Download - Pembahasan Soal Mtk UN 2013 Paket 02

SMP NEGERI 3 KALIBAGOR

Alfa Kristanti

1

PAKET 2


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3

Pelangi Matematika Viandre Al4-kristanty.blogspot.com

2−3 + 3−2 = 1

23+

1

32=

1

8+

1

9=

9

72+

8

72=

17

72

7 7 × 14 = 7 7 × 14 = 7 7 × 7 × 2 = 7 49 × 2

= 7 7 2 = 49 2

22

3∶ 1

2

3− 4

1

5=

8

3∶

5

3−

21

5=

8

3×

3

5−

21

5

= 8

5−

21

5= −

13

5= −2

3

5

Selisih = 4 − 3

4 + 3 × 560.000 =

1

7 × 560.000

= 80.000

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


Alfa Kristanti

4

b = 18

3= 6

b = 𝑈7− 𝑈4

7−4=

37−19

3

U4 = a + 3b

19 = a + 3(6)

19 = a + 18 a = 19 – 18

a = 1

Sn = 𝑛

2 ( 2a + (n – 1)b )

S24 = 24

2 ( 2(1) + (24 – 1) 6) = 12 (2 + (23) 6) = 12 (2 + 138)

= 12 (140) = 1.680

a = U1 = 7

b = U2 – U1 = 12 – 7 = 5

Un = a + (n – 1)b

U52 = 7 + (52 – 1) 5 = 7 + (51) 5

= 7 + 255 = 262

r = 𝑈2

𝑈1=

9

27=

1

3

a = U1 = 27

Un = a × r n – 1

= 27 × 1

3 𝑛−1

= 33 × 3−1 𝑛−1

Un = 33 × 3−𝑛 + 1 = 33 − 𝑛 + 1 = 34−𝑛

3x – 2 < 8x + 13

3x – 8x < 13 + 2

5x < 15

x > 3

I. 4x2 – 10x = 2x (2x – 5)

II. 7x2 – 49 = 7(x

2 – 7)

III. x2 – 3x – 18 = (x – 6)(x + 3)

IV. x2 + 5x – 36 = (x + 9)(x – 4)

×

×

m = 𝑦2− 𝑦1

𝑥2 − 𝑥1=

−3 − (−6)

−4 − −1 =

−3+6

−4+1=

3

−3= −1

y – y1 = m (x – x1)

y – (1) = 1 (x – (–6))

y + 1 = 1 (x + 6)

y + 1 = – x 6

y + x = – 6 – 1

x + y = – 7


Alfa Kristanti

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ax + by + c = 0

a = 8 ; b = 4

m = − 𝑎

𝑏=

8

− 4= −2

M = { 1, 3, 5, 7 }

N = { 5, 7, 11 }

M N = { 1, 3, 5, 7, 11 }

f(3) = 15

3a + b = 15

f(2) = 0

2a + b = 0

3a + b = 15

2a + b = 0

5a = 15

a = 3

2a + b = 0

2(3) + b = 0

6 + b = 0

b = 0 6

b = 6

f(5) = 3(5) + ( 6)

= 15 6

= 21

Misal :

Parkir mobil = p

Parkir motor = q

12 12 K

L

M

N

O

Lbelahketupat ABCD = 384

1

2 × KM × LN = 384

1

2 × 24 × LN = 384

12 × LN = 384

4p + 2q = 18.000

4p + 2(1.000) = 18.000

4p + 2.000 = 18.000

4p = 16.000

p = 4.000

20p + 30q = 20(4000)+30(1000)

= 80.000 + 30.000

= 110.000

3p + 5q = 17.000 × 4 12p + 20q = 68.000

4p + 2q = 18.000 × 3 12p + 6q = 54.000

14q = 14.000

q = 1.000

LN = 384

12 = 32 OL =

𝐿𝑁

2=

32

2 = 16

KL = 𝑂𝐾2 + 𝑂𝐿2 = 122 + 162

KL = 144 + 256 = 400 = 20

Keliling = 4× KL = 4 × 20 = 80

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

Jumlah bilangan terbesar dan terkecil

= 2

3 × jml ketiga bilangan

= 2

3 × 162 = 108


Alfa Kristanti

6

Q

30

24

18

P R B

C

A

12 9

15

𝐴𝐶

𝑃𝑄=

12

24=

1

2 ,

𝐴𝐵

𝑃𝑅=

15

30=

1

2 ,

𝐵𝐶

𝑄𝑅=

9

18=

1

2

FC = 4 × 20 + 6 × 5

4 + 6

= 80 + 30

10=

110

10 = 11

L daerah tdk diarsir

= LKLMN + LPQRS – 2 × L daerah diarsir

= 202 + 10 × 15 – 2 × 67

= 400 + 150 – 134

= 416

Banyak pohon = 𝐾𝑒𝑙𝑖𝑙𝑖𝑛𝑔 𝑘𝑒𝑏𝑢𝑛

𝑗𝑎𝑟𝑎𝑘 𝑝𝑜ℎ𝑜𝑛=

2(24+ 18)

3

= 2(42)

3=

84

3 = 28

B

A

C D

(3x 5) + (2x + 5) = 90

5x + 0 = 90

5x = 90

x = 18

Penyiku POR = ROQ = 2x + 5 = 2(18) + 5 = 36 + 5 = 41


Alfa Kristanti

7

Sudut keliling menghdp

busur yg sama maka

ABE = ACE = ADE

ABE = 96

3 = 32

AOE = 2 × ABE

= 2 × 32

= 64

= 676 − 100 = 576 = 24

luar = 262 − 12 − 2 2 = 676 − 102

LOBC = 𝐵𝑂𝐶

𝐴𝑂𝐵 × 𝐿𝑂𝐴𝐵

= 120

50 × 30

= 72

Panjang rusuk 1 balok = 4 (p + l + t) = 4 (40 + 24 + 36)

= 4 (100) = 400 cm = 4 m

Kawat tersedia = 10 m

Banyak kerangka balok yg dibuat = 10

4 = 2,5 2

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


Alfa Kristanti

8

dbola = rusuk kubus

dbola = 30, maka :

r = 30

2 = 15

Vbola = 4

3 π r

3 =

4

3 π × 15

3 =

4

3 π × 3.375

= 4 π × 1.125 = 4.500 π

Ldinding = 2 (pt + lt) = 2(8 × 5 + 6 × 5)

= 2(40 + 30) = 2(70) = 140

Biaya = 140 × Rp 50.000,- = Rp 7.000.000,-

s2 + s

2 = 8 2

2

2 s2 = 64 × 2

2 s2 = 128

s2 = 64 s = 64 = 8

8 2 s

s

Lkubus = 6 s2

= 6 × 8 2

= 6 × 64

= 384

d = 28 r = 14

Ltabung = 2πr (r + t) = 2 × 22

7 × 14 (14 + 26)

= 88 (40) = 3.520

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 2 3 4 3 2

Modus


Alfa Kristanti

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32 30

Selisih produksi pupuk Maret dan Mei = 10 – 6 = 4


Alfa Kristanti

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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 %