Page 58 - PRE-U STPM MATHEMATICS (T) TERM 1

Mathematics Term 1 STPM Answers

66. y 74. (a) 0°, 54°44´, 125°16´, 180°, 234°44´, 305°16´, 360°
(b) 257°35´, 349°47´
75. (a) 0°, 63°26´, 116°34´, 180°, 243°26´, 296°34´, 360°
y = 5 sin x
5 (b) 45°, 60°, 135°, 225°, 300°, 315°
76. 323 , – 36
325 325
y = 1 – 2 sin 2x 77. 18.4°, 45°, 198.4°, 225°
1 π
3
x 78. 4 sin 1 q + 2
0 90 180 7π π
–1 (a) min. –4, q = 6 ; max. 4, q =
6
6.5°, 143.5°, 366.5°, 503.5° (b) y
67. r = 13, a = 22.6°
(a) 13, 337.4°, –13, 157.4° 4
(b) y 2 3 y = 2 sin θ + 12 cos θ
2
13
x
0 __ π __ π __ π __ __ π 7π 4π 3π 5π 11π 2π
__ __ __ __ __
2π 5π
6 3 2 3 6 6 3 2 3 6
x –2
0
–22.6 90 180 270 360
–4
π 5π 3π 11π
π
,
–13 (c) q = , , , ; 5 q : , q , 5π 3π , q , 11π 6
2 6 2 6 2 6 2 6
(c) 85.3°, 229.5° 79. 90°, 306.87°
68.
y Chapter 2 Sequences and Series
y = cos 2x
1 Exercise 2.1
1 __ 1. (a) 25, 30; 5n (b) 16, 19; 3n + 1
2 (c) 14, 17; 3n – 1 (d) 32, 64; 2 n
n – 1
x (e) 3 , – 3 ; (–1) n – 1 3
0 __ π __ π __ π 2π 5π π 7π 4π 3π 5π 11π 2π 625 3 125 5
__ __ __ __ __
__ __
– 1 __ 6 3 2 3 6 6 3 2 3 6 (f) 9 11 ; 2n – 1
,
2 11 13 2n + 1
–1 (g) 625 3125 ; ( ) (h) 1 , 1 ; 1
,
5 n – 1
16 32 2 30 42 n(n + 1)
π π
,
{x : 0 < x , , , x , 2π 5π , x , 7π 4π , x , 5π , (i) 5, –6; (–1) n – 1 n
,
3
3
6
3
6 3
6
11π , x < 2π} 2. (a) 1 , 2 , 3 , 4 (b) 1 , – 1 , 1 , – 1
6 2 3 4 5 1! 2! 3! 4!
2
3
69. (a) 2 (b) m , – 1 (c) 1 2 , – 2x 4x 2 , – 8x 2 (d) – x , x 3 , – x 5 , x 7
2 ,
2 1 3 5 7 1.3 3.5 5.7 7.9
70. 8 (e) cos x , cos 2x cos 3x cos 4x
2 ,
3 ,
71. 15 cos (x – 0.6435) x 2x 3x 4x 4
(a) min. –15, x = 3.7851 rad; max. 15, x = 0.6435 rad 3. (a) (–1) (2n – 1) (b) 1 – (–1) n
n
(b) x = 2.2143, 5.3559 3n + 2 2
(c) y (c) n + 3 . 1 – (–1) n

15 n + 5 2
12 4. (a) 3, 2, 2, 3, 8, 35, … (b) 1, 3, 5, 11, 21, 43, …
10 (c) 1, 3, 7, 15, 31, 63, 127, …
1.485 6.086 5. (a) Convergent, 1 (b) Divergent
x (c) Convergent, 2 (d) Convergent, 3
0 0.6435 2.2143 3.7851 5.3559 2π 6. (a) 0 (b) 0 (c) ∞
(d) 1 (e) 2 (f) 2
5 3
10 3 50
∑ (2r – 1)
–15 y = 12 cos x + 9 sin x 7. (a) ∑ r (b) r = 1
r = 1
6
{x : 1.485 < x < 2.214, 5.356 < x < 6.086} 9 1 ∑ (–1) 1 2 r – 1
r – 1 1
(c) ∑ r (d) r = 1 3
r = 0 2
π
x
72. tan 1 – 2 , 2 + 1, 2 – 3 7 6
4 2 (e) ∑ (14 – 3r) (f) ∑ (3 + 2 )
r
73. (a) 1, 1 (b) 8 r = 1 r = 1
2 15 10 8 r
(g) ∑ (–1) rx r (h) ∑
r
r = 1 r = 1 (r + 1)(r + 2)
277
Answers STPM Math T S1.indd 277 3/28/18 4:25 PM