Page 55 - PRE-U STPM MATHEMATICS (T) TERM 1

Mathematics Term 1 STPM Answers

9. (a) sin 3x + sin x (b) cos 8q + cos 2q Exercise 1.16
1
3
(c) 3(cos x – cos 5x) (d) 1 (sin 6q – sin 2q) 1. –π , x , – π, π , x , π
2 4 4
π
(e) cos 2A + cos 2B (f) 1 (1 + 2 sin 2q) 2. – , x , 0.212π, 0.788π , x , π
4 2
10. (a) 2 sin 3x cos 2x 3. –π , x , –0.732π, 0.268π , x , π
(b) 2 cos 5A cos 2A 11 7 5 1
(c) –2 cos 4x sin x 4. – 12 π , x , 12 π, – 12 π , x , – 12 π,
(d) 2 sin 3A sin 2A 1 5 7 11
(e) 2 sin 45° cos 15° 12 π , x , 12 π, 12 π , x , 12 π
(f) 2 cos 60° cos 10° 5. –0.885π , x , –0.615π, –0.385π , x , –0.115π,
(g) 2 cos x sin y 0.115π , x , 0.385π, 0.615π , x , 0.885π
(h) –2 sin 2A sin A 1 1
11. (a) cos x (b) 0 6. – π , x , 0, π , x , π
4
4
12. (a) cot 5q (b) –tan 3q 7. –π , x , –0.580π, 0.580π , x , π
(c) cot 2x (d) –tan x
2
π
8. –π , x , – , 0 , x , π
Exercise 1.14 2 2
1. (a) 23°35´, 156°25´ (b) 60°57´, 240°57´ STPM PRACTICE 1
(c) 138°35´, 221°25´ (d) 226°3´, 313°57´ 1
2. (a) –49°28´, 49°28´ (b) 56°6´, 123°54´ 1. f : x ⟼ 1 x – 3 3 — –1
–1
2 ; graph of f is the reflection of the graph
(c) –37°36´, 142°24´ (d) –111°36´, 111°36´ 4
3. (a) 36°52´, 216°52´ (b) 135°, 315° of f about y = x.
–1
(c) 48°35´, 131°25´ (d) 48°11´, 311°49´ 2. fg : x ⟼ –ln x, f : x ⟼ e x
4. (a) 60°, 120°, 240°, 300° (a) graph of fg is the reflection of the graph of f about the
(b) 60°, 90°, 270°, 300° x-axis.
–1
(c) 0°, 78°28´, 180°, 281°32´, 360° (b) graph of f is the reflection of the graph of f about y = x
(d) 270° 3. (a) y
(e) 0°, 30°, 150°, 180°, 360°
(f) 56°19´, 90°, 236°19´, 270° 6
3
π
5. (a) – π, –0.148π, , 0.852π
4 4
(b) –0.920π, –0.080π
π
(c) – , 0, π 2
3 3
3
π
(d) –0.621π, – , 0.379π, π 0 x
4 4 –3 –2 –1 1 2 3
6. (a) 41°25´, 120°, 240°, 318°35´ –2
(b) 60°, 300°
(c) 70°32´, 120°, 240°, 289°28´ Range of f is [–2, 6]
(d) 19°28´, 30°, 150°, 160°32´
–1
(e) 18°26´, 135°, 198°26´, 315° (b) g : x ⟼ x – 4 – 1
(f) 45°, 75°58´, 225°, 255°58´ 4. (a) f (x) = 1 ± x – 1
–1
4
3
7. (a) 2 π, π (b) 0.232π, 0.768π, π (b) 4 < x < 3
3 3 2 3 2
7
3
5
(c) π , π, π, π (d) 0, 0.580π, π, 1.420π, 2π (c) No
4 4 4 4
5. f is a one-to-one function
1
1
1
1
1
Exercise 1.15 [–1, 1], [– π, π], π, , π
1. (a) 135°, 161°34´, 315°, 341°34´ 2 2 6 2 6
1
(b) 38°58´, 162°50, 218°58´, 342°50´ 6. (a) g : x ⟼ x + 1 (b) g : x ⟼ x + 1
2
2
2. (a) 2 cos (q + 45°); max. 2, q = 315°, min. – 2, q = 135° 7. (a) f : x ⟼ (x + 1) 2 (b) f : x ⟼ x – 1
2
(b) 2 cos (q + 30°); max. 2, q = 330°; min. –2, q = 150°
(c) 13 cos (q – 67°23´); max. 13, q = 67°23´; 8. f : No, [–1, 1]
min. –13, q = 247°23´ g : No, [1  2 ]
(d) 5 cos (q – 26°34´); max. 5, q = 26°34´; h : Yes, [–∞, ∞]
min. – 5 , q = 206°34´ — 1 3
–1
–1
9. (a) f (x) = x – 1 (b) g (x) = (x + 3)
3. (a) 74 sin (q – 0.951) (b) 3 5 cos (q – 0.464) y y g
(c) 5 5 cos (q + 0.464) (d) 65 sin (q + 0.519) f –1
f –1 g
4. (a) 26°10´, 110°14´ (b) 41°36´; 244°40´
(c) 180°, 313°36´ (d) 97°58´, 205°54´ 0 x 0 x
6. (a) 10°54´, 231°1´ (b) 257°36´, 349°48´
7. r = 5, s = 6, a = 36°52´
274
Answers STPM Math T S1.indd 274 3/28/18 4:25 PM