Edexcel A Level Maths – Pure 2023 With Verified and Elaborated Questions

Edexcel A Level Maths – Pure 2023 With Verified and Elaborated Questions Cosine Rule - Know 2 sides, and the angle in between. You want the missing side. Correct Answer a² = b² + c² - 2bcCosA Cosine Rule - Know 3 sides. You want an angle. Correct Answer Cos A = (b² + c² - a²) ÷ 2bc Sine Rule - Know 2 angles and a side. You want the missing side. Correct Answer (a ÷ SinA) = (b ÷ SinB) = (c ÷ SinC) Sine Rule - Know 2 sides and an angle. You want a missing angle. Correct Answer (Sin A ÷ a) = (Sin B ÷ b) = (Sin C ÷ c) Midpoint of a line segment on a circle. Correct Answer ( (x₁ + x₂) ÷ 2 ) , ( (y₁ + y₂) ÷ 2 ) Equation of a circle with centre (0,0) Correct Answer x² + y² = r² Equation of a circle with centre (a,b) Correct Answer (x - a)² + (y - b)² = r² Arithmetic nth Term Correct Answer uₙ = a + (n-1)d Arithmetic Series Correct Answer Sₙ = n/2 (2a + (n-1)d) Geometric nth Term Correct Answer uₙ = ar^(n-1) Geometric Series Correct Answer Sₙ = a(1-rⁿ) ÷ (1-r) Equation of a straight line Correct Answer y - y₁ = m(x - x₁) Distance between two points Correct Answer d = √(x₂ - x₁)² + (y₂ - y₁)² Vectors: Distance from origin to (x, y, z) Correct Answer √(x² + y² + z²) Vectors: Distance between (x₁, y₁, z₁) and (x₂, y₂, z₂) Correct Answer √(x₁ - x₂)² + (y₁ - y₂)² + (z₁ - z₂)² Angle between vector and axis for a vector a: xi + yj + zk Correct Answer x axis : cosθ = (x ÷ |a|) y axis : cosθ = (y ÷ |a|) z axis : cosθ = (z ÷ |a|) Vector: AB→ Correct Answer OB→ - OA→ Integration by substitution Correct Answer ∫f(x) = ∫f(x) × (dx÷du) Integration by parts Correct Answer ∫u (dv÷dx) = uv - ∫v (du÷dx)