = BA cosθ f(x) = Σ_n=0∞ (f⁽ⁿ⁾(a)/n!)(x-a)ⁿ f''(x) y - y₁ = m(x - x₁) a_n = ar^{n - 1} P_solution = X_solvent × P^°_solvent T = 2π√(L/g) ∫(dx/x) = ln|x| + C f(x) = Σ_n=0∞ (f⁽ⁿ⁾(0)/n!)xⁿ pK_a = -log K_a

1/f = 1/v + 1/u E = hf d/dx(e^x) = e^x π = MRT P(n, r) = n!/(n-r)! e^x = Σ xⁿ/n! (1+x)ⁿ = Σ ⁿ C _k.x^k Equivalent Weight = Molecular Weight/n A = ∫_a^b f(x) dx K.E. = ½mv² W = Fd cosθ sin A + sin B = 2 sin((A+B)/2) cos((A-B)/2) sin²(θ/2) = (1 - cosθ)/2 pH = -log[H⁺] cos²(θ/2) = (1 + cosθ)/2 U = mgh cos x = Σ (-1)ⁿ x⁽²ⁿ⁾/(2n)! sin x = Σ (-1)ⁿ x⁽²ⁿ⁺¹⁾/(2n+1)! F = q(E + v × B) A = ½ab sin C n₁ sinθ₁ = n₂ sinθ₂ E = VIt