Page 47 - Pra U STPM 2022 Penggal 2 - Mathematics

Mathematics Semester 2 STPM Answers
2t
2
(c) –3t (t – 1) 2 (d) 2
2
4
3. 2(2 – x) 4. –3x + 6x + 8x 3t + 1
3
2 2
(x + 2) 3 (x + 2x ) 2. (a) –cot q (b) –tan q
5. 2x cos x – sin x 6. (ln x) – 1 3. 1
2x x (ln x) 2 4. cos t
t
e
x
7. 1 8. e (x – 2) 5. (0, 2), (0, –2)
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1 + cos x (x – 1) 2 9. (2, 2), (2, –2)
2
9. sec x 10. –cosec x
2
11. sec x tan x 12. –cosec x cot x Exercise 2.9
x
13. 2 14. e 1. (a) 2 1 (b) 34
1 – sin 2x (2 + e ) (c) 2 (d) –1
x 2
4
15. 1 1
1
x (1 – x ) 2 2. –2, 2 2
Exercise 2.6 3. (a) – 10 (b) – 3
13
4
1. 3e 3x 2. 2x e x 2 4. (a) (3, –5) (b) (2, –8)
3. 2 4. 6(x + 1) 5 (c) (0, –8)
x – 1
π
2
1
3
5. 36x (2x + 1) 5 6. 8x 5. 2n π + , 1
2
2
x + 1 2
–2
7. 2 sin x cos x 8. – (x + 1) Exercise 2.10
π
2
9. 2x e (x + 3) 10. 3 cos (3x + ) 1. Increase for x . 3,
4 decrease for x , 3
2
11. 4x sin (x + 1) cos (x + 1)
2
12. 2 cot 2x 13. –(e + e )(e – e ) 2. Increase for x . 4,
–x –2
x
x
–x
decrease for x , 4

2
14. –cosec x 15. – 4x sin (2 + 2x )
3. Increase for x , –1,
16. (2x – 3)(43 – 6x) 17. –sin x decrease for x . –1
(3x + 4) 4 1 + cos x 4. Increase for x , –2 and x . 2,
2
18. x 19. 2 sec 2x decrease for –2 , x , 0 and 0 , x , 2
1 + x 2 tan 2x
4
20. 2x + 5 21. tan x Exercise 2.11
2
2 3) 1. – , – 25 2
(x + 5x +
1
1
24. – 1 3 25. –1 1 2 14 4
2 1 1 π – 1 2 — 2 2. 1 3 , – 27 2 , (3, –10)
2
3. (1, 0)
Exercise 2.7 4. (–2, 9)
1. (a) x + y dy = 0 5. (–1, –2), (1, 2)
dx
(b) 8x + 18y dy = 13 6. (2, 108), (0, 0), (5, 0)
dx 1 3
(c) 2x + y + (x + 2y) dy = 0 7. 1 4 ln , 12 2
2
dx
dy π π 5π 5π
(d) x + (y – 3) = 0 8. 1 , + 3 ), ( , – 3 2
2
2
dx 6 6 6 6
2
(e) 3x + y + (2xy – 5x) dy = 5y — 1 2 1
2
1
dx
2 3 9. e , 2e 2
2. (a) 2y – 2xy (b) cot x cot y 1
2 2
3x y – 4xy – 3 10. 1 2 ln 2, 2 2 2
(c) x (d) 2x + 5y + 2
y 2y – 5x + 3 Exercise 2.12
(e) sin 2x – cos 2x – 3y 1. (a) (0, 0) maximum, 1 2 –4 2 minimum
,
3 3x
x e x e 3 27
2 3x
6. 1 (b) (2, 10) point of inflexion
7. 3 (c) (2, 32) maximum, (6, 0) minimum
8. – 1 (d) (–1, –1) minimum, (0, 0) point of inflexion
3 2. (3, 9)
Exercise 2.8 3. (a) (0, 0) (b) (2, –11)
2
1. (a) 1 (b) 3(t + 1) (c) (–1, –25), (3, –173) (d) (2, 0), (1, –1)
t 2t
197
Ans STPM Math T Term2.indd 197 28/01/2022 5:52 PM