E . simbolon e51mb.blogspot.com
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1. ALJABAR 1.
Diketahui : a+b = 2000 dan c+d = 2012 Berapa nilai dari ac + bc + ad + bd = ?
2.
Diketahui : a = 112 , b = 175, c = 138 dan d = 225 Tentukan nilai ab+bc+ad+cd
3.
Diketahui : ab = 6 , bc = 10 dan ac = 15, nilai abc = ....
4.
Jika ac + ad + bc + bd = 68 dan c+d = 4, maka a+b+c+d= ….
5.
Diketahui : Diketahui :
a b
6.
Diketahui :
7.
Solve for x for x in the equation
8.
Diketahui :
c a
2
4 ; Tentukan nilai a b
c
c
2
(x - y) = 4 dan
−
b
12 dan
2
9.
10. 11.
Diketahui :
x
x
Diketahui : Diketahui :
y
x
x
y
y
2
y 2 x
x
=3
1
2
y x
y
2
y
y
2
x
2
x
= 51, 51 , Tentukan Tentu kan nilai : x 3
6 , Tentukan nilai
y 3 x
3 , Tentukan nilai
8
1
2
x +
x 2
5 , Tentukan nilai
x 2
2
x – y y
− −
= 6 . Tentukan nilai
y 2
2
2x – xy – xy – y y = 68 . Tentukan nilai
1
x-
a
y
x
2
y x
y 3 x 3
y 8
12.
Diketahui :
13.
Misalkan x dan y merupakan merupakan bilangan real positif yang memenuhi x +y = 1 dan
y
x
4
x y
4
2
4
+
4
=
17 18
2
. Nilai dari xy adalah ...
14.
Dua buah bilangan jumlahnya 6 dan jumlah kuadratnya 24 Berapa hasil kali kedua bilangan itu ?
15.
Jika selisih dua bilangan adalah 2 dan selisih kuadrat bilangan itu adalah 6, maka jumlah kedua kedua bilangan itu adalah …
16.
Tentukan nilai x , y dan z yang memenuhi
17.
18.
19.
xy x y
3,
xz x z
2x = 3y = 4z dan
6 dan 1
x
1
yz y z 1
1.
y z 6 1 2 1 ; dan 1 1 x 1 1 y x y x y
xy x y
1
;
2 y z
4 Hitung nilai
Hitung nilai y
;
1 x
1 y
yz
....?
x
1
;
xz
3 x z
1 7
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2
1
2
1
y
x y
21.
Jika nilai 50x+10y = 2010, maka nilai 35x+7y = ….
22.
Jika x = 9043 dan y = 6543, Tentukan nilai (x+y) – 4xy 4xy
23.
Diketahui a = 2010 dan b = 1810 , 3 3 Tentukan nilai a – b – 3ab(a-b) 3ab(a-b)
y
= 1 dan
8 nilai dari
Diketahui
x
+
1
20.
x
adalah ….
2
2
2
3
3
24.
Jika a + b = 2 dan a + b = 5 , maka nilai a + b = ...
25.
K + L + M = 34 ,
26.
x=
27. 28. 29. 30. 31. 32.
x
=
3
y
K L
2
dan z = y
3
z
=
4
L
dan
4
=
M
+
x
1
2
1
x
2
5
2
1
+
1
=
x3
24 = x , x =
3)x
Jika , x+
Hitung nilai L ?
3
x+2
2 +2x
1
x+y+z
= ….
= 2 , berapakah x3 +
x
;
2
= 194 , nilai
1+ 1 + x x 2
(x 2
3
dan x + y + z = 200 ; Hitung nilai
⋯ − − ⋯ −− − 2
1
; Hitung nilai maksimum dari x + y + z
5
y
1
=
. ?
.?
= 1 , x =….?
2
9
2
= 6 , hitunglah (x+2) +
(x+2)2
2
33.
Faktor dari x -2x+4y-y -3 adalah ...
34.
Jika x + y + z = 0 dan xz + xy + yz = -42 2 2 2 Berapa nilai x + y + z ?
35.
Jika a, b, dan c adalah anggota bilangan bilangan riil yang yang memenuhi 1 a
+
1 b
1
1
c
a2
+ = 2 dan
Maka carilah nilai dari 36.
Maka nilai
ab
b2
+ 1
+
bc
1
=1
c2
+
1 ac
1
a b+c
+
a+b
+
b c+a
+
x-3
1 b+c c
a+b
+
1 c+a
=
7 10
= ?
y
Diketahui : 2 = 3 ; 4 = 24 Maka
38.
1
1
Diberikan a, b, c adalah anggota bilangan riil ( nyata ) a+b+c =7 ,
37.
+
2 x y x y
= ….
Jika P dan Q keduanya adalah bilangan positif ganjil dan memenuhi
1 p
1
3
q
5
,
maka selisih dari P dan Q adalah … 39.
Diberikan dua buah bilangan bulat berbeda yang yang berjumlah 37. Apabila bilangan yang yang lebih besar dibagi degan bilangan yang lebih kecil, maka hasil baginya adalah 3 dan sisanya 5. Selisih kedua bilangan tersebut adalah …
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−− x
x2
x y
x 2 +y 2
40.
Jika x : y = 3 : 4 , maka nilai
41.
Jika 2x – 12y 12y = 5xy; dan y ≠ 0 , maka nilai
42.
Tentukan nilai xy dari system persamaan : 2 2 2 2 x - y = 1 ; (x – y y )(x – 2xy 2xy + y ) = 4
43.
a,b,c,d adalah empat bilangan asli berbeda yang yang memenuhi persamaan persamaan 2 2 2 2 a - b = c -d = 81. Nilai ac+bd+ad+bc = …
44.
Diketahui : a – b b = 2025 , a dan b bilangan asli. asli. Nilai a + b = ….
2
2
2
adalah …
x
adalah ...
y
2
2
4
3
3
2
2
2
4
45.
