293665438 Pembahasan Osn Matematika Smp

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www.siap-osn.blogspot.com @ Maret 2015

Sosuke D. Aizen 2 SMPN 1 Tambelangan

PEMBAHASAN

OSN MATEMATIKA SMP 2015 TINGKAT KABUPATEN

BAGIAN A : PILIHAN GANDA

1. Jawaban : . 3

Pembahasan :

∗ ∶

= −1∗

52= 5∗5 =4

53= 52∗5 =4∗5 =6

54= 53∗5 =6∗5 =2

55= 54∗5 =2∗5 =3

56_{= 5}5_∗_{5 =}₃_∗_{5 =}₁

57= 56∗5 =1∗5 =5

58= 57∗5 =5∗5 = 4

59= 58∗5 = 4∗5 = 6

52015 ∗ 2014 , ∶

2014=6 .335 + 4

52015 =3

6 1

2

3

4

5

6

(2)

2. Jawaban : . 1225

Pembahasan :

= 1, 2, 3,…, 50

= , , ∈ , ∈ , ∈ , < , <

= , , ∈ , ∈ , ∈ , =

∩ = , , ∈ , ∈ , ∈ , < , < , =

= 2,1,2 , 3,1,3 , 4,1,4 ,…, 50,1,50 , 49 3,2,3 , 4,2,4 , 5,2,5 ,…, 50,2,50 , 48 4,3,4 , 5,3,5 , 6,3,6 ,…, 50,3,50 , 47

49,48,49 , 50,48,50 , 2 50,49,50 1

∩ = 1 + 2 + 3 + + 49 =49 .(49+1)

2 =

49 .50

2 = 1225

∩ 1225

3. Jawaban : . 13

Pembahasan :

∶

= → = 10 ( )

=

= → = 4

, , , , =

= + + + +

5

=10+ + + +4

5

=14+ + +

5

4 10 ∶

3 .4 < + + < 3 .10 12 < + + < 30

5 = , , ,

∶

+ + = 16 , 21 , 26

, , + + 3,

(3)

=14+ + + 5

=14+21 5

=35

5

=7

= =7 , ∶

4, 7,7,7 , ,

, 10

1

4, 6,7,8 , ,

, 10

3! = 6

4, 5,7,9 , ,

, 10

3! = 6

13

4. Jawaban : . 2 5

Pembahasan :

∶

=

= = 2 .

= = = 1

∶

= =

= = 2 . = 2

− ∶

2+ 2= 12

2 2+ 2= 1

4 2+ 2= 1 5 2_{= 1}

2 =1 5

− ∶

₋ =1

2 . .

(4)

= 2 .1 5

=2 5

5. Jawaban : . 11

Pembahasan :

= 180 → = 4 . = 4 .180 = 720

= 72 →

= 60 →

=

. = .

.720 72 = .

720 60

.10 = .12

=12 10

=6 5

∶ = 6∶5 → = 6 = 5

+ = 6 + 5 =11

6. Jawaban : . 344

Pembahasan :

1418 = . + … 1 , 2134 = . + … 2 , 2850 = . + … 3 ,

2 1 ∶

2134 = . + 1418 = . +

716 = − .

716 = . … 4 ,

3 2 ∶

2850 = . + 2134 = . +

716 = − .

(5)

4 5 , ∶

716 = .

716 = 4 .179 → = 179 = 4

= 179 , ∶

1418 = 7 .179+165 → = 165 2134 = 11 .179+165 → = 165 2850 = 15 .179+165 → = 165

+ =179+165=344

7. Jawaban : . 1 18

Pembahasan :

= ,

= 2

= 1,1 , 1, 2 ,…, 6, 6

= 36

= . = 2 .36 =72

5 = 1,4 , 2, 3 , 3, 2 , 4, 1

5 = , 1,4 , , 2, 3 , , 3, 2 , , 4, 1

5 =4

5 = 4

72 =

1 18

8. Jawaban : . 14

Pembahasan :

