K13 Modul Matematika SMP/MTs Kelas VII Semester 1 1
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Soal Olimpiade Bilangan Pecahan Uji Kompetensi 4 1
1. Hitunglah
1× 2
+
1
1
+
2×3
3× 4
+
1 4×5
5
A.
C.
6 6
B.
+
D.
7
1 5×6
+
1 6× 7
=… (PASIAD 2008)
5 7 2 3
Knci !a"a#an$ B Gunakan aturan: 1 1× 2
+
1
+
2×3
1 k (k + 1)
1 3× 4
+
1
=
1 4×5
k
−
1 k + 1
1
+
5× 6
+
1 6×7
1 1 1 1 1 1 1 1 1 1 1 1 − + − + − + − + − + − 1 2 2 3 3 4 4 5 5 6 6 7
= = = = =
1 1 1 1 7 7 6
−
−
−
1 2 1
+
1 2
−
1 3
+
1 3
−
1 4
+
1
−
4
1 5
+
1 5
−
1 6
+
1 6
−
1 7
7 1 7
7
2005 −
2. 2002 +
20 17 = … (PASIAD 200%) 31 17
A. -2 B. -1
C. 0 D. 1
Knci !a"a#an$ D 2005 − 2002 +
17 × 2005 − 20
20
17 17 = 31 17 × 2002 + 31 17
17 17 × 2005 − 20
=
=
17
17 × 17 × 2002 + 31
17 × 2005 − 20 17 × 2002 + 31
YOYO APRIYANTO, S.Pd !"#"$%%3#5%1& 'mail( )*o*oa+ri*ato-mail.om *o*oa+ri*ato-mail.om00 -ui 2!1$ o4load ratis Modul Matematika 'disi S+esial S/MI, SMP/MTs, SMA/MA, da SMK/MAK Ku6ui 7e8site Yo*o A+ri*ato, S.Pd ( )9tt+(//ilmu:matematika.8los+ot.om ) 9tt+(//ilmu:matematika.8los+ot.om00
K13 Modul Matematika SMP/MTs Kelas VII Semester 1
P a g e | 5%
17 × (2002 + 3) − 20
=
17 × 2002 + 31 17 × 2002 + 51 − 20
=
17 × 2002 + 31 17 × 2002 + 31
=
17 × 2002 + 31
=1 1
3. Jika x =
, maka x = … (O&I'PIAD S!A*A +I'U, 20-0)
1
2+
2+
1 2
5
A.
12 4
B.
9
C.
4 12
D.
9
5
Knci !a"a#an$ A 1
x=
1
2+
2+
4. ilai !ari
1
=
1
2+
1
4
2
2
1 2× 4
+
+
1 4×6
1
=
1
2+
1
5
1 6×8
+
... +
2010
A.
C.
4024 1006
B.
2+
2 5
=
1 10 5
+
2 5
=
1 12
=
5 12
5
2
2
+
1
=
D.
4024
1 2008 × 2010 1005
+
1 2010 × 2012
=… (O'I+S 20-2)
4024 1004 4024
Knci !a"a#an$ . Gunakan aturan: 1 2× 4
+
1 4×6
+
1 k (k + 2 )
1 6×8
+
=
... +
1 1
1 − 2 k k + 2 1
2008 × 2010
+
1 2010 × 2012
2 2 2 2 + + + ... + + 2 2 × 4 4 × 6 6 × 8 2008 × 2010 2010 × 2012 1 1 1 1 1 1 1 1 1 1 1 − − = − + − + − + + 2 2 4 4 6 6 8 2008 2010 2010 2012 1 1 1 1 1 1 1 1 1 1 1 − − = − + − + − + + 2 2 4 4 6 6 8 2008 2010 2010 2012 1 1 1 = − 2 2 2012
=
1 2
YOYO APRIYANTO, S.Pd !"#"$%%3#5%1& 'mail( )*o*oa+ri*ato-mail.om0 -ui 2!1$ o4load ratis Modul Matematika 'disi S+esial S/MI, SMP/MTs, SMA/MA, da SMK/MAK Ku6ui 7e8site Yo*o A+ri*ato, S.Pd ( )9tt+(//ilmu:matematika.8los+ot.om0
K13 Modul Matematika SMP/MTs Kelas VII Semester 1
2 2012 2012 1 1005 = 2 2012 =
=
1 1006
P a g e | 55
−
1
1005 4024
". ilai !ari
1 3
+
1
+
15
1 35
+
1 63
+
... +
2012
A.
