15 May 2017

...................................................................................................................................................................... 1 ...................................................................................................................................................................... 5 ............................................................................................................................................................ 7 ..................................................................................................................................................................................... 9 ................................................................................................................................................. 13 ............................................................................................................................................................... 17 ............................................................................................................................................................... 25 ......................................................................................................................................................................................... 28 ............................................................................................................................................................. 30 ............................................................................................................................................................................. 38 ................................................................................................................................................. 41

1

(I)

3 (I+) (N) 1, 2, 3, ... (I0) 0 (I) 1, 2, 3, ...

: 1 1

(Q) ( 0)

1

5 = 51 , 2 =

2

1

( ) ( 0)

0.7 = 7

10 , 1.53 =

153

100

0. 3 = 39 , 0. 326 =

326

999 , 0.12356 =

1235612

99900=

12344

99900

(Q) 1.010010001 , 2.21452301520136455202 2 , 3 , 5 , 10 , ,

: 227

3.14 227 3.14

3.141592653589793238462643383279502884197169399 2: 2 3 (2 ~ 1.414 , 3 ~ 1.732)

(I)

(I+) (I0) (I)

(I)

(I+) (I0) (I)

(Q)

2

( 0)

2 3 = 6 = 2 8 = 16 = 4 =

(R) ( )

+ R Q R+ R Q+ Q

: 1

1. 1. 1 2. 2

3. 5 4. 2

5. 306 6. 0

7. 25 8. 227

9. 12.45254 10. 1.212121

11. 25 12. 0

(Q)

(R)

(I)

(I+) (I0) (I)

(Q)

3

13. 1

14. 1 + 2 15. 3 2

16. 2 18 17. 1+23

18. 19.

20. 21.

2. () 1. 2.

3. 3 4. 1

5. 8 6. 5

7. 2 8. 2

3. = 2 1.4 , = 3.1 = 53

1.63 , , [O-NET 56/3]

4. [O-NET 56/2] 1. 4 , 22

7 , 1.010010001 2. 23 , 8 , 2

3. + 1 , 16 , 0.101001000100001 4. 911

, 1.11111 , 83

5. 0.8 , 8 2 , 33

4

5. [O-NET 53/3] 1. 2.

6. [O-NET 52/5] 1. 2.

7. (3 1)2

[O-NET 54/4] 1. 2. 1.8

8. [O-NET 52/1] 1. 0 2. 0

5

5

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

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

3. = 1 1 = 4. = + 1 + 1 = + 2 = + 2

5. = 6 3 = 18 6. + 1 = 2 + 2 + = 5 + 1 = 5

7. + 2 = 6 8. 2 = 3 = 6

+ 2 + (2) = 6 + (2)

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

2 3 = 7 2 3 + 3 = 7 + 3 2 = 10

2 1

2 = 10

1

2

= 5

6

11. 3( + 1) = 6 + 1 = 2 12. + = = +

2.

5 3 = 23 5 = 23 + 3 18 = 3

6 =

= 6

1. ........................ 2. ........................ 3. ........................ 4. ........................

7

11

3 3 = 9 = 3

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

2 2 2 + (2) = (2) + 2 = 0 7 7 (7) + 7 = 7 + (7) = 0

32

32

32

+ (3

2) = (

3

2) +

3

2 = 0

0 0 0 + 0 = 0 + 0 = 0

2 12 2 1

2 =

1

2 2 = 1

32

23

32

2

3 =

2

3

3

2 = 1

23 3

2 ( 2

3) (

3

2) = (

3

2) (

2

3) = 1

0 0 1

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

( 0)

( + ) = ( ) + ( )

8

1. / 1. 2.

3. 4.

5. 6. 3

7. 8.

2. 1. + = +

2. 2 = 2

3. 2 + (3 + 4) = (3 + 4) + 2

4.

5.

6. + ( ) = ( + )( + )

3. 1. 8 2. 2 3. 1

2 4. 2

5. 0 6. 1 7. 1 8. 2 9. 1

2 10.

