105279281 Διαγωνίσματα Μαθηματικών Α Γυμνασίου
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2 0 0 7
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: T: :
Copyright
Copyright 2007:
EKOTIKO OPANIMO IBANH ABE
98 106 80 A. T.: 210 3661200, Fax: 210 3617791
http://www.livanis.gr
A , , , , -
, , , , , -
. N 2121/1993 E.
: E O
ISBN 978-960-14-1481-2
-
..
-
7
.....................................................................................................................9
1: .......................................................................13 2: .................................................................................17
3: ....................................................................21
4: . ......................................25 5: ...........................29
6: .......................................................35
7: .............................................................41 8: ......................................................45
9: .....................................................................................53
10: - - ...................................59 11: ..................................65
12: ..................................71
1: .......................................................................77
2: .................................................................................81 3: ....................................................................85
4: . ......................................89
5: ...........................93 6: .......................................................99
7: ...........................................................105
8: ....................................................109 9: ...................................................................................115
10: - - .................................121
11: ................................125 12: ................................131
-
8
-
9
.
12 , 10 2 , - .
, , , - .
.
, . .
-
10
-
11
-
12
-
13
1
1
: 1
1 . :
1. .............
, .................. ................., ............................ , ............................ .............................., = ....... + .........., < ... .... . = 0 = .......... ........................ .
(1,7)
2. : 1 = ..... .
..... : = 0. : ..... . ............................ ........................... . .................................... . ......... . , ... (, ) = ......... . ............................................. ... (, ) = .............. .
(1,7)
-
14
. :
+
.
.............................
+ = .... + .... = .... ....
+ ( + ) = (.... + ....) + .... ( ) = ...........
+ 0 = ....... .... =
0 = ....
( + ) = ........ + ........ ( ) = ........ .....
(1,6)
2 . , -
: 2 5 4 + 4 = 2 2 5 4 + 4 = 6 7 3 + 8 0 = 0 5 + 7 : 4 3 = 0 9 + 9 : 9 + 1 = 3
(2,5)
. :
418 100 31 23 7 12 1
(2,5)
-
15
3 . :
1. , = 1, :
. 1 = 1 . = 1 1 . = 1 = 1 . = 0 = 1
2. : 7 104 + 3 102 + 1 :
. 7.301 . 731 . 70.301 . 73.100
3. ;
. 5 + 0 + 0 + 4 . (5 + 0) (0 + 4) . (5 0) + (0 + 4) . 5 0 0 4
4. : x+ x+ x x x x x :
. x3 4 x B. x3 x4 . 3 x 4 x . 3 x x4
5. : x x x x = 0 :
. 2 . 3 . 4 . 5
6. 10 30;
. 4 . 5 . 6 . 7
-
16
7. 5 : . 5, 6, 7, 8 . 0, 2, 4, 6 . 0, 1, 2, 3, 4, 5 . 0, 1, 2, 3, 4
8. ;
. 0 = 3 0+ 0 . 40 = 6 6+ 4 . 83 = 10 8+ 3 . 91 = 10 8+ 11
2,4(8x0,3)
.
, .
3_ 6 _ 2
_ 2 _1 3
9 6 _ _ 3, 10 _ 3 6 _ 5, 9 2_ _ 4 2, 3, 4
3 _ _ _ 2, 3, 4, 5, 9, 10 (2,6)
4 . :
x = (23 10) 2, y = 14 + 24 + 34 = (23 + 5 2) : 32 + (15 3 5)5. x+ y+ , .
(2,5)
. = ... (6, 8) = ... (45, 60, 75) -
: = ( + )3 = 3 + 3 2 + 3 2 + 3
(2,5)
-
17
2
2
: 1
1 . :
i)
........ = ........
................... . .................................. , ............................. .
ii) 4
> 7 7
,
1 1 <
iii)
................................. .....................................................
.................... ....... .
(2,6)
-
18
. () (), 0:
i.
+= +
ii.
=
iii. 2
2
=
iv. :
: =
v.
1
+ = +
vi.
... (,) 1=
2,4(6x0,4)
2 . :
5
6
2
25
7
8
5
12
+ 22
25
27
16
(2)
. :
22 = , 20 5
24= , 21
28 4= , 3x x
4 = ,
5 7
11 11< < , 1 2
5 5< <
3 (6x0,5)
-
19
3 :
1. 2
1 1
2 2+ :
. 1
8 .
1
2 .
3
4 . 1
2. 1
2 33 :
. 2 . 1 . 7 . 3
3.
3 5
4 31 1
2 6
++
:
. 12
5 .
29
8 .
15
8 .
8
11
4. 3 22 71 2007
02 17 86 2008 :
. 2007 . 2008 . 86 . 0
5. x 5
x 6
++ :
. < 1 . > 1 . = 1 . = 0
6. 2 (x 3)
2 x 6
+ + :
. < 1 . > 1 . = 1 . = 0
7. 3 1 7 2
:4 4 6 3
+ :
. 4
3 . 12 . = 1 .
5
4 5 (7x0,7)
-
20
4
. 2
3 18 .
.
(2,5)
. :
22 7 1 1 13 1 1 2 (1 ) : ( 2 ) :
7 5 2 2 15 5 5 5
= + = +
= .
(2,5)
-
21
3
3
: 1
1 . -
:
1. 123: = 1,23 2. 1.000 = 57,4
3. 75 = 0,075 4. 32: 0,01 =
5. 0,00475 106 = 6. : 104 = 0,0302
7. 70.034 = 7,0034 8. 5 = 0,5
9. 3
0,01210
= 10. 11.092 11,09210
=
2,5(10x0,25)
-
22
. :
17,024 17,02
2.749
0,9156
304,9999
724.058
476,302
5 104 + 3 102 + 2 10 + 5 2,5
2 . -
= 2 ( + ), .
1 3,2dm 8dm
2 20cm 160cm
3 5m 180dm
4 400mm 80cm m
2 (4x0,5)
. .
. 5,23m 0,703m 2,023m 2m 0,7003m 0,052m . 0,023km 12,3m 134dm 1004cm 11011mm
1 (2x0,5)
-
23
. . -
.
160
4
523
100
41
6
523
10000
6,83333.... 40 0,0523 5,23
0,8 (4x0,2)
. .
3
5
21
25
3
800
1,2 (6x0,2)
-
24
3 x y cm, :
x = 15 + 0,02 (4,6 + 5,4)3 y = 0,2 2 102 = (0,1 + 0,12 + 0,13) 103. .
