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323

Halaman 1

PEMBAHASAN SELEKSI NASIONAL MASUK PERGURUAN TINGGI NEGERI (SNMPTN)

Mata Pelajaran : Matematika Dasar

Tanggal

: 12 Juni 2012

Kode Soal

: 323

1. Jawab: D

Eksponen

20 19 19 19

20 2 2 2 1 2

b

a = − = − =

2

a = b=19

21

a+b=

2. Jawab: A

Sistem Persamaan Linear

2 3

2 5

2 7

3 3 3 15

5

x y

y z

z x

x y z

x y z

+ =

+ =

+ = +

+ + =

+ + =

3. Jawab: D

Persamaan Kuadrat

1 1

x =p− x₂ =p+1

2

4 0

x − x+a=

1 2

b

x x

a

+ = −

2p=4→ p=2

1 1

x = x2 =3

1 2 x x =a

1 3⋅ =a→a =3

4. Jawab: B

Logaritma

3 2

2 3 9

a= →a= =

(

2

)(

)

2

a

a b =

2 2

2 2 4

b= →b= =

13

a+b=

5. Jawab: E

Fungsi Kuadrat

Puncak

(

α β

)

→y−β =a x

(

−α

)

2 Puncak

(

2 −1

)

y+ =1 a x

(

−2

)

2 Melalui

(

0 −5

)

− + =5 1 a

(

0−2

)

2

4 4a

− =

1

a= −

(

)

2

1 1 2

y+ = − x−

(

2

)

1 4 4

y+ = − x − x+

2

4 5

y= −x + x−

2

4 5

f x = −x + x−

5 25 20 5 10

f = − + − = −

6. Jawab: E

Matriks

1 2 1 1

1 5 3 2

a b

c d =

1 1 5 2

1

1 5 2 1 3 2 1 1

a b

c d

− =

⋅ − ⋅ −

5 1 2 1

1

3 15 2 6 2

− − +

=

− − +

4 1

3 3

13 4

3 3

− =

−

4 1 13 4

4

3 3 3 3

a+ + +b c d = − + − =

7. Jawab: A

Statistika

7 19

k

f = fk8 =22 fk =25

8 7 ₁₀₀ 3 ₁₀₀

25 k k

k

f f

f

−

⋅ = ⋅

323

Halaman 2 8. Jawab: C

Deret Aritmatika

1001

a =

997 1001 4

b = − = −

0 n

U <

(

1

)

0

a+ n− b<

(

)( )

1001+ n−1 −4 <0 1001−4n+4<0

4n 1005

− < −

4n>1005

1 4

251

n >

252

n =

9. Jawab: E

Fungsi

2

f x = x+b

( )

1

9 3

f− =

maka f(3) = 3 6 + b = 9

b = 3

2 3

f x = x+

(

3

)

( )

9 21

f f = f =

10. Jawab: D

Program Linear

(

)

3 4

f x y = x+ y

(

3 6

)

9 24 33

f = + =

(

6 4

)

18 16 34

f = + =

33

f =

11. Jawab: B

Statistika

1 9

n = x1 =61

2 1

n = x2 =

63 5

x =

1 2

1 2

1 2

n x n x

x

n n

+ =

+

2

9 61 63 5

10

x

⋅ +

=

2

635=549+x

2 86

x =

12. Jawab: D

Aritmetika Sosial

Sewa = 15.000.000 Banyak barang = 3.000 Bahan baku = 2.000

Biaya bahan baku total = 3.000 x 2.000 = 6.000.000 Modal = biaya + bahan baku = 15.000.000 + 6.000.000 = 21.000.000

Harga penjualan minimum agar tidak rugi 21 000 000

7 000 3 000

= =

13. Jawab: A

Deret Geometri

(

1

)

3 2 2 n n

S = − −

(

0

)

1 3 2 2 3

a= S = − =

1 1

2 2

r = − =

2 3 1 4

a+ r= + =

3 6

12 4

8

323

Halaman 3 14. Jawab: B

Bidang Datar

1 5 L=

1 1

5 5

xy y

x

= → =

2y =1

2 2

1

5x = →x = 5

15. Jawab: C

Pertidaksamaan

(

x+5

)(

x−3

)

< x−3

2

2 15 3

x + x− < x−

2

12 0

x +x− <

(

x+4

)(

x−3

)

<0

4 x 3

− < <

−4 3

− +