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# Nέο βιβλίο άλγεβρας Α λυκείου 2011-2012

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- . .. 2 . .. 2 . . . . . . , . . , . . , . . : 1991 : 1992, 1993, 1994, 1995, 1996, 1997, 1998 . . . / : / / : / : : .(2010) , . , . , . , . . . -: . (2010) . , . . -. (2010), . , . , . , . . . : 1 . . , .2, . 3 , 1 2 . , , 1 2 .412 , , 1 2 . 5 , - (pattern) . 6 . - . 7 , .- .. 1 92 13 1: 1.1 -201.2 29 2: 2.1 432.2 542.3 612.4 69 3: 3.1 1 793.2 863.3 2 88 4: 4.1 1 1014.2 2 1064.3 & 115 5: 5.1 1215.2 1255.3 1325.4 - 141 6: 6.1 1456.2 1526.3 (x) = x + 1596.4 - 1686.5 -- 175 7: 7.1 : (x) = x2 1887.2 : (x) = 1947.3 : (x) = x2+x+ 199 207- 213x .1 , , , , . - . . : , . : ,2 2 . 2 2 : 2 2a a . : PQ,,P Q ,PQ P Q . P Q P,Q.P ,Q (1). (1),,. . , , P Q -P., P Q , P Q -., . 10 10 :

2 2 = =(1) = + = + (2), , . : 9 , . 2 2 = = , ( )223 3 = , 3 3 = . 9 , , . , , : + = + = : = + = + . P Q ,,P, Q Q, P, P Q , , P Q P Q . P Q P Q. : , . , 0 =0 = . , 0 0 0 = = = - 11 11 P Q , P Q . P Q PQ .

2 21 0 x x x , 2x x 21 x , , : 2 20 1 0 x x x . : 91 x , 90 x 1 x -. : -, -. 0 z0 z, 0 0 z z 0 z P Q,PQ . P Q P Q . , ( 1) 0 x x( 1)( 1) 0 x x x , - 1 x. 12 12 I. ,- . . 1. 29 3 = = 2. 21 = = 3. 21 = = 4. 22 4 = = 5. 22 4 > > 6. 22 4 < < 7. 24 2 < < 8. 24 2 > > 9. 2 3 6 < < < II. . 1( ) 2 0 x x = 0 2 x x = =2( ) 2 0 x x = 2 x =3 24 x = 2 2 x x = =4 24 0 x x = < 0 x =5( ) ( ) 2 0 1 0 x x x x = = 0 2 x x = =6 24 0 x x = > 2 x = - 13 13 .2 ,.. ,,,,. ,.. ,- , .-,..-, .,-,,- . Cantor: , , . , , .,,. . -.,, -. 1000000, . , , . : 9` ,9] ,9_ 9\ . 14 14 e e x , xe x,x xe x . 35e`,35e_, 2 e], 2 e_, 2 e\. : ) , ,. .., 2, 4 6, : { } 2,4,6 = ,- , -.1 100 { } 1,2,3,... , 100 = , 1v, , - :1 1 1= 1,, , ,... 2 3 4 ` ) - .)-, , :{ }0 x x e > \ xe\, 0 x > . { } x x e] - 15 15 ,, , :^ ` x x x:, x .- . :^ ` 1,2^ `= ( 1)( 2) 0x x x \( 1)( 2) 0 x x12, . - . , . : , - . =. ^ ` = 1, 2, 3, ... , 15 ^ ` = 1, 2, 3, ... , 100- . ., . . : i) , . ii) , . iii) , =. 16 16 ^ `2 1 x x \ . , 21 x .,, { }.: . . Venn Venn.x, .,, , `] _ - =\.-, - . x , . ^ ` 1, 2, 3,...,10 : ^ ` 1, 2, 3, 4 ^ ` 3, 4,5, 6. x^ ` 1, 2, 3, 4,5, 6 , ,- . - 17 17 : ,- - . : { } x x x= e e e - { } 3, 4 . : , - - , : { } x x x = e e e , - = C, . -{ } 5, 6, 7,8, 9,10 , . : . : { } x x = e e18 18 I.1. - . 2. - ; 3. Venn - ` ,] ,_ \ . 3, 5 0 10135 2, 3205 1005 e`e] e_ e II. . 1. { }= 16 x x e` { }= 24 x x e` ,: ) =............................ ) =................ 2. { }= x x e { }= x x e . : ) =....... ) =...... )=......