Jika a- b = 1. Tentukan nilai dari dari : a – ab ab – a a b – b – 3a 3a b + 3ab + b
46.
Diketahui x -2x-2 = 0 , maka maka berapakah nilai x +
47.
Mis : a - 12a – 12a – b b + 41 = 0 dengan a,b
48.
Berapa nilai x+y , jika diketahui x + y - 4x +10y - 29 = 0 ?
49.
a dan b adalah digit digit pada bilangan ab dan ba, sehingga (ab) – (ba) (ba) = 1089 2 2 berapa nilai dari a + b ?
50.
Urutkan dari kecil ke besar bilangan bulat positif a,b dan c , jika
51.
Berapa nilai dari a + b + c , jika a + b = c+6 dan ab – ab – ac ac = bc – bc – 1 1 ?
52.
Tentukan faktorfaktor- faktor faktor dari x – y y – 6x – 6x – y -7 ?
53.
Diketahui persamaan 2x + (x+1) = 1. Carilah
54.
Diberikan sistem persamaan berikut :
2
2
2
2
∈
4 2
?
. Berapa nilai a untuk b yang paling minimum?
2
2
2
2
2
2
2
2
2
- 5
+
2
Carilah nilai x – y y ?
+
2
=6
= 40 + 12 2
55.
56.
(2x+y+1)(x-y-4) = 23, x+y = ...? ( x,y,z
57.
Some horses and some jockeys are in a stable. In all, there are 71 heads and 228 legs. How many jockeys are in the stable?
58.
1
2 +4
2
59. jika
60.
+
1
2 +4
=4 = 16 8 a 3 b
=
+4
=>
14 45
+
2
, berapakah nilai x + 3 ?
∈
+
Z )
= ..?
+b=3 +c =1
Diketahui
hitunglah a.b.c
83249 + 1675 16751 1 = 1082 108249 49 16751 + 8324 83249 9 = 4175 41751 1
, berapa nilai
=?
2
1
+
>
1
+
>
1
+
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61.
62.
= = =
12 35 28
=> a = ... ?
35 1 3
Diberikan a, b, c adalah anggota anggota bilangan riil ( nyata ) a+b+c =7 1 a+b
+
1
+
b+c
1 c+a
7
=
Maka nilai
10
2+
a b+c
+
b c+a
2
+
c a+b
− 2
2
63.
Aziz melakukan operasi : a O b =
64.
Dua bilangan real x real x,, y memenuhi Berapakah nilai x -y ?
65.
Diberikan tiga bilangan positif x positif x,, y, y, z semuanya berbeda. Jika
Jika
2ab ab
1,
+ 1+
2
+ 1+
ac ac
1 7
, dan
2
Misalkan a dan b bilangan real berbeda sehingga sehi ngga Tentukanlah nilai
67.
2
tentukan nilai 66.
dan a▲b =
= ?
bc cb
a
2,
maka
a2
1 a
+
+10
+10
1
1
c
b
2
= 1
− =
+
=
=2
68.
Jika a : b = 2 : 5 maka nilai
69.
Diketahui :
x+y+z =6 2 2 x +y +z = 14 nilai xy+xz+yz = ….
70.
Find the sum of x+y+z for the values of x,y,z that will solve the following system of equations. xy = 30 xz = 10 y+z = 20
71.
xy 4 and x y x 2 y xy 2
72.
If ax 3 y 5 and 2 x by 3 represent the same straight line. Find the value of a + b.
ab
a2
b2
=...
2
35 find
x 2
y 2 .
73.
A group of friends buy one coke, 3 burgers, and 7 cartons of fries for 23 euros. The next day they buy one coke, 4 burgers, and 10 cartons of fries for 29 euros. How much does one coke, 1 burger, and 1 carton of fries cost?
74.
Solve the following system for (v, w, x, y, z): v+w+x+y=6 v+w+x+z=4 v+w+y+z=1 v+x+y+z=0 w+x+y+z=5
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2.
BILANGAN
1.
25 x 42 : 6 + 28 x 35 : 4 + 63 : 9 x 40 - 80 x 56 : 8 =....
2.
If the product
3.
123456789 + 987654321 + 22282125+ 44444444+ 6666666666+777777777 jika dibagi 5 berapa sisanya ?
4.
Berapa sisa pembagian 123456789 : 8 ?
5.
a22282125b habis dibagi 18, nilai b adalah ….
6.
Sisa pembagian 3
7.
Berapa sisa pembagian
8.
Berapa sisa pembagian 474747
3 2
×
4 3
2012
5
×
4
×
6 5
…
.×
= 2012 . what is the sum of a and b?
: 7 adalah …. 2012
3
: 11 ?
…… …
47 dibagi 9 ?
108
999999999
9.
Jika 10
10.
Jika bilangan bulat x dan y dibagi 4 maka bersisa 3. Jika bilangan x - 3y dibagi 4 maka bersisa . . .
11.
Suatu bilangan jika dibagi 3 sisa sisa 1, jika dibagi 4 sisa sisa 2 dan jika dibagi 5 sisa sisa 3, bilangan apakah itu ?
12.
Suatu bilangan jika dibagi 4 sisa 1, jika dibagi 5 sisa 2 dan jika dibagi 6 sisa 3, bilangan apakah itu ?
13.
Umur Pak Simlon jika dibagi dibagi 4 sisa sisa 1 , jika dibagi 5 sisa sisa 2 dan jika jika dibagi 6 sisa sisa 3. Berapa umur Pak Simlon ?
14.
Sebuah bilangan asli lebih dari 11 mempunyai sisa yang sama (bukan nol) jika terbagi 3, 5, 7 dan 11. Bilangan Asli terkecil terkecil yang memenuhi adalah …
15.
Suatu bilangan kuadrat jika dibagi 3, maka kemungkinan sisanya adalah ...
16.
