-
- IV
1. : : x,
: : 4x + 1, (4 )
: : 5x + 1,
: : 5x = 55,
55 : 5 = 11; 11 4 = 44; 44 + 1 = 45; : x = 11.
, 45 (8 ), 11 (8 ).
2. .
0 1, .
2,
(12). 3, (13,
23). ... 9,
(19, 29, 39, 49, 59, 69, 79, 89). ,
3687654321 =+++++++ (20 ). ( (
, ) 10
.)
3. 1008 1010
(10 ). -
1004 1006 (10 ).
4. 2010 9
(20 ):
5.
4
= (8+18+10+24) 410 = 20, = 20cm (20 ).
.
2 0 1 0
0 0 0 0
1 0 1 0
0 0 0 0
2 0 1 0
0 0 0 0
1 0 1 0
0 0 0 0
2 0 1 0
0 0 0 0
1 0 1 0
0 0 0 0
1
1
1000
1002
1010
1008
-
- V
1. 20
.
2. o180 (5 ).
=++ o180842
(5 ).
o1808
7=+
, o96= (10 ).
3. 9
9. 9
a98765 , 1=a , 36156789 =+++++ . (8 )
9 x10234 , x
5, 6, 7, 8 9. 8=x (12 ).
4.
4
= (8,6 + 22,2 + 6,4 + 18,6) 4 10 =15,8; = 15,8cm (20 ).
5. 115210 = , 1, 1, 2 5 (10 ). 2009
1 1125, 1152, 1215, 1251, 1512,
1521 (10 ).
.
1
6
12
7
2
1
4
3
5
12
12
1
3
1
1
4
2
3
-
- VI
1.
1
2 3
3 2
+
= 6
5(20 ).
2. 45 75 : 45
, 75
30 .
D C.
ACD BCD ,
. 20 .
3. 18 234991 ba + , (5 ). n 9 n
9. 9
baba ++=+++++++ 28432199 (10 ). 8=+ ba 17=+ ba .
(0, 8), (2, 6), (4, 4), (6, 2) (8, 9). (5 )
4. ACD , AC = CB = CD (5 ).
D .
1) D . ACD
ooo 1506090 =+ , oCDACAD 15== (3 ).
oooADB 451560 == (5 ). 2) D
. ACD ooo 306090 = , oCDACAD 75== (3
). oooADB 1357560 =+= (4 ).
5. 1,
11, 12, 13, 14 15. -
2
22 23 (5 ). -
1, 2, 3, 4, 5, 4 6
25 (5 ). -
(10 ):
( 20
( )).
.
C
B
D
C
B
D
-
- VII
1. : 2 2
2 2
2 2
1 1 1 1 82 100 102 2 2
9 9 3x x x x
x x x x
+ = + + = + + = + = =
1 10
3x
x+ = (7 ). ,
2 21 8
3x
x
=
1 8
3x
x = (8 ).
10 8 182 6
3 3 3x = + = = , 3x = . (5 )
2. 12x mm= .
0 1 2 2(3 )x x+ =
10x . 1 1 0,
1 3 2x (5 ).
10 0 2 10 10 2 5 5x x x x x x x x+ + + + + + + + ,
3 10 2 5 2 3x x x x+ + + (7 ).
12 (3 10 2 5 2 3) 12 (3 3 2 2,2 1,4 3) 12 17,8 213,6 + + + >
+ + + = =
(8 ), 210mm. 3. , 5 cm (10
). .
2 2 2(12 ) 5a a + = , 169
24a = (5 ).
169 8455,
24 24a h P = = cm2 (5 ).
4. n- ( 3)
2
n n . -
( 3)
20102
n nn
= + (5 ). -
( 5) 4020 2 2 3 5 67n n = = (5 ). n
5n 5, ( 5)n n
25 5. 2 2 3 5 67
-
5, ( 5) 4020n n = ,
(10 ).
.
5. 44n 4 6, n
. 4344 4,
4444 6 (10 ). 44
43 4344 4444 44 222 2
= =
4344 4, 4444
2
8 (10 ).
.
-
- VIII
1. 2( )xy x y= + . -
4
2 2 4 4xy x y + = , ( 2)( 2) 4x y = (10 ). 4
= 41 = 22 2 4x = 2 1y = , 6x = 3y = ,
2 2x = 2 2y = , 4x = 4y = (10 ).
, 6 3 4 4.
2. ,
2.
2 2 2(4 ) (2 ) 2x x+ = , 220 4x = , 1
5x = (10 ). -
21 ,
2 2 2 128 (2 ) 125
x x x + = = .
9 12
5 (10 ).
3. (32, 76)
xxy8
19
32
76== (5 ).
x 0 32. x
8 (7 ). , x 0, 8, 16 32, (0,0), (8,19), (16,38),
(32,76) (8 ).
4. P MN. P
BD. MND1 ABC
1 45oDPD = (5 ). 1 10DP DD= = .
BMN 2
xBP PN PM= = = ,
BN BM x= = (5 ). 10 2 102
xBD DP PB= = + = +
(20 10 2)BN x cm= = (10 ).
5. .
24 (10 ).
, 18 (10
).
