MEI OCR Maths Formulas

The Circle Formula - ANS-(x - a)² + (y - b)² = r² Where (a,b) is the centre and (x,y) is any point on the circle. The Discriminant - ANS-b² - 4ac Where 0 gives a tangent (repeated root); 0 gives two real roots; 0 gives no real roots; d²y/dx² 0 = minimum point SUVAT - ANS-v = u + at s = ut + 0.5at² v² = u² + 2as s = vt - 0.5at² s = 0.5t(u + v) Product Rule - ANS-dy/dx = u(dv/dx) + v(du/dx) Quotient Rule - ANS-dy/dx = (v(du/dx) - u(dv/dx)) / v² Where the original equation is y = u/v. Chain Rule - ANS-dy/dx = (dy/dt)(dt/dx) Where t can be any variable. The Trapezium Rule - ANS-AREA = 0.5(Width of strips)(FirstHeight + 2(Σ Middle Heights) + FinalHeight) Trigonometric Differentiations - ANS-dSinθ/dx = Cosθ dCosθ/dx = -Sinθ dTanθ/dx = Sec²θ Trigonometric Identities - ANS-Sinθ/Cosθ = Tanθ Cosθ/Sinθ = Cotθ Cos²θ + Sin²θ = 1 Sinθ = Cos(90 - θ) Cosθ = Sin(90 - θ) Trig Derivations - ANS-cotθ = 1/tanθ secθ = 1/cosθ cosecθ = 1/sinθ sec²θ = 1 + tan²θ cosec²θ = 1 +cot²θ R and α - ANS-Asinx + Bcosx = Rsin(x+a