Ada berapa bilangan asli kurang dari 579 yang habis dibagi 3 atau 5 ?
17.
Banyaknya bilangan bulat positif yang tidak lebih dari 1000 dan tidak habis dibagi oleh 4 maupun 7 adalah ... Jika bilangan bulat x dan y dibagi 4 maka bersisa 3. Jika bilangan x - 3y dibagi 4 , maka bersisa . . .
18.
dibagi 7, maka sisanya adalah …
19.
Diberikan dua bilangan bulat yang berjumlah 37 . Jika bilangan yang lebih besar dibagi dengan bilangan yang lebih kecil, maka hasil baginya adalah 3 dan sisanya 5. Selisih kedua bilangan tersebut adalah ...
20.
How many three-digit numbers, when divided b y the sum of their digits, give 25 as the answer?
21.
If we type seven consecutive integer numbers and the sum of the smallest three numbers is 33, which is the sum of the largest three numbers?
22.
Diketahui “ a*b “ artinya 2ab dan “ a▲b “ artinya a – b b Nilai dari ( 5*2) ▲ (7▲3) = ….
23.
Dua buah bilangan berjumlah 148 , bilangan yang besar dibagi bilangan yang kecil hasilnya 17 dan
2
2
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24.
Jika angka pertama dan angka kedua dari sebuah bilangan dua angka dijumlahkan maka hasilnya adalah 12. Jika letak kedua angka tersebut dipertukarkan, dipertukarkan, maka selisih bilangan sekarang dengan bilangan sebelumnya adalah 18. Maka bilangan pertama adalah...
25.
1-2+3-4+5-6+…….+2011 1-2+3-4+5-6+…….+2011--2012 = ….
26.
Hasil dari 2+3-4+5-6+……..+2011 2+3-4+5-6+……..+2011--2012 = …
27.
Dua buah bilangan FPB dan KPK nya berturut turut turut 36 dan 432, Jumlah kedua bilangan itu adalah
28.
Dua buah bilangan FPB dan KPK nya nya berturut turut 14 dan 392, Selisih kedua bilangan itu adalah
29.
Sekarang hari Sabtu , hari apa apa 2012 hari lagi ?
30.
O,L,I,M,P,I,A,D,E, O,L,I,M,P,I,A,D,E, ........ Huruf apa yang menempati urutan yang yang ke 2012 ?
31.
Digit terakhir 2012
32.
1 1 1 1 = ... 1 2 1 2 1 2 .....1 2 2 3 4 2012
33.
If
97 19
34.
1
w
x 1
c
Tentukan nilai a+b+c+d
73
d
1
8 ,
Tentukan nilai abcd
35
1
b
c
36.
30 ,
1
1 a
, where w, x, y are all positive integers, then w x y equals
1
b
35.
adalah ...
y
1
a
1
2012
0,222… +
1 d
=
1 1,999... 2
1 2
, nilai a+b = ...
1
+
1
1
= , maka p – p – q q=…
37.
Jika P dan Q keduanya adalah bilangan Asli ,dan p>q memenuhi
38.
Jika P dan Q keduanya adalah bilangan Asli dan memenuhi 1 1 2 , maka nilai pq = ….
39.
Jika P dan Q keduanya adalah bilangan Asli dan memenuhi
40.
Two numbers and are such that x + y = 20 and
p
1
+
1
=
1 2
7
q
− 1
1
9
=
3 10
, maka nilai p+q =… 2
2
. What is the value of x y = xy ?
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46.
Hasil kali dari 99999999 . 100000001 adalah ….
47.
3 4 5 5
48.
Himpunan semua bilangan prima yang kurang dari seratus dan kuadrat bilangan tersebut ditambah dua juga merupakan bilangan prima adalah ….
49.
The sum of two numbers is 52. If the larger is divided by the the smaller, What is the numbers ?
50.
1 1 1 + 2! 3! 4! 1 1 1 + 2! 3! 4!
51.
(2,397+0,3x0,01) : 0,001 – 0,001 – 400 400 = ... ?
52.
(0,75) - (0,75)(0,5) – (0,75)(0,5) – (0,25) (0,25) = ...?
53. 54.
♥ ♥ ♥ ♥
7 8 9 7
= 6 = 8 = 10 = ...?
− − ∶ −
3!+4! 5! 4!
= ...?
2
2
0,xy+0,00xy 0,xy
= ...?
2012201220122012 2012
=
⋯
55.
A+B+C = 11 , CAC + BCA + ABB = ..? ( Ketiganya bilangan 3 digit)
56.
20102012 . 20122010 - 20122012 . 2010210 = ....
57.
Digit terakhir (1! . 2! . 3! . ...... . 2012! ) : 625 = ...
58.
Apakah bilangan terakhir bilangan (1!+2!+3!+......+ (1!+2!+3!+......+ 2012!)
59.
Diketahui m dan n adalah bilangan bulat positif, dan m + n + mn = 34 Berapa nilai dari m + n ?
60.
m dan n dua bilangan bulat positif sehingga m+n+mn = 24. Berapa m+n ?
61.
Sebuah angka 6 digit cdbcda dapat dibagi 11 dan a+b = 10, maka nilai nilai ab = ...
62.
Ada berapa kemungkinan bilangan asli n, sehingga
63.
a dan b adalah digit digit bilangan ab dan ba, sehingga ab-ba = 72. 2 2 Maka berapakah a + b ?
64.
a,b,c,d bilangan bulat positif. Jika a dibagi b = 15 sisa sisa 7, b dibagi 6 = c sisa 3 dan a dibagi 18 = d sisa x Berapa nilai x ?
65.
Berapa nilai maximum dari
8
?
3n+21 n+3
2012
?
adalah bilangan asli asli ?
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69. 70.
a, b, c 1 4×9
+
∈
R
1 9×14
-
+
,
5
5
=
1 14×19
8
+
=
⋯
..