)B=......III.. 1. . : ) _ ) _ ) _ ) _2. . : ) _) _ ) _ ) _IV. . 1. ,C _ .:) = C ) =)() = ..2. _ .) = ) = . 1 . - Pascal Fermat 17 . - , - , , , 16 17 .. ' - , , . . 18 Bernoulli, Moivre, Laplace Gauss. Laplace . Laplace - , . , -Gauss. - , -20 1. . , 19 ,, . ,(Chebyshev,Markov,VonMises,Kolmogorov .., . .- , ,,,, , . . - . -, .1.1- , 100 ,760 mm Hg, . , , t. - (deterministic) . ,(-).-(randomexperiment).,- , 1.1- 21 . :1. .2. .3. .4. .5. .6. .7.,5.., -.8. 1.9. . . - (sample space) . 1,2,..., , : = {1, 2,...,}. , , , = {, }. , 1, 2, 3, 4, 5, 6. , ={1,2,3,4,5,6}. - (event) . , = {2,4,6}, B = {1,3,5} = {6} . 22 1. , 6.- . . , , . , - , . - . , , ={2,4,6},- 2 4 6. -,, . . . .(). , = {1,2,3,4,5,6} = {2,4,6} () = 3, () = 6 (} = 0. , . -, - , . , , : , , .1.1- 23 , -, , . ', -, . ' - ._,--, . _ = '. . - , - . - ' ( ) ( )' - ( ') 24 1. , = {1,2,3,4} = {2,4,6}. 1, , , - , ' , ', , ( )', ( - ), .-- , ={2,4,6}={1,3,5}. - , - . . : , = . - .1 .i) . ii) :1: 2: 2 3: 2 4: 5: iii) '3, 5 2, 5 4.i) , :1.1- 251 2 3 , - = {, , , , , , }.ii) :1={, , , }2 = {, , }3 = {, , , } ( 3 = 1)4 ={, }5 = {, , , }.iii) '3 3, 2. , '3 ={, , , }. 52 52, , . -, 5 2={, }. 5 4 . , 5 4 = {, , , , }.2 . Venn - : i) . ii) . 26 1.i) , - , . - - . , ( - ) ( - ) ( ') (' ).ii) , . -- , ( )'.'1. , , . :,- . . ( ).i) ; ii) ; iii) ;2., -. ( -).1.1- 273. . . , . , :i) ii) : .4.. ,. : , i) ii) : iii) : iv) ) : , - ( ) .5. , , , . 0 1, , , , , , . . :i) .ii) : , iii) : , iv) : .6. :i) . 3 . ii) . , iii). 30 30 , iv) . .7. - - . .'1. - . , - .2. . :: 1 - 2 .: - : 5 , , , ( ) .28 1. , , . , , - . ' , - . (). ; - ; . -, . = {1, 2,...,} {1}, {2 },..., {) 1,2,..., -, :1. 0 i 1, i= 1,2,..., ( 0 i ) 2. : . - 10, 20, 30,...,200 1 .1.230 1. 10 7 0,70020 13 0,65030 16 0,53340 23 0,57550 26 0,52060 31 0,51770 33 0,47180 39 0,48890 43 0,478100 46 0,460110 53 0,482120 61 0,508130 66 0,508140 70 0,500150 73 0,486160 81 0,506170 87 0,512180 89 0,494190 93 0,489200 99 0,495{}, {} . (), . , , - . ..- . 1 0,5 , 0,5. - , , -,1.2 31 {}, {} . - {1},{2},{3},{4},{5} {6} . - , , . . , . 2 4 6 , ., . ' :, , Laplace 1812. : 1. 2. 3. 0 () 1, - .32 1. , . , -. , . , . = {1,2,...,} . {i} - , (i), : 0 (i) 1 (1) + (2) + ... + () = 1. (i) {i}. () = {1, 2,...,} (1) + (2) + ... + (), () = 0. (i) = , i = 1,2,..., , . = {1, 2,...,} , (i) =, i = 1,2,..., . ,. . .1.2 331. :( ) = () + () () = () = , + , . , ( ) = + = () + ().: (simply additive law) . , - , :( ) = () + () + ().2. ' :(') = 1 - () ' = , ' , , :( ') = () + (')() = () + (')1 = () + (').(') = 1 - ().3. :( ) = () + () - ( )34 1. ( ) = () + () - ( ), (1)()+() . (1) () : ( ) = () + () - ( ). (additive law). , () () :

