ANSWERS
嚜澤NSWERS
1.3 EXERCISE
1. (i) {2}
(ii) {0, 1}
2. (i) {0, 每1, 1}
(ii)
3.
?11
3
(iii)
{?
3, ? 2, 2, 3
}
{1, 2, 22, 23, ...2P 每 1,(2p 每1}
4. (i) True
(ii) False
7. (i) {2, 4, 6, 8, ... , 98}
8. (i) {4, 8, 12}
9. (i) {4, 5, 6, ....10}
10.
13.
16.
24.
25.
28.
30.
34.
(iii) {1, p}
(ii) {7, 8, 9}
(iii) True
(iv) True
(ii) (1,4, 9, 16, 25, 36, 49, 64, 81,}
(iii)
(ii) {5}
1 3
,1,
2 2
(iv) {0, 1, 2}
(iii) {1, 2, 3, 4, 5}
11.
True
14. False
15. True
True
17. True
22. T = {10}
(i) 2 (ii) 3 (iii) 3 (iv) 9
25
26. 20
27. (a) 3300 (b) 4000
(i) 6, (ii) 3, (iii) 9, (iv) 1, (v) 2, (vi) 6, (vii) 30, (viii) 20 29. C
B
31. B
32. D
33. C
D
35. B
36. B
37. C
18/04/18
304
38.
42.
46.
49.
51.
53.
57.
EXEMPLAR PROBLEMS 每 MATHEMATICS
C
39.
B
43.
n (B)
47.
{0, 1, 2, 3, 4, 5, 6, 8}
A ﹍ 弛∩
52.
True
54.
True
58.
C
40. A
41. B
C
44. [1,2]
45. 1
A ﹎ B∩
48. {耳, {1}, {2}, {1, 2}
50.(i) {1,5, 9, 10 } (ii) { 1, 2,3, 5, 6, 7, 9, 10 }
(i) ?(b) (ii) ?(c) (iii) ? (a) (iv) ?(f) (v) ?(d) (vi) ? (e)
False
55. False
56. True
False
2.3 EXERCISE
1.
(i) {(每 1, 1), (每1, 3), (2, 1), (2, 3), (3, 1), (3, 3)}
(ii) {(1, 每1), (1, 2), (1, 3), (3, 每1), (3, 2), (3, 3)}
(iii) {(1, 1), (1, 3), (3, 1), (3, 3)}
(iv) {(每1, 每1), (每1, 2), (每1, 3), (2, 每1), (2, 2), (2, 3), (3, 每1), (3, 2), (3, 3)}
2. {(0, 1), (0, 2), (1, 1), (1, 2), (2, 1), (2, 2)}
3. (i) {(0, 3), (1, 3)}
(ii) {(0, 2), (0, 3), (0, 4), (0, 5), (1, 2), (1, 3), (1, 4), (1,5)}
4.
5.
6.
7.
8.
9.
10.
(i) a =
2
11
and b =
3
3
(ii) a = 0 and b = 每 2
(i) {(1, 4), (2, 3), (3, 2), (4, 1) }
(ii) {(1, 1), (1, 2), (1,3),(2, 1), (2, 2), (3, 1)}
(iii) { (4, 5), (5, 4), (5, 5)}
Domain of R = {0, 3, 4, 5} = Range of R
Domain of R1 = [每5, 5 ] and Range of R1 = [每3, 17 ]
R2 = {(0, 8), (8, 0) (0,每 8), (每 8, 0)}
Domain of R3= R and range of R3 = R+ ﹍ {0}
(i) h is not a function (ii) f is a function (iii) g is a function
function(v) t is a constant function
11. (a) 6
(b)
1364
4
12. (a) x = 4
(b) x > 4
2
13. (i) (f + g) x = x + 2x + 2
(c) 13
(iv) s is a
(d) t2 _ 4 (e) t + 5
(ii) (f 每 g) x = 2x 每 x2
18/04/18
ANSWERS
305
? f ?
2x + 1
(iv) ? ? x = 2
x +1
?g?
