menu utama
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MENU UTAMA. Pendahuluan Standar Kompetensi Kompetensi Dasar Indikator Pencapaian Materi Pokok Alokasi Waktu Tujuan Pembelajaran Metode Pembelajaran. Materi Pertemuan 1 Materi Pertemuan 2 Materi Pertemuan 3 - PowerPoint PPT PresentationTRANSCRIPT
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MENU UTAMA
Pendahuluan
Standar Kompetensi
Kompetensi Dasar
Indikator Pencapaian
Materi Pokok
Alokasi Waktu
Tujuan Pembelajaran
Metode Pembelajaran
Materi Pertemuan 1
Materi Pertemuan 2
Materi Pertemuan 3
Materi Pertemuan 4
Aktivitas Siswa
Uji Kemampuan Tinggi
Pekerjaan Rumah
Penutup
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logaritmadan akar, pangkat,bentuk
denganberkaitan yangmasalah Memecahkan
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logaritma
danakar pangkat,aturan n Menggunaka
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.sebaliknyadan
positifpangkat kebentuk bilangan suatu
dari negatifpangkat bentuk Mengubah 2.
.berpangkat
bilangansuatu bentuk nakan Menyederha 1.
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2 x 45 Menit
1 Kali Pertemuan
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sebaliknyadan positif,pangkat bentuk
kebilangan suatu dari negatif,pangkat
bentukmengubah dapat didik peserta b.
.berpangkatbilangan suatu bentuk
nakanmenyederhadapat didik peserta a.
ini materi imempelajarSetelah
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Kelompok Diskusi 3.
Jawab Tanya 2.
Ceramah 1.
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Ilmiah Notasi b.
nol,dan
negatifbulat pangkat positif,bulat pangkat
dengan berpangkatbilangan sifat -Sifat a.
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Ilmiah notasigunakan
meng serta noldan negatifbulat pangkat
positifbulat pangkat dengan berpangkat
bilangansifat -sifat n tentangmenjelaska
Guru Jawab Tanya metodeDengan
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Sifat-sifat bilangan berpangkat
1.
bilanganbuah n perkalian
a x a x .....a x a x a x a a n
2. q-pqp a a : a
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3. 0 kecuali 1 a0
4. definisi tidak ter 00
5.n-
nn
n-
a
1 aatau
a
1 a
6.n10 x a
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25
8
4
7
353
9kx k
3k c.
6p
p x 2p b.
0 n,2n
5m d. 5a x 2a a.
:berikut bentuk -bentukan Sederhanak
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3
3
33
333
7-825
8
25
8
44
8
4
71
4
7
85353
8n
125m
n2
m5 0 n,
2n
5m d.
3
1k
3
1
k
k
9
3
9kx k
3k c.
p3
1
p
p
3
1
p
p
6
2
6p
p x 2p b.
a10)(2x5)(a 5a x 2a a.
k
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9
5 e.
)(3 d.
9 x 4 c.
7:7 b.
5x 5 a.
berikut berpangkatbilangan bentuk an Sederhanak
7
46
55
721
425
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7
77
246x446
5555
147-21721
29425425
9
5
9
5 e.
3 3 )(3 d.
36 9) x (4 9 x 4 c.
77 7:7 b.
5 5 5x 5 a.
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Sifat-sifat bilangan pangkat positif
0 b ,b
a
b
a 5.
b x a b x a 4.
a a 3.
a a : a 2.
a a x a 1.
n
nn
nnn
mnnm
nmnm
nmnm
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1634) x (30
4x 17) x (15 bahwaTunjukan .5
16x 6
3x 2 4.
3(2pq) 3.
a
a .2
5 x 3 x 5 x 3 1.
:berikut bentuk -bentukanlah Sederhanak
5
75
125500
5001000
4
2
6
5432
Menit 10
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1.
86
5342
5432
5 x 3
5 x 3
5 x 3 x 5 x 3 1.
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4
2-62
6
a
a a
a .2
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44
44
4444
q48p
)q3(16p
)qp3(2 3(2pq) 3.
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1
2
2
2x 2
1
2x 6
3
)(2 x 6
2x 3
16x 6
3x 2 4.
500
500500
5001000500
1254500
1000500
125500
5001000
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Terbukti 16
4
4
4
4
4 x 4
1
2) x (2
4 x 1 x 1
34) x (30
4x 17) x (15 : Bukti
1634) x (30
4x 17) x (15 bahwaTunjukan .5
2
5-7
5
7
75
5
75
5
75
5
75
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1-
n-4-
7-
3-3-
5p
1 3.
0 a ,a
1 5. 2a .2
p
2a 4. 2 1.