5
4 = 2 , = 0,8 , = 0,5 , = 9,6 , = 0,01 , :
= 2 (3 : + 2 : ) = (3 ) + : (3 : 4)2 5
-
25
4
4 5 1.
2. : 1
1 () : .
1. x + = . x = :
2. x = . x = 3. x = . x = 4. x = . x = 5. x : = . x = :
6. : x = . x = +
1 2 3 4 5 6
2,5
-
26
.
1. x 4
03
= . 3
2. x 12
120
+ = . 4 3. 2(x 3) = 8 .
4. 12 2x = 7x 15 .
5. x 1 4
15 5
+ = . 7 6. 3 : x = 1:3 . 9
7. (7 7)x = 0 . 2
8. (4 3 1)x = 2 . 8
A 1 2 3 4 5 6 7 8 B
2,5
2 () .
60 cm.
1. : . x2 + 2x = 60 B. x 2x = 60 . x + 2x + x + 2x = 60 . (1 + 2 + 1)x = 60
-
27
2. . 3. . 4. .
2,5
. = 30 2 5, = (22 + 2) 5 = (23 22)3 : 22 + 2 17
: ( + + ) x = 2 + 2 + 2 .
2,5
3 () :
1. 31,4% :
. 31,4
100 B.
31,4
10 .
314
100 .
314
1000
2. 200% 200 :
. 200 . 400 . 4000 . 40000
3. 4
5 :
. 40% . 50% . 60% . 80%
4. % :
.
100
+ . 100
. : 100
.
:100
5. 3% 1m :
. 3m B. 3dm . 3 cm . 3 mm
6. 50 80 : . 30% . 40% . 50% . 60%
7. 32 14 -
: . 40% . 43,75% . 42,15% . 49,12%
5 (7x0,7)
-
28
4 () 500. 12 10% 12 8%. - 10% + 8% = 18%; .
5
-
29
5
6
: 1 30
1 . : x y x , y ................................... .
x y .............................................. ........................................ .
x y .................................... .
(x, y) ................. .................... .
(2,5)
. x y ; 1.
x 10 20 30
y 60 120 180
-
30
2.
3. . 4. . 5. y = x
6. y = 3
7 x
7. y = 3
x
8. 9.
10.
2,5 (10x0,25)
x 6 15
y 4 12
-
31
2 . : x y x y ........................... .
.............................. x y ............................ .
(x,y) ........................................... ...................................... .
2,5(5x0,5)
. : x y
......
yx
= . - .
1,1
. x y ; 1. . 2. 12 cm2. 3. 4.
x 1 2 3 4
y 6 3 2 1,5
-
32
5. y x = 1000
6. y = 2
3
x
7. y = 0,01
x
1,4 (7x0,2)
3 :
= 10,5 x y , : ) :
(2)
) x y; .
(2)
x = 2 3 4
y = 6 10,5
-
33
) (x,y) ) , x y.
(1)
4 120 50 . ) 40
;
(2,5)
) ( 120 . ) -
1 ;
(2,5)
-
34
-
35
6
7
: 1 30
1 . : , ..... - , .
, .. .. .
..... .
....... , .. . . .
. .
1,8 (9x0,2)
. : 1.
;
-
36
2. ; 3. .
.
1,2 (3x0,4)
. .
:
1. 0 .
2. -
.
3. -
.
1 2 3
1
. :
-
. , , :
1.
2. x =
3.
4.
> 0
5.
1 (5x0,2)
-
37
2 . :
+ 12,64
+ 104,23 16
3
0
2 (4x0,5)
.
:
1. ( + 2) + ( 3) ( + 3) 2. (2) (3) + ( + 3) 3. ( + 2) ( + 3) + (3) 4. (2 + 3 + 3) 5. (2 + 3 3) 6. + ( 2 + 3 3)
. 2 3 3 . 2 + 3 + 3 . 2 3 3 . 2 + 3 + 3 . 2 + 3 3 . 2 3 + 3
1 2 3 4 5 6
3 (6x0,5)
3 . : 1. = 2, :
. + 2 . 2 . + 2 2 .
-
38
2. = 3, : . + 3 . 3 . + 3 3 .
3. :
. 8,64 < 3
2 < 1000 < 0 < 1
5 < + 4 < 100
. 1000 < 8,64 < 3
2 < 0 < 1
5 < + 4 < 100
. 1000 < 3
2 < 8,64 < 0 < 1
5 < + 4 < 100
. 1000 < 3
2 < 8,64 < 1
5 < 0 < + 4 < 100
4. 3
5 :
. 5
3 . 5+
3 .
3
5 . 3+
5
5. , = :
. = . > . + = 0 . = 1 6. 5
-
39
4 . :
1) ( 8) (2) ( 1) = + 16
2) [( 5) ( 3)] : [( + 1) ( 1)] = 15
3) ( 4) ( 5) = +
4) ( + 3) ( 1) 5 = 0
5) 5 8 + 2 = 20
6) (7 10) = 12
7) : (2
3 ) =5
2,1 (7x0,3)
B. 1. N :
4 4 3 4 10,2 3 10,2
3 3( 1)( 3)( 4)
6
18
4 ( 10)
= + + + + = = +
1,2 (3x0,4)
2. , -
: ( 2)
( ) ( 2)
+= 1
3. :
: x=, , , .
0,7
-
40
-
41
7
7
: 1 30
1 . : 1. , > 1, -
... . 2 .. . .. .
2. 1 = . = ., 0 = , 0
3. > 0 ..0 < 0 < 0 < 0 > 0
4. = .. 5. : = , 0 6. = .
-
42
7. ..... .
8. .....
........
......
= 9. . ..... .
10. ( ) .......... ........ = 2,5 (10x0,25)
. , -
.
1. x5 : x3 = x2
2. x5 = x5
3. x3 x4 = x12
4. (x3)2 = x5
5. (x)4 = x4
2,5 (5x0,5)
2 . N : 1. , ( + )2008 :
. 1 . + . 0 . 2008
2. ( )3 < 0, : . , . , . , . = = 0
3. =( 1)0 + ( 1)1 + ( 1)2 + ( 1)3 :
. 0 . 1 . 2 . 3
-
43
4. x : 1014 = 1010 : . 102 . 102 . 1014 . 1024
5. : 0,00001 x = 107 :
. 1011 . 1012 . 1013 . 1014
2,5 (5x0,5)
.