+1

4. [O-NET 52/4] 1. + = 0 = + 2. = 1 =

9

25 , 342 , 532 , 2 , 6 , , 21 , 0

,

25 + 35 = 55 32 + 2 = 42 22 2 = 22 2 ( )

32

2 2 = (3

2 1) 2 = (

31

2) 2 =

1

22

22 3 = 632 32 2 = 322

12

2 4

32 =

2

34

63

23=

32

2

1 25 + 4 + 5 , 32 + 2 2 , 6 32 , 23

25 + 4 + 5 3 25 , 4 , 5

() , () , () () () () = 25 + 4 + 5 (1) = 2(1)5 + 4(1) + 5 = 11 (2) = 2(2)5 + 4(2) + 5 = 67 () = 6 32 (0) = 6 3(0)2 = 6 (1) = 6 3(1)2 = 3

25 342 532 2 6 21 0 2 3 5 1 6 1 21 0

5 6 6 2 0 1 2

25 + 4 + 5 32 + 2 2 6 32 23 5 3 2 0

10

(25 + 4 + 5) + (5 2 2) = 35 2 + 2 + 5 (2 2 1) (22 2) = 2 2 1 22 + + 2 = 2 + 1

(22 + 4 + 5)(2 2) = 24 42 + 43 8 + 52 10 = 24 + 43 + 2 8 10

(2 2 + 5) ( + 2) = ( ) + 2 2 + 5 = ( + 2)( 4) + 13

3 + 2 + + = 23 32 + 5 = 2 , = 3 , = 0 , = 5

1. () = 2 1 , () = 3 + 2 , () = () () (2)

2. () 2 1 + 2 ()

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

4 + 2 2 2 + 5

2 + 2 4 + 5 4 8

13

11

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

5. ( + 2)( ) = 32 + + 10 + +

6. ( + )2 = 42 12 + > 0 + +

7. (())2 = 2 + 6 +

12

8. () = 23 + 2 + + 3 () = (2 + 1)() (1)

9. , , ( 1)2( + ) = 3 + + 4 + + + [O-NET 54/25]

13

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

1. 32 1222 + 62 = (3)( 4 + 2) 24 43 + 32 = (2)(22 4 + 3)

2. 3 22 + 3 6 = (3 22) + (3 6) = 2( 2) + 3( 2) = (2 + 3)( 2) 3 2 3 + 3 = (3 2) (3 3) = 2( 1) 3( 1) = (2 3)( 1)

3.

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

42 3 = (2)2 (3)2

= (2 3)(2 + 3)

83 27 = (2)3 (3)3 = (2 3)(42 + 6 + 9) 646 1 = (83)2 (1)2 = (83 1)(83 + 1) = ((2)3 13)((2)3 + 13) = (2 1)(42 + 2 + 1)(2 + 1)(42 2 + 1)

4. 2 + +

2 + 5 + 6 = ( + 2)( + 3) 2 + 7 + 6 = ( + 1)( + 6)

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

2 + 2 + 2 = ( + )2 2 2 + 2 = ( )2 3 + 32 + 32 + 3 = ( + )3 3 32 + 32 3 = ( )3

2 + +

( + ? )( + ? )

+ 2

14

2 + 2 8 = ( 2)( + 4) 2 2 8 = ( 4)( + 2) 2 4 + 3 = ( 1)( 3) 4 62 + 8 = (2 4)(2 2)

5. 2 + +

22 + 7 + 6 = (2 + 3)( + 2) 62 17 3 = (6 + 1)( 3) 42 4 3 = (2 1)(2 + 3) 42 11 + 6 = (4 3)( 2) 6 22 = (3 2)(2 + ) 24 52 + 2 = (22 1)(2 2)

6. 6.1.

6.1.

1 2 1 2

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

2 + +

(1 + 1)(2 + 2)

2 6 7 = 2 2(3)() + 32 32 7 2 2 + 2 = ( )2 = ( 3)2 32 7 = ( 3)2 16 = ( 3)2 42 2 2 = ( )( + ) = ( 3 4)( 3 + 4) = ( 7)( + 1)

2

2 + 2 5 = 2 + 2(1) + 12 12 5 = ( + 1)2 12 5 = ( + 1)2 6

= ( + 1 6)( + 1 + 6)

2 + 3 + 1 = 2 + 2 (3

2) + (

3

2)

2

(3

2)

2

+ 1

= ( +3

2)

2

(3

2)

2

+ 1

= ( +3

2)

2

5

4

= ( +3

2

5

2) ( +

3

2+

5

2)

22 7 1 = 2 (2 7

2

1

2)

= 2 (2 2 (7

4) + (

7

4)

2

(7

4)

2

1

2)

= 2 (( 7

4)

2

57

16)

