【精选】121915 step formula booklet.pdf

Sixth Term Examination Papers              MATHEMATICS LIST OF FORMULAE AND STATISTICAL TABLES Pure Mathematics Mensuration 2 Surface area of sphere = 4π r Area of curved surface of cone = π r × slant height Trigonometry 2 2 2 a = b + c − 2bc cos A Arithmetic Series u = a + (n − 1)d n S = 1n(a + l) = 1n{2a + (n − 1)d} n 2 2 Geometric Series n−1 u = ar n n a(1 − r ) S = n 1 − r a S∞ = 1 − r for |r | 1 Summations n ∑ r2 = 1n(n + 1)(2n + 1) 6 r=1 n 3 1 2 2 ∑ r = 4 n (n + 1) r=1 Binomial Series n + n = n + 1 r r + 1 r + 1 (a + b)n = an + n an−1b + n an−2b2 + . . . + n an−r br + . . . + bn n ∈ , 1 2 r n n n ! where r = Cr = r !(n − r)! n n(n − 1) 2 n(n − 1) . . . (n − r + 1) r (1 + x ) = 1 + nx + x + . . . + x + . . . |x | 1, n ∈ 1.2 1.2.3 . . . r Logarithms and exponentials x ln a x e = a Complex Numbers n n {r(cos θ + i sin θ )} = r (cos nθ + i sin nθ ) iθ e =