:
1. 2 = 1
2. 2 = 1
4
3. ( 2) = 8 4. ( 2) = 16 5. (2)3 = 64
. = 2
. = 0
. = 2
. = 3
. = 4
1 2 3 4 5
2,5 (5x0,5)
3 N :
1 3
4
3
3
1
3 3 9
2 32 + ( 3)2 3 1 0
3 23 2 2 23 24
4 4 3
4 3
8 4
4 2 4 8 12
-
44
5 ( 3)0 1 1 3
6 4
2
3
81
16 16
81
81
16
7 (56)2 121
5
4
1
5
12
1
5
8 6 2
8
6 6
( 3)
2
6 28 68
9 3 3 3
1 3 4
2 2 3
27
64 1
64
27
10 ( 1) + 1
2 0 2
5 (10x0,5)
4 . :
x = 24 + 2 ( 3)2 [23 ( 3)3] : 7
B. -: = 9 xx + 1 2 x2 + 18 xx + 3
5 (2x2,5)
-
45
8
1
: 1 30
1 . : 1.
.
2. . . . .. . .
3. - . . . .
4. .... . . .
5. ... .
2,5 (5x0,5)
-
46
. -:
1.
2.
3. 4.
5.
6. 7.
8. 9.
10.
2,5 (10x0,25)
-
47
2 .
:
1.
.
2.
.
3.
.
4.
.
5.
.
-
48
6.
.
7.
.
8.
.
9.
.
1 2 3 4 5 6 7 8 9
1,8 (9x0,2)
-
49
B. N x : 1.
= 12cm
x = 2.
x= ....
3.
x= .... 4.
x= ....
3,2 (4x0,8)
3 A. N : 1. , -
:
. . . .
-
50
2. 3/10 : . 54 . 98 . 102 . 108
3. :
. l l . l . l . l l ,
4. ,
: . 45 . 65 . 90 . 120
5. 2/5 .
: . 8 . 18 . 72 . 108
2,5 (5x0,5)
. lxOy . , , .
2,5
4 . :
1. ....... .
2. . .
0,5 (2x0,25)
-
51
. :
1. 70
2.
0,5 (2x0,25)
. (,2cm). x
. :
x
. 2 cm
1
E
1
. x :
1.
x =
2.
x =
-
52
3.
x =
4.
x =
5.
x =
1,5 (5x0,3)
E. l = 50 , l lA . p ;
1,5
-
53
9
2 B
: 1 30
1 . : 1. , , ....... .
2. ........................... .................. .
............................... .
3. , ............... ................................................................... .
1,5 (3x0,5)
-
54
. :
2 1.
.
2. .
1
.
3,5
2 . (1,3), (2,0),
(0,4), M(4,4) :
2,5
lxOy (1,3)
(2,0)
(0,4)
M(4,4)
-
55
. 3 cm = 4cm. ( ). ) . ) ,
. ) ;
) pA = 40 lBOK . 2,5
3 . : 1. -
.............. .
1
2.
.............................. . .............................. . : ......., ....... ..., ......... .
// , =............. // , + = ............ = , ............. .
1
-
56
. . :
2
. :
1
4 . //. .
1,5
120
-
57
. l l l l, B, .
1,5
. // l . , , , .
2
-
58
-
59
10
3 B - -
: 1 30
1 . : 1. ......................................................
.................................................... .
2. ............ .
3. ............................. .
4. ...... ................. . ...................... .
......... .................................. .
5. ................... . ........... . .......................... ............ .
2 (5x0,4)
-
60
. :
1 . :
1. l l 2. l 90 3. l 90 = + 4. l l = +
2 (4x0,5)
2 . l l l, B, -
, .
l lB l
;
80 40 110 75 60 30
60 60 92 40 45 45
100 40 52 52
1,4
-
61
. x. 1.
x = .... 2.
x = .... 3.
x = .... 4.
x = ....
5.
x = ....
-
62
6.
x = ....
3,6 (6x0,6)
3 . l 2/5 lB
l . . 2,5
. . ,, .
2,5 .
.
. . . . .
2,5 (5x0,5)
-
63
. (,2cm) (,4cm). . , , , . ; .
2,5
-
64
-
65
11
: 2
1 . : 1. -
0 .................................. .
2. ................... . ........................................... .
3. ....................... .
4. .................. .
5. ........................................... ............................ .
6. ............................. ......................................... : = + .......... .
7. ............................. ......................................... : : = .
8. 0 ...................... ...................... . : = ....... .
2,4 (8x0,3)
-
66
. :
1.
;
2.
+ = ;
3.
++ = + ; 4.
; 5. -
;
6. ;
7. ; 8. ,
; 9.
; 10. -
o + ;
11. , , 2 = 2;
12. 12345 3, 5 9;
13. x = 4, |x 4| + |2 x| + |x + 2| = 6;
2,6 (13x0,2)
-
67
2 . : 1. , = 1 :
. = 1 = 1 . = 0,5 = 2 . 1 1= + = + 1 1= = .
2. 120 350 -
: 120 = 23 3 5 350 = 2 52 7
...(120,350) : . 2 5 . 23 3 5 . 22 3 52 . 23 3 5 7 ...(120,350) : . 2 5 . 23 3 5 . 22 3 52 . 23 3 52 7
3.
: . (12 5) 2 . 3 (4 5 6 : 7) . 2 (4 + 7 32) . 7 + (2 5)+(3 : 4)
4. 5cm. ,
(%) ; . 100% . 200% . 300% . 400%
5. 3 5
2 , :
+= . 3 . 5 . 8 . 11
6. , x
:
. x = 2 B. x = 3 . x = 4 . x = 5
-
68
7. 1;
. ( 1) ( 2) ( 3)
6
. 2 ( 1) ( 3)
( 3) 2 5
+ +
. 6 4 8
3 2 4
+ + . 25 4 5 30 : 15
8.
36 12, :
. = 2 = 12 . = 2 = 3 . = 1 = 3 . = 2 = 4
9. (2) (3) (+4) (2)> 0, : . > 0 . < 0 . = 0 . .
10. = 10 232
: . 10 2 9 8 9 72 = = . 210 6 10 36 26 = = . 10 2 9 10 18 8 = = . 2 2 2(10 2 3) (10 6) 4 16 = = =
2,4 (10x0,24)
B. 1. 5 -
. :
5 5 5 5 5
1,3
-
69
2. x :
15
2
3 -
7
3
4 25
1,3
3
. : + 7 2 5 5x = 4 y = (3 )3 3 4 2
x .
2
.
y2 : x2.
1
. 20 x%
, y
x . ( x y -
. ). : i. . ii. (%) .
2
-
70
4 // . -
: l 3 2 3 2A = (2 2 7) [(2 2 ) : 2 6] 5 . l l l , x .
