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

Cosine Rule - Know 2 sides, and the angle in between. You want the missing side. a² = b² + c² - 2bcCosA Cosine Rule - Know 3 sides. You want an angle. Cos A = (b² + c² - a²) ÷ 2bc Sine Rule - Know 2 angles and a side. You want the missing side. (a ÷ SinA) = (b ÷ SinB) = (c ÷ SinC) Sine Rule - Know 2 sides and an angle. You want a missing angle. (Sin A ÷ a) = (Sin B ÷ b) = (Sin C ÷ c) Midpoint of a line segment on a circle. ( (x₁ + x₂) ÷ 2 ) , ( (y₁ + y₂) ÷ 2 ) Equation of a circle with centre (0,0) x² + y² = r² Equation of a circle with centre (a,b) (x - a)² + (y - b)² = r² Arithmetic nth Term uₙ = a + (n-1)d Arithmetic Series Sₙ = n/2 (2a + (n-1)d) Geometric nth Term uₙ = ar^(n-1) Geometric Series Sₙ = a(1-rⁿ) ÷ (1-r) Equation of a straight line y - y₁ = m(x - x₁) Distance between two points d = √(x₂ - x₁)² + (y₂ - y₁)² Vectors: Distance from origin to (x, y, z) √(x² + y² + z²) Vectors: Distance between (x₁, y₁, z₁) and (x₂, y₂, z₂) √(x₁ - x₂)² + (y₁ - y₂)² + (z₁ - z₂)² Angle between vector and axis for a vector a: xi + yj + zk x axis : cosθ = (x ÷ |a|) y axis : cosθ = (y ÷ |a|) z axis : cosθ = (z ÷ |a|) Vector: AB→ OB→ - OA→ 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) How do you convert from degrees to radians? × (π÷180) How do you convert from radians to degrees? × (180÷π) Radians: Arc length rθ Radians: Sector Area ½r²θ Radians: Segment Area ½r²(θ - sinθ) Radians: Triangle Area ½r²sinθ ∫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