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05.03.2011 - III
1. 4 a, b, c d, b, c b, da . ( ) ( ):
a b c dab
cd
2. 2009. . (5. 2011. )?
3. 8.
4. 2, 5, 7, 13, 16 21 .
5. 1 , 2 , 5, 10 15 . 7 . 2 , , ?
20 .
120 . .
>> 13 (20 ).
5. 2 15 + 2 10 + 2 5 + 2 = 62 (10), 2 1 + 2 2 + 2 5 + 10 = 26
(10 ).
.
a b c d
a b c d
>>
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05.03.2011 - IV
1. 44cm 16cm 16cm. ?
2. 4, ?
3. , . , . 210 ?
4. .
5. - (). -
6cm.
AB = 4cm, BC= 3cm,EF= 5cm, FG = 2cm,
ABCDEFGHA.
20 . 120 . .
25 55
66 42
63
4cm
3cm
5cm2cm
B
C D
EF
GH
- IV
1. (XLIII, ML2) 4cm (5 ). 11 4 = 44 (15 ).
: , , 5 .
2. 2 ( ) (5 ) 6: 2020, 2011, 2002, 1120, 1111, 1102 (15 ). 2 .:
, .
3. (XLV, ML2) M , 2M (3 ), 3J 6M (3 ). , 6 + = 210 (5 ), 30 (3
), J 60 (3), 180 (3 ).
4. (XLIII, ML4) 2 .
5. ABCDEFGHA
je:2 (AB + FG + FE + BC) + 6cm = 34cm(20 ).
.
5 11 7
5 25 55 35
6 30 66 42
9 45 99 63
B
C D
EF
GH
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05.03.2011.
V
1. 1
2
2, 100.
2. . :) 73;) 73;) 273.
3. a + b = c + d = e + f
30. a,b, c, d, e f.
4. a. 2cm, 96cm2 . .
5. 2011.
?
20 . 120 . .
- V
1.2 3 99 1
98 494 6 198 2
+ + + = = (20 ).
: 10 .
2. (XLV, ML2) ) = 36 30, = 143 30 (6 );) = 53 30, = 126 30 (7 );
) = 87, = 93 (7 ).
3. 30 : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 (5 ). 13 + 17 = 11 +
19 = 7 + 23 (15 ).:
.
4. 6 96 : 6 = 16cm2 (5 ). - 2cm, 2cm a, 4cm2( ). , 2a + 2a + 4 =
16, a = 3cm (10 ). ,
P = 6 a2 = 54cm2 (5 ).
5. (XLV, ML3) .abcd :
2011
2011 1000 100 10
2011 1001 101 11 2
abcd a b c d
a b c d a b c d
a b c d
= + + + +
= + + + + + + +
= + + +
a = 1. 101b + 11c + 2d = 1010.
b 9. 11c+ 2d= 101. c 9, d= 1. , 1991. (20 ).: .
.
2 2 4
2
2
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05.03.2011.
VI
1. x = 12 + 4,y= 12 : 4,z= 12 4, :
) (x + y) (xz), ) ,z x
x y
) .
:
x y z
z x
+
2. 6cm, 10cm 8cm. .
3. a, b p |a b| p = 4022.
4. 8.
.
5. :) , ) 7560, 1.
20 .
120 . .
- VI
1. (XLV, ML2) x= 8,y= 3, z = 48 (5 ).) 440 (5 ); ) 8 (5 ); ) 4
(5 ).
2. (XLIII, ML2) 10cm 5cm (10 ).
, .5
cm3
(10 ).
3. p = 2, 8 ( a {2011, 2011} b {1, 1} a {1, 1} b {2011, 2011})
(10 ).
p = 2011, 8 ( a {1, 1} b {2, 2} a {2, 2} b {1, 1}) (10 ). 1
.
4. , (180 8) : 3 = 57 20, 65 20 (10 ). , (180 16) : 3 = 54 40,
6240 (10 ).
5. 7560 = 2 2 2 3 3 3 5 7 (5 ) ) 75333222 (5 );) 35789 (10
).
.
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05.03.2011.
VII
1. : ) ( )4
251 3 ;9
)
( )
4 3
4
4 125.
50
2. ABCD AC 2cm 5cm. 3cm, ABC ACD.
3. ( )2
2 1 7.x + =
4. .
5. 4
( ). 200cm2 MV.
20 .
120 . .
M
V
- VII
1. (XLV, ML2) ) 9 (10 ); ) 80 (10 ).
2. (XLIII, ML1) ACD ABC(10 ). DC= 2 2 =
4cm, AB = 2 5cm = 10cm, 2
5ACD
ABC
P
P=
(10 ).
3. x 2 0, . x 2 (5 ).
( )
2
2 2,x x = -
|x 1| = 7 (5 ). x 1 > 0 (5 ), x 2, x 1 = 7, x= 8 (5 ).
4. .ab 2ab ba c + = 11(a + b) = c2 (5 ). 2 a + b 18, a + b = 11
(5). 29, 38, 47, 56, 65, 74, 83 92 (10 ).
5. 50cm2, 5cm 10cm (10 ). MV2 = 202 + 102, 10 5cmMV = (10 ).
.
M
V
A B
CD
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05.03.2011 - VIII
1.
2010.x x x+ + =
2. 16 3cm.
30.
3. 4 2 . , . .
4. ( ) 6
7 ,
3
4
. 7cm .
5. a, b c, , S
.| | | | | | | |
a b c abc S
a b c abc = + + +
20 . 120 . .
- VIII
1. (XLV, ML2) x 0: x= 670 (10 ). x< 0: x= 2010 (10).
2. (XLV, ML2) 8 3cmH= (5 ), 12 2cma = (5 ),2(288 384 6 )cmP= +
(5 ), 32304 3cmV= (5 ).
3. () () :, , , , , , , ,, (20 ).: 2 .
4. r. 2 2 2 21 1
7 cm cm7 4
r = (10
), 28cm2 (10 ).
5. x 0 1| |
x
x= (4 ). a, b c , abc
(4 ). S 4 4 (4 ). a, b c , a, b, c abc (4 ) S = 0 (4 ).: S, ,
5.
.
.