6
1 1999×2004
Find the value of
72.
n – m m = 2323 , n+m = ...
73.
1 1.2.3.
?< ? < ? = ...
1×5×18+2×10×36+3×15×54
71.
2
=>
9
1×3×9+2×6×18+3×9×27
2
+
1 2.3.4
+
1 3.4.5
+
⋯
+
1 2000.2001.2002
=
⋯
74.
Delapan bilangan asli memiliki rata-rata 6,5. Empat dari delap an bilangan tersebut adalah 4, 5, 7, dan 8. Selisih antara bilangan terbesar dan terkecil adalah 10. Jika kedelapan bilangan diurutkan dari kecil ke besar, maka banyaknya susunan adalah …
75.
Two 3-digit numbers, abc and def, have the following property: abc +def 1000 None of a, b, c, d, e, or f is 0. What is a + b + c + d + e + f?
76.
The mean (average) of 6, 9 and 18 is equal to the mean (average) of 12 and y. What is the value of y?
77.
Four of the six numbers 1867, 1993, 2019, 2025, 2109, and 2121 have a mean (average) of 2008. What is the mean (average) of the other two numbers?
78.
In the figure there are nine regions inside the circles. Put all the numbers from 1 to 9 exactly one in each region so that the sum of the numbers inside each circle is 11.
79.
Jumlah setiap baris , kolom dan diagonal sama Nilai p adalah ...
?
24
p
4 12
80.
81.
A paper strip was folded three times in half and then completely unfolded so that you can still see the 7 folds going up or down. Which of the following views from the side cannot be obtained in this way?
Carmen selects four different numbers from the set {1, 2, 3, 4, 5, 6, 7} whose sum is 11.
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3. B I L A N G A N BERPANGKAT & AKAR 1.
64+ 64+ 36 36
The value of
is
64+36 64+36
(A) 7
(B) 16
(C) 1
(D) 24
8
(E) 14
4
2.
The number 8 is obtained from the number 4 by raising this number by the power of n. What is the number n? A) 2 B) 3 C) 4 D) 8 E) 16
3.
10 0,0036 3 1 3 4 x 9 =… 5 1 5
4.
2 3
1
27.
2
0,04 ...
2
3
5.
2.
6.
k adalah bilangan real. real. Berapa Berapa nilai k untuk persamaan disamping ? 0,4 .0,5 .k 103
7.
Seorang pedagang membeli sebuah barang seharga Rp.3 , kemudian barang tersebut dijual lagi 34 dengan harga Rp.3 . Berapa persentase untung Pedagang itu ?
... 3 3
33
50502 49502 = …
8.
2007
. 5
2008
9.
2
10.
Semua bilangan bulat x sehingga
11.
Express
12.
5
2+ 2+
1 2010
= …
2010
1
−
1
2+ 2
1
+
2 2
1 2010
2009
1
1 2 x
1 2 x
merupakan bilangan bulat Adalah …
in its simplest form
1 2010
5555
2008
4444
3333
2222
14.
Berapakah jumlah dari akar akar penyelesaian persamaan 4
1
Jika
16.
22012 22009 =... 22 0 0 8 22 0 0 6
17.
2 +2 = 10 ; 4 + 4
18.
Carilah x untuk (6,25)
x
2
-x
dibagi 9, maka sisanya adalah ...
x
+
, 5
2010
Urutkan bilangan-bilangan 2
15.
, 4
1
13.
311
, 3
. ..............
-x
= ... 3x-3
= (0,064)5
−
x2
2010
1
1005 2010
....?
dari yang terkecil sampai yang terbesar x+1
x
- 9. 2 + 2 = 0 ?
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x
x+3
83 + 3 2y+1 = 5
y+1
24.
Diketahui : 2
25.
Jika 9
26.
Jika 9 + 9 = 7 , maka 27 + 27
27.
Diketahui : 4 + 4 + 2 + 2
28.
- x
+ 9
= 7 ; maka nilai 27
x
– x
1
-x
1
2008
2x+1
x
-x
2008
2007
– x x
= ... x
= 10 ;
1
1
; Tentukan nilai xy
= ...
x
x
2008
= 35 dan
Tentukan nilai 2 + 2
1
2008
1
2006
........ 5
1 2008
2
Jika hasil perkalian perkalian dua bilangan cacah cacah sama dengan 2 , 3, 5 , 7 maka hasil penjumlahannya akan habis dibagi ....
30.
Jika ( 0,25)
=
1
2 x 2
2 x 1 28 ;
32.
4 x 1
2 2 x 1 72
34.
0,036 0,009
4
x
3
x =…
; x =…
=…
4
8
x
5
; x = …
35.
Sederhanakan.
20 8 6
36.
Rata rata dari :
4
37.
2 )(2
3 )(1
12
+
4
(x+1)
Jika
39.
Sederhanakan
1
287 287
1
289
= ...
3)
= ....
1 2
12
x + 1 = 8 , maka nilai x = …
1
= ...
2 )(2
38.
40.
=…
1 (1
1
= ...
, berapakah nilai x ?
64
31.
33.
2008
3
29.
x+1
-x
2
1 3
3
4
41.
Berapa hasil h asil penjumlahan dari :
42.
Hasil dari
43.
Hasil dari
16 16 x 2 12
12
12
12
.....
1 99
100
....
1
17+ 17+ 16 16
+
9 9 x 2 ... .. . ...
=…
1
18+ 18+ 17 17
+
1
19+ 19+ 18 18
+
……
.+
1
99+ 99+ 98 98
+
1
100+ 100+ 99 99
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47.
8
48.
1999.2000.2001.2002
49.
2003.2001.1999.1997
50.
48
8
48 = ....
Tentukanlah nilai x jika
16 =...
x
1 51.
1 = …
Tentukan nilai x dari : 2
x
( x 2) 2
2010 2010 + 2000 2000 = a, nilai
52.