= 2 ( 7

4

57

4) (

7

4+

57

4)

2 4 + 7 = 2 2(2) + 22 22 + 7 = ( 2)2 22 + 7 = ( 2)2 + 3

= ( 2 2 )

4 + 2 + 1 = 4 + 22 + 12 22 + 2 = (2 + 1)2 2 = (2 + 1)(2 + + 1)

15

1. 1. 2 + 12 2. 2 6 16

3. 32 + 24 4. 42 19 + 12

5. 62 3 18 6. 4 53 + 62

7. 332 242 8. 23 + 2 8 4

9. 4 202 + 64 10. 6 + 73 8

16

11. 3 32 6 + 8 12. 2 + 52 + 12

2. 1. 2 + 2 1

2. 2 4 + 1

17

2 3 + 2 = 0 {1, 2} 1 2

1

2 2 + + = 0 2 + + 0

2 + + = 0 2

2 3 + 2 = 0 2 (3)2 4(1)(2) = 9 8 = 1 > 0

4 + 5 = 2 13 4 2 = 13 5 2 = 18

= 18

2 = 9

5 + 22 = 9 4 2 32 + 4 4 = 0 (3 2)( + 2) = 0

= 2

3 , 2

3 2 = 0 =

2

3

+ 2 = 0 = 2

5 + 22 = 9 4 2 32 + 4 4 = 0

= 4424(3)(4)

2(3)

= 464

6 =

48

6

= 4

6 ,

12

6

= 2

3 , 2

= 3 = 4 = 4

=24

2

o 2 4 > 0 2 o 2 4 = 0 1 o 2 4 < 0

18

- 2 + + = 0 2

2 3 + 2 = 0 (3)1

= 3 21

= 2

22 4 + = 0 2 + + = 0 1 2 4 = 0

= 2 , = 4 , = (4)2 4(2)() = 0 16 8 = 0 2 = #

22 + 6 = 0 32

1 3

2

32

2 #

2 32

22 + 6 (2 3)(? + ? )

2 2 #

3 -

2 + + = 0

22 + 6 = 0 62 = 3

2 (32)

2

(3

2) + 6 = 0

9

2

3

2+ 6 = 0

9 3 + 12 = 0 21 = 3 = 7

= 3

2 , ?

(2 3)(? + ? ) = 0 22 + 6 = 0

22 7 + 6 = 0 (2 3)( 2) = 0

= 3

2 , 2

22 + 6

(2 3)(? + ? )

1 2

o 2

o 2

19

32

32 3

2 #

2 1 2 0

3 32 4 + 12 = 0 0

{2, 2, 3} #

1.

2. 3. 2 4. ( , )

3 90 1.

2.

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

3. 90 ()(2 + 3) = 90

3

2 = 3

= 3 2

3 = 2

2( 3) 4( 3) = 0

(2 4)( 3) = 0

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

= 2, 2, 3

20

4.

= 152

6 6 = = 6 = 2 + 3 = 2(6) + 3 = 15 #

1. 1. 2 5 + 4 = 0 2. 42 3 = 9

2

3. ( 3)( 5) = 11 4 4. 3 22 + 2 = 0

5. 2 + 1 = 0 6. 2 + 4 + 1 = 0

2. 1. 2 5 + 6 = 0 2. 2 = 9

()(2 + 3) = 90 22 + 3 = 90 22 + 3 90 = 0 (2 + 15)( 6) = 0

= 15

2 , 6

21

3. 2 + + 1 = 0 4. 22 + 3 6 = 0

5. 2 + 6 + 9 = 0 6. 2 + 1 = 0

3. 2 + 1 = 0 12

4. 2 + 9 = 0 1

5. 2 [O-NET 51/6] 1. ( 2)2 + 1 = 0 2. (2 + 2)(2 1) = 0 3. ( 1)2(2 + 2) = 0 4. (2 1)( + 2)2 = 0

22

6. 1+2

+ = 1 [O-NET 57/9]

7. (2 + 1)(22 6 + ) = 0 1 [O-NET 54/7]

1. (0 , 3) 2. (3 , 6) 3. (6 , 9) 4. (9 , 12)

8. 34 42 + 6 = 0

[O-NET 53/6]

9. = 12 2 + 3 1 = 0

[O-NET 50/6]

23

10. 65 3 [O-NET 52/21]

11. 3 7 [O-NET 56/11]

12. 600 75% [O-NET 53/14]

