www.siap-osn.blogspot.com @ Maret 2015
Sosuke D. Aizen 2 SMPN 1 Tambelangan
Pembahasan OSN Matematika SMP 2015 / Page 1 Download Soal dan Pembahasan OSN Matematika SMP Lainnya di www.siap-osn.blogspot.com
PEMBAHASAN
OSN MATEMATIKA SMP 2015 TINGKAT KABUPATEN
BAGIAN B : ISIAN SINGKAT
BAGIAN B : ISIAN SINGKAT
1. Jawaban : = 4,1
Pembahasan :
2 + 5 + 6
2 + 5 + 6 = + 2 . ( + 3)
+ 2 < + 3 = 2, 3, 5, 7, 11,
= 2
2 + 5 + 6 = + 2 . + 3 = 2 = 1 .2 = 2 . 1
+ 2 . + 3 = 1 .2
+ 2 = 1 + 3 = 2
= 1 2 = 2 3
= 1 = 1 ( )
+ 2 . + 3 = 2 . 1
+ 2 = 2 + 3 = 1
= 2 2 = 1 3
= 4 = 4 ( )
= 3
2 + 5 + 6 = + 2 . + 3 = 3 = 1 .3 = 3 . 1
+ 2 . + 3 = 1 .3
+ 2 = 1 + 3 = 3
= 1 2 = 3 3
= 1 = 0 ( )
+ 2 . + 3 = 3 . 1
+ 2 = 3 + 3 = 1
= 3 2 = 1 3
= 5 = 4 ( )
= 5
2 + 5 + 6 = + 2 . + 3 = 5 = 1 .5 = 5 . 1
+ 2 . + 3 = 1 .5
www.siap-osn.blogspot.com @ Maret 2015
Sosuke D. Aizen 2 SMPN 1 Tambelangan
Pembahasan OSN Matematika SMP 2015 / Page 2 Download Soal dan Pembahasan OSN Matematika SMP Lainnya di www.siap-osn.blogspot.com
+ 2 = 1 + 3 = 5
= 1 2 = 5 3
= 1 = 2 ( )
+ 2 . + 3 = 5 . 1
+ 2 = 5 + 3 = 1
= 5 2 = 1 3
= 7 = 4 ( )
3
= 4,1
2. Jawaban : 12
Pembahasan :
= 2 + + (2, 6)
= 1
, ,
2
, 6
= 2 + +
6 = . 2 2 + . 2 +
6 = 4 2 +
4 2 + = 6 1
= 1 =
2
1 =
2
2 =
= 2 2
2 1
4 2 + = 6
4 2 . 2 + = 6
4 4 + = 6
= 6
= 6 , = 2 , ,
2
, 4 =2
, 6
+ + = 2 + 4 + 6 = 12
www.siap-osn.blogspot.com @ Maret 2015
Sosuke D. Aizen 2 SMPN 1 Tambelangan
Pembahasan OSN Matematika SMP 2015 / Page 3 Download Soal dan Pembahasan OSN Matematika SMP Lainnya di www.siap-osn.blogspot.com
3. Jawaban : 7 3 + 12 2
Pembahasan :
, ,
= = = = = = 90
=
= = = 1
= 3
3
= 60
= 180 90 60 = 30
= = 60
= 180 90 60 = 30
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Sosuke D. Aizen 2 SMPN 1 Tambelangan
Pembahasan OSN Matematika SMP 2015 / Page 4 Download Soal dan Pembahasan OSN Matematika SMP Lainnya di www.siap-osn.blogspot.com
= 180 90 60 = 30
= = 30
= 180 60 60 = 60
= 180 60 30 = 90
= 2 + 2 = 3
3
2
+ 12 = 3
9+ 1 =
3
9+
9
9=
12
9=
12
9=
4 .3
9=
2 3
3
= + = 1 +2 3
3
=
1=
1+2 3
3
3
3
= 1 +2 3
3 .
3
3
=3
3+ 2
=3
3 . 3
3+ 2
= 3 + 2
= = 3 + 2
= = + = 3 + 2 + 3 + 2 = 2 3 + 4
=
3
3
=2 3+4
1
= 2 3 + 4 . 3
3
= 2 +4 3
3
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Sosuke D. Aizen 2 SMPN 1 Tambelangan
Pembahasan OSN Matematika SMP 2015 / Page 5 Download Soal dan Pembahasan OSN Matematika SMP Lainnya di www.siap-osn.blogspot.com
=1
2 . .
=1
2 . 1 +
2 3
3 . 3 + 2
=1
2 . 3 + 2 + 2 +
4 3
3
=1
2 .
3 3
3+ 4 +
4 3
3
=1
2 .
7 3
3+ 4
=7 3
6+ 2
=
=7 3
6+ 2
=1
2 . .
=1
2 . 2 3 + 4 . 2 +
4 3
3
=1
2 . 4 3 + 8 + 8 +
16 3
3
=1
2 .