5. ( - ) = () - ( ).- ( - ) ( ) = , : () = ( - ) + ( ). (A - B) = (A) - ( B).1.2 351 . ., , . 2 1 1 2 3 4 5 61 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)36 , () = 36 . : , = {(1,2), (2,1), (2,3), (3,2), (3,4), (4,3), (4,5), (5,4), (5,6)(6,5)} () = 10 ,, 0,28 , , 28%.2A () = 0,5, () = 0,4 ( ) = 0,2. :i) . ii) .i) ( )'. 36 1.(( )') = 1 - ( ) = 1 - (() + () - ( )) = 1 - (0,5 + 0,4 - 0,2) = 1 - 0,7 = 0,3.ii) ( - ) ( - ). -- , :(( - ) ( - )) = ( - ) + ( - ) = () - ( B) + () - ( ) = () + () - 2( ) = 0,5 + 0,4 - 2 . 0,2 = 0,5.3(A)=0,6 P(B) = 0,5.i) , ii) 0,1 ( B) 0,5 .i) , - :( B) = () + () = 0,6 + 0,5 = 1,1,,{)>1,. , .ii) , ( ) () ( ) (), ( ) 0,5(1)1.2 37 :( B) = () + () - ( ) ( ) = 0,6 + 0,5 - ( B). ( ) 1.: 0,6 + 0,5 - ( ) 10,6 + 0,5 - 1 ( )0,1 ( ). (2) (1) (2) :0,1 (A B) 0,5.'1. 52 . - i) ii) .2. .3. : 10 , 15 , 5 10 . . :i) ii) iii) .4.30, . :4 11 9 3 2 10 1 2 3 4 5 , - .38 1.5.={/1020},={/ 3} = { / 4}. , i) ii) .6. 30%, 20% 40%. i) ii) .7.

. ( ).8. ,. ().9. - () = (), ( ) = 0,6 ( ) = 0,2. ().10. . ( ).11. ( ) () + ().12. D V. 25% D,55%V15% . ;13. 10% , 6% - 2% . ) ;) ;1.2 3914. 80% , 30% 20%. . .'1. () = , () = ( ) = , :i) ii) iii) .2. 15% , 40%10% .. .3. () (').4. 0 < () < 1, 5. () = 0,6 () = 0,7 , 0,3 ( ) 0,6.6. - () - (') ( ).40 1.1. ,,, , . ; ;2.5. , - .3. , , , - . - , .() ;() (i) 3 6(ii) 36(iii) 63(iv) 3 63. ( )( 4 - 6 - . ).4. 0,4, -;() 0,2 () 0,8 () 0,6 () 1,4.5. () = 12, () = 12,( B) =, ( ); () 1()()()() .11.2 416. Venn ;() ) '() - () - . ( 7 - 9 . , , , ).7. .8. .9. , - ' ' . 10. , () + () = 1,3;- .11.- Venn:i)iii)ii)iv) 1.1 ( ) , . : 9 ( ) , - , , , 0 z . 9 - , , . ,142,85 ,91, 258 ,605, 4511 ,2252, 25100 2302,3299 . , 2 , 3, , S ., , , ,0 z (,, ). . 12 2.1 ( - )442. 201. , , . - , . + = + =( ) ( ) + + = + + ( ) ( ) = 0 + = 1 =/ ( ) 0 + =11, 0 = = ( ) + = +,, ,- . 0 , -.1-, . ,,-- . , 3 2 2 3 2 5 2 3 3 2 2 5 2 2 5 + + + + = + + + + = . ,- - . , ( ) ( ) ( ) ( )2 1 5 1 2 53 6 4 3 6 4 245 3 2 3 5 2| || | | | | || || | = = | ||| | |\ .\ . \ . \ .\ .\ . 2.1 451.1 21 (-). - : ( )1 : ( 0) = + = = =: o | , , , 0 =, - . , - , 0 = . - - : 1. ( ) = = + = +, . 2. ( ) = = =, . 3. = + = +, . 4. 0, : == = , . 5. 0 0 0 = = = 462. 221. , , . : 0 0 0 = = = + = + = - = , . ,, . 1 = . : ( )( ) ( )22111 11 1 1 11 10 = = = = + = + == 1 = ,10. , ( )( ) ( ) 1 1 1 1 + = ( ) 1 ,, . -.,, : , = "