24

13. 2

100 800 200 1,100 [O-NET 56/35]

14. 5 60 4 [O-NET 57/38]

15. 1 3 4 100 250 50 100 100 20 % [O-NET 51/37]

25

< < < < + < +

o < 5 < 5 o < 5 > 5

< < + < + = + () > < < < < 2 1

6 < < 15 1 < < 4 1

2 < < 14 #

0 < < 0 < < <

2

0 < < 0 < <

> 4

0 < < 0 < <

<

( )

0 < <

0 < 1

<

1

<

26

1. 1. < < 2 2. < 1

<

1

3. 0 < < 1

< 1

4. < < 0 1

<

1

5. < 2 < 2 6. < <

7. 0 < < < 8. < < 0 >

9. < > 0 < 10. < < <

11. < < <

12.

13. 6 < < 10 2 < < 4 4 < < 6

2. 6 < < 12 2 < < 3 1. + 2.

3. 4.

5. 2 3

27

3. , [O-NET 56/1] 1. = = 2. < 2 < 2 3. < < <

4. , , < < [O-NET 53/4] 1. < 2. <

5. 3 3 5 1.732 2.236 [O-NET 52/3]

1. 2.235 + 1.731 5 + 3 2.237 + 1.733 2. 2.235 1.731 5 3 2.237 1.733

6. = 18 12 = 75 50 [O-NET 57/3] 1. 2. 3 < 2 3. + < 2

28

/

[1, 5] 1 5 ( 1 5 ) { | 1 5 } [4 , 3) 4 3 ( 4 3) { | 4 < 3 } (2, ) 2 ( 2) { | 2 < } (, 2] 2 ( 2 ) { | 2 }

, , , , , 2 (0, 5) 6 (, 2] {2} (0, 5) (1, 3] (, 3]

(1, 5] (2, 6) = (1, 6) (1, 5] (2, 6) = (1, 2] (1, 5] (2, 6) = (2, 5]

(, 2] {0} = (, 0) (0, 2] (2, ) = (, 2] {1} = (, 1) (1, )

1. 1. (1, 10) (1, 2] 2. (, 2) (1, 0]

(, ____ ____ , )

[ (

] )

,

[4, 3)

(2, )

0 2 3 4 5 1 4 3 2 1 5

[1, 5]

(, 2]

(1, 5]

2 5 6 1

(2, 6)

29

3. (3, 3) (1, 1] 4. (, 2) (1, )

5. ( 12 , 2) (

1

3 , 3) (

1

4 , 4) 6. ( 1

2 , 2) (

1

3 , 3) (

1

4 , 4)

7. (, 5) (1, 5] 8. [2, ) (1, 2)

9. [8, 8) [1, 1) 10. [5, 8)

2. 1. 1 < 9 2. > 1

3. 3 4. > 1 1

5. < 2 > 2 6. > 2 < 2

7. 2 8. 4 2

30

3 6 10 55 2 2.5 2

2 > < ()

1

(, )

2 4 < 2 < 2 + 14

2 + 3 4 5 2 4 5 3 2 8

8

2

4

3 < 6

> 6

3

2 5

(5)(2)

> 3 2 < (3)(2)

2 > 8 > 8 + 2

+2

> 5

+ 2 ? 5 !

4 < 8

< 8

4

4

(, 4]

(4, 2)

2 4 < 2 < 2 + 14 2 4 2 < 2 2 < 2 + 14 2 4 < 2 3 < 14 4 2 < 2 3 2 < 14 2 6 < 3 < 12

6

3 >

3

3 >

12

3

2 > > 4

2

2

3 ()

5 3

5 3 (,)

4 2 > 2 + 5

4 > 5

31

1. 1. 3 < 2 1 3 2. 1 1 4+2

3 3

3. 1 2 + 1 < 5 4. 2 < 1 2 < + 4

> 4

2 4

< 2

(4, 2)

2 4 < 2 < 2 + 14

2 4 < 2 2 + < 2 + 4 3 < 6 < 2

2 < 2 + 14 2 < 14 2 3 < 12 > 4

32

2 0 0 + , + , , + , > 0 + < 0

2. 1. 2 5 + 6 < 0 2. 2 + 7 + 12 > 0

3. 2 4 > 0 4. 1+2

< 1

+1

2 4 5 > 0 ( + 1)( 5) > 0

(, 1) (5, ) 1 5

+ +

2 + 6 < 0 ( 2)( + 3) < 0

+ +

(3, 2) 3 2

(2)