2011(2011 + 2 )
C.
4026 2012
B.
1
D.
4028
=… (O'I+S 20-2)
2011 4028 2012 4024
Knci !a"a#an$ A Gunakan aturan: 1 3
= = = = = = = =
+
1 15 1
1× 3
+
+
1 35
+
1 3× 5
+
+
... +
1 5× 7
+
1 1
1 − 2 k k + 2 1
2011(2011 + 2 ) 1 7×9
+
....
1 9 × 11
+
1 2011 × 2013
2 2 2 2 2 + + + + .... + 2 1 × 3 3 × 5 5 × 7 7 × 9 9 × 11 2011 × 2013 1 1 1 1 1 1 1 1 1 − − − + − + ... + + 2 1 3 3 5 2010 2011 2011 2013 1 1 1 1 1 1 1 1 1 − + − + ... + − + − 2 1 3 3 5 2010 2011 2011 2013 1 1 1 − 2 1 2013 1 2013 1 − 2 2013 2013 1 2012 2 2013 2012 4026
B.
63
k (k + 2 )
=
1 2
#. ilai !ari 1 − A.
1
1
1 20 21 40
1 1 1 1 1 1 − 2 1 − 2 ...1 − 2 1 − 2 =… (PASIAD 20-2) 2 2 3 4 19 20
C. D.
21 2 21 20
YOYO APRIYANTO, S.Pd !"#"$%%3#5%1& 'mail( )*o*oa+ri*ato-mail.om0 -ui 2!1$ o4load ratis Modul Matematika 'disi S+esial S/MI, SMP/MTs, SMA/MA, da SMK/MAK Ku6ui 7e8site Yo*o A+ri*ato, S.Pd ( )9tt+(//ilmu:matematika.8los+ot.om0
K13 Modul Matematika SMP/MTs Kelas VII Semester 1
P a g e | 5$
Knci !a"a#an$ B Gunakan aturan: a
2
−b
2
=
(a + b )(a − b)
1 1 1 1 1 1 − 2 1 − 2 1 − 2 ...1 − 2 1 − 2 2 3 4 19 20 1 1 1 1 1 = 12 − 2 12 − 2 12 − 2 ...12 − 2 12 − 2 2 3 4 19 20 1 1 1 1 1 1 1 1 1 1 = 1 + 1 − 1 + 1 − 1 + 1 − ...1 + 1 − 1 + 1 − 2 2 3 3 4 4 19 19 20 20 1 1 1 1 1 = 1 − 1 − 1 − ...1 − 1 − 4 9 16 361 400 3 1 4 2 5 3 20 18 21 19 = ... 2 2 3 3 4 4 19 19 20 20 3 4 5 20 21 1 2 3 18 19 = ... . ... 2 3 4 19 20 2 3 4 19 20 21 1 = 2 20
21
=
40
$. ilai !ari A. B.
1 1× 4
+
1 4×7
+
1 7 × 10
+
1
15
10 × 13 5
16 5
16 2
C.
D.