1 > 1, = 1. = 0 = , : 01 =

1= 2.1 471.1 23 , = , = ,,- ( )222 2 = , 2 2 = . , . + = =( ) = | |= |\ . ( ) = .,- . : ( )22 22 + = + + ( )22 22 = + ( ) ( )2 2 = + ( )33 2 2 33 3 + = + + + ( )33 2 2 33 3 = + ( ) ( )3 3 2 2 + = + + ( ) ( )3 3 2 2 = + +( )22 2 22 2 2 + + = + + + + +482. 241. 1) , 0 + + = 3 3 33 + + = , :3 3 3 0, 3 + + = + + = . 0 + + = , ( ) = + , : ( )( )( )( )33 3 3 3 333 33 2 2 3 3 32 23 33 333 , . + + = + ( + + = + + += + += = += + = 0 + + = 3 3 33 + + = . . 1) ., ( )22 22 + = + + , , R e , : ( ) ( )( )( ) ( )22 22 22 + = + += + + += + + += + + | || || || | 2) , .- .,, , , x y : 2.1 491.1 25 ( )( ) ( ) ( )2 22 2 2 2+ x y x y y x + + = + : ( )( ) ( ) ( )2 22 2 2 22 2 2 2 2 2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2+2 2, . x y x y y x x y x y x xy y y xy x x y x y x y x y+ + = + + + + = + + + + + + + = + + + 3) , , , . 0 > 2 > , 12= 214 = , 2 < . 2) :, , 2 , : . , 2 1 = + , , : ( )( )222222 14 4 12 2 2 12 1 ( 2 2 ). = += + += + += + = + 22 1, = + e', 2 . 2.,- . .- -.- .502. 261. - . 1 : ) 0 :.i == = = ) 0 :.ii == = = = ) 0 :1 1iii =+ += + = + =( ) ) 0, , : , ( )., , iv + = = == = + = ++ += = =+ + 22 ., ,2 2 .( )( )( )( ) ( )) 0) 0) 0) 0 i ii iii iv = = == = =+ += = =+= = = + =+2.1 511.1 27 2 . 2= ,, ( ). : ( )22222 2222 | |= |\ .== 2 ,(.25), =2. : 2 , . , , (). 1- 1. 2 . = 2 -xxM-22 . ( )2 2222 22 222 24 22 ====522. 281. 1. ( ) ( )332 42 3 31xx y xyy| | (= : | ( \ .. i) 9 9 x y = . ii) 12010 2010= = x y . 2. ( ) ( )22 11 3 7 : xy x y ( ( = 0, 4 2, 5 x y = = . 3. : i) 2 21001 999 ii)99 101 iii) ( ) ( )2 27, 23 4, 2311, 46. 4.i) ( ) ( )2 24 + = . ii) : 2 2999 1000 999 10001000 999 1000 999| | | |+ ||\ . \ .. 5.i) ( )( )21 1 1 + = . ii) : ( )21, 3265 0, 3265 2, 3265 . 6.- ( ) . 7., 1 22 2 2 + ++ + - 7. 2.1 531.1 29 1. : i) 3 222 +ii) ( )222 21 + . 2. i) ( )23 2311 + | | |\ . +ii) 2 231 11 1 + + +

3. i) ( ) ( )221 1x y x y + +ii) 1 12 2x y x yx y x y + . 4. 3 3 22 2: 1x y xyx y x y| | | | + = || \ . \ .. 5.,. : i) = = . ii)- - - = = . 6.,4 L = 2E = , . 7. : i) , . +ii), 0, , . = 1.2

, , , : , > , . - < : - . - . : 0 > > > ,- . > = ,> : . -, : - ( ) 00 0 > > + >( ) 00 0 < < + < - , 0 0, 0 0 > > < < 2.2 2.2 551.2 31 - ( )20, 0 > e=

