-
1
,
23.05.2012 . 1 1. 20. !
1. [ ]1; 1 ? A)
215
) 17 .49 ) 31
2
) 14625
2.
625 81 :
) 16
) 42 34
) 4
) 34
3. 3 133
x
xx
++
:
)
( );3x )
( ];3x )
( ) ( );0 0;3x )
( )3;x
4. 2 4 02
xx :
) ( ] [ ); 2 2; ) ( ] ( ]; 2 0; 2 ) [ ] [ )2; 0 2; ) [ ) [ )2; 0
2;
5. 6log1 .6 64
xx=
x :
) 8 )
4,8 ) 172
)
8
6. 1x 2x 20,5 22,5 2 0x x + = , :
) 1 0x > 2 0x < ) 1 0x < 2 0x < ) 1 0x > 2 0x
> ) 1 2x x=
7. 4 2 0ax bx c+ + =
13
2 . :
) 12
3 ) 2
3
)
2 ) 2 13
-
2
.
A B
C
H
b
.
. O
H A B
C
8. 6pi
= sin 3 cos 2 :
) 32
) 12
)
12
) 32
9. ABC 8=AB cm . O
CH 2:5 . AC
:
) 6 cm
) 10 cm
)
16 cm
) 20 cm
10. AB ABC ,H
HCB CAB = = . AC b= ,
HCB :
) .sinb ) .cosb ) .b tg ) 1 .2
b tg
11. ( )f x ( )g x . (0;2)A
(3;5)B . ( ) ( )f x g x> : ) ( ;0) ) (0;3) ) ( ;0) (3; ) )
(3; )
12. ,na n
, 3 2?
) 3 2na n= + ) 3 1na n= ) 3 2na n= ) 2 1na n= +
13. , 2 6 3a a+ = 13
26 , .
) 16
) 13
)1 ) 6
14. 2 , 3 , 5 2 .
, , ? ) 12 ) 24 ) 30 ) 60
O x
y
(0;2)A
(3;5)B( )f x ( )g x
-
3
H
C
M
B
. . A
15. 25.04.2012 . 12 .
?
)
1 ) 4 ) 6 ) 11
16. 12 cm 60. :
) 3 cm ) 3 3 cm ) 6 cm ) 6 3 cm
17. ABCD e
120DAB = . 12cmBD = ABC ADC = ,
AC :
) 8 3 cm ) 8 2 cm )
6 3 cm ) 4 3 cm
18. ABC , 3cmAC = ,
6cmBC = 120ACB = .
( )CL L AB
:
) 2 cm )
3cm ) 2 3 cm ) 2 7 cm
19. ( || )ABCD AB CD 10=AB , 7=BC , 4CD = 5=AD , :
) 2 6 ) 6 6 ) 14 6 ) 42 6
20. ABC
, : 5 : 2BM CM = . ( )H AB ABC , :AH HB .
) 1: 5 ) 3: 5 ) 3: 7 ) 2 : 7
t
( C) 10
15
20
25
n
( t C) 3 4 1 2
A 120
B
C D
-
4
21. 25.
!
21. ( )2
1sin cos 1 sin
2 2
+ +
, sin 1 .
22. 22 2x x x = .
23. n . 45. n .
24. .
.
..,
, ,
.
12500 . , ?
25. 5 cm 6 cm.
26. 28. !
26. x
( )1 2 sin cos 2 sincos 2 4
tg x x x xx
pi + =
.
27. 3cmAB = ,
A - B .
1 cm, 2 cm, 4 cm, 5 cm 9 cm.
?
28. ABCD 7=BC 25
O , AB . ACD 108 .
.
-
2 0ax bx c+ + = , 0a 2 4D b ac= 1,2 2b D
xa
= 0D
( )( )2 1 2ax bx c a x x x x+ + = : 1 2b
x xa
+ = 1 2c
x xa
=
2 , 0y ax bx c a= + + ;2 4b Da a
.
