A

–

–

©

– 9

1.

18

26

2. ( + ) ( ) 42 ( + )( ) 48 ( + ) ( ) 52

3. –

65

– 70 –

76

– 80

85

94

– 98

– 103

4.

122

126

131

139

155

… a A

8

9

1. ( 2) ( 3) ( 2) + ( 3) ( 2) ( 3) 2 + 5 3 3 + 4 | 5| ( 3 5) ( 4) ( 3) ( 5) (+4) ( 3) ( 1) + ( 5) (+4) ( 3) + ( 5) ( 1) ( 5) ( 4 + 3)

2. ,

21, , 8, , , 9 , 2, 9

3. 81 27 5 16 81 16

4. 8 2 2 + 3 5 2 7 + 4 ( 5 ) ( 4 ) ( 2 ) (2 ) ( 6 ) (30 ) ( 5 ) ( 18 ) ( 6 ) ( 2 ) ( ) + 5 6 ( 2 ) (3 )

5. 2 (3 + 5) 3 (2 1) ( 2)( + 2) (2 + 3)( + 2) (4 5)(2 1) ( + )( ) (3 1)( 2) 10 3 ( 2 ) 3 (2 ) 3 ( 2 + 3) (2 ) 2(3 + 4 2) + (2 1)

10

6. = 3( 2 ) 2 + 5( + 1).

= 2 = 1. = 15.

7. 20

4 .

8. (8 10 ) (2 ) (9 6 ) ( 3 ) (9 24 ) ( 3 ) ( 4 ) ( 4) ( 12) ( 4) (25 + 10 + 4) (5 + 1)

9. = 4 + 7, = + 5 5 = + 1 + ( + ) 2

10. ( ) = 7 5 + 4 ( ) = 3 + 5 9. ( 1) (+2) ( ) = ( ) + ( ) ( 2)

11

11. 2 6 = 4 2 3( 1) + 3 = 33 5( + 1) = 2 3 5( + 2) 3(1 ) = 8 + 6 = + ( ) = 1 +

12. 3 46 c ,

13. = 1 2 + = 4

+ 2 = 3 3 + 4 = 7

14. « ».

-

90°

-

-

-

12

15. , y, z

16. .

, .

17. = 2 . (2,1) ( 2, 4) .

. = 2 = 1.

18. y = + (0, 4) (1, 2).

.

19. 5 + 6 = 30.

, .

.

13

20..

. . = 6 3 .

.

21. 10

15 , 11 , 10 , 10 , 14 , 16 , 19 , 18 , 13 , 17 10 10

22. To

14

23. 6, 5,

, 4, : .

1

:

16

1:

E-82

3

-

000

17

1:

-

–

E- = =

-

PISA 2012

=

250

m250 m

18

1:

19

1:

( , 7)

( , 4)

( , 3).

( , 6)

20

1:

21

1:

, ,

, ,

.

-

.

, ,

22

1:

, =

=

= .

= =

=

23

1:

24

1:

1 .

, , , , , , , ,

= = = = =

25

1:

| | = 3 = 3=

= =

2

4 .

26

1:

+ =

27

1:

+ + =

= =

+ = + =

= = .

.

-

,

.

28

1:

.

= + ( )

+ + +

: + = + = + = + =

. = + = + = = + = + = 2. , .

+

29

1:

+

+ ( ) =

30

1:

.

+ = + = + + = + = + + + =

+ + + + + + +

31

1:

= =

+

32

1:

+ + + +

.+ = 2

= = , ,

33

1:

8 80 80 /

5 1,5

4

( 1)

5 , 6 , 8 2 .( 2)

=

1 = 1852

(nm

34

1:

. =

, ,

+ + + + + +

, ,

+ + = ,

35

1:

= . =

, , , , , , ,= = , , , ,

36

1:

0 0.

+ = +

= = = =

,

= 6 + 7

2

:

: ( + ) = + + ( ) = + ( + )( ) = ( + ) = + 3 + + ( ) = 3 +

38

2:

O Jean

29% 32% 41% 71%

20%

= 10000 (1,5 0,2) = 10000 (1,5 0,8) = 10000 (1,2 0,2) = 10000 (1,2 0,8)

39

2:

:

/

/

/

/

PISA 2012

2000 2001 2002 2003 2004 2005 2006 2007 2008 0

0,8

0,2

0,4

0,6

1,0

1,2

40

2:

…

· = = ( ) = · ( ) = · = , 0 = = , 0

= , 0 = , 0 = , , 0 = · , , 0 = , 0, > 0 = , 0, > 0

.

: 3 5

: 2 2 2 2 13

.

.

8 2) 2 +2

41

2:

.

3 7 = (3 7) = 4

( 2 ) (3 ) = ( 2 3) = 6 = 6

: (8 ) (4 ) = = = 2 =

2 5 + 2: 2 , 5 2

3 + 2 2 3 2 + 3 3

(2 5 + 2) ( 4 + 1) = 2 5 + 2 + 4 1 = 2 5 + 4 + 2 1 = + 1

( 2) ( + 4) = ( + 4) 2 ( + 4)= + 4 2 8= + 2 8

42

2:

( ± )

: 41 101 999 105

( + ) ( )

( + ) ( )

«C_En _ »

,

41 =101 =999 =105 =

43

2:

:

. . 45 , 105 , 567 , . . ».

