www.siap-osn.blogspot.com @ Maret 2015
Sosuke D. Aizen 2 SMPN 1 Tambelangan
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
www.siap-osn.blogspot.com @ Maret 2015
Sosuke D. Aizen 2 SMPN 1 Tambelangan
+ 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
www.siap-osn.blogspot.com @ Maret 2015
Sosuke D. Aizen 2 SMPN 1 Tambelangan
3. Jawaban : 7 3 + 12 2
Pembahasan :
∶
, − , ∶
∠ =∠ =∠ =∠ =∠ =∠ = 90
→ =
= = = 1
= 3
3
∠ = 60
− ∶
∠ = 180 −90 −60 =30
− − ∶
∠ =∠ = 60
− ∶
www.siap-osn.blogspot.com @ Maret 2015
Sosuke D. Aizen 2 SMPN 1 Tambelangan
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
www.siap-osn.blogspot.com @ Maret 2015
Sosuke D. Aizen 2 SMPN 1 Tambelangan
7. Jawaban : 1∶2
Pembahasan :
∶
=
= 2 .
= = = =
⊥ ⊥
∶
= = =
. ∶ . =
. .
= . .
. .
= 1
2 . . . . .
= 1
2 . . . . .
=1 2 = 1∶2
. . 1∶2
8. Jawaban : 28
Pembahasan :
→ , , , → , , , → , , ,
, ,
∶
, , , , , , , , ,
, , 3
www.siap-osn.blogspot.com @ Maret 2015
Sosuke D. Aizen 2 SMPN 1 Tambelangan
, , 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 , �
www.siap-osn.blogspot.com @ Maret 2015
Sosuke D. Aizen 2 SMPN 1 Tambelangan
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! /