Diberikan
53.
Sederhanakan : 3
1
16
1+ 1 x x 2 24 = x
.... x
.3 ( x 2).( x 2) 3
54.
x
3
12
3
2
2010 2010 - 2000 2000
dalam bentuk a adalah ….
9
; Nilai x = ....
− ⋯ − − ⋯ −− − − ⋯ − − 7
(x+1)
x+1
x+1
55.
Jika
56.
Jika n = 2009 + 2010 , maka
57. 58. 59. 60. 61. 62.
2
x
1
x
x
2n 2n
1
x3
3)x
24 = x , x =
2 +2x
250
( 3 1)49 .( 3+1) 3+1)50
m
2
= 2 , berapakah x3 +
1+ 1 + x x 2
(x 2
= 2 2 , maka nilai x = …
=
1
. ?
.?
= 1 , x =….?
.
n = 2 , mn = 4
1. 2. 3
=
1 =…
3
. hitunglah m m 12 5
n n
carilah nilai
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69.
70. 71.
19
Ahmad menghitung nilai 3 = 11a2261467 dan Ahmad yakin bahwa semua angka tersebut adalah benar kecuali angka (digit) ke-3 yaitu a. Berapakah nilai a?
− −
104 102 10 105
104
= ….
−
3
5+2 -
3
5
s
2 = ….
t u
72.
Jika 1800 = p q r , { p,q, r} r} p + q + r + s + t + u = ….
73.
Given 2 A) 0
74.
2
75.
n + 2003
x+1
x
y-2
2 1+2 1+2 2
bilangan prima
y
+ 2 = 3 – 3 3 , where x and y are integers. What is the value of x? B) 3 C) -1 D) 1 E) 2
+ 2
n +2003
= ...
1
∈
+
1
3 2+2 2+2 3
+
1
4 3+3 3+3 4
+ ....... +
1
15 14+14 14+14 15 15
⋯ −
+
1
16 15+15 15+15 16 16
= ...
76.
…
77.
Solve for x in the equation
78.
Solve for x in the following equation: 5x
79.
Diketahui untuk setiap bilangan real x , x x menyatakan menyatakan bilangan bulat terbesar yang
2+3 22 +32
.. 22048 +32048 +24096 32048
=
x+9
x=2 2
−
35
⌊ ⌋
kurang dari atau sama dengan . Nilai dari a
b
= 25x
2010 2 010 +
⋯ 201 2 010 + 2010 2 010 +
c
adalah
80.
If 3 x10 +5x10 +7x10 = 5073, and a, b and c are non-negative integers, what is the value of a + b + c?
81.
Solve for n:
82.
What is the value of
− 1+
2 + n = 2. 17 17
12 2 + 1
17+12 2 ?
x
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4.
PERSAMAAN
1.
Tentukan nilai x dari dari : 3x + 2 - 9 – 6x – 6x = 9x – 9x – ( ( 2x + 1 ) + 6
2.
Tentukan nilai 2a – 2a – b b dari persamaan ( a + 2b )( a – a – b b ) = 10 ; a dan b Bilangan bulat positif
3.
Bilangan 45 dapat dinyatakan sebagai selisih selisih dari bilangan bilangan kuadrat, 2 2 yakni a – b b , dengan a dan b adalah bilangan asli. 2 2 Semua pasangan bilangan asli a dan b yang memenuhi a – b b = 45 adalah …
4.
Suatu halaman rumah berbentuk persegi panjang luasnya 165m , jika panjangnya (2x-3) m dan lebarnya (x+2)m , maka keliling halaman rumah itu adalah ….
2
5.
Jika a + b = 40, b + c = 50 dan a + c = 60, maka a + b + c = …
6.
Tentukanlah nilai 2x + 3y dari sistem persamaan :
7.
Tentukanlah nilai x - y dari sistem persamaan :
2
8
8.
a 3 b
9.
b 3
2
7x + 13y = 68 13x + 27y = 12 123x + 321y = 345 321x + 123y = 543
, hitunglah abc
c 1
xy x y
2,
xy
3 ; Hitung nilai xy
y x
10.
1 2 x 2 y 2 4 Diketahui x dan y bilangan real 1 2 12 2 y 2 x
11.
Tentukan nilai x + y dari persamaan
12.
Tentukan nilai
2
x y
xz
12
2
x
dari system persamaan : yz
2
2
2 x
y
−
2
, nilai x – y y = ….
2
1 y
x 2 dan =2;
1 x
2
3 x
2
y
+ = 11 y
2
y 2
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20.
Peserta upacara bendera yang dihadiri oleh 600 siswa disusun dalam x baris. Tiap barisnya diisi oleh y siswa. Jika susunan barisan diubah dengan menambah 5 baris, maka tiap barisnya berkurang 6 siswa. Tentukan banyaknya baris sebelum diubah?
21.
Diketahui bahwa 13 buah anggur mempunyai berat yang sama dengan 2 apel ditambah 1 buah pear. Sedangkan 1 buah pear sama beratnya dengan 4 buah anggur ditambah 1 buah apel. Berapa banyak buah anggur yang seberat dengan 1 buah pear?
22.
Umur Pak Tono sekarang 33 tahun, adalah tepat tiga kali umur Tini pada waktu Pak Tono masih berumur sama dengan umur Tini sekarang. Berapakah umur Tini sekarang?
23.
Suatu kereta api hanya dapat menampung maksimum 78 penumpang. Kereta api tersebut berangkat tanpa penumpang dari stasiun awal dan menaikkan 1 orang penumpang pada pemberhentian (stasiun) pertama, 2 orang pada pemberhentian ke dua, 3 orang pada pemberhentian ke tiga, demikian seterusnya. Setelah berapa kali pemberhentian kereta api tersebut akan penuh?
24.