1 2 33510501

44

2:

( + ) = +

( + ) = + +

( + 3) = + 2 3 + 3= + 6 + 932 = (30 + 2) = 30 + 2 30 2 + 2= 900 + 120 + 4= 1024

:

= ( + )

= ( + )( + ) = + + + = + + + = + + = B

( + ) = + + ( + )2 = 2 + + 2

+

-

( + )

+ 2 +

= … = = =

,

= = =

45

2:

:

( ) = +( 3) = 2 3 + 3= 6 + 919 = (20 1) = 20 2 20 1 + 1= 400 40 + 1= 361

: = ( )

= ( )( ) = + = + = + = B

( ) = +

N ( + 2) (2 3 ) 2 5 + 2

( + 2) = + 2 2 + 2 = + 4 + 4 (2 3 ) = (2 ) 2 2 3 + (3 ) = 4 12 + 9 2 = 2 2 + 2 = 2 + 4 5 + 2 = 5 + 2 5 2 + 2 = 5 + 4 5 + 4 = 9 + 4 5 ( + 1) 1 = ( + 2)

= ( + 1) 1= ( + 2 1 + 1 ) 1 = + 2 + 1 1= + 2= ( + 2)=

=

46

2:

= ( + 1) 1= ( + 2 1 + 1 ) 1 - = + 2 + 1 1= + 2 = ( + 2) = + 2 -

= ( + 1) 1 = ( + 2)

+ 2 + + 3,

+ = 0+ 2 + + 2 + + 3 = ( + ) + 3 = 0 + 3 = 3

,

= 56 = 4 + 2 0 = 0= 1 += 0 2( + ) = 2 +

N ( + 1) ( 3) (7 ) (6 + ) (4 1) (3 + 2) (5 ) 5 + 2 (2 + ) 3 +

47

2:

( 1) + ( + 1) (2 + 1) 2 (2 ) (2 + 3) (1 2 ) (2 3) + ( 1)( 1)

N , ( + ) = + 4 + 4 ( + ) = 9 + 6 +( + ) = 25 + + 10 ( ) = 20 + 4 + 25(5 ) = + 16 40 ( + ) = + +

4 + 4 9 + 6 + 14 + 4 + 25 + 8 166 + 3 2 + 1

:

+ 2 + + = 5 2 + = 2 + 6 + 9 + 2 = 1 :

( 2) ( + 2) = 8 ( + ) 4 = ( ) ( + ) ( ) = 4 + 2 = + 2 ( + + ) = + + + 2 + 2 + 2

= 90

+ +

-( ± )

48

2:

( + ) ( )

–

,

«C_En _ »,

( )( + ) = ,

( )( + ) =

49

2:

: ( )( + ) =

( 3)( + 3) = 3 = 932 28 = (30 + 2)(30 2)= 30 2 = 900 4= 896

:

= ( )( + ) = + = = B

, ( )( + ) =

N : ( 5)( + 5) (2 3)(2 + 3) (2 )( + 2) 2 ( 1)( + 1)

( 5)( + 5) = 5 = 25

2 3 2 + 3 = 2 3 = 4 3 = 1(2 )( + 2) = (2 )(2 + ) = 2= 4

50

2:

2 ( 1)( + 1) = 2 ( 1) = 2 + 1= 1 -

N

( 3)( + 3) (2 1)(2 + 1) ( 1)( + 1) ( 2 )( + 2 ) + (5 2)(5 + 2) (3 1)(1 + 3 ) (3 + 5)(5 3 )

N ,

4 + 1 = 1 + 8 = 2 + = 64 + 5 =

N : ( 3)( + 3)( + 9) ( + 2)( 2) + 3 5 ( 1)( + 1)( + 1) 1 (4 1)(4 + 1) + (4 + 2)2 (2 + 3)(2 3) ( 1)(1 + )

,

103 29 29101 99 198 202

51

2:

: ( 1) + 2 = ( 1)( + 1) + 2 ( )( + ) + 2 = ( ) + 2 ( 1)( + 1)( + 1)( + 1) = 1 [( ) + ]( 9 ) = 81

( + )( ) = :

1 2 + 1 2 1

= (3 + 1) + ( 3) + 10(1 )(1 + )

y = 1 , :

= ( ) ( 3)( + 3)

52

2:

( + ) ( )

( + ) ( + )

«C_En , ( + )

( )

( + ) = + + +

(2 + ) = 2 + 3 2 + 3 2 + = 8 + 12 + 6 +

53

2:

= ( + ) = ( + ) ( + )

= ( + ) ( + + ) = + 2 + + + + = + 3 + + = ( + ) = + 3 + +

( ) = +

( 5) = 3 5 + 3 5 5 = 15 + 75 125

A’ = ( ) = ( ) ( + )

= ( ) ( + ) = 2 + + = 3 + = ’ = ( ) = + ( ) = + 3 ( ) + ( ) + ( ) = 3 + = ( ) = 3 +

( + 3 )2

( + 3 ) = ( ) + 3 ( ) (3 ) + 3 ( ) (3 ) + (3 ) = + 3 (3 ) + 3 ( ) (9 ) + 27 = + 9 + 27 + 27

54

2:

:2 = (2 ) 3 (2 ) + 3 (2 )

= 8 3 (4 ) + 3 (2 ) = 8 4 + ( ) = 5 1 ( ) = 4 5,

( ) + 1 ( + 1)