(iii) ( f g) x = 2x3 + x3 + 2x + 1
14. (i) f = {(每1, 0), (0, 1), (3, 28), (7, 344), (9, 730)}
15. x = 每1 ,
4
3
16. Yes, 汐 = 2 , 汕 = ?1
17. (i) R 每 {2n羽 : n﹋Z}
(iv) R 每 {每1, 1}
18. (i) [
3
,﹢)
2
(ii) (每 ﹢, 1]
(ii) R +
(v) R 每 {4}
(iii) R
(iii) [ 0 , ﹢)
(iv) [ 每 2, 4]
?2 x , ? 3 ≒ x < ? 2
19.
f ( x) =
4 , ? 2≒ x < 2
2 ,2≒ x≒3
21. (i) (f + g) x =
x+x
(ii) (f 每 g ) x =
? f ?
1
?x=
x
?g?
3
(iii) (fg) x = x 2
22.
24.
28.
32.
36.
38.
42.
x 每x
(iv) ?
Domain of f = (5, ﹢) and Range of
D
25. D
B
29. B
C
33. A
{2, 3, 4, 5}
37. (a) ? (iii) (b)
False
39. False
True.
f = R+
26. B
27.
30. A
31.
34. B
35.
? (iv) (c) ? (ii) (d)
40. True
41.
C
C
A
? (i)
False
3.3 EXERCISE
4.
56
33
5.
2cos x
cos 2 x
18/04/18
306
EXEMPLAR PROBLEMS 每 MATHEMATICS
1
2 +1
8.
16. 牟 = 2n羽 +
18. 牟 =
15. 牟 = n羽 + (每1)n
7羽
4
17. 牟 = 2n羽 ㊣
羽 5羽
,
3 3
19. x =
22. 1
25.
23
17
3 ?1 1
+
2
2
羽
4
3
2
27. n羽 ㊣
28.
n羽 羽
㊣
2 8
29. 牟 = 2n羽 ㊣
30.
34.
38.
42.
46.
50.
54.
C
B
A
A
C
C
A
D
C
B
D
C
B
B
58. B
59. D
62. tan 汕
63.
x2 ?
32.
36.
40.
44.
48.
52.
56.
羽 羽
+
4 12
D
B
D
C
C
C
A
33.
37.
41.
45.
49.
53.
57.
C
C
D
B
B
C
B
60. 1
61.
1
8
1
[4 每 3(a2 每 1)2] ,
4
2
x + 1 65. 13
sin 2A
68. True
69. False
72. False
73. True
76. (a) ? (iv) (b) ? (i) (c) ? (ii) (d)
64.
羽
3
羽 羽 羽
, ,
6 4 2
26.
31.
35.
39.
43.
47.
51.
55.
羽 羽
?
4 4
2 ? a2
66. [每3, 3]
67. 2
70. False
74. True
? (iii)
71. True
75. True
18/04/18
ANSWERS
307
4.3 EXERCISE
1. P(n) : 2n < +n
2. P(n) : 1 + 2 + 3 + ... + n =
26. A
29. 4
27. B
30. False
28.
n (n + 1)
2
A
5.3 EXERCISE
1.
2n
2. 每1 + i
5.
(1, 0)
6. icot
13. 1:3
2 ㊣ i 2, ? 2 ㊣ i 2
23.
2 cos
(a
牟
2
11.
10
2
,0 ,
3
3
14.
21.
25. (i)
3. (0, 每 2)
3
每 2i
2
12.
15. 1
2
5
1
每 2i
2
18. 0
22. 每2 每 i
5羽
5羽
+ i sin
12
12
2
+ b2
)( z
1
(iii) 每2 (iv) 0 (v)
2
+ z2
2
)
(ii) 每15
1 i
?
2 2
(vi) z1 (vii) 0
(viii) 6 and 0 (ix) a circle
26. (i)
(v)
27. (a)
(d)
(g)
4.
F
T
? (v),
? (iv),
? (viii) and
(ii)
(vi)
(b)
(e)
(h)
(x) 每 2 3 + 2i
F
T
? (iii),
? (ii),
? (vii)
(iii)
(vii)
(c)
(f)
T
F
? (i),
? (vi),
(iv) T
(viii) F
18/04/18
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