Pelajaran Matematika Semester 2 kelas 11

1. Tugas Selama Belajar Dirumah
10-13 April 2017
Kelas XI MIPA 5 alewoh.com

2. Data Frekuensi
10-19 2
20-29 8
30-39 12
40-49 7
50-59 3
1. Perhatikan table berikut
Data Frekuensi Xi FiXi
10-19 2 14,5 29
20-29 8 24,5 196
30-39 12 34,5 414
40-49 7 44,5 311,5
50-59 3 54,5 163,5
Tentukan rata-rata dari data pada table di atas…..
𝑥 =
𝑓𝑖𝑥𝑖
𝑓𝑖
=
114
32
= 34,8
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3. Jawaban nomor 2
• Letak =
𝑖
4
. 20
• =
3
4
. 20 = 15
• 𝑄3 = 𝑡𝑏𝑄3 + 𝑝
3𝑁
4
−𝐹𝑘𝑢𝑚
𝐹𝑄3
• 𝑄3 = 85,5 + 5
15−12
5
• = 85,5 + 3
• = 88,5
nilai frekuensi
71-75 4
76-80 2
81-85 6
86-90 5
91-95 3
Jumlah 20
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4. 3. Tabel :
Jawaban :
𝑀𝑜 = 𝑡𝑏𝑀𝑜 + 𝑝
𝑑1
𝑑1 + 𝑑2
𝑀𝑜 = 10,5 + 5
6
6 + 2
𝑀𝑜 = 10,5 + 5
6
8
𝑀𝑜 = 10,5 + 3,75
𝑀𝑜 = 14,25
Data Frekuensi
1-5 6
6-10 8
11-15 14
16-20 12
21-25 10
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5. 4. Tabel
Jawaban :
Me = tbMe +
𝑁
2
−𝐹𝑘𝑢𝑚
𝐹𝑀𝑒
161
6
= 23,5 +
27+𝑎+𝑏
2
−(2+𝑎)
18
4
161
6
-
235
10
=
(27+𝑎+𝑏)
2
−(2+𝑎)
18
4
1610−1410
60
=
27+𝑎+23−𝑎−4−2𝑎
2
18
4
200
60
=
46−2𝑎
2
18
4
20
6
=
92−44
18
360 = 552 – 24a a + b = 23
-24a = 552 – 360 8 + b = 23
-24a = 192 b = 23-8
a = 8 b = 15
Me = 26
5
6
27 + a + b = 50
a + b = 50 – 27
a + b = 23
b = 23 – a
nilai f xi
16-19 2 17,5
20-29 21,5
24-27 18 25,5
28-31 29,5
32-35 6 33,5
36-39 1 37,5
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6. 5. Tabel :
Jawaban :
𝑀𝑒 = 𝑡𝑏𝑀𝑒 + 𝑝
𝑁
2
− 𝐹𝑘𝑢𝑚
𝐹𝑀𝑒
𝑀𝑒 = 77,5 + 5
40
2
− 18
9
𝑀𝑒 = 77,5 + 5
20 − 18
9
𝑀𝑒 = 77,5 + 5
2
9
𝑀𝑒 = 77,5 + 1,1
𝑀𝑒 = 78,6
Data Frekuensi
63-67 3
68-72 5
73-77 10
78-82 9
83-87 8
88-92 5
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7. 6. Jawaban :
3 x 4 x 3 x2 = 72
3 4 3 2
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8. 7.
7 sahabat terdiri dari dari 2 laki-laki (misalkan A dan B), 3 laki-laki
(misalkan C,D,dan E), dan 2 perempuan (misalkan F dan G)
𝐶
𝐷
𝐸
𝐷
𝐸
3 × 2 × 1 = 6 cara
2 1 (A dan B ) 2 × 1 = 2 cara
2 1 (F dan G) 2 × 1 = 2 cara
3 2 1 (Secara acak) = 6 cara
Total = 6 × 2 × 2 × 6 = 144 cara
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9. 8. Jawaban :
1
9!
+
5
10!
=
10!+5.9!
9!10!
=
10.9!+5.9!
9!10!
=
9!(15)
9!10!
=
15
10!
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10. 9. Jawaban :
(n+1)! = 9n!
(n+1) n! = 9n!
n+1 = 9
n = 9-1
n = 8
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11. 10.
n + 1P3 = 12 × nP2
n + 1P3 = 12 × nP2
𝑛+1 𝑛!