(+3) < 0

+ +

(3, 2) 3 2

+ +

( + 1)( 2)( + 3) < 0

(, 3) (1, 2) 1 2 3

+ + +

(+1)(2)

(+3)(5) > 0

(, 3) (1, 2) (5, ) 2 5 1 3

33

3. 1. 22 3 2 0 2. 62 + 5 1 0

3. (2 1) 15 4. 33 + 22 3 2 0

5. 35+1

0 6. 35+1

1

2 + 6 0 ( 2)( + 3) 0

[3, 2] 3 2

+ + + + +

(2)(+3)

(+1)(5) 0

(, 3] (1, 2] (5, ) 2 5 1 3

34

() + + ()

4.

1. ( + 1)3( 2)4( + 3)5 < 0 2. (1)2(2)

+1 0

3. (2 1)( + 1) 0 4. (1)4(2)3

(3)2(4) 0

( ) 1 22 + 3 + 2 0 22 3 2 0 ( + 2)( + 1) > 0 ( 2)( + 1) < 0 ( + 2)( + 1) > 0 ( 2)( 1) > 0 ( 1 ) ( + 2)4( + 1) > 0 ( 2)4( 1) < 0 ( ( + 2)4 = ( 2)4)

(3)2(21)

(+2)(+1) 0

1 3 2 12

+ + +

(, 2) (1, 12 ] {3}

(1)4(2)3

(3)2(4)> 0

2 4 1 3

+ + +

(, 1) (1, 2) (4, )

35

5. 1. 4 2 0 2. (1)(+2)

2 0

3. (3)2(12)

(2)(+1) 0 4. (1)

4(2)3

(3)2(4) > 0

( 2 + 1) (2 + 1)( 3)( + 1) > 0 2 + 1 2 + 1 ( 3)( + 1) > 0

6.

1. 352+5

0 2. 32+1

2 0

36

3. 2 + 4 > 0 4. 2 + 4 0

7. 1 2 + 12

1 [O-NET 51/4] 1. [2 1, 1] 2. [2 1, 2] 3. [3 22, 1] 4. [3 22, 2]

8. = { | (2 + 1)(4 3) > 0 } [O-NET 56/6] 1. (1.2, 0.2) 2. (0.9, 0.3) 3. (0.6, 1.2) 4. (0.4, 1.5) 5. (0.3, 1.3)

37

9. 2 + 4 = 0 [O-NET 50/26] 1. (5, 5) 2. (, 4) [3, ) 3. (, 0) [5, ) 4. (, 3) [4, )

10. 120 1,240 [O-NET 56/36]

11. 25 120 18 500

[O-NET 57/37]

38

|| |2| = 2 , |5| = 5 , |3| = 3

||

||2 = 2

|| = |||| |

| =||

||

| + | || + || | | || || | + | || + || 2 = ||

0 < 0

1. 1. < || 2. || = ||

3. ||

=

|| 4. ( ||)2 42

5. < || < || 6. || < || <

7. || < || 2 < 2 8. || ||

9. |2 3| = 2 3 10. < 2 | 2| = 2

11. || || 12. || > || || > ||

13. || = || 14. 2 = < 0

15. | | = | | 16. ||

{1, 1} 0

17. || 2

|| = { 0 < 0

|| ()

39

2. > 1 |1 | < 2

3. , [O-NET 49/1-17] 1. < 2 < 2 2. < < 0 < 2 3. || < || < 4. 2 < 2 <

4. [O-NET 54/5] 1. || < || 3 < 3 2. , = =

5. , ||3 > 0 [O-NET 54/6] 1. > 0 2. > 0

6. , [O-NET 57/1] 1. = = 2. || < 0 < 0 || < 0 3. > 0 > 0 + 2

40

7. 5 [O-NET 50/4] 1. 2 25 2. || 5 3. || 25 4. ( ||)2 25

8. { | = ( + 1||

)2

(|| 1

)

2 0}

[O-NET 51/21]

9. ( , ) | 1| + |6 3| < 17 > 2 + [O-NET 54/27]

41

1.

