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