𝑛+1−3 !
= 12 ×
𝑛!
𝑛−2 !
𝑛+1 𝑛!
𝑛−2 !
= 12 ×
𝑛!
𝑛−2 !
𝑛 + 1 = 12
𝑛 = 11
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12. 11.
10P4 =
10!
10−4
=
10x9x8x7x6x5x4x3x2!
6𝑥5𝑥4𝑥3𝑥2!
= 5040
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13. 12.
BOROKOKOK
B = 1 R = 1 O = 4 K = 3
= 9P(4,3) =
9!
4!3!
=
9 𝑋 8 𝑋 7 𝑋 6 𝑋 5 𝑋 4!
4! 3!
=
1520
6
= 2520
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14. 13.
80
100
× 50 = 40 𝑠𝑜𝑎𝑙
40C15=
40!
25!15!
=
40×393×38×37×36×35×34×333×324×31×30×29×282×273×26×25!
25!15×14×13×12×11×10×9×8×7×6×5×4×3×2×1
= 3 × 38 × 37 × 34 × 3 × 4 × 31 × 29 × 26
= 4.022.534.510
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15. 14.
P = ( n – 1 )
= 4!
Peluang o & j berdekatan
P(A) =
𝑛(𝐴)
𝑛(𝑠)
=
2.4!
5!
=
2.4!
5.4!
=
2
5
n(A) o & j = 2 X 4!
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16. 15.
6
C2
10
C2
=
6!
4!2!
10!
8!2!
=
6!5!4!
2!4!
10!9!8!
2!8!
=
15
45
=
1
3
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17. 16.
Diket : n 𝑚𝑎𝑡𝑒𝑚𝑎𝑡𝑖𝑘𝑎 : 14
n 𝑓𝑖𝑠𝑖𝑘𝑎 : 10
n 𝑚𝑎𝑡 ∩ 𝑓𝑖𝑠 : 4
Dit : p(tidak suka mat&fis) : 1 orang dipanggil
Jawab :
P 𝑚𝑎𝑡 ∪ 𝑓𝑖𝑠 : p 𝑚𝑎𝑡 + p 𝑓𝑖𝑠 - p 𝑚𝑎𝑡 ∩ 𝑓𝑖𝑠
:
14
32
+
10
32
-
4
32
:
20
32
:
5
8
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18. 17.
p(ℎ ∩ 𝑝) = p(h) . p (p/h)
=
7
9
.
2
8
=
14
72
=
7
36
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19. 18.
P(x,y)
𝑀𝑥=2
(2a-x , y)
P(7,8)
𝑥=2
(2.2-7 , 8)
P(7,8)
𝑥=2
(-3,8)
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20. 19.
P 2, −2
Q 0,1
R 2,3
𝑣𝑒𝑘𝑡𝑜𝑟 𝑎,𝑏
𝑅′ 4,6
2a – b = 2 2 – 3 =1
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21. 20.
𝑥′ −2
𝑦′ −1
=
cos (−60) −sin(−60)
sin (−60) cos (−60)
𝑥 −2
𝑦 −1
𝑥′ −2
𝑦′ −1
=
1
2
1
2
3
−
1
2
3
1
2
1− 3
1+ 3
𝑥′ −2
𝑦′ −2
=
1
2
−
1
2
3 +
1
2
3+
3
2
−
1
2
3+
3
2
+
1
2
+
1
2
3
𝑥′
𝑦′
= 2
2
+ 2
1
= 4
3
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22. 21.
(x,y)
𝑀𝑦= −1
(x,2(-1)(-y))
x’= x
y’= -2-y
x= x’
y= -y-2
y-2𝑥2- 8x +11
-y’-2 =2(𝑥′)2- 8(x’)+11
-y’=2𝑥′2-8x’+13
y’ = -2x’2+8x’-13
y’= 2x’2+8x’-13
Titik puncak kurfa
= −
𝑏
2𝑎
, −
𝑏2−4𝑎𝑐
4𝑎
= −
8
2(−2)
, −
82−4(−2)(−13)
4(−2)
=(2,-5)
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23. 22.