( ) + 1 = 5 1 + 1 = 5 ( ) = 5 1 ( + ) = ( + ) 5( + ) 1

: = + 3 + 3 + 1 5( + 2 + 1) 1 = + 3 + 3 + 1 5 10 5 1 = 2 7 5

+ = 5,

+ +

+ = 5, + = 5 + 2 + = 25 + 2 + = 25 + = 25 2 + = 23

+ = 5,3 ( + ) = 3 53 + = 3 + = 15

+ = 5+ 3 + 3 + = 125+ 3 + + = 125+ 15 + = 125 + = 125 15 = 110

= = ,

55

2:

( + 3) (2 ) ( + 3) ( 3 ) (2 1)

( 2) ( 3)( + 3) + 4 (1 + ) 2 (2 + 1) ( 2) + (2 3)(3 + 2 )

( + 2) 2 = 6( + 1) + ( 1) + (3 7) = ( 2)( + 2) 1

+ = ( + ) 2 + = ( + ) 3 ( + ) + + + = 2 = 8

+ = 3 = 2 + + ( )

5 3

6410

:

GeoGebra CAS

(Calculate Algebra System) -

”

CAS”

-

!

56

2:

(2 + 5) + (2 ) 2 7 ( + 3)( + 3) ( 5 1)( 5 + 1) ( + )( ) ( )( + ) ( 5) (2 3 ) (1 + )( + 1)( 1)(1 + )

+ + = + 25 + 1 + = + + + 25y = 4 + + 9 = 4 = + 3 + = + = y + 8y + = + + + = + 27 + 1 + + = +

: ( + ) ( + ) = 2 ( ) + ( )( + ) ( + ) ( ) = 2 ( + 3 ) = ( + 1) = ( ) + 2( ) + 1

57

2:

:

4

N = 2015 2014 = 1,61 1,6

P( ) = 2 + 2 + 80 ( 1) P( ) P( 1) = 4 4 .

P(100) P(99) + = 2 = 3 + = 10 + = 26 ( ) = 16

N , + , , , 0

-

(0 < < < ) + = .

58

2:

= ( 1) ( 4 2) + 7, = + 5 + 6. = 5 + 7 = ( 1)( + 1)

= 9

= (3 ) (3 2)(3 + 2)

+ = 3 ( + 1) + ( + 1) ( ) 2

: ( + 5) = (3 ) + 24 3( 3) + 2( 3)( + 3) = 5(2 1) 15

59

2:

= 2 15 = 6 10: ,

2.

( )( ) ( ) ( )

3. : = 2015 + (2 2016)

Blaise Pascal (1623 – 1662).

:

( + ) , ( + ) = ( + )1 = + ( + )2 = + + ( + )3 = + + + ( + )4 = + + + + ( + )5 = … + … + … + … + … + … ( + )6 = … + … + … + … + … + … + …

( + ) ( + ) ( )

60

2:

(S)

(F) (E)

(T)

Ca 3 3

Sp 3 3 3 3 3

KK 3 3

= x + + + «Ca»

«Ca»

«Ca»

= x + x + x + x

= 140

m 70 0,80

:

3

62

3:

= : : :

:

PISA 2012

63

3:

(9 6 ) 3 = (9 3 ) (6 3 ) = 3 2

84 = 2 3 7

( ) ( ) ( ) 0 ( ) ( ) ( ) ( )

( ) = ( ) ( ) + ( ) ( ) ( )

6 + 5 + 3 6 3 +2 + 3 2 1 +2

2 + 1

6 + 5 + 3 = (2 + 1)(3 + 1) + 2( ) = 3 + 1 ( ) = 2

3 + 1

84 120120 = 2 3 5 (84,120) = 2 3 = 12

64

3:

6 = 2 3

6 88 = 2 (6,8) = 2 3 = 8 3 = 24

4 + 3 = 5 5 3 4 + 3 = 5 5 3 4 5 + 3 = 5 3 2 = 8 = = 4

65

3:

__________________________________________________________

__________________________________________________________

__________________________________________________________

__________________________________________________________

__________________________________________________________

__________________________________________________________

__________________________________________________________

2

2.3 + 2 = ( 2)( 1) 2 4 + 3 = 2 ( 2) + 3 3 12 + 12 = 3( 2) 4 = ( 2)( 2) + 2 9 = ( 2)( 2)

2 6 + 12 8

66

3:

(12 , 24 , 36 ) = 12 (4( )( + ), 6( + ) , 2( + )) = 2( + )( ) ( ) ( ) 0 ( ) ( )( ) ( ) ( ) = ( ) ( ) + ( )

( ) ( ) ( ) = 0 ( ) ( ) ( ) ( )

6 + 8+ 42 + 82 804

( ) = 0

2 ( ) = ( ) ( ) + ( ) ( 6 + 8) = ( 4)( 2)46 + 8

9 + 2 7 3 2

9 + 2 7 3 2

-

67

3:

9 + 0 7 + 2

3 2 -

= 33

9 + 0 7 + 29 + 6 +6 7 + 2

3 2 3(3 2)3 (3 2) = 9 6 A

-9 + 6 -

3

-

9 + 0 7 + 2 9 + 6 +6 7 + 2 6 + 4 3

3 2 = +2+2 (3 2) = 6 4

-6 + 4-

3 + 2

-

9 + 0 7 + 2 9 + 6 +6 7 + 2 6 + 4 3 + 2 +3 2 0

3 2 = 11(3 2) = 3 + 2-+3 2

3 + 2 1

9 + 2 7 = (3 2)(3 + 2 1)9 + 2 7 3 + 2 1 .