5
-
71
12
: 2
1 . x :
1. 2
3 x 37 = , x .....= 2. ( 1)( 2)( 3) x ( 1)( 2)( 3)( 5) 0 + + = ,
x .....=
3. (6 x) : 9 0 = , x .....= 4. (x 3) : 3 1 = , x .....=
5. x 5
53
= , x .....= 6. x
31
7
= , x .....=
7. x10 0,0001= , x .....= 8. 2 6 75 10 x 10 10 = , x .....=
9. 4
x
10 10 1
10 10
= , x .....= 10. 129 9x= , x .....= x .....=
2,6 (10x0,26)
-
72
. - :
1.
.
2. .
3. , .
4. . 5.
.
6. .
7. 180.
8. .
2,4 (8x0,3)
2 . -
l =40:
1. lAOB ...................................... . 2. o ................... 3. p = ....... . 4. p = ........... . 5. p o ......... ,
........................... .......................... ........................ .
1,5 (5x0,3)
-
73
. + :
/ +
1,5 (5x0,3)
. //.
: . . . . . , -
. . x.
2 (4x0,5)
3
l l = = 45 . cm 30:(x-2)=5, cm :
2 2y 2
1
2
= ... (2, 3, 10) + ... (2, 6, 10).
-
74
1. . 2. .
5 (22,5)
4 16 cm = x + 2
= x cm. p = 140.
1. .
2,8
2. , , , , , , , , , o o .
2,2
-
76
-
77
1
1 . 1.
, , , = + , < 0. = 0 = .
2. : 1 =
0 : = 0 : 0
- .
.
2.
... (, ) = 1.
... (, ) = .
-
78
.
+ = + =
+ ( + ) = ( + ) + ( ) = ( )
+ 0 = 0 1 = 0 = 0
( + )= + ( ) =
2 .
2 5 (4 + 4) = 2, : 2 5 8 = 10 8 = 2 2 (5 4) + 4 = 6, : 2 1 + 4 = 2 + 4 = 6 (7 3 + 8) 0 = 0, : (4 + 8) 0 = 12 0 = 0 (5 + 7) : 4 3 = 0, : 12 : 4 3 = 3 3 = 0 (9 + 9) : 9 + 1 = 3, : 18 : 9 + 1 = 2 + 1 = 3
.
418 162 100 31 23 8 13 7 12 15 1 4
1.
2. = 23 7 + 1 = 161 + 1 = 162
418 31
= 5 13 =
-
79
3. = + , < 100 = 12 + , <
3 .
1. 2. , 7 10.000 + 3 100 + 1 = 70.000 + 300 + 1 = 70.301. 3. , : ) 5 + 4 = 9, ) 5 4 = 20, ) 0 + 4 = 4, ) 0. 4. 5. , : x3 x = 0 x3 = x, = 3. 6. , : 11, 13, 17, 19, 23, 29. 7. , .
.
3062
6201
9600 4365 2004 3600
4 .
x = 13 2 = 26 y = 1 + 16 + 81 = 98 = (8 + 10) : 32 + (15 15)5 = 18 : 9 + 05 = 18 : 9 + 0 = 2 + 0 = 2 x + y + = 26 + 98 + 2 = 126 = 2 32 7
100 12
= 4 8 =
:
.
.
-
80
. 6 = 2 3, 8 = 23 ... (6, 8) = 3 23 = 3 8 = 24, = 24 45 = 32 5, 60 = 22 3 5, 75 = 3 52, ... (45, 60, 75) = 3 5 = 15, = 15 = (24 + 15)3 = 393 = 59.319 = 243 + 3 24 152 + 3 242 15 + 153 = 13.824 + 3 24 225+3 576 15 + 3.375 =
= 13.824 + 16.200 + 25.920 + 3.375 = 59.319 = .
-
81
2
1 .
i)
= .
-, .
ii) :
8 4
7 7> 1 1
4 3<
iii)
.
1 .
. i.
ii. iii. iv.
v. :
1 1
+ = + = + = + vi.
-
82
2 .
61
48
4
5
+ 41
24
1. (6,8) 245 7 5 4 7 3 20 21 41
6 8 6 4 8 3 24 24 24
= + = + = + = + =
2. 22 2 20 20 : 5 4
25 25 25 25 : 5 5
= = = =
3. (16,12) 4827 5 27 3 5 4 81 20 61
16 12 16 3 12 4 48 48 48
= = = = = .
1, 221
=
6, 20 20 : 4 524 24 : 4 6
= =
3, 21 21: 7 328 28 : 7 4
= =
43
, 4 3
x x 1 x3 4
= =
6 ,11
5 6 7
11 11 11< <
:
: 1 1 4 4
5 5 4 20
= = 2 2 4 8
,5 5 4 20
= =
:7
20.
-
83
3
1. : (2,4) 4
2
1 1 1 1 2 1 3
2 2 2 4 4 4 4
=+ = + = + =
2. : 1 7
2 3 3 73 3 = =
3. :
3 4
(4,3) 12
(2,6) 63
2
3 5 3 5 9 20 2929 6 294 3 4 3 12 12 12
1 1 3 1 4 12 4 81 12 6 6 6 62 6
=
=
+ + + = = = = =+ ++
4. 5. , x + 5 < x + 6 6. , 2 (x + 3) = 2x + 6 7. :
1
2
3 1 7 2:
4 4 6 3
3 1 7 2 2 3 1 7 4: :
4 4 6 3 2 4 4 6 6
3 1 3 3 1 1: :
4 4 6 4 4 2
3 1 2 3 2 5
4 4 1 4 4 4
+ = = + = + =
= + = + =
= + = + =
4 . 2/3 18 1/3 18 : 2 = 9
3/3 3 9 = 27 .
-
84
. 2 7 1 1 13
A [ (1 ) ] :7 5 2 2 15
= + = 2 7 2 1 1 13 2 7 1 1 13
[ ( ) ] : ( ) :7 5 2 2 2 15 7 5 2 2 15
= + = + = ...(5,4) 202 1 13 2 4 1 5 13
( ) : ( ) :5 4 15 5 4 4 5 15
= = + + = = 8 5 13
( ) :20 20 15
= + = 13 15 15 15 : 5 3
20 13 20 20 : 5 4= = = =
2 21 1 2 1 2 2 ( 2 ) : ( ) :
5 5 5 5 5 5= + = + =
3 4 3 5 3:
5 5 5 4 4= = =
= .
-
85
3
1 .
