Pembahasan mtk un 2013 paket 04
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Transcript of Pembahasan mtk un 2013 paket 04
SMP NEGERI 3 KALIBAGOR
Alfa Kristanti
1
PAKET 4
SMP NEGERI 3 KALIBAGOR
Alfa Kristanti
2
SMP NEGERI 3 KALIBAGOR
Alfa Kristanti
3
Pelangi Matematika Viandre Al4-kristanty.blogspot.com
2−1 + 3−1 = 1
21+
1
31=
1
2+
1
3=
3
6+
2
6=
5
6
7 7 × 14 = 7 7 × 14 = 7 7 × 7 × 2 = 7 49 × 2
= 7 7 2 = 49 2
31
2+ 2
2
5∶ 1
1
5= 3
1
2+
12
5∶
6
5= 3
1
2+
12
5 ×
5
6
= 31
2+
2
1=
7
2+
4
2=
11
2
Selisih = 5 − 3
5 + 3 × 24 =
2
8 × 24 = 6
Bunga 9 bln = 9
12 × 12% × 𝑇 = 9% 𝑇
Tabungan setelah 9 bln = 100% T + 9% T = 109% T
109% T = 3.815.000 T = 3.815.000
109% =
3.815.000109
100
= 3.815.000 × 100
109
= 3.500.000
SMP NEGERI 3 KALIBAGOR
Alfa Kristanti
4
b = 𝑈7− 𝑈3
7− 3=
22 −10
4
b = 12
4= 3
U3 = a + 2b
10 = a + 2(3)
10 = a + 6 a = 10 – 6
a = 4
Sn = 𝑛
2 ( 2a + (n – 1)b )
S30 = 30
2 ( 2(4) + (30 – 1) 3) = 15 (8 + (29) 3) = 15 (8 + 87)
= 15 (95) = 1.425
a = U1 = 3
b = U2 – U1 = 7 – 3 = 4
Un = a + (n – 1)b
U45 = 3 + (45 – 1) 4 = 3 + (44) 4
= 3 + 176 = 179
r = 𝑈2
𝑈1=
32
64=
1
2
a = U1 = 64
Un = a × r n – 1
= 64 × 1
2 𝑛−1
= 26 × 2 𝑛−1
Un = 26 × 2−𝑛 + 1 = 26 − 𝑛 + 1 = 27−𝑛
x – 3 ≤ 5 – 3x
x + 3x ≤ 5 + 3
4x ≤ 8
x ≤ 2
I. 2x2 + x – 3 = (2x + 3)(x – 1)
II. x2 + x – 6 = (x + 3)(x – 2)
III. 4x2 – 9 = (2x)
2 – 3
2 = (2x + 3)(2x – 3)
IV. 6x2 – 15x = 3x(2x – 5)
× ×
m = 𝑦2− 𝑦1
𝑥2 − 𝑥1=
2 − −5
3− 1=
2 + 5
2=
7
2
y – y1 = m (x – x1)
y – (5) = 7
2 (x – 1)
y + 5 = 7
2 (x – 1)
2(y + 5) = 7(x – 1)
2y + 10 = 7x – 7
2y – 7x = – 7 – 10
– 7x + 2y = – 17
7x – 2y = 17
SMP NEGERI 3 KALIBAGOR
Alfa Kristanti
5
ax + by + c = 0
a = 6 ; b = 3
m = − 𝑎
𝑏=
− − 6
3=
6
3= 2
Jumlah bilangan terbesar dan terkecil
= 2
3 × jml ketiga bilangan
= 2
3 × 84 = 56
M = { 1, 3, 5, 7 }
N = { 5, 7, 11 }
M N = { 1, 3, 5, 7, 11 }
f(5) = 15
5a + b = 15
f(5) = 5
5a + b = 5
5a + b = 15
5a + b = 5
10a = 20
a = 2
5a + b = 5
5( 2) + b = 5
10 + b = 5
b = 5 + 10
b = 5
F(1) = 2 (1) + 5
= 2 + 5
= 3
Misal :
Harga pulpen = p
Harga pensil = q
5p + 4q = 30.000 × 3 15p + 12q = 90.000
2p + 6q = 23.000 × 2 4p + 12q = 46.000
11p = 44.000
p = 4.000
2p + 6q = 23.000
2(4000) + 6q = 23.000
8.000 + 6q = 23.000
6q = 15.000
q = 2.500
3p + 2q = 3(4000)+2(2500)
= 12.000 + 5.000