Positifbulat pangkat
dalamberikut bilangan -bilanganh Nyatakanla
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33-
2
1 2 1.
a
2 2a .2
44-
5
p
5p
1 3.
1-
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3
7
7-
-3
a
2p
p
2a 4.
n
n
n-a
a11
0 a ,a
1 5.
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1
1-9
5-6
01-1-
32
7
24243-2
b81a
b3a .3
)6 x 6 - 6 x 2(6 .2
y2
)x(:
y
)(2x 4. )cb(a 1.
contoh sesuai
positifpangkat dalam hasilnyanyatakan dan
inidibawah bentuk -bentukanlah Sederhanak
Menit 10
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cba )cb(a 1. -86-424-32
6
10
)6
52(
)6
1 - 1 2( )6 x 6 - 6 x 2(6 .2 01-1-
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43
9-
56-1
1-9
5-6
b27a
ba811
ba31
b81a
b3a .3
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6
14
7
8
6-
32
7
24
y
8x
y
4x x
x
2y
y2
)x(:
y
)(2x 4.
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0,000001 10 1.000.000 10
0,0001 10 1000 10
0,001 10 100 10
0,01 10 10 10
0,1 10 1 10
6-6
4-3
3-2
2-1
-10
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7.802.000 5.
0,0057 4.
0,0003 3.
257.000 2.
40.000 1.
ILmiah notasi
dalamberikut bilangan bilangan Nyatakan
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6
3-
4-
5
4
10 x 7,802 7.802.000 .5
10 x 5,7 0,0057 .4
10 x 3 0,0003 .3
10 x 2,57 257.000 .2
10 x 4 40.000 1.
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9550,00001004 5.
0,00443 4.
0931.500.00 3.
0,000316 2.
3.752.000 1.
ILmiah notasi dalamberikut bilangan Nyatakan
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10 x 3,752 3.752.000 1. 6-410 x 3,16 0,000316 2.
810 x 9,315 0931.500.00 3. -310 x 4,43 0,00443 4.
-510 x 1,004955 9550,00001004 5.
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Qdengan an dilambangk
rasionalBilangan 0. bdan bulat bilangan ba,dengan b
abentuk dalam dinyatakandapat yangbilangan Adalah
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berulang.
tidakdesimal bilangatau berulang, desimalbilangan berupabaik
desimal,bilangan bentuk dalam dinyatakandapat rasionalBilangan
0 berulangatau bulat bilangan 3,0000... 3
terbatas tapiberulang tidak 0,25 4
1
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6 berulang 1666... 0, 6
1
27 berulang 2727... 0, 11
3
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tersebut.berulang
yang angka diatas garis n tandamembubuhkadengan
singkat didapat berulang desimal bilangPenulisan
0,27 2727... 0,
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0 bdan bulat
bilangan ba,dengan ,b
abentuk dalam dinyatakan
dapat tidak yangbilangan adalah IrasionalBilangan
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tas. tak terbaberulang tak desimalbilangan
bentuk dalam dinyatakandapat IrasionalBilangan
2,7182... e 4.
3,1415... π3.
.2,236067..- 5- 2.
.1,414213.. 2 .1
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3
2
16 12. 100 9. 2 6. 27
9 .3
48 11. 2
3 8. 3 log 5. 25 .2
8 10. 8log 7. π4. 20 1.
akarbentuk dan Irasional
rasional,bilangan merupakan yang inidibawah
bilangan-bilanganmanakah sikan Identifika
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12dan ,11,1,4,5,6,10
nomor soaladalah akar bentuk atau
irasionalbilangan merupakan yangsedangkan
9dan 2,3,7,8,nomor soal
adalah rasionalbilangan merupakan Yang
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0,99dan 1,01 d. 1,1dan 0,9 b.5
4 -dan
5
1- c. 1-dan 0 a.
:berikut
bilangan duadiantar rasionalbilangan igaTulislah t
4...0,56456456 3.
...28571428570,14285714 2.
.0,333333.. 1.
bukanatau rasional
bilanganberikut bilangan -bilanganh Selidikila
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:berikut sebagaiakar sifat -sifatn menggunakadengan
akandisederhandapat 125 ,24 ,8akar Bentuk
AKAR SIFAT-SIFAT
amn m
nnn
nn n
a 3.
ab b . a 2.
a a a 1.
a
n
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3
2 c.
9 e. 54- b.
2
1 d. 8 a.
:anlah Sederhanak
43
3
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33 3 3 9 e.
42
1 4.
8
1 4.
8
1
2
1 d.
63
1 6 .
9
1 6.
9
1
3
2 c.
23- 2 x 27- 2 x 27- 54- b.
22 2 x 4 2 x 4 8 a.