68

3:

2 4

2 4

4

2=

+ 0 4 + 2 + 0 +2 4

2 2( 2 ) = 2-+ 2-

+ 0 4 + 2 + 0 +2 4 2 + 4

2 = +2+2 ( 2 ) = +2 4

-2 + 4+ 2

2+ 2 44 = ( 2 )( + 2 )

69

3:

16 , 36 y 30( 1)( + y) , 18( 1) , 42( 1)

(16 , 36 ) = 4[30( )( + ) , 18( ) , 42( ) ] = 6( 1)

: ( 2) ( + 1) 5 + 2 4 6

: + 6 2 + 13 27 + 4 8 3 9 6 +

2 + 3 + 4 1 4 22 + 32 8 2 4 + 2 3 + 12 4 3

24 , 15 , 6 16 , 4 , 12 9 ( ) , 6 ( ) ( + )

: + = + 3 (2 5) = 6 15 ( 2) = 3 6 = 3 15

70

3:

6 12 = 2(3 6 ) 6 12 = 3(2 4 )

6 12 = (6 12) 6 12 = 3 (2 4)6 12 = 6 ( 2)

–

1

H

3:

, ,

+ 5 ( + 5)

+ + ( + + 1)

+ + 5+ 5 ( + )+ 5( + ) ( + )( + 5)

«C_E _ exe» 5

72

3:

, - .

4 2 = 2 (2 1)

5 5 + 5 = += ( + ) - 5512 8 = 3 2= (3 2 ) - 4

+ + + =-

+ + + =( + ) + ( + ) = ( + )( + ) ( + )

-( 1) -

-’

-

-

73

3:

10 + 10 3 2 ( + ) + 5y( + ) 10( y) + 2 (y )

10 + 10 = 10 ( + 1) --103 9 =3 ( 3) --32 ( + ) + 5 ( + ) = ( + )(2 + 5 ) 2 ( + ) 5 ( + )-( + )10( ) + 2 ( ) =

10( ) 2 ( ) = 2( )(5 ) 10( ) 2 ( )

( ) -2 ( )

+ 21 + 7 + + 12 +

+ 21 + 7 + 3 =

3 -

= ( + 7) + 3( + 7)-( + 7) = ( + 7)( + 3)

+ 21 + 7 + 3 = ( + 7)( + 3)

( ) = +( + )

= ( )

74

3:

+ = = ( ) + ( ) ( )

= ( )( + ) + = ( )( + )

12 8 9 + 6 = 43 = 4 (3 2 ) 3 (3 2 )

(3 2 ) = (3 2 )(4 3 ) 12 8 9 + 6 = (3 2 )(4 3 )

+ 7 + 7 7 3 3 + 6 7 14

7 + 7 6 612 6 8 6 4 8 5 + 10 4 18 + 16 15 + 30 10

75

3:

2 ( + ) + 5 ( + ) 3( ) + ( )( + 1) 2(1 + ) 4 (2 5) + 9 (5 2 )( 2 ) 5(2 ) ( + ) + 3( + )( + ) 3 ( + ) ( ) +

+ 5 + 2 + 10 3 + 3 + 8 12 10 + 15 5 + 5 2 + 3 2 3 + = 4 = 3

: = 4 + 4 = 2 + 2 = + + + = +

+

( )

: = ( 3) 4 2

:

76

3:

–

115.

15

= ( )( + )

25 = = ( + 5)( 5)(2 1) = (2 1 + )(2 1 )–

= ( )( + + ) + = ( + )( + )

27 = 3 = ( 3)( + 3 + 3 )= ( 3)( + 3 + 9)8 + = (2 ) + = (2 + )[(2 ) 2 + ] = (2 + )(4 2 + )

.

x

x

y

y

77

3:

4 9 8 + 27 3 24 + +

4 9= (2 ) (3 )= (2 3 )(2 + 3 )

8 + 27= (2 ) + (3 )= (2 + 3 )(4 6 + 9 )

3 24 = 3( 8) = 3( 2 )= 3( 2)( + 2 + 4)+ + = ( )( + ) + ( + )

= ( + )( + 1)

+ = 5 = 4+

( + ) = + 3 + 3 ++ = ( + ) 3 3+ = ( + ) 3 ( + )+ = 5 3 4 5 + = 125 60 = 65

78

3:

+ = ( + )( + )

( + ) = + 2 + + = ( + ) 2 + = 5 2 4 + = 25 8 + = 17

+ = ( + )( + ) + = 5 (17 4) + = 5 13 + = 65

4 49 94 9 81 + 16 49 3 3 2 3225 1 81 16 18 50

(2 1) (5 + 1) 4 4 ( ) ( + ) 16 ( + ) ( + )( ) + ( ) ( ) ( 2 )

5 5 4 + 4 ( 3) ( 3) 16( + 4) ( + 4) ( 3 ) + 2( 9 ) ( )(2 + ) ( )(4 )

79

3:

– 8 125 + + + 2 54 3 24 + 1

( ) + ( ) 2( )+ 3( + ) ( 1) 2( 1)

: 100 99 805 795

= 2 + 2 = 2 2

( )

80

3:

( –

1

«C_E ggb»

: ( ( + 4 + 3 ( + 3)( + 1) + 3 + 2 + 4 + 4 + 5 + 6

+ + = ( + )( + )

3:

= 4 + 4 + 1 = + 5 + 4

+ + 0

= 1+ + , = + =

+ + = ( + )( + ) + 3 10 = ( 2)( + 5) +3 10 2+5

22( ) )

( )(x xx x xx x

82

3:

+ 2 + = ( + ) 2 + = ( )

4 + 12 + 9 = (2 ) + 2 2 3 + 3 = (2 + 3) 12 + 36 = 2 6 + (6 ) = ( 6 )

----

.

