shw 6-01 total: 14 marks (a) review exercise 6 (p. 6.5)personal.tsss.edu.hk/roh/f4/solutions...
TRANSCRIPT
1
SHW 6-01 Total: 14 marks
Review Exercise 6 (p. 6.5)
9.
x
x
xxx
xx
818
8
2)2(
1
)3(4
313
4
31
4
=
=
=
=
−
−−−
×−
−
−
−
1M+1A
11.
qppqqppq
8
818)2(
3
3302
=
÷=÷ −
1M+1A
12.
4
16
)4(1
)4(44
4
1
4
4
1
134
1
3
81
3
3
33
abab
ab
ab
bab
=
=
⎟⎟⎠
⎞⎜⎜⎝
⎛=
⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛
−×−
−×−−
−
−
−
−
−
−−−
−
−
1M+1A 13. (a)
12
)1(1
5
555+
+++
=
=•n
nnnn
1A
(b)
913
3333
2
)12()1(12
1
=
=
=
−
+−−++
−• nnnn
nn
1A
14. (a)
n
n
n
n
236
36
=
⎟⎠
⎞⎜⎝
⎛=
1A (b)
n
nn
nn
nnnn
3
)22()2(
222
12212
2
2
22
)2(242
=
=
•=
•=•
−++
−+
−+−+
1A
15. (a)
913
3333
)3(3)3(
9327
2
)22(3
22
3
12
3
1
=
=
=
•=
•=
•
−
+−−
+
++
nnn
nn
n
nn
n
nn
n
1M+1A (b)
82
22
22)2(
)2()2(8164
3
)36(4)62(
36
462
123
432
12
3
=
=
=
•=
•=
•
+−++
+
+
+
+
+
+
nnn
n
nn
n
nn
n
nn
1M+1A
2
SHW 6-A1 Total: 20 marks 1. (a)
21
61
361
3)(
a
aa
=
=×
(b)
52
54
21
54
21
54
)()(
a
a
aa
=
=
=
×
(c)
21
21
)2(23
223
243
2
1
)(
a
a
a
aaaa
=
=
=
×=×
−
−+
−−
1M+1A+1M+1A+1M+1A
2.
2433
3
33
)3()3(279
5
)2(3
23
32
323
232
23
=
=
=
÷=
÷=÷
−−
−
−−
1M+1A
3. (a)
4
56
542
56
54
2
352
54
2 )(
aa
aaa
aaa
=
=
÷×=
÷×
⎟⎠
⎞⎜⎝
⎛−−+
−
−
1M+1A
(b)
45
45
23
21
43
23
21
21
321
43
23
21
21
21
21
3
43
21
3
43
4
2
)2(2
82
)8()2(82
a
a
a
a
aa
aa
aaa
a
=
×=
××=
×=
×=×
+
−+
1M+1M+1A
(c)
34
65
34
65
131
21
34
21
31
34
131
3 4 )(
b
a
ba
ba
ba
baabba
=
=
=
×=
×
−
−−−
−−
1M+1M+1A
4. (a)
162)(
2
4441
41
=
=
=
xx
x
1M+1A
(b)
102421
21
161)(
161
10
25
4
25
25
52
52
=
⎟⎠
⎞⎜⎝
⎛=
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛=
⎟⎠
⎞⎜⎝
⎛=
=
−
−
−−−
−
x
x
x
1M+1A
3
SHW 6-A2 Total: 20 marks
1. (a)
6
23)4(
23
423
4 )(1
aa
aa
=
=
=⎟⎠
⎞⎜⎝
⎛
⎟⎠
⎞⎜⎝
⎛−×−
−−
−
1M+1A
(b)
41
21
21
21
21
21
)(
a
a
a
aa
=
=
=
=
×
1M+1A
(c)
51
561
56
1
352
1
3
3
3
)(
3
a
a
a
a
a
a
=
=
=
⎟⎠
⎞⎜⎝
⎛−−−
−
−
−
−
1M+1A
2.