= 17.000
26 26
26 26
10 10 A
B
C
D
E
S = 𝐾
4=
104
4= 26
DE = 𝐴𝐷2 − 𝐴𝐸2 = 262 − 102 = 676 − 100 = 576 = 24
BD = 2 × DE = 2 × 24 = 48
Lbelahketupat ABCD = 1
2 × d1 × d2 =
1
2 × AC × BD = =
1
2 × 20 × 48 = 480
Pada gambar di samping:
ABC KLM maka
AB = LM, BC = KL,
AC = KM L
M
K 62
o
80o
B
A
C 62
o
80o
38o
38o
SMP NEGERI 3 KALIBAGOR
Alfa Kristanti
6
P
16
12 10
Q R A
B
C
6 5
8
𝐴𝐶
𝑄𝑅=
8
16=
1
2 ,
𝐴𝐵
𝑃𝑅=
5
10=
1
2 ,
𝐵𝐶
𝑃𝑄=
6
12=
1
2
KL = 3 × 12 + 2 × 27
3 + 2
= 36 + 54
5=
90
5 = 18
L daerah tdk diarsir
= LEFGH + LABCD – 2 × L daerah diarsir
= 42 + 12 × 8 – 2 × 8
= 16 + 96 – 16
= 96
Banyak pohon cemara = 𝐾𝑒𝑙𝑖𝑙𝑖𝑛𝑔 𝑡𝑎𝑚𝑎𝑛
𝑗𝑎𝑟𝑎𝑘 𝑡𝑎𝑛𝑎𝑚=
2(48+ 32)
4
= 2(80)
4 = 40
Q
P
R
(3x 6) + (4x + 25) = 180
7x + 19 = 180
7x = 180 – 19
7x = 161
x = 23
Pelurus AOC = COB = 4x + 25
= 4(23) + 25 = 92 + 25 = 117
SMP NEGERI 3 KALIBAGOR
Alfa Kristanti
7
Sudut keliling menghdp
busur yg sama maka
ABE = ACE =ADE
ABE = 96
3 = 32
AOE = 2 × ABE
= 2 × 32
= 64
= 289 − 64 = 225 = 15
dalam = 172 − 5 + 3 2 = 289 − 82
LAOD = 𝐴𝑂𝐷
𝐵𝑂𝐶 × 𝐿𝐵𝑂𝐶
= 40
100 × 50
= 20
Panjang kawat minimal = Panjang rusuk balok
= 4 (p + l + t) = 4 (40 + 40 + 35)
= 4 (115)
= 460
Garis pelukis
BC = 𝐾𝐴𝐵𝐶𝐷
4=
72
4 = 18
t
9
15 t = 152 − 92 = 225 − 81
t = 144 = 12
Vlimas = 1
3 La × t =
1
3 × 18
2 × 12 = 324 × 4 = 1.296
SMP NEGERI 3 KALIBAGOR
Alfa Kristanti
8
dbola = rusuk kubus
dbola = 24, maka :
r = 24
2 = 12
Vbola = 4
3 π r
3 =
4
3 π × 12
3 =
4
3 π × 1.728
= 4 π × 576 = 2.304 π
Ldinding = 2 (pt + lt) = 2(6 × 4 + 8 × 4)
= 2(24 + 32) = 2(56) = 112
Biaya = 112 × Rp 50.000,- = Rp 5.600.000,-
s2 + s
2 = 10
2
2 s2 = 100
s2 = 50
s = 50 = 25 × 2 = 5 2
10 s
s
Lkubus = 6 s2
= 6 × 5 2 2
= 6 × 50
= 300
Ltabung = 2πr (r + t) = 2 × 22
7 × 35 (35 + 10)
= 220 (45) = 9.900
Jumlah siswa = 18 + 22 = 40 anak
Jml tinggi = 18 × 156 + 22 × 152 = 2.808 + 3.344 = 6.152
Rata-rata tinggi = 𝑗𝑚𝑙 𝑡𝑖𝑛𝑔𝑔𝑖
𝑏𝑎𝑛𝑦𝑎𝑘 𝑠𝑖𝑠𝑤𝑎=
6.152
40 = 153,8
Data 5 6 7 8 9
frekuensi 3 2 3 4 2
Modus
SMP NEGERI 3 KALIBAGOR
Alfa Kristanti
9
32 30
Banyak siswa dapat nilai kurang dari 8 = 1 + 4 + 5 = 10
SMP NEGERI 3 KALIBAGOR
Alfa Kristanti
10
n(S) = 2 × 2 × 2 = 8
3 gambar = GGG
P (3 gambar) = 1
8
6
5 5
2 2
4
3 3
Banyak kelereng = 6 + 5 + 3 + 3 + 2 + 4 + 2 + 5 = 30
Kelereng merah = 6
P ( 1 merah) = 6
30 × 100 % = 20 %