5 6 + 6 + 9 3 + 6 24 10 + 25

5 6 = ( 6)( + 1)

3 + 6 24 = 3( + 2 8)= 3( + 4)( 2)

+ 6 + 9 = ( + 3) 10 + 25 = 10 + 25= ( 5)

= ( 5 )( 5 + )

83

3:

+ ( + ) + + ( + )( + ) + 2 8 2 + 8 2 8 ( 2) ( + 8)+ + + + + +

«C_E

9 + 20 2 15+ 5 + 6 6 + 8 + 8 6 ( 15) + 56 + 90 y 5y 150y + 2 2 14 + 205 4 5 6

18 + 81 64 16 +25 + 30 + 9 4 + 12 + 9 6 + 9 16 + 24 + 9

84

3:

= 4 = 2 8 + 4 25 30 + 9

992 + 2 8 992 + 8 0,58 + 0,42 + 2 0,58 0,42

2 + 16 + 8 1+ + + 2 + 1 1 2

( + )( + ), , + 7 + + 10 8 + , > 0 5 + , > 0

85

3:

1, 3, 6, 10, …

1 4 6

- = ( + )

55 120 150 200

86

3:

:

+ 4 + 4+ 4 + 3+ 4 + 5 + 4 + 4 = 0+ 4 + 3 = 0+ 4 + 5 = 0

( ) ( ) = 0 ( ) = 0 ( ) = 0

( ) ( ) … ( ) = 0 ( ) = 0 ( ) = 0 … = 0

( ) ( ) … ( ) = 0

( 2) (2 + 3) = 0 2 = 0 2 + 3 = 0

= 2 = ( 2) ( + 5) = 0 = 0 2 = 0 + 5 = 0

= 0 = 2 = 5 + + = 0 0

2 1 = 0

+ = 0 , 0

=

-

87

3:

4 0 + + = 0 , 0 = =

, = ±

2 1 = 0 = 2 , = 1, = 1 , = ±= ( )± ( ) ( ) = ±

= == 1

== =

+ + = 0, 0 4 + 4 + 4 = 0 4 + 4 + 4 = 0 (4 + 4 + ) + 4 = 0 , . (2 + ) = 4

4 0

2 + = 42 = + 4=2 + = 42 = 4=

+ + = 0, 0 , = ±

88

3:

(2 1)( 1)( + 2) = 0 2 + 2 = 0 3 = 64 ( 18) + 81 = 0

: H ( ) ( ) … ( ) = 0

(2 1)( 1) = 0 = 0 2 1 = 0 1 = 0 = 0 2 = 1 = 1 = 0 = = 1

H ( ) ( ) … ( ) = 02 + 2 = 0 2 = 0 + 2 = 0

= 2 = 2 ( ) ( ) … ( ) = 0 3 = 64 64 = 0 -

( 64) = 0 -

( 8)( + 8) = 0

-

-

= 0 8 = 0 + 8 = 0

= 0 = 8 = 8

89

3:

( ) ( ) … ( ) = 0 ( 18) + 81 = 0 18 + 81 = 0 -

+ 2 + = ( + ) ( 9) = 0

9 = 0 = 9 -9

1 15

== + 1. = = 15 ( +1) = 15

( + 1) = 30 2 + 30 = 0 ( 5)( + 6) = 0 ( 5) = 0 ( + 6) = 0

= 5 = 6

5 6 (2 5) = 25 4 + 4 + 10 = 02 6 = 0 + 3 + 1 = 0

90

3:

: (2 5) = 25 (2 5) = (+5) (2 5) = ( 5)2 5 = 5 2 5 = 52 = 5 + 5 2 = 5 + 52 = 0 2 = 10= 0 = 5 4 + 4 + 10 = 0

4 + 4 + 10 = 0= 4 , = 4 , = 10

H

, = ± = ±= ± 244 + 4 + 10 = 0

4 + 4 + 10 = 04 + 4 + 1 1 + 10 = 04 + 4 + 1 + 9 = 0(2 + 1) + 9 = 0(2 + 1) = 9(2 + 1) 0(2 + 1) = 9

3:

2 6 = 0 = 2 , = 1 , = 6 H, = ± = ( )± ( ) ( )= ±= ±

= = = 2 = = =

+ 3 + 1 = 0 , = 1 , = 3 , = 1 H , = ± = ± ( ) = ±

= = = =

( + 5) = 0 ( 7)( + 5)(2 3) = 0 5 10 = 0 (2 5)( 6 + 5) = 0 4 = 0 25 10 + 1 = 0 5 + 6 = 0 ( 9)(9 6 + 1) = 0

92

3:

= 25 = 12 = 35 2 = 2 + = 2 ( 6) = 9 ( + 4)( 3) = 3 ( 10) + 25 = 0

2 5 + 10 = 0 5 4 1 = 02 2 3 = 0 2 + 1 = 0 3 + 2 = 0 ( 7 + 12)(2 5 + 2) = 0

: + 1 = 0 (2 ) = 0 ( 2) = 4 (3 1) + 9 = 0 4 + 12 + 8 = 0 9 6 + 2 = 0 25 20 + 12 = 0 16 + 40 + 20 = 0

( ) = ( + 1) + ( 1) + 7: ( ) = 2 + 5 + 7 ( ) = 0

9 6 + 2 = 0

93

3:

74

8 4

:

( 3,14)

3 cm 16

100 5 = 0)

«C_ ggb»= 0)

94

3:

2 1!!!