Y =-X +7
Y+X = 0 → Y = -X
. 𝑋′
𝑌′
=
0 −1
−1 0
𝑋
𝑌
=
−𝑌
−𝑋
X’ = -Y →Y = -X’
Y’ = -X → X = -Y’
∴ Y = -X + 7
-X’=-(-Y’) +7
-X’ = Y’+7
Y’ = -X’-7
Bayangannya
Y = -X-7
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24. 23.
2x2 + 3x – 6
𝑥′
𝑦′
=
𝑐𝑜𝑠 − 90 sin 90
sin −90 cos −90
𝑥
𝑦
𝑥′
𝑦′
=
0 1
−1 0
𝑥
𝑦
𝑥
𝑦
=
0 1
−1 0
−1
𝑥′
𝑦′
𝑥
𝑦
=
1
0−(−1)
0 −1
1 0
𝑥′
𝑦′
𝑥
𝑦
= −𝑦′
𝑥′
y = 2x2+3x-6
x’= 2(-y)2 + 3(-y’)-6
x’ = 2y’2 - 3y’ – 6
x = 2y2 – 3y – 6
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25. 24.
. 𝑥′
𝑦′
=
𝑘 𝑜
𝑜 𝑘
𝑥−𝑎
𝑦−𝑏
+ 𝑎
𝑏
𝑥′
𝑦′
=
2 0
0 2
𝑥−1
𝑦−2
+ 1
2
𝑥′
𝑦′
= 2𝑥−2
2𝑦−4
+ 1
2
𝑥′+1
2
𝑦′+2
2
= 𝑥
𝑦
(x-5)2 + (y+1)2 = 25
𝑥′+1
2
−
10
2
2 +
𝑦′+2
2
+
2
2
2 = 25
𝑥′−9
2
2 +
𝑦′+4
2
2 = 25
(𝑥′−9)2
4
+
(𝑦′+4)2
4
= 25
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26. 25.
P = 8 L = 8 × 5 = 40
l = 5
L’ = det (A)× 𝐿
L’ = det
2 0
0 2
40
L’=det =ad-bc
L’= 2 × 2 − 0 × 0
= 4 × 40
L’=160
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5 -4 -3 -2 -1 0 1 2 3 4 5
y
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27. 26.
lim
𝑥→∞
𝑥3 − 2𝑥2 − 5
2𝑥3 − 𝑥
lim
𝑥→∞
𝑥3 − 2𝑥2−5
𝑥3
2𝑥3 − 𝑥
𝑥3
lim
𝑥→∞
1 −
2
𝑥
−
5
𝑥3
2 −
1
𝑥2
=
1−0−0
2−0
=
1
2
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28. 27.
. lim
𝑥→∞
(2𝑥−2)3
(3𝑥+3)3
. lim
𝑥→∞
(2𝑥−2)3
𝑥
(3𝑥+3)3
𝑥
. lim
𝑥→∞
(2−
2
𝑥
)3
(3+
3
𝑥
)3
.
(2−0)3
(3+0)3
.
8
27
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29. 28.
. lim
𝑥→∞
5−2𝑥 5
2𝑥2 −5𝑥+7 2 4𝑥2+3
. lim
𝑥→∞
5−2𝑥 5
4𝑥4−20𝑥3+53𝑥2−70𝑥+49 2𝑥+ 3
. lim
𝑥→∞
5−2𝑥
𝑥
5
4𝑥4
𝑥5 −
20𝑥3
𝑥5 +
53𝑥2
𝑥5 −
70𝑥
𝑥5 +
49
𝑥5
2𝑥
𝑥5+
3
𝑥5
=
0−25
0−0+0−0+0 0+0
= -32
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30. 29.
. lim
𝑥→∞
16𝑥2 − 6𝑥 + 7 - (3+4x)
. lim
𝑥→∞
16𝑥2 − 6𝑥 + 7 − (4𝑥 + 3)2
. lim
𝑥→∞
16𝑥2 − 6𝑥 + 7 − 16𝑥2 + 24𝑥 + 9
.
𝑏−𝑞
2 𝑎
−6−24
2 6
−30
8
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31. 30.