6
+
1 13 × 16
=… (PASIAD 20-/)
3
Knci !a"a#an$ . 1 1× 4
+
1 4×7
+
1 7 × 10
+
3 3 3 3 + + + + 10 × 13 13 × 16 3 1 × 4 4 × 7 7 × 10 10 × 13 13 × 16 1 1 1 1 1 1 1 1 1 1 1 = − + − + − + − + − 3 1 4 4 7 7 10 10 13 13 16 1 1 1 1 1 1 1 1 1 1 1 + − + − = − + − + − 3 1 4 4 7 7 10 10 13 13 16 1 1 1 = − 3 1 16 1 16 1 = − 3 16 16 1 15 = 3 16 1
1
+
=
=
1 3
5 16
YOYO APRIYANTO, S.Pd !"#"$%%3#5%1& 'mail( )*o*oa+ri*ato-mail.om0 -ui 2!1$ o4load ratis Modul Matematika 'disi S+esial S/MI, SMP/MTs, SMA/MA, da SMK/MAK Ku6ui 7e8site Yo*o A+ri*ato, S.Pd ( )9tt+(//ilmu:matematika.8los+ot.om0
K13 Modul Matematika SMP/MTs Kelas VII Semester 1 3 4
%. 1 : 1,125 − 1,75 : A. 2 B.
2 5 .1 =… (PASIAD 20-/) 3 7
3
C.
4
−1
P a g e | 5#
5
D.
6
−
2
1 5
6 11
Knci !a"a#an$ B 2 5 3 7 1125 175 2 12 − : . 1 : 1,125 − 1,75 : .1 = : 4 3 7 4 1000 100 3 7 7 1000 175 3 12 = × − × . 4 1125 100 2 7 7 1000 12 175 3 12 = × × × × − 4 1125 7 100 2 7 1000 × 3 25 = × 3× 6 − 1125 100 3000 1 = − × 18 1125 4
= = =
8
−
9
3 2 16 27 −
6 6 11
−
6 5 = −1 6
&.
20122011 20122010 1006
A. B.
2
+
2
20122012
2
−
2
=… (PASIAD 20-/) C.
2011 2011
1 2
D. 1
2012
Knci !a"a#an$ . 20122011 20122010
2
+
2
20122012
2
−
2
=
20122011 20122010
2
−1+
2
20122012
2
−1
2
=
20122011
(20122010
2
) (20122012
−1 +
2
)
−1
2
=
20122011
(20122010
2
2
−1
) (20122012 +
2
−1
2
)
YOYO APRIYANTO, S.Pd !"#"$%%3#5%1& 'mail( )*o*oa+ri*ato-mail.om0 -ui 2!1$ o4load ratis Modul Matematika 'disi S+esial S/MI, SMP/MTs, SMA/MA, da SMK/MAK Ku6ui 7e8site Yo*o A+ri*ato, S.Pd ( )9tt+(//ilmu:matematika.8los+ot.om0
K13 Modul Matematika SMP/MTs Kelas VII Semester 1 = = = = = = = = 6
10. ilai !ari
1 10
+
1 40
+
1 88
+
P a g e | 5" 20122011 × 20122011
(20122010 − 1)(20122010 + 1) + (20122012 − 1)(20122012 + 1) 20122011 × 20122011
(20122009 )(20122011) + (20122011)(20122013) 20122011 × 20122011
(20122011)(20122009 + 20122013) 20122011
(20122009 + 20122011 + 2 ) 20122011
(20122009 + 2 + 20122011) 20122011
(20122011 + 20122011) 20122011 2(20122011) 1 2
a!alah… (I'.S 20-)
1 154
A. 24 B. 3#
C. 42 D. "4
'. #3
Knci !a"a#an$ . 6 1 10
+
1 40
+
1 88
+
1 154
=
6 1 1
1 1 1 + + + 2 5 20 44 77
=
12 1 5
=
=
+
1 20
308 1540 12
+
+
1 44 77
1540
+
1
=
6
×
2
1 1 1 1 1 + + + 5 20 44 77
()*) !ari ", 20, 44, !an $$ a!alah 1"40+
77 12 +
35 1540
+
20 1540
440
1540 1540 = 12 × 440 154 = 3× 11
= 3 14 = 42
YOYO APRIYANTO, S.Pd !"#"$%%3#5%1& 'mail( )*o*oa+ri*ato-mail.om0 -ui 2!1$ o4load ratis Modul Matematika 'disi S+esial S/MI, SMP/MTs, SMA/MA, da SMK/MAK Ku6ui 7e8site Yo*o A+ri*ato, S.Pd ( )9tt+(//ilmu:matematika.8los+ot.om0