, ( )( ) ,

95

3:

H ( )( )( 1)( + 1) 0, 1 1. , ,

.

3 3( 1)( + 1) = 3( 1) ( 1)( + 1) = 3+ 1

1 1

0 0

+ 5 05

0

-

0 0

--

, 0, =

= 0

96

3:

4 0 ( 2)( + 2) 0 2 2= ( )( ) =

( )( )

= =( )( ) =

= ( )( )( ) =

97

3:

, 0

( )

( )( )

( )( ) ( )( ) ( )( )

= { 6, 3}

98

3:

–

40

kwh

3

20

8 3

, , , = , =

:

1 1

99

3:

: = =

= : = === ( )( )( )( )

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:

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3:

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20 75 1 1 60

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= , , 0

3:

10 / / 72 / /

( ) ( )

: : : :

: :

22 32 3 2

2

x xx x x

x 32 ( 2)

xx x ( 1)

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xx

x x

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2

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= 2013

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3:

–

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3:

+ = + , =

= ( ) = =

(2 , + 1) = 2 ( + 1)+ = ( )( ) = ( ) = ( )

( )( ) = 0 ( ) = 0 ( ) 0. ( )( ) = 0 ,

( ), ( ).

= 0 2 = + 3 03 = 2

+

3:

+ = + =

=

---

= ( )( )= ( )( )( )= ( )( )

-

= ( + 1)( 1) = ( )( )

=

+ = 2 3 + 2 4 = 25 + 6

2 3 + 2( 2) = 2( 2)( 3)

2( 2) 2 3 + 3 2( 2) = 2 2 ( 2)( 3)

4( 2) + ( 3)2( 2)( 3) = 42( 2)( 3)

4( 2) + ( 3) = 4 4 8 + 3 4 = 0 + 12 = 0 ( + 4)( 3) = 0 + 4 = 0 3 = 0 = 4 = 3

H = 4 = 3

-

= 2( 2)( 3)2( 2)( 3) 02 0 3 0

-

E

-

2 3

3:

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+ 2 1 0

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1 + + : 1 + :

= 0 = 0= = 2 = 1 + = 2 + = + =

= 0 1) = 0 = 3 ( ) = 0 2) = 2

= 0 = 3

= 1 4) = 1 5) = 0 = 1 = 1

3:

3 + 3 5 + 10 15 7 + 10 12 8 4 2 2 + + 5 + 5 6 + 8 27 16 8 +

( + 1) 9 3 3 + 2 2 (3 + 2 ) 16 4 ( 1) + 4 (1 ) 3 + 3 3 3 10 + 25 + 4 20 3 3 + 3 3 10 + 25 3 + 2 2 + + + ( )2 ( + 1)2 (3 9)( 9) ( 3) 2 + 4 36 12 + 2

=

+

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+

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.

3:

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( 2)( + 8) = 0 3 (5 2) = 0 3( + 5) = 0 = 9 ( + 3) = 4 16 8 + 1 = 0 ( + 1) = 3 ( + 1) ( 3)( + 2) = +6

5 24 2 10

20

= 0 ( ) = = 2 = = 2 + =

( ) = + =

3:

:

+ = 1 ( + 2 ) + (2 ) = 5

3:

, , 0 + + = 0

= ( ) = + 1 = 1

= ( )= + 1 ( 1,0) = 1

= = ( )( ) 2013 + 1 2014

= 1 1 1 … 1 1

= ( ) :

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118

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A

154 :

: 155

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9

1. 6 5 10 4 217 17 352. , 8, , 9, 2 21, 93. 6 1

364. 6 5 5

20 4 12 6 3 7 12

5. 6 + 10 6 + 3 4 2 + 7 + 6 8 4 10 + 5 3 17 + 2 3 3 6 6 + 9 + 2 6 6 + 3

6. + 5 8 207. 0 < < 10 4 80 + 400 576 8. 4 5 3 + 2 3 + 8

2 + 1 + 1 + 3 = 5 + 1 = 3

9. 5 4 + 13 3 + 310. 16 11 4 5

1111. = 2 =

A = 5 = 012. = 130 13. = 1 , = 2 = 1, = 1

156 :

14.

-

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15. = = 119, = 61 = 90, = 37, = 5316. = 4 = 2

17.( 2, 4) (0,0)

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: 157

19. ( 6,0)(0,5) = 15 . .

20. = 3 = 3 + 6

21. 14,3 14,5 50%22. 2 2 123. ( ) = ( ) = ( ) =

( ) = ( ) =

:

23

1. 2. , , . .

158 :

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= , = = = == == =

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8. = = , ,

30

1.

3.