1. 123 : 100 = 1,23 2. 0,0574 1.000 = 57,4 3. 75 0,001 = 0,075 4. 32 : 0,01 = 3.200 5. 0,00475 1.000.000 = 4.750 6. 302 : 10.000 = 0,0302 7. 70.034 0,0001 = 7,0034 8. 5 : 10 = 0,5 9. 12 : 1.000 = 0,012 10. 11.092 : 103 = 11,092
.
17,024 17,02
2.749 2.750
0,9156 0,9
304,9999 305
724.058 724.100
476,302 476
50.325 50.000
-
86
2 . = 2 ( + )
= 2 + 2.
1 : = 2 (3,2+8) = 2 11,2 = 22,4dm 2 : = 20cm = 2( + ), : 160 = 2(20 + ) 160 : 2 = 20 + 80 = 20 + = 80 20 = 60cm 3 : = 180dm = 180:10 = 18 m = 2( + ), + = : 2, + = 18 : 2 = 9, + = 9 + 5 = 9, = 4 m. 4 : = 400mm = 400 : 1000 = 0,4m = 80cm = 80 : 100 = 0,8m = 2 (0,4 + 0,8) = 2 1,2 = 2,4m
1 3,2dm 8dm 22,4dm
2 20cm 60cm 160cm
3 4m 5m 180dm
4 400mm 80cm 2,4m B. . 0,052m < 0,7003m < 0,703m < 2m < 2,023m < 5,23m
. .. m :
0,023km = 0,023 1000 = 23m 12,3m = 12,3m
-
87
134dm = 134 : 10 = 13,4m 1004cm = 1004 : 100 = 10,04m 11011mm = 11011 : 1000 = 11,011m : 10,04m < 11,011m < 12,3m < 13,4m < 23m
1004cm < 11011mm < 12,3m < 134dm < 0,023km.
. .
.
() ()
160
4
523
100
41
6
523
10000
6,83333.... 40 0,0523 5,23
3
5 3 : 5 = 0,6
6
10
21
25 21 : 25 = 0,84
84
100
3
800 3 : 800 = 0,00375
375
100000
: 160
160 : 4 404
= = 523
523 : 100 5,23100
= = 41
41: 6 6,8333......6
= =
523523 : 10000
100000,0523
= ==
-
88
3 x = 15 + 0,02 103 = 15 + 0,02 1000 = 15 + 20 = 35 cm y = 0,2 2 100 = 0,4 100 = 40 cm = (0,1 + 0,01 + 0,001) 1000 = 0,111 1000 = 111 cm = (x + y) = 111 (40 + 35) = 111 75 = 36 cm.
4 = 9,62 (23 : 0,8 + 0,52 : 0,01) = 9,62 (8 : 0,8 + 0,25 : 0,01) = 9,62 (10 + 25) =
= 9,62 35 = 92,16 35 = 57,16.
= (23 0,8 0,5) 2+9,6:0,01 (23:24)2 = (8 0,8 0,5) 2+9,6:0,01 (8:16)2 = = (8 0,4) 2 + 9,6 : 0,01 0,52 = 7,6 2 + 9,6 : 0,01 0,25 = = 15,2 + 960 0,25 = 975,2 0,25 = 974,95.
-
89
4
1. 2.
1 . :
1 2 3 4 5 6
. 1. 0 0, :
x 4 = 0, x = 4. ().
2. 1 , : x + 12 = 20, x = 20 12 = 8. ().
3. : 2x 6 = 8 . 2x = 8 + 6 2x = 14 x = 14 : 2 = 7. ().
4. x = 3. x = 3 : 12 2 3 = 7 315 12 6 = 21 15 6 = 6 . ().
5. 2 : 2 1 4 1 4 5
1 , . 1 , . 15 5 5 5 5
+ = + = = , . ().
-
90
6. : 3 1
x 3= 1 x 3 3 = x 9= .
().
7. : 0x = 0 - . ().
8. 0x = 2, . ().
:
A 1 2 3 4 5 6 7 8
B
2 . 1. . -
. 2. 1 , :
6 x = 60 3. x = 60 : 6 = 10 cm. 10 cm 20 cm. 4. = 10 20 = 200 cm2. B.
= 30 10 = 20 = (4 + 2) 5 = 6 5 = 30 = (8 4)3 : 4 + 2 17 = 43 : 4 + 2 17 = 64 : 4 + 2 17 = 16 + 34 = 50
: + + = 20 + 30 + 50 = 100 2 + 2 + 2 = 400 + 900 + 2500 = 3800
: 100 x = 3800 x = 3800 : 100 = 38.
3
1. : 314 314 : 10 31,4
31,41000 1000 : 10 100
= = = %
-
91
2. : 200% 200 200
200 2 200 400100
= =
3. : 4 4 20 80
805 5 20 100
= = = % 4.
5. 1m = 100cm 3% 100cm 3
100 3100
= cm 6. 30 :
30 30 2 6060
50 50 2 100
= = = %
7. : 14 43,75
14 : 32 0,4375 43,7532 100
= = = = %
4
10 : 10 5000
500 50100 100 = = .
500 + 50 = 550. 12 8% 550 :
8 4400550 44
100 100 = = 550 + 44 = 594, . -
594 500 = 94.
: 94 94 : 5 18,8
18,8500 500 : 5 100
= = = % 18%.
-
92
-
93
5
1 . x y x , y .
x y .
x y y = x
(x, y) . .
1. , : 60 120 180
610 20 30
= = =
2. , : 4 12
6 15
3. , x ,
4x : 4
4
= = .
-
94
4. , x , -: 1, 2, 3, 4, ..., x2, -: 12 = 1, 22 = 4, 32 = 9, 42 = 16, ...
:
1 2 3 4 ...
1 4 9 16 ...
1 2 3 4 ...
5. , y = x . 6. , . 7. , y = x x y. 8. , x y -
. 9. , . 10. , .
2 . x y x y .
x y
yx
=
(x, y) - x, y.
-
95
. y x = 6, 6
yx
=
. 1. , 10 6
, 20 3 . 2. , = x y
= x y = 12 = .
-
96
:
x 12 6 4 3 2 1
y 1 2 3 4 6 12
E = x y 12 12 12 12 12 12 3. , . 4. , . 5. , x y 1000.
6. , x, y
y , 0x
= .
7. , x, y
y , 0x
= - .
3 ) x , y y = 3x.
x = 2 3 3,5 4 y = 6 9 10,5 12
) :
6 9 10,5 123, 3, 3, 3,
2 3 3,5 4= = = =
x y : y
3x= y = 3x.
-
97
) :
4 . ) x -
. 120+x . :
(./) 120 120 + x
() 50 40 A - :
40 (120 + x) = 50 120 4800 + 40x = 6000 40x = 6000 4800 40x = 1200 x = 1200 : 40 = 30
-
98
30 . 40 .