12 3
3+ 16 +
16 3
3
=1
2 .
28 3
3+ 16
=14 3
3+ 8
= + +
= 7 3
6+ 2 +
7 3
6+ 2 +
14 3
3+ 8
=14 3
6+ 12 +
14 3
3
=7 3
3+ 12 +
14 3
3
=21 3
3+ 12
= 7 3 + 12
7 3 + 12 2
4. Jawaban : 55 153
Pembahasan :
= 2 11
= 3 5
=
www.siap-osn.blogspot.com @ Maret 2015
Sosuke D. Aizen 2 SMPN 1 Tambelangan
Pembahasan OSN Matematika SMP 2015 / Page 6 Download Soal dan Pembahasan OSN Matematika SMP Lainnya di www.siap-osn.blogspot.com
=2
2+11 . =
2
13
=11
2+11 . =
11
13
=3
3+5 . =
3
8
=5
3+5 . =
5
8
+ = + =2
13+
3
8=
16
104+
39
104=
55
104
+ = + =11
13+
5
8=
88
104+
65
104=
153
104
+ + =++
=55
104153
104
=55
104 .
104
153=
55
153= 55 153
55 153
5. Jawaban : 19
Pembahasan :
= 209 2
= + 2 2 , <
= + 2 2
209 2 = 209 + 2 2 209 2 2
209 22 = 209 2 + 4 + 42 209 2 4 + 42
209 22 = 209 2 4 42 209 2 + 4 42
209 22 = 209 2 4 42 209 + 2 4 + 42
209 22 = 8
209 = 22 8
19 .11 = . 8 = 19
8 = 11
= 19 , <
= 19
= 1 . 19 = 1
= 19
=
19
1= 19
www.siap-osn.blogspot.com @ Maret 2015
Sosuke D. Aizen 2 SMPN 1 Tambelangan
Pembahasan OSN Matematika SMP 2015 / Page 7 Download Soal dan Pembahasan OSN Matematika SMP Lainnya di www.siap-osn.blogspot.com
6. Jawaban : 10080
Pembahasan :
1 + 2 + 3 + 4 = 70 4 = 70
5 + 6 + + 16 = 690
1 + 2 + + 16 = 760
16 = 760
=
2 . 2 + 1 .
4 =4
2 . 2 + 4 1 . = 70
2 . 2 + 3 = 70
2 + 3 =70
2
2 + 3 = 35 (1)
=
2 . 2 + 1 .
16 =16
2 . 2 + 16 1 . = 760
8 . 2 + 15 = 760
2 + 15 =760
8
2 + 15 = 95 (2)
2 (1):
2 + 15 = 95
2 + 3 = 35
12 = 60
=60
12
= 5 1 :
2 + 3 = 35
2 + 3 . 5 = 35
2 + 15 = 35
2 = 35 15
2 = 20
=20
2
= 10
= + 1 .
2015 = 10 + 2015 1 .5
= 10 + 2014 .5
= 10 + 10070
= 10080
2015 10080
www.siap-osn.blogspot.com @ Maret 2015
Sosuke D. Aizen 2 SMPN 1 Tambelangan
Pembahasan OSN Matematika SMP 2015 / Page 8 Download Soal dan Pembahasan OSN Matematika SMP Lainnya di www.siap-osn.blogspot.com
7. Jawaban : 1 2
Pembahasan :
=
= 2 .
= = = =
= = =
. . = .
.
= . .
. .
=1
2 . . .
. .
=1
2 . . .
. .
=1
2
= 1 2
. . 1 2
8. Jawaban : 28
Pembahasan :
, , ,
, , ,
, , ,
, ,
, , ,
, , ,
, , ,
, , 3
, 2
www.siap-osn.blogspot.com @ Maret 2015
Sosuke D. Aizen 2 SMPN 1 Tambelangan
Pembahasan OSN Matematika SMP 2015 / Page 9 Download Soal dan Pembahasan OSN Matematika SMP Lainnya di www.siap-osn.blogspot.com
, , 3
, 2
, , 3
, , 3
, , 3
, 2
, 2
, , 3
, 2
28
28
9. Jawaban : 8, 6 , 8, 10 , 4, 6
Pembahasan :
, = 3 ,
, 8, 0 , 8,4 , 4, 0
,
= 3 ,
8, 6 , 8, 10 , 4, 6
www.siap-osn.blogspot.com @ Maret 2015
Sosuke D. Aizen 2 SMPN 1 Tambelangan
Pembahasan OSN Matematika SMP 2015 / Page 10 Download Soal dan Pembahasan OSN Matematika SMP Lainnya di www.siap-osn.blogspot.com
10. Jawaban : 61600
Pembahasan :
= 3
= 3 = 3 = 3 = 3
= 12
2
4
2
4 ,
, ,,
, , =12!
3! .3! .3! .3!
, ( ,
) , ,
3 ,
= 3!
(
)
=12!
3! .3! .3! .3! . 3! /
= 61600