MEI OCR Maths Formulas

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)