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Form Five                                                            Form Five


          Answers to Revision Exercise 9

                 2         3                   x 5   3
          1.    (a)    (3x −  1) +  2  c    (b)   +  x +  c
                 9                              5
         FOR ONLINE READING ONLY
                 1                             1
                          1
                 (c)  ln e 2x  ++ c         (d)   x +  5  3x +  4  16x +  3  32x +  2  c
                 2                             5
                 2       5  2       3           x 3        1     1
                                                                       +
                 (e)  ( x −  ) 1  2 +  ( x −  ) 1  2 +  c    (f)    tan x −  − 1  x +  2  ln (1 x +  2 ) c
                 5          3                   3          6     2
              π            ln 3
          2.            3.
              12            4
                  116                      2      1   
                                                         θ 
          4.   (a)  −                 (b)   tan − 1    tan   + c
                  15                       3       3    2
                (c)                      (d)   x e −  2 x  2xe +  x  2e +  x  c


          5.   0.1794

                1                  −  x +  2  4       1        1
          7.  (a)   ln 3          (b)   −  +  c          (c)   (sin x −  sin 7 )x +  c
                4                   4x                2        7
                  e x  cos x  e x  sin x       2         4      θ      1 
                (d)  −    +         +  c     (e)    tan − 1  tan   +       +  c
                                                                
                     2         2               23          23       23   
                                                                  2
                1    − 1   θ − 3                               1
                                                                        6x
                (f)   2  tan      2     + c               (g)  2.3752             (h)  6ln 24 24 + c

                                                          2
          9.  (a)  sin(x −  2  5) c+                       (b)  cos(x−  3  − 2x ++
                                                             1) c
                           x
                                      1 sin (3 )z   2sin (3 )z  sin (3 )z   13
                                          
                                                          11
                                              9
                (c)  2 2 cos−   +  c  (d)        −           +           +  c
                           2
                                       3    9         11          13   
                1               3     1                1
                      3
                (e)     cos 2 sin 2t  t +    2t −  sin8t     +  c  (f)  cos(cos3 )x + c
                2               8     4                  3
                  
                       3
                                  5
                1 tan 3y     2 tan 3y   tan 3y   7
                (g)       +          +          +  c
                3    3         5          7   
                                  205
                                             Mathematics for Advanced Secondary Schools

                                                                        30/06/2024   18:02:55
   ADVANCED MATH F.5 TG CHAPTERS.indd   205                             30/06/2024   18:02:55
   ADVANCED MATH F.5 TG CHAPTERS.indd   205
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