361616
)6(
])23[(
])2(3[)83(
2
2
34
23
34
23
34
21
323
34
23
=
=
=
=
×=
×=×
−
−
−
−−
1M+1M+1A
3. (a)
2
23
21
23
21
)2(43
21
2411
21
2
41
21
212
421
3
3
3
3
)(3
9)9(
aa
aa
aa
aa
a
aaaaa
=
=
÷=
÷=
÷=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛÷=⎟⎟
⎠
⎞⎜⎜⎝
⎛÷
⎟⎠
⎞⎜⎝
⎛−−
−
−×
−−
−−
1M+1M+1A
(b)
2
21
31
65
2
65
31
265
3
631
)
ab
ba
bb
abb
a
=
=
×=×(
−−
−−
1M+1M+1A
(c)
47
41
)1(43)1(
43
21
1
143
43
211
43
)(
ba
ba
babaa
baaba
=
=
××=⎟⎠
⎞⎜⎝
⎛××
−−−++
−
−−
1M+1M+1A
4.
9)3(
27)(
27
32
3
32
32
23
23
=
=
=
=
x
x
x
1M+1A
4
SHW 6-B1 Total: 20 marks 1. (a)
∴
13322
8233
3
=
=
=
=
xx
x
x
1M+1A
(b)
∴
12155
)5(5
255
21
121
11
−=
−=−
=
=
=
−−
−−
−−
xx
x
x
x
1M+1A
(c)
∴
41212
66
6)6(
636
21
2
21
2
=
=
=
=
=
x
x
x
x
x
1M+1A 2. (a)
∴
53222
82
24)2(3
24)12(2
242)2(2
2422
24)2(22
32
2
2
22
222
2
3
=
=−
=
=
=
=−
=−
=−
=−
−
−
−
−
−−
−
−
xx
x
x
x
x
xx
xx
xx
1M+1A
(b)
∴
2312244414
43)14(4
434)4(4
4344
43)4(4
43164
122
22
22
2222
2232
1232
132
−=
−=+
=
=
=−
=−
=−
=−
=−
−+
+
+
++
++
++
++
x
x
x
x
x
xx
xx
xx
xx
1M+1A
3. (a)
∴
3221
66
)6(6
366
221
121
11
=
−=+
=
=
=
−+
−+
−+
xxx
xx
xx
xx
1M+1A
(b)
∴
155
843922
)2()2(
168
8439
24133
213
=
=
+=+
=
=
=
++
++
++
xx
xx
xx
xx
xx
1M+1A
(c)
∴
75573614
33
3)3(3
)3(])3[(3
27)9(3
3614
364
2322
22
=
=
−=+
=
=
=
=
−+
−
−
−
x
xxx
xx
xx
xx
xx
1M+1A
4. (a)
∴
233
93
45)3(5
45)133(3
453)3(3)3(3
45333
2
2
2
12
=
=
=
=
=−−
=−−
=−− ++
x
x
x
x
x
xxx
xxx
1M+1A
(b)
∴
12255
255
225)5(9
225)1515(5
225)5)(5(35)5(5
225)5(355
225)5(3)5()5(
225)5(32525
22
2
2
22
2222
12222
12212
121
=
=
=
=
=
=−−
=−−
=−−
=−−
=−−
++
++
++
xx
x
x
x
x
xxx
xxx
xxx
xxx
1M+1A
5
SHW 6-B2 Total: 20 marks 1. (a)
∴
2
12
33
)3(3
273
12
31
32
31
2
=
=
=
=
=
x
x
x
x
x
1M+1A
(b)
∴
433422
)2()2(
324
34
53
522
53
2
−=
−=
=
=
=
−
−
−
x
x
x
x
x
1M+1A
(c)
∴
6
32
77
)7()7(
49)7(
32
23
221
23
−=
=−
=
=
=
−
−
−
x
x
x
x
x
1M+1A
2. (a)
∴
32155255100)15(51005)5(510055
21
1
1
11
1
=
=−
=
=
=−
=−
=−
−
−
−
−−
−
xx
x
x
x
xx
xx
1M+1A
(b)
∴
23212339336)13(3363)3(33639
212
12
12
1212
12
=
=−
=
=
=+
=+
=+
−
−
−
−−
−
x
x
x
x
x
xx
xx
1M+1A
(c)
213622812
89)2(9
89)12(2
89)2()2(
8948
36
6
6
36
32123
312
−=
−=
=
=
=
=+
=+
=+
−
+
+
x
x
x
x
x
x
xx
xx
1M+1A 3. (a)
7117
243333927
2433
121
=
=
+=−
=
=+−
+−
x
xxx
xx
xx
1M+1A
(b)
242232
55)5(255
232
32
−=
−=
+=−
=
=+−
−
xx
xx
xx
xx
1M+1A
(c)
∴
181845
9225
22
)2(22
])2[(2)2(
)4(832
36225
62325
32325
32
=
+=
+=
=
=
=
=
++
+
+
+
xxx
xx
xx
xx
xx
xx
1M+1A
4.
