FORMULAE LIST
                                               Standard derivatives                                                                                     Standard integrals
                                                                                                                                                                                           fxdx
                                         fx                                           fx                                                       fx                                             ()
                                            ()                                          ′()                                                       ()                                   ∫
                                                                                         1                                                                                          1
                                       sin−1x                                                                                              sec2 ax                                      tan(ax)+c
                                                                                      1−x2                                                          ()                              a
                                       cos−1x                                     −         1                                                     1                                  sin−1 x +c
                                                                                                 2                                               22                                                
                                                                                        1−x                                                   ax−                                               a
                                       tan−1x                                            1                                                         1                              1tan−1 x +c
                                                                                              2                                                 22                                                   
                                                                                     1+x                                                     ax+                                  a              a
                                         tanx                                        sec2 x                                                       1                                     ln|xc|+
                                                                                                                                                  x
                                                                                               2                                                    ax                                   1 ax +
                                        cotx                                   −cosec x                                                           e                                      aec
                                        secx                                     secxxtan
                                      cosecx                                 −cosecxxcot
                                          lnx                                            1
                                                                                         x
                                            ex                                           ex
                       Summations
                                                                                                                                              1       21
                                                                     (Arithmetic series)                                            Sn=+ an− d
                                                                                                                                      n                        ()
                                                                                                                                             2                               
                                                                                                                                                          n
                                                                                                                                             ar1−
                                                                     (Geometric series)                                             S = (                   )
                                                                                                                                      n          1−r
                                                                          n                                 n                                                n               22
                                                                                        ()1                                 ()11()2                                            ()1
                                                                                      nn+                         2      nn++n                                     3       nn+
                                                                              r =                    ,          r =                                   ,          r =
                                                                         ∑∑∑
                                                                                            2                                         6                                            4
                                                                         r==r                                                                               r=
                                                                            1                                 1                                                1
                       Binomial theorem
                                                                                   n        n n                                      n                            n!
                                                                                                          nr−    r                                 nC
                                                                        ab+           =                ab                                      ==
                                                                      ()                                               where 
                                                                                          ∑                                          r              r
                                                                                          r=0 r                                                            rn!(     −r)!
                       Maclaurin expansion
                                                                                                                                                                   iv
                                                                                                                                   234
                                                                                                                            0                     0                    0
                                                                                                                      fx()                 fx()                  fx()
                                                                                                                        ′′                   ′′′
                                                                                          00
                                                                        fx()=+ff()                      ()x+                          +                     ++...
                                                                                                      ′                    2!                   3!                    4!
                                                                                                               Page two
                                           FORMULAE LIST (continued)
           De Moivre’s theorem
                                                  n   n
                                  r(cosθ +=isinθ)    rncos θ+insin θ
                                                        ()
                                 []
           Vector product
                                                      ijkaaaa aa
                                                  ˆ                  2313 12
                                       ===−+
                                    ×        sinθ     aaa
                                   ab ab n                        i         j         k
                                                       123bbbb bb
                                                      bbb 2313 12
                                                       123
           Matrix transformation
                                                                      cosθθ−sin
           Anti-clockwise rotation through an angle, θ about the origin, ⎡⎤
                                                                     ⎢⎥
                                                                      sinθθcos
                                                                     ⎣⎦
                                                   Page three