2 2k ka a= 2 1 2 1k ka a+ + = k 1
, 0mm
a aa
= m
n m na a= n k nka a= nk nmk ma a= 0, 2, 2a k n , ,m n k
logx aa b b x= = loga ba b= log xa a x= 0, 0a b> > 1a
n : ( ). 1 ...3.2.1 !nP n n n= = n k - : ( ) ( ). 1 ... 1knV n n
n k= +
n k - : ( ) ( )( )
. 1 ... 1. 1 ...3.2.1
kk nn
k
n n n kVCP k k
+= =
A:
( ) , p A
= ( )0 1p A
: ( )1 1na a n d= + ( )11 2 1
2 2n
n
a n da aS n n+ +
= =
: 11.n
na a q= 1
1, 1
1
n
n
qS a qq
=
: . . 1100
n
n
n
pK K q K = = +
-
: 2 2 2c a b= + 1 12 2 c
S ab ch= = 2 1a a c= 2
1b b c=
21 1ch a b= 2
a b cr
+ = sin a
c = cos
bc
= tg ab
= cotg ba
=
:
2 2 2 2 2 2 2 2 22 cos 2 cos 2 cos 2sin sin sin
a b ca b c bc b a c ac c a b ab R= + = + = + = = =
:
( ) ( ) ( )2 2 2 2 2 2 2 2 2 2 2 21 1 12 2 2 2 2 24 4 4a b c
m b c a m a c b m a b c= + = + = +
: a n
b m=
2cl ab mn=
: 2 2 2 21 2 2 2d d a b+ = +
: 12 c
S ch= 1 sin2
S ab= ( )( )( )S p p a p b p c=
S pr= 4abcS
R=
: aS ah= sinS ab= : 2a bS h+=
: 1 21
sin2
S d d=
: S pr=
0 30 45 60 90
rad 0 6
4
3
2
sin 0 12
22
32
1
cos 1 32
22
12
0
tg 0 33
1 3
cotg 3 1 33
0
-
90 90+ 180 sin sin cos cos sin cos cos sin sin cos tg tg cotg
cotg tg
cotg cotg tg tg cotg
( )sin sin cos cos sin = ( )cos cos cos sin sin =
( )tg tg
tg1 tg tg
=
( )
cotg cotg 1cotg
cotg cotg
=
sin 2 2sin cos = 2 2 2 2cos 2 cos sin 2cos 1 1 2sin = = =
22 tg
tg 21 tg
=
2cotg 1cotg 2
2cotg
=
( )21
sin 1 cos 22
= ( )21
cos 1 cos 22
= +
sin sin 2sin cos2 2
+ + = sin sin 2sin cos
2 2 +
=
cos s 2 s cos2 2
co co+
+ = cos cos 2sin sin2 2
+ =
21 cos 2sin2
= 21 cos 2cos2
+ =
( ) ( )( )1
sin sin cos cos2
= + ( ) ( )( )1
cos cos cos cos2
= + +
( ) ( )( )1
sin cos sin sin2
= + +
-
,
23 2012 .
1
1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2
10 2 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 3 21 1 4 22
1x = 4
23 10n = 4
24 4 4 25 2 2 211 3cm 2 cm 2,75cm
4 4S = = = 4
26 _ 10 27
5, 15
P = 10
28 192=ABCDS 62=ABCDP 10
-
26. 26
:
1. ( 1 ) 1 1 sin 22cos 2 cos 2
xtg xx x
= .
2. ( 2 ) 1 sin 2cos 2
xx
=
2
2 2(sin cos )cos sin
x x
x x
.
3. ( 2 ) ( )( )2
2 2cos sin(sin cos )
cos sin cos sinx xx x
x x x x
=
+.
4. ( 1 ) cos sin .(sin cos ) cos sincos sin
x x x x x xx x
+ = +
.
5. ( 3 ) cos sin cos cos 2sin sin2 4 4
x x x x xpi pi pi
= =
.
6. ( 1 ) 2 22sin sin sin 2 sin4 4 2 4 4
x x xpi pi pi pi
= =
.
:
1. ( 1 ) ( )1 2 sin cos 2 sin 0cos 2 4
tg x x x xx
pi + =
2. ( 2 ) ( )1 sin 2 sin cos 2 sin cos cos sin 0cos 2 4 4
xx x x x
x
pi pi + =
.
3. ( 3 ) ( )2 21 2sin cos sin cos cos sin 0cos sinx x
x x x xx x
+ + =
.
4. ( 2 ) 1 2sin cos cos sin 0cos sin
x xx x
x x
+ =
.
5. ( 1 ) 2 21 2sin cos cos sin cos sin cos sin 0
cos sinx x x x x x x x
x x
+ + =
.
6. ( 1 ) 0 0=
-
A B
C
D .
C
27. 27.
1. (4 ) 3AB = cm , ( );A Ak A r ( );B Bk B r A Br r< .
, 3A Br r+ = 3B Ar r = .
1 2, 1 4, 2 5.
2. ( 3 ) , 3, Ar Br .
2 4 4 5.
3. ( 1 ) 2
. 5.
4. ( 1 ) Ar Br 255.4 101.2
C = = .
5. ( 1 ) 2 110 5
P = = .
28. 28
1. ( 1 ) AB -, 90== ADBACB , 90>ADC .
2. ( 1 ) 24=AC .
3. ( 1 ) 84ABCS = 192=ABCDS .
4. ( 2 ) 2524
sinsin == ADCABC , 7cos cos25
ADC ABC = = .
5. ( 1 ) 225. =DCAD .
6. ( 1 ) 45022 =+ CDAD .
7. ( 2 ) 15== DCAD 30AD DC+ = .
8. ( 1 ) 62=ABCDP .