Formasi tempat duduk di suatu ruangan kelas k elas terdiri dari beberapa baris, di mana masing-masing baris terdiri dari beberapa kursi yang berjumlah sama. Jika setiap baris baris terdiri dari 4 kursi, ada 3 siswa yang tidak kebagian kursi. Jika setiap baris terdiri dari 5 kursi, ada 2 kursi kosong yang tidak ditempati siswa. Berapakah sedikitnya jumlah siswa dalam kelas tersebut?
25.
Tiga pipa air digunakan untuk mengisi suatu kolam renang. Jika pipa pertama saja yang dipergunakan mengisi sampai penuh kolam renang tersebut, maka diperlukan waktu 8 jam. Jika pipa kedua saja dipergunakan maka diperlukan 12 jam, sedangkan jika digunakan pipa ketiga saja diperlukan waktu 24 jam. Jika ketiga pipa dipergunakan secara bersamaan, berapa lama kolam renang tersebut akan terisi penuh?
26.
Wati mencatat
3 20
dari total siswa di kelas IX adalah laki - laki.
Sedangkan menurut catatan Budi,
1 7
dari total siswadi kelas IX selain dirinya adalah laki - laki.
Banyak siswa laki - laki kelas IX di sekolah mereka adalah . . . 2
2
27.
If r is a number such such that r − 6r 6r + 5 = 0, what is the value of (r – (r – 3) 3) ?
28.
The integer numbers x and y satisfy satisfy 2 x = 5 y. y. Only one of the following can be x be x + y. y. Which is it? A) 2011 B) 2010 C) 2009 D) 2008 E) 2007
29.
Himpunan penyelesaian dari pertidaksamaan
30.
Tentukan semua bilangan real x yang memenuhi pertaksamaan
−
2 +5 2
< 1 , adalah ...
− ≥ 1
+1
2 !
Sekumpulan bilangan asli memiliki rata-rata x . Semua bilangan asli tersebut
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5.
FUNGSI
1.
F( 2x – 2x – 3) 3) = 4x + 5 ,
f(x) = ….. ?
2.
f(x + 3ax + 1) = 2x-1 dan f(5) = 3. hitung nilai a
3.
F(x) adalah sebuah fungsi sehingga f(2011) = 2020 dan f(x+1) = 2f(x) – 2f(x) – 2004. 2004.
2
untuk x adalah bilangan bulat maka nilai dari f (2010) adalah …. ….
f (b) f (a)
4.
Jika f(z) = az + b, maka nilai dari
5.
Diberikan fungsi kuadrat f(x) = ax – 3x 3x + c. jika f(1) = 4 dan f(2) = 7, maka f(-1) f(-1) = …
6.
Dik : f(x) = 10x + 11a + 12 f(2008) = 2009; f(2010)= ... ?
7.
F(x+1) =
2
—
1+ ( ) 1
( )
dan f(1) f(1) = 2
hitung f(2010) 8.
3
Nilai dari f 9.
f(x) = 4x – 2000x 2000x +14
1+ 1997 1997 2
f(2x+1) = 4x – 4x – 2006 2006 f(2009) = .... ? 2
10.
f(x) = 2x +bx + c f(2008) = 0 ; f(2009) =0 ; f( 210) = .... ?
11.
f(x) = ax +bx - 12 f(1) = 0 ; f(3) = 0 ; f(5) =….
12.
f(x) = x +bx + c f(9) = f(10) = 5 ; f( 2010) = …. ?
2
2
= ….
ba
adalah ....
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6. HIMPUNAN & PERBANDINGAN 1.
Dalam suatu ruangan terdapat 165 orang orang siswa, diantaranya 110 orang suka suka minum susu dan 132 orang suka minum kopi. Banyaknya yang suka minum susu saja adalah ….
2.
Diketahui Himpunan P = { Bilangan Prima < 10} dan Q = { m, t, k } Banyaknya pemetaan dari Himpunan Q ke Himpunan P = …
3.
Dalam Suatu Kelas terdapat 30 orang siswa, Tercatat 2 4 orang suka matematika, 10 orang suka IPA , 15 orang suka B.Inggris, 9 orang suka suka Matematika dan B.Inggris, 10 orang suka B.Inggris dan IPA dan 4 orang suka Matematika dan IPA Berapa orang yang suka ketiga-tiganya ? n 1 H adalah himpunan semua bilangan asli n demikian sehingga bentuk menghasilkan n3 bilangan bulat kurang dari 1. maka banyaknya himpunan bagian tak kosong dari H adalah …
4.
5.
Jika H adalah himpunan semua pembagi positif dari 2007, maka banyak himpunan bagian dari H yang tidak kosong adalah …
6.
60 children go on holiday. Among any 10 children there are at least 3 who live in the same village. Show that there must be at least 15 children who live in the same village.
7.
Setiap dung adalah ding. Ada lima ding yang juga dong. Tidak ada dung yang dong. Jika banyaknya ding adalah 15, dan tiga di antaranya tidak dung dan tidak dong, maka banyaknya dung adalah …
8.
100 students attended at least one of three concerts: Pop, Country, and Blues. 48 heard Pop, 36 heard Country, 60 heard Blue, 12 heard Pop and Country, 20 heard Country and Blue, and 16 heard Pop and Blue. How many attended all three?
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14.
5 Orang tukang jahit dalam 5 hari dapat membuat 5 potong jas Berapa waktu yang diperlukan 4 orang tukang jahit untuk membuat 4 potong jas ?
15.
6 Orang tukang kayu dalam 6 hari dapat membuat 6 buah lemari Berapa waktu yang yang diperlukan 3 orang tukang kayu untuk membuat 3 buah lemari ?
16.
Pembangunan sebuah gedung direncanakan selesai dalam waktu 20 hari bila dikerjakan oleh 20 orang. Setelah dikerjakan 5 hari, pekerjaan dihentikan selama 5 hari. Supaya pembangunan itu selesai tepat pada waktunya, maka diperlukan tambahan pekerja sebanyak ….