2
1
4
24 24
33333
33333
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sederhana paling yang
akarbentuk dalam iniberikut bilangan Nyatakan
5002 f).
994 e).
96 d).
50 c).
44 b).
27 a).
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520)510(25 x 1002 5002 f).
1112)113(4)11 x 94( 994 e).
64 6 x 16 6 x 16 96 d).
25 2 x 25 2 x 25 50 c).
112 11 x 4 11 x 4 44 b).
33 3 x 9 3 x 9 27 a).
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nnn
nnn
xb) (a xb xa .2
xb) (a xb xa 1.
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34 - 36 32 3.
27 - 23 .2
24 23 1.
:anlah Sederhanak
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27 24)(3 24 23 1.
24- 27)-(3 27 - 23 .2
)3(4
34)-6(2 34 - 36 32 3.
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2xy 4x 8x .3
125 400 - 80 2.
2
14 182 1.
:anlah Sederhanak
4 626 93
64
yy
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28
22 26
22
14. 22.3
2.4
14 9x22
2
14 182 1.
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53
55254
55254
5 16x25- 16x5 125 400 - 80 2.
3.2 32.2 2
6 3464
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xy
xyxyxy
xyxy
xyxy
yy
21)2y(
22y2y
222xy
222xy
2xy 4x 8x .3
2
132
13
4
236
33
4 626 93
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32323 81838x .3
15
1
5
32
3
53 .2
321850 1.
iniberikut akar bentuk anlah Sederhanak
xyxy
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223232 .7
322322 .6
32 .5
2 x 3 .4
5 x 3 .3
2 x 2 .2
24 x 32 1.
:anlah Sederhanak
2
32
36
4
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68 2 x 34) x (2 24 x 32 1. 4444 24 82 x 4 2 x 2 2 x 2 .2
6
6
6 2636
75
25 x 3
5 x 3 5 x 3 .3
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6
6
66
6 26 332
108
4 x 27
4 x 27
2 x 3 2 x 3 .4
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62 5
3 62 2
33222 32 .5222
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5
3-0-8
3 62 62 22
322322 .62
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65 10
46646
222 x 32 x 3432
223232 .722
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ab2b)(a )ba( Jadi
ab2b)(a
bab2 a
2a )ba(
1. : Misalnya
kuadratakar menarik Teknik
222
bba
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ab2b)(a )ba( Jadi
ab2b)(a
bab2 a
2a )ba(
2. : Misalnya
kuadratakar menarik Teknik
222
bba
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192-14 4.
140-12 .3
608 .2
625 .1
baatau babentuk dalam
iniberikut bilangan -bilanganNyatakan
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2 3
2 x 322)(3 625 .1
3 5
3 x 523)(5
1528 608 .2
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57
5 x 72-5)(7
352-12 140-12 .3
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68
6 x 82-6)(8
482-14 192-14 4.
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3
1 .3
66
2 x433 .2
3
6 1.
inidibawah akar bentuk an Sederhanak
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23
6
3
6 1.
2
12
6
6
6
12
66
612
66
24 x 33 .2
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3 3
1
3.9
1
3
1
3
1
3
1 .3
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adiagonalny panjangdan luash Tentukanla
cm.)3-(5 lebarnyasedangkan cm,)3(5
panjang mempunyai panjang persegiSebuah
6Nomor 11Halaman 4.Latihan TeksBuku Buka
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cm, )35(
cm, )35(
cm 56 AC diagonal Panjang Maka
cm. 56 28 28
)31028()310(28
)331025()3310(25
)35()3(5AC
BCABAC SMP di Pithagoras RumusIngat 222
222
A B
CD
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2cm 22
325
)3-(5 x )3(5
Lebar x Panjang Panjang Persegi Luas
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rasional kalinya hasildan Jumlah
jikasekawan dikatakan akar Dua
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)ba(- sekawannyaakar )ba( .4
)b(-a sekawannyaakar )b(a 3.
) b-(a sekawannyaakar )b(a 2.
a sekawannyaakar a .1
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b
a
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25
2 .3
3
1 .2
5
20 1.
: iniberikut pecahan penyebut n Rasionalka
3
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545
520
5
5 x
5
20
5
20 1.
33
3 2
3 2
339
3
1
3
9
3
3 x
3
1
3
1 .2
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25
1
5
2
10
22
2
2 x
25
2
25
2 .3
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b-a
catau
ba
c
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25
25 .3
23
1 .2
2-2
1 1.
iniberikut pecahan penyebut n Rasionalka
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2
22
24
22
22
22 x
2-2
1
2-2
1 1.