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

{3, 1, 1} #

|| = 3 + 4 = 3 + 4 = (3 + 4) 3 + 4 0

3 + 4 0 :

{1} #

|2 1| = 3 = = 3 0

#

2.

|3 2| 5 5 3 2 5 5 0

[1, 4] #

2 + 2 3 = 0 ( 1)( + 3) = 0 = 1, 3

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

2 = 4 = 2

= 3 4 4 = 4 = 1

3(2) + 4 = 2 0 3(1) + 4 = 1 0

8 2 2 4 1

| | = = = 0

| | < < < > 0

42

|5 2| < 1 ( 1) < 5 2 < 1 1 > 0

(, 4) (2, ) (1, ) = (2, 4) #

| + 1| 1 < < 1 > 0

#

3.

| + 2| + 4 + 2 + 4 + 2 ( + 4) + 4 0

(, 3] (, 4] = (, 3] #

|3 + 2| > 1 > < 1 < 0

R #

|13

| > 2 1

3> 2 1

3< 2 2 < 0

(, 5) (7, ) #

1 > 6 > 7

1 < 6 < 5

( 1) < 5 2 + 1 < 5 2 < 4

5 2 < 1 6 < 3 2 <

> 1

1 2 4

> 1

> 2

< 4

2 4

+ 2 4 2 6 3

4

4 3

< 4

< 3

< 5

5 7

> 7

| | > > < < 0

43

4.

|2 3| | 4|

(, 1] [ 32 , ) #

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

{ 13 , 12 , 3 } #

: /

1. / 1. | + 2| = 5 2. |2 1| = 1

|2 3|2 | 4|2 (2 3)2 ( 4)2 (2 3)2 ( 4)2 0

((2 3) ( 4))((2 3) + ( 4)) 0

(2 3 + 4)(2 3 + 4) 0 (4 + 6)(2 2) 0 (2 + 3)( 1) 0

1 32

+ +

|2 4 5|2 = |2 3 + 8|2 (2 4 5)2 = (2 3 + 8)2 (2 4 5)2 (2 3 + 8)2 = 0

((2 4 5) (2 3 + 8))((2 4 5) + (2 3 + 8)) = 0

(2 4 5 2 + 3 8)(2 4 5 + 2 3 + 8) = 0 ( 13)(22 7 + 3) = 0 ( 13)(2 1)( 3) = 0

= 13 , 1

2 , 3

| | = | | , | | > | | , | | < | | (||2 = 2) 2 2 = ( )( + )

| | = = = 0

| | < < < > 0

| | > > < < 0 | | = | | | | < | | | | > | |

||2 = 2

44

3. 2 + 4 = 4|| 4. |2 + 5| 3

5. |2 + 4| > 5 6. |2| > + 6

7. | + 3| < 2 8. |3 4| 2 1

9. | 3| 5 10. |2 1| 2

45

11. |2 + 1| | + 2| 12. |2 5 + 1| < |2 4 + 3|

13. |2 3 8| = 2 + 3 14. |1 3|1 3|| =

2. | 7| = 6 [O-NET 52/6] 1. 10 15 2. 14 3. 2 4. 3

3. 2|5 | = 1 [O-NET 53/5] 1. (10, 5) 2. (6, 4) 3. (4, 5) 4. (3, 6)

46

4. 3 2 = || [O-NET 51/24]

5. | 3| 4 [O-NET 56/33]

6. = { | | + 1| + 1 > 2 } [O-NET 57/10] 1. (4, 2] 2. (3, 1) 3. [1, 0) 4. [0, 2) 5. [2, 3)

7. = { | | 2| < 3 } = { | 2 3 4 > 0} [O-NET 57/11]

8. I = { I | |1|1|1|

2

3}

[O-NET 49/1-20]

47

1. 1 , 3 , 5 , 9 , 11 , 13 , 14 , 17 , 19 , 20 , 21 2. 1. 1 2. 3. 4 4. 5. 1 6. 7. 8. 3. < < 4. 1 5. 1, 2 6. 1 7. 1 8. -

1. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 2. 1. 2. 3. 4.