17.
Sebuah Tabung jika diisi kran A akan penuh selama 3 jam dan jika dibuka kran B selama 3 jam akan berkurang
1
nya . Berapa lama lama tabung penuh jika kran dibuka kedua duanya ?
3
18.
Jika perbandingan A : B = 2 : 3 ; C : D = 4 : 5 dan D : B = 6 : 7, maka A : C adalah ...
19.
Sekarang umur saya
1 3
dari umur Ibu, 5 tahun lalu umur u mur saya
1 4
dari umur Ibu.
Berapa tahun umur saya sekarang ? 20.
Perbandingan jumlah siswa perempuan dan laki-laki di suatu kelas adalah 10 : 9 . jika laki-laki keluar 2 orang maka perbandingan perempuan dan laki-laki di kelas itu menjadi 5 : 4 Banyak laki laki di kelas itu adalah ….
21.
Antara jam 8 dan jam 9. Jarum jam dan jarum menit berimpit pada jam …..
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7. BARISAN BILANGAN & DERET
1.
1+2-3-4+5+6-7-8+…………2005+2006 1+2-3-4+5+6-7-8+…………2005+2006-2007-2008+2009-2010+2011-2007-2008+2009-2010+2011-2012 2012 = …
2.
Tentukan hasil penjumlahan berikut 20 + 22 + 24 + ….. + 98+100
3.
Jika a, b, 15 , c, d membentuk barisan barisan aritmatika , maka a + b + c + d = …
4.
(1 + 2 + 3 + ..... + 2011 ) – ) – ( ( 1x3 + 2x4 + 3x5 + .... + 2010x2012 ) = ...
5.
Hitunglah ( 1+3+5+7+......+ 2013) - ( 2+4+6+8+.......+20120) ?
6.
Seorang siswa menjumlahkan halaman sebuah buku tapi ada yang terhitung dua kali sehingga jumlahnya 2000. Halaman berapakah yang dihitung dua kali ?
7.
Diberikan sebuah persegi dengan panjang sisi 6 satuan panjang. Di dalam persegi tersebut digambar persegi dengan menghubungkan titik tengah dari persegi dan cara tersebut terus berulang. Tentukan keliling persegi yang ke -9
8.
Seorang pendaki sebuah gunung. Pada satu jam pertama, dia mendaki sejauh 800 m. setiap satu jam jam selanjutnya dia mendaki sejauh kurang dari 25 m nya. Berapa jam yang dibutuhkan oleh pendaki tersebut jika ketingggian yang harus dicapai yaitu 5700 m ?
9.
Bilangan asli n terbesar terbesar sehingga jumlah 1+3+5+…+(2n1+3+5+…+(2n-1) lebih kecil 2010 adalah…
10.
Sebuah barisan bilangan didapat dengan cara mengalikan bilangan sebelumnya dengan 2 dan menambahkan a ke hasilnya. Jika suku ke-6 dan suku ke-9 barisan tersebut tersebut adalah 70 dan 609,
2
2
2
2
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18.
Sebuah bola dijatukan dari ketinggian 10 m. kemudian bola selalu memantul
3
bagian dari tinggi
4
sebelumnya. Berapa jarak yang dilalui bola sampai berhenti ? 19. 20.
Bilangan asli n terbesar sehingga jumlah 1+3+5+…+ n < 1000 adalah… 3 1.4
+
5 4.9
+
7 9.16 2
+
⋯ 2
.+
2011 1005 2 .1006 2 2
2
=… 2
21.
The sum 100 - 99 + 98 - … +2 - 1 equals
22.
1 246 3 5 7 9 11 8 10 12 14 16 18 20 13 15 17 19 21 23 25 27 29 22 24 26 28 30 32 34 36 38 40 42 ... ......................................................... th Which number is at the end of 10 row?
23.
If a – a – 1 1 = b + 2 = c – c – 3 3 = d + 4 = e – e – 5, 5, then which of the numbers a, b, c, d, e is the largest?
24.
How much is 12 + 23 + 34 + 45 + ......+ 221 ?
25.
If 991 + 993 + 995 + 997 + 999 = 5000 – 5000 – N, N, then then N =
26.
Calculate 1 – 1 – 2 2 + 4 – 4 – 8 8 + 16 - ….….- 512
27.
Banyak bola pada pola yang yang ke 40 adalah .... (1)
(2)
(3)
(4)
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8. GEOMETRI
1.
Tentukan Luas segitiga ABC ABC . B A C
2.
Perhatikan gambar di samping. Jika jarak titik horizontal dan vertikal adalah 2 satuan, maka luas daerah persegi yang diarsir adalah … satuan luas
3.
Diketahui : Keliling persegi kecil 56 m Keliling persegi besar 104 m Tentukan Luas daerah yang diarsir
4.
Sebuah segi empat dibagi menjadi 7 buah persegi Sisi persegi yang diarsir 16 cm. Tentukan Luas persegi yang besar yang tidak diarsir
5.
ABCD adalah persegi dengan panjang sisi 12 cm. Titik P, Q, R berturut turut terletak tepat ditengah BC, CD, dan DA. Luas daerah yang diarsir adalah ...
16cm p
D R
Q
C P
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11.
Pada gambar di samping, segitiga PSR adalah segitiga siku-siku dan S sebagai sudut siku-siku. Dan segitiga PRQ juga merupakan segitiga siku-siku dengan R sebagai sudut siku-siku. Jika PS = 12, SR = 9, dan PQ = 25, tentukan panjang SQ!
12.
Pada gambar berikut, ABC = BCD = 90 . Jika AB = 9, BC = 24 dan CD = 18. Serta diagonal AC dan BD dari segiempat ABCD A BCD berpotongan di titik E, tentukan luas ΔDAE!
13.
Rectangle ABCD is inscribed in a quadrant of a circle, as shown. If the length of BC is 6, and the length of CE is 4, what is the length of AB?