) :
(./) 120 120 x
() 50 60
60 (120 x) = 50 120 7200 60x = 6000 60x = 7200 6000 60x = 1200 x = 1200 : 60 x = 20
20 . .
-
99
6
1 . , , .
, .
- .
- , .
+. . 1.
. 2. . , . 3. :
- . - . - .
-
100
.
1 2 3
. 1. . .
2. . x = x = : =
3. . 4. . , . 5. .
2 .
+ 12,64 12,64 12,64 12,64
104,23 + 104,23 104,23 104,23
16
3 16+
3
16
3
16
3
0 0 0 0 . : . +, , -
+, ( ), .
. .
1. (+ 2) + ( 3) (+ 3) = 2 3 3 . 2. ( 2) ( 3) + (+ 3) = 2 + 3 + 3 . 3. (+ 2) (+ 3) + ( 3) = 2 3 3 . 4. ( 2 + 3 + 3) = 2 + 3 + 3 . 5. ( 2 + 3 3) = 2 3 + 3 . 6. + ( 2 + 3 3) = 2 + 3 3 .
-
101
1 2 3 4 5 6
3 1. . || = 2, = + 2 = 2. 2. .
, - .
3. . 3 1
1,5 0,22 5
= = .
4. . 3
5 5 ,
3 5
3 5
3+
5. . 0. 6. . 5 8, 6
7. : |x| = 6 x = + 6 x = 6 |x| = 7 x = + 7 x = 7. 4 : 6, + 6, 7, + 7.
. 1. = 5, = + 7
+ = ( 5) + (+ 7) = 5 + 7 = 2 = 5 (+ 7) = 5 7 = 12 = ( 5)(+ 7) = (5 7) = 35
: = ( 5) : (+ 7) = (5 : 7) = 5
7
2. 1 1
, 3 3
= = 1 1
( ) 03 3
+ = + = 1 1 1 1 2
( )3 3 3 3 3
= = + = 1 1 1 1 1
( ) ( )3 3 3 3 9
= = = 1 1 1 1
: : ( ) ( : ) 13 3 3 3
= = =
-
102
3. 1 1 1
( )2 2 2
= = + = +
4 4 4 ( )
3 3 3
= = + =
3 2
1 4 1 4 3 8 11 ( )
2 3 2 3 6 6 6+ = + = = =
3 2
1 4 1 4 3 8 5 ( )
2 3 2 3 6 6 6 = = + = + =
1 4 1 4 4 2 ( ) ( ) ( )
2 3 2 3 6 3 = = + = =
1 4 1 4 1 3 3 : ( ) : ( ) ( : )
2 3 2 3 2 4 8= = + = =
4 1. (+ 8)( 2)( 1) = + (8 2 1) = 16 2. [( 5)( 3)] : [(+ 1)( 1)] = (+ 15) : ( 1) = 15 3. ( 4) ( 5) = 4 + 5 = + 1 4. (+ 3) 0 ( 1) 5 = 0 5. 5 8 + 2 x = 7 8 x = 1 x
1 x = 20 x = 1 + 20 = 19 : 5 8 + 2 19 = 5 + 2 8 19 = 7 27 = 20
6. 7 10 = 3 3x = 12 x = ( 12) : ( 3) = + 4 : (7 10) 4 = 3 4 = 12
7. x: (2
3 ) = 5
x = 5 2 2 10
( ) (5 )3 3 3
= =
: 10 2 10 2 10 3 10
: : 53 3 3 3 3 2 2
= + = = =
-
103
.
1. = 4 4
3 4 10,2 3 10,23 3
+ + + = 3 3 + 4 = 6 + 4 = 2
( 1)( 3)( 4) 12
2 26 6
+ += = = + =
18 18 18 3 3
4 ( 10) 4 10 6
= = = = + = +
2. ( 2) 2 2( 2 2 3)
( ) ( 2) [2 ( 2)] ( 2 2 2)
+ + = = = 2 2( 2 6) 2 2 4 2 8 10 5
(2 2) ( 2 4) 4 ( 6) 24 24 12
+ = = = = =+ 3. : x = || | | | |
: x = |2| |+ 2| |+ 3| A : x = 223 A : x = 3
( )
5:x 3
12
5 5 5 1 5x : 3 :3
12 12 12 3 36
= = = = =
.
- .
-
104
-
105
7
1 . 1. , > 1,
, .
2 .
3.
2. 1 =
= 1, 0 =
1
, 0
3. > 0 > 0
< 0 < 0 . < 0 > 0 .
4. = + 5. : = , 0 6. = () 7. -
.
-
106
8.
=
9.
10. () =
. 1. x5 : x3 = x53 = x2
2. x5 = 5
1
x
3. x3 x4 = x3+4 = x7 4. (x3)2 = x32 = x6 5. ( x)4 = x4
2 . 1. . , + = 0 ( + )2008 = 02008 = 0 2. . , < 0.
. 3. . = ( 1)0 + ( 1)1 + ( 1)2 + ( 1)3 = 1 + ( 1) + 1 + ( 1) = 1 1 + 1 1 = 0 4. . x = 1010 1014 = 1010 + 14 = 1024 5. . 0,00001 x = 107
105 x = 107 x = 107 : 105 = 107 ( 5) = 107 + 5 = 1012 . 1. 2 = 1, = 0
2. 2 = 1
4
2 = 22, = 2
3. ( 2) = 8 ( 2) = ( 2)3, = 3
4. ( 2) = 16 ( 2) = 24 ( 2) = ( 2)4, = 4
-
107
5. (2)3 = 64 2 3 = 26 3 = 6 = 6 : 3 = 2
1 2 3 4 5
3
1. 3
4
3
3 . 334 = 31 =
1
3
2. 32 + (3)2 . 9 + 9 = 0
3. 23 2 . 23 21 = 23+1 = 24
4. 4 3
4 3
8 4
4 2 .
4 38 4
4 2
= 24 23 = 16 8 = 8
5. ( 3)0 . 1
6. 4
2
3
. 4 4
4
3 3 81
2 2 16
= =
7. (56)2 . 5(6) 2 = 512 =
12
1
5
8. 6 2
8
6 6
( 3)
.