213+ 210+ 2 = 23+10+ 210+ 2

= 23 . 210+ 210 + 2

=8 . 210+1 . 210 + 2

=9 . 210+2 → 2 =16 . 210 = 24 . 210 = 24+10 = 214 → =14

=9 . 210+16 . 210

=25 . 210

= 52 . 210 ( 2)

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9. Jawaban : .−31

Pembahasan :

�� ∶

= 2 −1+ 2 −2 +1

1 = 21−1+ 21−21+1= 20+ 21−22= 1 + 2−4 =−1

2 = 22−1+ 22−22+1= 21+ 22−23= 2 + 4−8 =−2

3 = 23−1+ 23−23+1= 22+ 23−24 = 4 + 8−16 =−4

4 = 24−1+ 24−24+1= 23+ 24−25 = 8 + 16−32 =−8

5 = 25−1+ 25−25+1= 24+ 25−26 = 16 + 32−64 =−16

1 + 2 + 3 + 4 + 5 =−1 + −2 + −4 + −8 + −16

=−1−2−4−8−16

=−31

�� ∶

= 2 −1+ 2 −2 +1

=2

21+ 2 −2 1_{. 2}

=1

2 . 2 +1 . 2 −2 . 2

=1 2 . 2 +

2

2 . 2 −

4 2 . 2

=−1 2 . 2

=− 2 −1

1 =− 21−1=− 20=−1

2 =− 22−1=− 21=−2

3 =− 23−1=− 22=−4

4 =− 24−1=− 23=−8

5 =− 25−1=− 24=−16

1 + 2 + 3 + 4 + 5 =−1 + −2 + −4 + −8 + −16

=−1−2−4−8−16

(7)

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12. Jawaban : . 36

Pembahasan :

∶

= = 12

= +

= −

− ∶

2 = 2+ 2

+ 2= − 2+ 122

2+ 2 . . + 2= 2−2 . . + 2+ 144

2+ 2 . . + 2− 2+ 2 . . − 2= 144

4 . . = 144

. =144 4

. =36

13. Jawaban : . 26

Pembahasan :

= 2015−25 = 1990

1991 2014

∶

1991 1 + 9 + 9 + 1 =20 2015−1991 =24 1992 1 + 9 + 9 + 2 = 21 2015−1992 = 23

1993 22 22

1994 23 21

1995 24 20

1996 25 19

1997 26 18

1998 27 17

1999 28 16

2000 2 + 0 + 0 + 0 = 2 15

2001 3 14

2002 4 13

2003 5 12

2004 ₆ ₁₁

2005 7 10

2006 8 9

2007 9 8

(9)

2009 ₁₁ ₆

2010 2 + 0 + 1 + 0 = 3 5

2011 4 4

2012 5 3

2013 6 2

2014 ₇ ₁

=4+22=26

14. Jawaban : . 581.040,00

Pembahasan :

∶

16.00−19.00 40.000,00

3 3 . 40.000,00 = 120.000,00

19.00−06.00 30.000,00 11 . 30.000,00= 330.000,00

06.00−07.00 20%

1 30.000,00+ 20% . 30.000,00= 36.000,00

07.00−08.00 20%

1 36.000,00+ 20% . 36.000,00= 43.200,00

08.00−09.00 20%

1 43.200,00+ 20% . 43.200,00= 51.840,00

581.040,00

15. Jawaban : . 20 2

Pembahasan :

∶

. = 64000 3

= = = 3 . = 64000

3

= 40

∶ = 2∶1 → =1

2 . = 1

2 .40 = 20

=1

2 . = 1

(10)

− ∶

=1

2 . .

=1

2 .20 .40 = 400

∶

=

1

2 . . = 400

1

2 .40 . = 400 20 . = 400

=400 20 = 20

− ∶

= 2₊ 2

= 202_{+ 20}2

= 400 + 400

= 800

= 400 .2

= 20 2

20 2