12222412
87
21212
87)2(
21)2(22
87224
22
2
2
222
1212
−=
−=
=
=
=⎟⎠⎞
⎜⎝⎛ ++
=++
=++
−
−+
xx
x
x
x
xxx
xxx
1M+1A
6
SHW 6-C1 Total: 26 marks
1. (a)
fig.) sig. 3 to(cor. 8.7477)1.2()4.1( 1.24.1
=
+=+ ff
(b)
fig.) sig. 3 to(cor. 378.077)2.1()7.0( 2.17.0
=
•=−• −ff
(c)
fig.) sig. 3 to(cor. 0.0968
77
(3)(1.8)
3
1.8
=
=ff
3A 2. (a) Sam’s present weight
kg 80kg ]3.1[80 )0(02.0
=
= −
(b) Sam’s weight after 20 weeks
kg)nearest the to(cor. kg 72
kg )80(1.3
kg ]3.1[800.4
)20(02.0
=
=
=−
−
2A 3.
(a) From the graph, 6.5 31.7 =
(b) From the graph, 15.5 32.5 =
(c) 1.2
1.211.2
3
)3(31
=
=⎟⎠
⎞⎜⎝
⎛ −−−
From the graph, 1031 1.2
=⎟⎠
⎞⎜⎝
⎛−
3M (for the arrows) +3A 4. (a)
∵ 2.7)2( =f
∴
52.744.12.7)2.1( 2
=
=
=
kk
k
(b) From (a), f(x) = 5(1.2x).
fig.) sig. 3 to(cor. 9.17
)2.1(5)7( 7
=
=f
2A 5. (a)
∵ 4)1( =−f
∴
422
2)2(
221
165.0
445.0
4
41
4
)1(
=
=
=
=⎟⎠
⎞⎜⎝
⎛
=
=
−−
−
−
−
b
b
b
b
b
b
(b) From (a), we have 45.0)(4x
xf =
fig.) sig. 3 to(cor. 0.0146
45.0
45.0)1()2(
)1(4)2(4
−=
−=− ff
2A 6. (a) When t = 0, N = 200.
200
)15.1(200 0
=
=
AA
(b) Number of insects after 4 weeks
integer)nearest the to(cor. 350
)15.1(200 4
=
=
1M+2A 7. (a)
(i) From the graph, 2.54.0 8.1 =−
(ii) 4.2
4.24.2
4.052
25
−
−
=
⎟⎠
⎞⎜⎝
⎛=⎟
⎠
⎞⎜⎝
⎛
From the graph, 925 4.2
=⎟⎠
⎞⎜⎝
⎛
2M (for the arrows) +2A
(b)
(i) From the graph, x = −2.6.
(ii)
94.0
952
925
=
=⎟⎠
⎞⎜⎝
⎛
=⎟⎠
⎞⎜⎝
⎛−
x
x
x
From the graph, x = −2.4. 2M (for the arrows) +2A
7
SHW 6-C2 Total: 21 marks
1. (a)
fig.) sig. 3 to(cor. 4.30)5.1(46.0)5()8( 58
−=
−=− gf
(b)
fig.) sig. 3 to(cor. 5.80
)4(1.54
0.6(0.9)4
(3.6) 0.93.6
=
+=+ gf
(c)
fig.) sig. 3 to(cor. 1.33
6.0)]5.1(4[3
2.4)(2.4)(3
4.2
4.2
=
=−−
−
−
fg
3A 2. The required height
fig.) sig. 3 to(cor. m 3.56m )75.0(15 5
=
=
1A 3.