86 2 6 2 88
8 8 8
6 6 6 6 62
3 3 3 3
+ = = = =
9. 3 3 3
1 3 4
2 2 3
. 3 3
31 3 4 12 1 12 2 3 12
= = =
10. ( 1) + 1
. (1) = 1, , 1 = 1
: ( 1) + 1 = 1 + 1 = 2
-
108
4 . x = 24 + 2 ( 3)2 [23 ( 3)3] : 7 = 24 + 2 ( 3)2 [8 ( 27)] : 7 =
= 24 + 2 ( 3)2 (8 + 27) : 7 = 24 + 2 ( 3)2 35 : 7 = = 16 + 2 9 35 : 7 = = 16 + 18 5 = = 16 5 + 18 = = 21 + 18 = 3
x = 3 . = 9 xx+1 2 x2 + 18 xx+3 = 9 ( 3)3+1 2 ( 3)2 + 18 ( 3)3+3 =
= 9 ( 3)2 2 9 + 18 ( 3)0 =
= 2
19 18 18 1
( 3) + =
19 18 18 1
9 + =
,
,
.
-
109
8
1 . 1.
.
2. . . 90 180 .
3. - . .
4. - . - - .
5. .
. 1. , . 2. , , ,
.
-
110
3. :
, .
4. , x x :
5. ,
6. , 90, 90 -
.
7. , 180 180 .= = 8. , 90 180,
180. 9. , . 10. , .
-
111
2 .
1 2 3 4 5 6 7 8 9
. 1. , = = 12 : 2 = 6cm.
, = 6 : 2 = 3cm. = + = 3cm + 6cm = 9cm. x = 9cm.
2. x = 360 35 = 325. 3. x + x + 110 = 180
2x = 180 110 2x = 70 x = 70 : 2 = 35.
4. :
x + 5 = 70 x = 70 5 = 65.
3 . 1. , -
.
2. , o
o o3 1080360 10810 10
= =
3.
4. , 180 45 = 135, - 90 45 = 45. : 3 45 = 135.
5. , o
o o2 360180 72 .5 5 = = : 90 72 = 18.
-
112
.
lxy , 70= . , 70 - :
70 180
70 70 180
140 180
180 140 40 .
+ + =+ + =+ == =
70 : 70 .= - 70 : 180 70 110 .= =
4 . 1. . 2. . . 1. , :
p o 70 , 70= = p o .
2. .
-
113
.
x
.
1) 2 cm T 2
2) 2 cm E 1
3) 2 m E 0
1) 2) 3) .
1. p , x = 180. 2. p , x = 90. 3. p = 50 360. x = 360 50 = 310.
-
114
4. l l ( ) . . x = 40.
5. , , l = 90. x = 90 55 = 35.
.
l 50= . l = 50 : 2 = 25. l l : 180 l = 180 50 = 130. l l 130 : 2 65 .= = l : l l l = + =25o + 65o = 90o, .
p = 90.
-
115
9
1 . 1. , , .
2. - .
.
3. , .
.
2
1. -
.
2. . 1
.
1
1
.
-
116
3 .
1
.
2 2 -
-
. 1
2 2
. 1
4
2
2
.
1
. . 1 .
2 A.
(1,3) (7,5)
(2,0) (6,8)
(0,4) (8,4)
M(4,4) (4,4)
-
117
.
) = = 3cm, -
. ) ,
. = 2 = 2 3 = 6cm .
) , , = .
) lAO , 40. - lAO l , l = 40. l l l = + =40 + 40 = 80. l = 180 80 = 100 ( lAOB ).
(1,3) (3,1)
(2,0) (0,2)
(0,4) (4,0)
M(4,4) (4,4)
-
118
3 . 1. -
.
2. , . , . : , , . // = . // + = 180. , -.
.
1. : 180 120 60= = .
2. , 120= . 3. , 60= . 4. , 60= . 5. , 120= . 6. , : 60= . 7. -
, 180 60 120= = .
120 60 120 60 60 120 60 120
-
119
. 300 = 360 300 = 60. l : l + = 60 + 120 = 180. //.
4 . 50 : = 180 50 = 130.
140 : = 180 140 = 40. , : = = 40. x 50 360 x= = 360 50 = 310.
. 180 75 105= = . , 180 105 75= = . l 180+ = , l 180 75 105= = l l 180+ = , l 180 105 75= = .
. 72 : = 72. :
180 (90 ) 180 (90 72 ) 180 162 18= + = + = = . 18= .
-
120
-
121
10
- -
1 . 1. ,
, o .
2. 180 .
3. , 90.
4. 2 . .
.
5. . 60 . .
. .
. .
. 1) .
2) , 90. 3) ,
. 4) , , : l l 180 = .
-
122
2 . 180. -
:
;
80 40 60
110 75 ,
180.
60 90 30
60 60 60
92 40 48
45 45 90
40 100 40
52 76 52
. 1) 2x + 3x + 4x = 180, 9x = 180 x = 180 : 9 = 20. 2) :
x + x + 50 = 180, 2x = 180 50 = 130, x = 130 : 2 = 65. 3) T .
30 + 30 = 60, x = 180 60 = 120.
4) : x + 2x = 90 3x = 90 x = 90 : 3 = 30.
5) x : x = 40 + 70 = 110. ( : 180 (40 + 70 ) = 180 110 = 70. x 70 x = 180 70 = 110).
6) 72 + 48 = 120. 180 120 = 60. 2x = 60 x = 60 : 2 = 30.
-
123
3
. l
2 2 90 180 90 365 5 5
= = = = . l l l 180 , 180 36 144 + + = + = = - 144 : 4 : 144 : 4 36= = . l = . l 3 = = 3 36 = 108 > 90 - . . 70= 180 120 60= = 180 , 180 (70 60 ) 180 130 50+ + = = + = = = , 50 .=
4 .
()
()
. . . -
. .
.
: = = 2cm = = 4cm, - , -.
-
124
-
125
11
1 . 1. -
0 .
2. . .
3. .
4. .
5. .
6. - . = + ( )
7.
. : = 1
8. 0 1
. =
1
-
126
.
1. . -.
2. .
. :
= .
3. . .
:
++ = .
4. .
5. .
:
= .
6. . . .
7. . , -.
8. . . .. ( 2)4 = + 16.
9. . () = .
10. . + .
11. . 3 +3 , ( 3)2 = (+ 3)2 = 9.
12. . 12.345 3 1 + 2 + 3 + 4 + 5 = 15 3, 5 - 5, 9 15 9.
13. .
|x 4|+|2 x |+|x + 2|=
=|4 4|+|2 4|+|4 + 2|= 0 +| 2|+|6|= 0 + 2 + 6 = 8.
-
127
2 . 1. . : (+ 1) (+ 1) = 1 ( 1) ( 1) = 1 , -
= 1.
2. ... - : . ... : .