1. 1. + , 2. 3. + , 4. + , 5. + 6. + , 7. + , 8. 2. 2 , 4 , 5 3. 1. 8 2. 1

2 3. 1

2 4. 1

2

5. 0 6. 1 7. 1 8. 22

9. 22

10. +1

4. 1

1. 5 2. 22 + 3 2 3. 23 + 32 4 4. 3 5. 15 6. 8 7. 9

(())2 2 + 6 + (())2 2 () 1 () = + ( )

(())2 = 2 + 6 + ( + )2 = 2 + 6 + ( + )( + ) = 2 + 6 + 22 + + + 2 = 2 + 6 + 22 + 2 + 2 = 2 + 6 +

2 = 1 2 = 6 2 =

48

8. 10 () = (2 + 1) () () 1 () = +

9. 2

1. 1. ( + 4)( 3) 2. ( + 2)( 8) 3. (3 8)( + 3) 4. (4 3)( 4) 5. 3(2 + 3)( 2) 6. 2( 2)( 3) 7. 32( 2)(2 + 2 + 4) 8. (2 + 1)( 2)( + 2) 9. ( + 2)( 2)( + 4)( 4) 10. ( 1)(2 + + 1)( + 2)(2 2 + 4) 11. ( + 2)( 1)( 4) 12. ( + 22)( + 32) 2. 1. ( + 1 2)( + 1 + 2) 2. ( 2 3)( 2 + 3)

1. 1. 1 , 4 2. 34 ,

3

2 3. 2 4. 1, 1, 2

5. 152

6. 2 3 2. 1. 2, 5, 6 2. 2, 0, 9 3. 4. 2, 3

2 , 3

5. 1, 3, 3 6. 3. 1 4. 6, 6 5. 4 6. 2 7. 2 8. 2 9. 1

5 10. 36

11. 22 + 814 12. 120 13. 500 14. 30 15. 12

1. 3 , 4 , 9 2. 1. 8 15 2. 3 10 3. 12 36 4. 2 6 5. 3 18

3 2

() = (2 + 1)() 23 + 2 + + 3 = (2 + 1)( + ) 23 + 2 + + 3 = 3 + 2 + +

2 = = = 3 =

49

3. - 4. 2 5. 1 6. 1, 2

1. 1. (1, 10) 2. (, 2) 3. (1, 1] 4. 5. ( 1

2 , 4) 6. ( 1

4 , 2) 7. (, 1] 8. [2, )

9. [8, 1) [1, 8) 10. (, 5) [8, ) 2. 1. [1, 9) 2. (1, ) 3. (, 3] 4. (1, 1] 5. (, 2) (2, ) 6. (, ) 7. (, 2) (2, ) 8. [4, 2) (2, )

1. 1. (1, 2] 2. [5, 1] 3. [2, 2) 4. (1, 1) 2. 1. (2, 3) 2. (, 4) (3, ) 3. (, 2) (2, ) 4. (, 2) (1, )

3. 1. [ 12 , 2] 2. (, 1] [ 1

6 , ) 3. (, 5

2 ] [3, )

4. (, 1] [ 23 , 1] 5. (, 1) [ 5

3, ) 6. (, 1) [3, )

4. 1. (3, 1) 2. (, 1) {1} [2, ) 3. {1} [1, ) 4. (, 2] (4, ) 5. 1. [2, 2] 2. (, 2] [1, 2) 3. (, 2) (1, 1

2 ] {3}

4. (2, 3) (3, 4) 6. 1. [ 5

3 , ) 2. (, 1] (2, ) 3. R

4. 7. 3 8. 5 9. 4 10. 680 11. 89

1. 3 , 4 , 7 , 8 , 9 , 10 , 13 , 14 , 15 , 16 , 17 2. (1, 3) 3. 2 4. - 5. 2 6. 3 7. 3 8. 2 9. 8

1. 1. 3, 7 2. 3. 2, 2 4. [4, 1] 5. (, 1) (1, ) 6. (, 2) (6, ) 7. (3, ) 8. [1, 3] 9. (, 4] 10. (,)

50

11. (, 1] [1, ) 12. (2, 12) (4, )

13. 2 14. 1

4 ,

2

5 ,

1

5 ,

1

2

|1 3|1 3|| =

1 3|1 3| = 1 3|1 3| = 0 1 = 3(1 3) (1 ) = 3(1 3) 1 + = 3(1 3) (1 + ) = 3(1 3)

2. 3 3. 4 4. 3 1 5. 9 6. 5 7. 5 8. 6

081-8285490 John Quod

1 = 3|1 3| 1 + = 3|1 3|

1 0 1 + 0 1 = 3 9 8 = 2

= 1

4

1 + = 3 9 10 = 4

= 2

5

1 + = 3 9 10 = 2

= 1

5

1 = 3 9 8 = 4

= 1

2

1 0

1 + 0