Edexcel A Level Maths - Pure|2023 LATEST UPDATE|GUARANTEED SUCCESS

Equation of a straight line y - y₁ = m(x - x₁) Distance between two points d = √(x₂ - x₁)² + (y₂ - y₁)² Integration by substitution ∫f(x) = ∫f(x) × (dx÷du) Integration by parts ∫u (dv÷dx) = uv - ∫v (du÷dx) Trapezium Rule A = ½h (y₀ + 2(y₁ + y₂ ... yₙ-₁) + yₙ) ∫eⁿ eⁿ + c ∫1÷x ln|x| + c ∫cosx sinx + c ∫sinx -cosx + c ∫sec²x tanx + c ∫cosecxcotx -cosecx + c ∫secxtanx secx + c ∫cosec²x -cotx + c ∫tanx -ln|cosx| = ln|cosx|-¹ = ln|1÷cosx| = ln|secx| + c ∫cotx ln|sinx| + c ∫secx ln|secx + tanx| + c ∫cosecx -ln|cosecx + cotx| + c ∫sin²x ½x - ¼sin2x + c ∫cos²x ½x + ¼sin2x + c ∫sin³x -cosx + 1/3cos³x + c ∫cos³x sinx - 1/3sin³x + c Quadratic formula x = (-b ± √(b²-4ac)) ÷ 2a Discriminant rules b² - 4ac > 0 = Two distinct real roots b² - 4ac = 0 = One repeated root b² - 4ac < 0 = No real roots Chain Rule y = (f(x))ⁿ dy/dx = n(f(x))ⁿ-¹ × f'(x) Product Rule y = f(x)g(x) dy/dx = (g(x) × f'(x)) + (f(x) × g'(x)) Quotient Rule y = f(x)÷g(x) dy/dx = ((g(x) × f'(x)) - (f(x) × g'(x)) ÷ (g(x))²