3. . 7+(2 5) + (3 : 4) = 7 + 2 5 + 3 : 4 = 7 + 10 + 0,75 = 17,75.
4. 5 cm 4 5 = 20 cm. 2 5 = 10 cm
4 10 = 40 cm. 40 40 5 200
200%20 20 5 100
= = = . .
5. 3 5 3 5
3 5 3 2 5 6 5 11
+ = + = + = + = + = . .
6. : x + 3 = 9 x,
x + x = 9 3, 2x = 6, x = 6:2 = 3. .
7. . 2 ( 1) ( 3) 2 3 1
1( 3) 2 5 6 5 1
+ += = = + + . = 6
16
= , = 2 + 2 + 2 = 2, = 25 20 2 = 3.
8. . 1 36
36 123 3 = = .
9. . 3 , . < 0.
10. . , .
. 1. : = + , < .
5 : 0, 1, 2, 3, 4. = 0, = 5 ( = ), = 5 5 + 0 = 25, = 1 = 5 = 5 5 + 1 = 25 + 1 = 26, ...
-
128
0 1 2 3 4
5 5 5 5 5
5 5 5 5 5
25 26 27 28 29 2. 1 :
A x x + 1 : x + x + 1 = 15 2x + 1 = 15 2x = 15 1, 2x = 14, x = 14 : 2 = 7. H x = 7.
2 : x :
2 7 7 2 95x , 5x , 5x , 5x 3 , x 3 : 5 0,6
3 3 3 3 3 = = + = = = = .
3 :
4 : x = 25 4 : x = 1 4 1
, , x 4 32 12832 x 32
= = = .
15
2x + 1 = 15 x = 7
-
2
3 -
7
3
5x 2 7
3 3= x = 0,6
4 25
4 : x = 1
32 x = 128
-
129
3 .
2 4
7 8 15x 5
3 3 3
5 3 5 5 6 5 5 1 5 2 3y ( ) ( )
4 1 2 4 2 2 4 2 4 4 4
=
= + = =
= = = = =
.
22 2 2 2
2 2
3 3 1 9 1 9 25 225y : x ( ) : 5 : :
4 4 5 16 25 16 1 16 = = = = =
.
i. 5% , 5 5 20 100
20 1100 100 100
= = = .
ii.
3y 3 1 3 3 5 154 15%x 5 4 5 20 20 5 100
= = = = = = .
4 2 2
o
A (8 14) [(8 4) : 2 6] 5 ( 6) [(8 4) : 2 6] 5
36 (4 : 2 6) 5 36 (2 6) 5 36 ( 4) 5
36 ( 20) 36 20 56
= = == = = == = + =
: 56 + B 180+ = , 180 56 124+ = = .
: ,= = l l 124 ,+ = l 2 124 ,= l 124 : 2 62= = . x lA //, lx = 56. l l //, l = 62. ( l l l, x, , - o180 l l l o x 180 ,+ + = l l o o ox 56 62 118+ = + = , l o o o 180 118 62= = ).
-
130
-
131
12
1 .
1. 2
3 x 3,7 = 2
7 x , .
7x
2=
2. ( 1)( 2)( 3) x ( 1)( 2)( 3)( 5) + , x= 5
3. 6x
0,9
= 6x 0, . x=0
4. x 3
1,3
= x= 1
5. 5 x= 3 6. x 0= 7. x 410 10= x 4= 8. -2 6 75 x 10 10 10 = -2 (-6) 7 -8 7 -7 85 x 10 10 , 5 x 10 10 , 5 x 10 : 10+ = = =
-7-(-8) -7 85x 10 , 5x 10 += = 15x 10=
5x 10= x 10 : 5 2= =
-
132
9. 1 4 5
x x
10 1 10 1 ,
10 10 10 10
+= =
x 510 10 10= , x 1 510 10 += , x 610 10= x 6=
10. x 9= : 1 2 12
9 19 9
9 9 = = =
x 9= ( )1 2 1
2 2
9 9 19 9
9 99
= = = =
B. 1. . .
2. .
3. . , 180.
4. . 60, , 90.
5. .
6. . , , , 180.
7. . :
l l ,, : l l 180 , 180 , 180 : l l l l (180 ) (180 ) (180 ) 3 180 ( ) 540 180 360 + + = + + = =
8. . .
2 .
1. lAOB . 2. o l 3. p = 40 , . 4. p = 140 o , -
: 180 40 = 140.
-
133
5. p o 40 , .
.
/ +
+ +
+ + + +
+ + + + + . . : , . . : .
. : l l l l . : l l , l l , l l , l l , l l , l l .
// : l , l l , l l .
. //, :
l x= = . l lZ =2x= .
l l 180+ + = , : 39 + x + 2x = 180 39 + 3x = 180 3x = 180 39 = 141 x = 141 : 3 = 47.
3 x = 8 30 : (8 2) = 30 : 6 = 5 .
-
134
: : 5 (x2) = 30 5x10 = 30 5x = 30+10 5x = 40 x = 40 : 5 = 8
= 8cm. ...(2,3,10) = 30 ...(2,6,10) = 2
: 2 2y 2
2
1
= 30 + 2 2 2y 22 = 32 2 4 2y = 32 8 2y = 32 2y = 32 : 8 2y = 4 y = 2,
= 2cm. 1. : l 45= = l //. l l 180 180 45 135= = = . 135= l l
.
2. l l , . 90 l 45= l 45= , . = = 2cm. = = 2cm. = = 8 2 2 = 4 cm. -, = 2cm.
4 1.
+ + + = x + 2 + x + x + 2 + x = 4x + 4.
-
135
16cm, 4x + 4 = 16 4x = 16 4 4x = 12 x = 12 : 4 = 3cm
= 3 + 2 = 5cm, = 5cm = 3cm, = 3cm.
2. - , 140 .= . , .= 180+ + =
180 180 140 40+ = = = 40 : 2 20 .= = =
// 20 .= 20 .= = ( 90 ),= 90 20 70 .= = 70 .= = = l l (-) : p o 140 .= = p o 180+ = () o p 180 180 140 40 .= = =
-
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/CreateJDFFile false /Description > /Namespace [ (Adobe) (Common) (1.0) ] /OtherNamespaces [ > /FormElements false /GenerateStructure false /IncludeBookmarks false /IncludeHyperlinks false /IncludeInteractive false /IncludeLayers false /IncludeProfiles false /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe) (CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector /DocumentCMYK /PreserveEditing true /UntaggedCMYKHandling /LeaveUntagged /UntaggedRGBHandling /UseDocumentProfile /UseDocumentBleed false >> ]>> setdistillerparams> setpagedevice
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