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= = += + = +5. + + = + + = 2 = =7.

= == 2 == = = 2= 2 =

: 159

33

1.

2. 22 3 2 5. | | = 5 , = 8 | | = 107. = 58.

= 2== +=

36

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160 :

:

( ± ) 6

1.

2. + 2 + 1 6 + 9 14 + 49 + 12 + 36 16 8 + 1 9 + 12 + 4 25 10 + 10 2 + 27 + 4 + 4 + 9 + 2 + 1

3. 4 + 4 8 + 16 10 + 25

4. 2 + 2 6 + 1 16 + 8 5 14 + 10

5. ( + 2 ) = + 4 + 4 ( + 3 ) = 9 + 6 + 5 + = 25 + + 10 ( 2 5 ) = 20 + 4 + 25 (5 4 ) = 25 + 16 40 ( + ) = + + 2

6. 4 + 4 9 + 6 + 1 2 + 17. 25 4

19. 10. 4 4

( + )( ) 50

1. 9 4 1 1 4

: 161

239 1 25 92. 4 1 4 + 1 = 16 1 8 + 8 = 64

2 + 8 8 2 = 64 4 5 + 5 = 25

3. 81 + 3 9 2 32 + 16 + 3 2 + 9

4. 10609 841 9999 39996

7. = 5 28. = 209. = 7

( ± ) 55

1. + 9 + 27 + 27 8 12 + 6 + 9 + 27 + 27 9 + 27 27 8 12 + 6 1 3 +

2. 3 + 12 + 1 7 5 + + 1 5 6 + 3 8

4. + = 20 + = 565. 5 9

16. 13 7. 188. 2015

56

1. 4 + 20 + 25 + 2 + 4 + 4 11 4 7

162 :

+ 6 + 9 4 15 + 75 125 8 36 + 54 27 1

2. + 2 + = + 25 + 1 + 10 = 5 + 1 16 + 40 + 25y = 4 + 5 2 + 9 2 9 = 4 81 = + 3 3 + = 9 + = y + 8y + 16 = + 4 + + = + 27 + 1 + 27 + 9 = 3 + 1

5. = 4029 = 0,03217. 2 + 6 + 76 39611. 20 2

412. = = 2

9

1. 33. 17 4.

( + ) = + 5 + 10 + 10 + 5 + ( + ) = + 6 + 15 + 20 + 15 + 6 + ( ) = 6 + 15 20 6 + 15 + 5. 15

6. 0,5 89,6 5,38

: 163

3: –

9

1. 2 5 18 38 122.

3.

2 + 3 + 4 1 2 44 22 + 32 8 4 14 + 4 24 + 2 23 + 12 4 + 4 34. 3 4 3 ( )5. 66. + 3 = + 3 3 (2 5) = 6 15

3 2 = 3 6 3 5 = 3 15 - 7

1.

+ ( + )7 + 7 7 7 7 ( + )3 3 + 6 3 3( + 2)7 14 7 7 ( 2)2. 7( + ) 6( 1) 6(2 )

( ) 2 (4 3) 4 ( 2 ) 5 (1 + 2 ) 2 (2 + 9 8) 5 (3 + 6 2 ) (1 2 )

3. ( + )(2 + 5 ) ( )(3 + ) ( + 1)( 2) (2 5)(4 9 ) ( 2 )( + 5) ( + )( + + 3) ( + )( + 3 ) ( )( 1)

4. ( + 5)( + 2) ( 3 )( + ) ( )( + )

164 :

(2 3 )(4 5) ( 5)( 1) (2 + 3 )( )5. = 16 = 72

= 16 = 307. = ( 3) 35 8. = 2 (4 ) = 4( + + 4)

- 78

1. ( 2)( + 2) ( 7)( + 7) (3 )(3 + ) (2 3 )(2 + 3 ) ( 9)( + 9) + 7 + 7 3 ( 1)( + 1) (5 1)(5 + 1) 2( 4)( + 4) (3 2 )(3 + )(9 + 4 ) 2(3 5 )(3 + 5 )

2. (2 1 )(2 1 + ) (5 1)(5 + 3) ( + )(3 ) ( + 2 4)( + 2 + 4) ( )( + + ) ( )( + + ) ( )( + )( + ) (2 3 )

3. ( + )( 5) ( )( + 4) ( 3)( )( + ) ( + 4) (4 ) ( 3 )( 2 + 6 ) ( )(2 + )(2 )

4. ( 2)( + 2 + 4) (5 + )(25 5 + ) ( )( + + ) + + + + ( )( + + ) 2( 3 )( + 3 + 9 ) 3( 2)( + 2 + 4) ( + 1)( + 1)

5. ( )( + ) ( + ) ( )( + + 2 2 ) ( + )( + 3) ( 1) ( + 1)

6. 199 160007. 2 = 4

: 165

- 3

1.