(a) From the graph, 5.34 9.0 =
(b) From the graph, 7457
=
(c) 9.1
9.119.1
4
)4(41
=
=⎟⎠
⎞⎜⎝
⎛ −−−
From the graph, 1441 1.9
=⎟⎠
⎞⎜⎝
⎛−
3M (for the arrows) +3A 4. (a)
∵ 125)3( =f
∴
2581258125125)(8
3
3
3
=
=
=
=
a
a
a
(b) From (a), we have x
xf ⎟⎠
⎞⎜⎝
⎛=
258)(
fig.) sig. 3 to(cor. 0.259
25824.5)(2
5.4
=
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛=−
−
f
2A
5. The required increase
integer)nearest the to(cor. 154)000(1.0136 10)000(1.0136 10 910
=
−=
1M+1A 6.
(a) When n = 0, A = 35 000.
000 35
)02.1(000 35 0
=
=
pp
(b) Amount received after 5 years )000(1.02 35$ 5= The required percentage change
fig.) sig. 3 to(cor. %4.10
%100000 35
000 35)000(1.02 35 5
=
×−
=
1A+1M+1A 7. (a)
(i) From the graph, 5.102 4.3 =
(ii) 6.2
6.212.6
2
)2(0.5
=
= −−−
From the graph, 65.0 6.2 =−
2M (for the arrows)+2A
(b)
(i) From the graph, x = 3.9. (ii) From the graph, x = 5.
2M (for the arrows)+2A
8
SHW 6-R1 Total: 30 marks
10. 23
25
23
25
221
121
2
1
b
abaab
baabba
===×
× −
−
−
−
−
1M+1A
11. 81
41
81
1438
143
43
61
1 1)(
baba
aba
aba
===−−
−−−
1M+1A
12. [ ]babababa2
1231
363 36 64)8()8()8( =−=−=− −−−
1M+1A
20.
1515
53)25(5
53)5(25 1
−=
=
=−
=−+
x
x
x
xx
1M+1A 21.
1022125)21(252)2(
22
222
221
=
=−
=
=+
=+
−
−
−
xx
x
x
xx
1M+1A 22.
10331215)12(21522
1528
33
433
3313
131
=
=−
=
=−
=−
−=
−
−
−+
+−
xx
x
x
xx
xx
1M+1A
25. (a) [ ] )4(3)2(3)2(3)2(9)()()( 2 xxxxxgxfxh ==÷== −
1M+1A (b)
∴ 344
644
192)4(3
192)(
3
=
=
=
=
=
b
bh
b
b
b
1M+1A
27. (a) The amount of drug intake = 25(0.85)0 mg = 25(1) mg = mg 25
1M+1A (b) Percentage of drug left after 4 hours
fig.) sig. 3 to(cor.%2.52%100
mg 25mg)85.0(25 4
=×=
1M+1A 30. (a)
(i) From the graph, 2132 50
..
=⎟⎠
⎞⎜⎝
⎛−
(ii) 233
32
32
278
⎟⎠⎞
⎜⎝⎛=⎟
⎠⎞
⎜⎝⎛=
From the graph, 50278 .=
2M (for the arrows)+2A (b)
(i) From the graph, x = –1.7.
(ii)
332
31
23
31
23
11
=⎟⎠
⎞⎜⎝
⎛
⎟⎠
⎞⎜⎝
⎛=
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛
=⎟⎠
⎞⎜⎝
⎛
−−
x
x
x
From the graph, x = −2.7. 2M (for the arrows)+2A
47.
∴
[ ]
244
164
80)4(5
80)32(4
80)4(3)4(2
80)2(3)4(2
80)2()(2
2
2
=
=
=
=
=+
=+
=−−
=−
k
kgkf
k
k
k
k
kk
kk
1M+1A
(a)(ii) (a)(i)