2-3
23
23
23
23 x
23
1
23
1 .2
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3
1027
25
21025
25
25x
25
25
25
25 .3
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cba
c
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321
1
anlahSederhanak
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4
622
2
2x
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321
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3)21(
321
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3)2(1 x
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1
321
1
2
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532
2 a. .3
23
2-3 c.
32
2 b.
2-1
2 a. .2
2
1 c.
53
9 b.
3
3 a.
berikutPecahan Penyebut n Rasionalka 1.
3
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rq-p-
r-q-p
rq-p
rqp
r-qp
r
qp
a E.
a D.
a C.
a B.
a A.
...dengan sama a
a x a
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4
4
3
3
3
223
8a E.
2a D.
8a C.
4a B.
2a A.
... 2a : )(4a
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31
2 E.
2 D.
2 C.
2 B.
2 A.
...dengan sama )(4
12-
3-
6
12
2-3
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3
11
11
1112
10 C.
10 E. 9
10 B.
9
10 D.
9
1 A.
... 9
1010
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38 E.
53 D.
35 C.
34 B.
33 A.
...48 dari sederhanaBentuk
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0 E.
22 D.
2 C.
22- B.
2- A.
...2501654
3
3
3
3
333
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6
6
6
6
6
3
306 E.
108 D.
16 C.
12 B.
6 A.
... 3 x 2
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44 E.
38 D.
28 C.
7 B.
2 A.
...)5234)(523(4 dari Hasil
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102
5 E.
105
2 D.
105
1 C.
52
5 B.
55
2 A.
...5
2 dari sederhanaBentuk
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53 E.
54 D.
53 C.
54 B.
53 A.
... 53
4 dari sederhanaBentuk
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13
106-13 C.
13
10623 E.
23
10613 B.
13
106-23 D.
23
106-23 A.
adalah... yasederhananbentuk 106
10-6pecahan penyebut kan merasionalDengan
![Page 110: MENU UTAMA](https://reader037.vdocuments.pub/reader037/viewer/2022102908/56812bd8550346895d9048a9/html5/thumbnails/110.jpg)
16
1 C.
4
1 E.
32
1 B.
8
1 D.
64
1 A.
...8 dari Nilai 3
2
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62 E.
6 D.
2 C.
1 B.
0 A.
...2
6
6-4
5
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3
2
3 4
4 3
3
6
1
4
1
3
2
xE.
xD.
x C.
x B.
x A.
...:.x xx
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ab C.
ab E. b
a B.
ba D. a
b A.
menjadi...akan disederhandapat
ba
baBentuk
3
2
2
3-1-
3-2
1
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125
16 C.
2.000 E. 125
16- B.
100 D. 2.000 - A.
...
y
yx nilai maka 64,ydan 25 xJika
2
1
3
1
3 22
3-
x
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7 E.
6 D.
5 C.
4 B.
3 A.
adalah...n nilai maka,64
63
2
1-1 Jika
n
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5 E.
4 D.
3 C.
2 B.
1 A.
adalah...273persamaan Akar 31-5x x
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2
14 E.
2
13 D.
2 C.2
11 B.
0 A.
ialah... 93persamaan an Penyelesai 212x x
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3-2-
2-2-
3-2
32-
32
26
54
nm E.
nm D.
nm C.
nm B.
nm A.
dengan... samanm
nmBentuk
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4 E.
3 D.
2 C.2
3 B.
2
1 A.
adalah...
2781
279 x 3 dari sederhanaBentuk
3
4
4
3
12
3
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628 E.
68 D.
6 C.
62-8 B.
6-8 A.
...)32123(2 dari Nilai
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)3-(4 E.
)3(4 D.
)3(47
13 C.
)3-13(4 B.
)313(4 A.
...3-4
13Bentuk
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5 E.
2 D.
2- C.
5- B.
10- A.
adalah...1288 memenuhi yang x Nilai 113x x
![Page 123: MENU UTAMA](https://reader037.vdocuments.pub/reader037/viewer/2022102908/56812bd8550346895d9048a9/html5/thumbnails/123.jpg)
4 E.
3 D.
0 C.
3- B.
4- A.
adalah... 813
13 memenuhi yang x Nilai 3-2x
![Page 124: MENU UTAMA](https://reader037.vdocuments.pub/reader037/viewer/2022102908/56812bd8550346895d9048a9/html5/thumbnails/124.jpg)
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" tantanganmenghadapi
meskipun tepat,yangsaat pada benar, yang
tujuanmencapaiuntuk an Berketetap"
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a NilaiTentukan ,
...1
11
1
2
313 Jika .2
10099
1...
43
1
32
1
21
1
anlahSederhanak 1.
aa
aa
a
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Esis Karangan Sulistiyono,Sri Kurnianingsih dan Kuntari Jilid 1A
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