∠ ∠
0
A
B
14.
Diberikan sebuah persegi dengan sisi a satuan, sebagaimana tampak tampak pada Gbr. empat buah segitiga siku-siku dipotong dari persegi tersebut seperti digambarkan
D
C
E
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19.
Diketahui panjang jari-jari ½ lingkaran 10 cm Luas daerah yang diarsir adalah ...
20.
Diketahui sisi persegi 35 cm. Tentukan Keliling dan Luas bangun 35cm
35cm 21.
Diketahui sisi persegi 14 cm. Tentukan Luas daerah yang diarsir 14cm
22.
Jika jari-jari lingkaran kecil = 3,5 cm Tentukan Luas yang diarsir
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28.
Dua buah lingkaran di samping masing masing Mempunyai jari-jari 50 cm untuk lingkaran luar , dan 20 cm untuk lingkaran dalam. Berapa luas daerah yang diarsir ?
29.
Kedua persegi menyinggung lingkaran, Diketahui sisi persegi luar 12 cm. Tentukan luas daerah yang diarsir 12cm
30.
31.
Tentukan luas daerah yang diarsir
Luas daerah yang diarsir setengah dari luas daerah yang tidak diarsir panjang AB dibagi panjang AC adalah …
C B
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37.
D
Perhatikan gambar . AK = BL = 4 cm Dan AB = 5 cm Tentukan Luas ABCD.
C
7 K
38.
2
Perhatikan gambar . jika Luas daerah yang diarsir 22 cm Tentukan panjang CD.
A
Seorang pemain bilyard menyusun ketiga bola bilyard dalam posisi seperti gambar di samping ini. Jika masing-masing bola bilyard mempunyai diameter 4 cm, berapakah nilai d ?
L
B 4
D
A 39.
5
C
E
B
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45.
Two semicircles are constructed, as shown in the figure. The chord CD is parallel to the diameter AB of the greater semicircle and touches the smaller semicircle. If the length of CD is 4, what is the area of the shaded region?
C
A
46.
Dua lingkaran dengan jari-jari yang sama 10 cm. Keduanya saling tumpang tindih dengan masing-masing menutupi 25% dari keliling yang lainnya, seperti pada gambar. Luas daerah yang diarsir
47.
Pada gambar berikut, PQRS adalah persegi panjang, dan T adalah titik tengah RS. Lingkaran dalamdari ΔPTS dan ΔRTQ masing-masing masing-masing berjari-jari 3. Sedangkan lingkaran dalam dari ΔQPT berjari-jari berjari-jari 4. Tentukan ukuran persegi panjang PQRS
48.
Diketahui DC setengah lingkaran, AE= 3cm dan AD = 9 cm Panjang AB = ….
A 3 E 9
D
B
B
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53.
Perhatikan gbr. besar sudut α = …..
1150 α 100 55
54.
0
0
In the figure D ABC D ABC has a right angle at C and angle A measures 20 degrees. If BD is an angle bisector of angle ABC, then the measure of angle BDC=?? A
55.
Berapa besar sudut sudut CDA ?
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2
2
2
62.
Luas sisi sisi sisi suatu balok adalah 48cm , 54 cm dan 72 cm . Tentukan volum balok
63.
Selembar seng berbentuk
3 4
lingkaran dan jari-jarinya jari-jarinya 28 cm, akan dibuat menjadi kerucut.
Volum kerucut yang terbentuk adalah …
64.
Sebuah wadah berbentuk tabung berisi penuh air minum , jari-jarinya 20 cm dan tinggi 30 cm. Air tersebut akan dituangkan ke dalam gelas berbentuk kerucut yang jari jari terbesarnya 5 cm dan tingginya 10 cm Berapa gelas volum tabung tersebut ?
30cm
40cm
10cm
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72.
Tentukan perbandingan luas daerah ADC dan luas daerah BCD!
73.
Diketahui ABCD persegi 2 Luas segitiga EBF = 3 cm 2 CDE = 4 cm 2 AED = 5 cm Tentukan Keliling segitiga AEF
B
E 5 cm
C 3 cm F
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81.
Diketahui E dan F titik tengah AD dan BC
A
B
1
Luas segitiga BDC = luas ABD 4
Luas CDEF : Luas Luas ABFE = ….
E
F D
82.
2
Diketahui luas persegi ABCD 144 cm , E dan F titik tengah AB dan BD Tentukan luas CDFP
C
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88.
2
The surface area of a large cube is 5400 cm . This cube is cut into a number of 3 identical smaller cubes. Each smaller cube has a volume of 216 cm . How many smaller cubes are there ? (A) 25 (B) 125 (C) 164 (D) 180
(E) 216
89.
PQRSTU is a regular hexagon and V is the midpoint of PQ. What fraction of the area of PQRSTU is the th e area of triangle STV?
90.
Angle b is 25 % less than angle c and 50 % greater than angle a. Which of the following is true about angle c?
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96.
In the diagram, 4PQR is right-angled at P and has PQ = 2 and PR = 2 3. Altitude PL intersects median RM at F. What is the length of PF?
R
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9. A. ( P
− −
PERMUTASI =
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)
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B.
PERMUTASI DENGAN UNSUR SAMA
(
… !
!
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)
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11.
Lima orang pemuda pergi berekreasi menggunakan mobil. Mobil yang digunakan memiliki dua tempat duduk di depan termasuk supir dan tiga tempat duduk di belakang. Dari kelima pemuda tersebut hanya dua yang bisa supir. Berapa cara mereka duduk di mobil tersebut ?
12. Indonesia akan mengirimkan delegasi Olimpiade Sains Internasional thn 2010. delegasi itu tiga
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10 . PELUANG P(A) =
1.
( ) ( )
Di dalam sebuah kotak terdapat 10 kartu k artu yang diberi nomor 1 sampai 10. jika diambil sebuah kartu