+ ( + ) + + ( + )( + )+ 2 8 2 + 8 2 8 ( 2) ( + 8)+ + 2 8 2 + 8 2 8 ( + 2) ( + 8)

8 2 8 + 2 8 2 ( 8) ( + 2)+ ( 8) ( 2) 8 2 8 2 ( 8) ( 2)+ ( 4) ( 4) 4 4 4 4 ( 4)+ + 16 1 16 + 1 16 1 ( + 16)( + 1)3. ( 5) ( 4) ( 5)( + 3) ( + 2) ( + 3)

( 4) ( 2) ( 4) ( 2) ( 7)( 8) ( 9) ( + 10) ( 15) ( + 10) ( 1) ( + 2) 2 ( 5) ( 2) ( + 1) ( + 4) ( 6) ( + 1)

4. ( 9) ( 8) (5 + 3) (2 + 3 ) ( 3) (4 + 3 )

5. = ( 2)( + 2)= (2 1)( 2)( + 2)= ( 2)( + 2)( 1)

6. = 4(5 3 )7. 1 000000 18. ( )( + ) ( 4 1)( + 4 + 1)

( + 1)( + + 1) (1 )(1 + + )9. = ±6 = ±7 = ±11

= 16 , = 15, = 7, = 12 = 6 = 4 91

1. = 0 = 5 = 7 = = 5 = 0 = 2 = = 1 = 5= 0 = 2 = 2 = = 2 = 3 = 3 = 3

2. = 0 = 5 = 5 = 3 = 4

166 :

= 7 = 5 = 0 = 2= 0 = 2 = 1 = 3= 6 = 2 = 0 = 5 3. = = 1= = = 1 = = 1 = = = 2 = 3 = 4 4. = 2= 0 = 4 = 2 = 1 = =5. = 1 =6.

7. 5 + 6 = 0= 2 = 38. = 49. 5 ,7 5, 710. 10 , 6 11. = 10 = 7 12. 3, 13. = 514. = 20

96

1. {±5} { 7,2} {3}2. , .3. .4. ( )

( )5. ( )6. 2019

: 167

- 100

1. 75

2. 36 / 20 /3. ( ) ( ) 4. 1

( ) ( ) 5. 6. 2013 7. 9

( ) -

106

1. 3

2. .

3.

13004. ( ) ( )( ) ( )

( )( )( ) ( )

5. + , + + , +

6.

7. 2 6 ( )

8. = 7 = 3

168 :

y = 1 y = 5 = 1 = 3 = 2 = 0 = 2 = 8 = 2

9. 3) 1) 2) 4)

108

1. 3 ( + ) 5 (2 + 3 ) ( 5)( 2) ( 4) ( 2) 4 (2 ) 2 ( 1) ( + 1)( + )( + 5) ( 4) ( + 3) ( 3) ( + 3 + 9) (4 )

2. ( 2) ( + 4) ( )(3 + + ) (3 2 ) (3 + 6 ) 4( )( + )( 1)( + 1) ( + )( + 3) ( 5) ( 1) ( + 1)( )( + + ) ( 5 )( 5 + ) ( + 1)( + + ) ( + 1)(2 + 1) (3 + 8) ( 3) ( + 6)( + 6 2)

3. ( ) 364. ( + )( 1)5. 3

6. ( )1 ( ) ( )( )( )

: 169

( ) ( ) ( )7.

( ) ( )( )8.

9.

( ) 10. = 2 = 8 = 0 =

= 5 = 0 = 9= 4 = 1 = = 0 = 1 = 3 = 411. = 3 = 8 12. = 8 = 6 13. = 0 = 4 = 514. = 2 == 3 == 14 = 3= 10 = 415. To 116.

= 3 .= 4 .= 5 .

112

1. ( + )[ ( ) + + ]

170 :

3. = 2 , 0

= 2 3, 2

4. + 1

5.

7.

8.

1 1 82 4 16

3 9 24

4 16 32

5 25 40

= 89. 14 37 75

: 171

4:

A T 125

1. , , , , = , = , =( ) ( ) ,,2.

3. = 1,2,3, … ,11,12= 8,9,10, …4. >

- 129

1. = , = , =4.

5.= , = , = , == , = , = , == 20°

135

1. = = 50°, = = 100°, = = 30°2.

172 :

3.= = == = = = = =

4. - - - - - -

5. )6.

- -

- -

1

1.

2.

3.

4.

1 7

1.

2.

4. 7 49 6. < 33 < 44

{ } =

{1,2,3,4, . . . }

{0,1,2,3,4, . . . }

{0, ±1, ±2, ±3, ±4, . . . }

{1,2,3,4, . . . } { 1, 2, 3, 4, . . . }

{ / : ,

/

o

=

·

Ans

^

SHIFT 2nd F

AC

DEL

Abs

(-)

a b/c 23

S D a b/c

CLR

M+

M-

M

3 + 4 3+4 7 2,34 – 1,1 2.34 – 1.1 1.243 2 3 2 6 2 2 2 32 5 10 5 3 5 103 5000

3 4 2

2

2 3 4 4 4 2 5 5 25 2 (7 3) 2 (7 3) 8 2 (7 3) 2 8 2 ( 3) 2 ( 3) 5 | 3| | 3| 3 0,25

9 6 2

9 – 6 2 + 6

3 (9 6: 2) 6: (9 6: 2) 3 – 6 17

+ = 3 4

· – 2 3 4 1 · 1 =

3 x 2 =

2 5 =

5 P 3 =

3 a b/c 4 =

3 a b/c 4 =

SHIFT 23 2 3 4 =

2 a b/c 3 a b/c 4 =

4 =

5 X² =

= 3 – 7 ( x 2 )

x 2 = 3 – = 7 Ans

2 ( (-) 3 ) =–

= 3 (-) Abs

S D

a b/c SHIFT

= 2 ÷ 6 – 9

3 – 6 ÷ =