• lim
𝑥→∞
9𝑥2 + 18𝑥 + 3 + 4𝑥2 + 8𝑥 + 1 - 252 − 10𝑥 + 6
• lim
𝑥→∞
( 9𝑥2 + 18𝑥 + 3 - 9𝑥2 + 0𝑥 ) + ( 4𝑥2 + 8𝑥 + 1 − 4𝑥2 + 0𝑥 ) +
( 25𝑥2 − 10𝑥 + 6 - 25𝑥2 + 0𝑥
• =
18−0
2 9
+
8−0
2 4
+
−10−0
2 25
• =
18
6
+
8
4
+
−10
10
• =3+2-1
• =4
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32. 31.
lim
𝑥→0
sin 𝑎𝑥
tan 𝑏𝑥
= 0,2
lim
𝑥→0
sin 𝑎𝑥
tan 𝑏𝑥
= 0,2
=
𝑎
𝑏
= 0,2
• FPB 𝑎 = 1 𝑏 − 𝑎 = 5 − 1
•
1
𝑏
= 0,2 = 4
• 𝑏 = 5
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33. 32.
• lim
𝑥→2
𝑥 tan(𝑥−2)
𝑥2−4
• lim
𝑥→2
𝑥
𝑥+2
.
tan(𝑥−2)
(𝑥−2)
• lim
𝑥→2
2
4
.1 =
1
2
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34. 33. . lim
𝑙𝑖𝑚→0
𝑐𝑜𝑠7𝑥−𝑐𝑜𝑠5𝑥
1−𝑐𝑜𝑠3𝑥
. lim
𝑙𝑖𝑚→0
−2 sin
1
2
7𝑥+5𝑥 sin
1
2
(7𝑥−5𝑥)
1−(1−2𝑠𝑖𝑛2 3
2
𝑥)
. lim
𝑙𝑖𝑚→0
−2 sin
1
2
12𝑥 sin
1
2
(2𝑥)
1−1+2𝑠𝑖𝑛2 3
2
𝑥)
. lim
𝑙𝑖𝑚→0
−2𝑠𝑖𝑛6𝑥𝑠𝑖𝑛𝑥
2
3
2
𝑥
3
2
𝑥
. lim
𝑙𝑖𝑚→0
−2
2
𝑠𝑖𝑛6𝑥
𝑠𝑖𝑛
3
2𝑥
𝑠𝑖𝑛𝑥
𝑠𝑖𝑛
3
2𝑥
= -1 . 6
2
3
. 1
2
3
= -1 .4 .
2
3
= -
8
3
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35. 34.
• lim
𝑋→0
sin 7𝑥−tan 5𝑥
tan 4𝑥−3𝑥
•
• lim
𝑥→0
sin 7𝑥
tan 4𝑥
−
tan 5𝑥
7𝑥
• =
7
4
-
5
3
• =
21−20
12
• =
1
12
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36. 35.
• lim
𝑥→0
tan 4𝑥−sin 4𝑥
𝑥𝑠𝑖𝑛24𝑥
• lim
𝑥→0
sin 4𝑥
cos 4𝑥
− sin 4𝑥
𝑥𝑠𝑖𝑛24𝑥
• lim
𝑥→0
sin 4𝑥−sin 4𝑥 cos 4𝑥
cos 4𝑥
𝑥𝑠𝑖𝑛24𝑥
• lim
𝑥→0
sin 4𝑥 ( 1−cos 4𝑥 )
𝑥𝑠𝑖𝑛24𝑥 .cos 4𝑥
• lim
𝑥→0
sin 4𝑥 ( 1− 1−2 sin22𝑥 )
𝑥𝑠𝑖𝑛24𝑥 .cos 4𝑥
• lim
𝑥→0
(sin 4𝑥 )( 2𝑠in22𝑥 )
𝑥𝑠𝑖𝑛24𝑥 .cos 4𝑥
• lim
𝑥→0
sin 4𝑥
𝑥
.
sin 2𝑥
4𝑥
.
sin 2𝑥
4𝑥
.
2
cos 4𝑥
• lim
𝑥→0
4
1
.
2
4
.
2
4
.
2
cos 4𝑥
• lim
𝑥→0
2
cos 4𝑥
• lim
𝑥→0
2
cos 4 0
=
2
1
= 2
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37. Nama Anggota Kelompok
( diikuti nomor soal yang dikerjakan)
 Raja Angraini : 1,7,13,19,25,31
 Ayu Aulia O. : 2,8,14,20,26,32
 Difa Aulia Putri Rizal : 3,9,15,21,27,33
 Ayunda Bestarina E. : 4,10,16,22,28,34
 Nuriah Agrina : 5,11,17,23,29,35
 Natasya : 6,12,18,24,30, ^..^
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