: 2 22 20 0 00 0 0+ = = =+ > = = 0 > > , : 1.( ) > > > 2. - > + > +-0 > , : > > -0 < , : > < 3. -( ) > > + > +- , , , : ( ) > > > 3. . :9( )1 1 2 2 1 2 1 2 ...... ... > > > + + + > + + +9, , , : ( )1 1 2 2 1 2 1 2 ...... ... > > > > (*) . 4. , : > >562. 32 1. x ! . , (*), 1 2... 0 ! 1 2... 0 ! , : ! . x . ! d . : 9 , (), 9 , ( ). , ! . : , : x . , , - , . x . z . : 9 ! , (4), ! (), 9 , (4), (). , . 1 3, -,.- . , 10 6 7 2,10 7 6 2 ! !. 2o, 3, ,,, . . , 2.2 571.2 33 24 1024 10 6 2, 6 2! !. x x d d - [ , ] .[ , ] - - , . - . , . : 9 [ , ) x d x 9( , ] - x d x . , ,9 x d x [ , ) f , 9 x d x ( , ] f .( , ) f ( , ) f . ff, , . : 582. 34 1. x s s [ , ] x s < [ , ) x < s ( , ] x < < ( , ) x >[ , ) + x >( , ) + x s( , ] x ii) , 2 22 + >iii)0 > , 12 + > i), 0 > . : 1 1 1 1 < < < > . ii): ( )22 2 2 22 2 0 0 + > + > > , iii): ( )22 212 1 2 1 2 0 1 0 + > + > + > > , . 2.2 59 1.2 35 2 1 32 4x < > > > + > +> 1. . :i)1 + ii)1 >, +> , 1 + > + . 3., , ( )1 14| |+ + > |\ . . 4. :i) 2 20 + + > ii) 2 20 + > 2.3 1.3

. ,, . :x 13 132 2, , 2 25 5 : , 0 ! .: . x 13 132 2, , 2 25 5 : , 0 . : . x0 0. , . : , 0, 0 t

622. 38 1. : -0 = >- > > - 22 = 0 > , :-x x x = = = -x x x = = = ,95 5 5 x x x = = = 92 3 2 3 3 2 = = = 42 3 = = ,- : 1. = 2. =3. + s +,, . 1. = , : ( )22 = = 2 2 2 = ( )22 2 = , . 2. . 2.3 631.3 39 3. + s + - , :

( )22 + s + + s +( )2 2 22 + s + + 2 2 2 22 2 + + s + + s , . = 0 > , . - = . -: 1 2 1 2... ... = 1 2... = = = = , : =- + s + . : 1 2 1 2... ... + + + s + + + -,2 3,- . 2 3.- ( ) ( ) ( ) 5 2 3 3 2 = = = . , . 642. 40 1. ,- , d . : , d , , d d . , [ , ] . x [ , ] . 0x AB,

0 0( ) ( ) , , MA MB d x d x 0 0x x 0 0x x ,0 x 02x 02 x

2 [ , ] , 2

[ , ] . ,, ,[ , ) ( , ] , [ , ] . xx 3 2 x . 2.3 651.3 41 : ( ) 3 2 , 3 2 x d x < 3 2 3 2 x x < > +( ) ( ) , 3 2 3 2, x e + + . : 662. 42 1. 0 0, : x e > ( ) ( )0 0 00 0, ,x x x x x x x x x > e + + < > + x 0x x > ( ) x x x ( )0 x . 00 x = , :x > x x < > : 2 x > 2 2 x x < > . 1. . i)3 ii)4 iii)3 4 + iv)2 3 3 2 . 2.3 4 x < < , 3 4 x x + 3. 3 4 x x , : i)3 x . 2.3 671.3 43 4. = , . 5.0 x = 0 y = , x yx y= +6. 2,37dm. - 0,005dm. D -, : i) ii) D.7. . 4 2 x s ( , 4) 2 d x s| |2, 63 4 x + < 4 2 x > 3 4 x + > ( , 5) 1 d x < ( , 1) 2 d x > ( , 5) 1 d x > ( , 1) 2 d x s ( ) 2, 2 | | 5, 1 ( | | ) , 2 2, + ( ) ( ) , 5 1, + 682. 44 1. 1. d. 2. ! , : i) 2

ii) 2

3. x y : i) 0 x y ;ii) 0 x y! ; 4.0 . i) 1, . ii) - 1 . 5.2 0,1 x4 0, 2 y , : 2.4 1.4 - . : H , , . : 0 t , 2x . : x 2 x x

- 64 . x , 3x -: 364 x. x , ,64. ,, . 702. 461. 4, 34 64.464 364 . 364 =4. ., . - (1) , , . 1 2 . : 0 t , x . 410 10000, 410000 10. 410 10000 . , 410000 10 ,, , 410000 410000 x. - , - : x0 t , : x0 d , : . (1) . 2.4 711.4 47 : 6 62 2 = , ( )662 2 2 = = . , : , 0 > , : 1. = 2.( 0) = =3. =4. = 1.:( ) ( )( ) ( ), . = = = = 2. 1. 3.: ( )( )( )( ), . = = ( = ( = 4.: ( ) = = = 1.-. , 1 2, , ... , : 1 2 1 2... ... = 722. 481. 1 2... 0 = = = = > , : ( ) = , , 1, , 0 > = . a , 0 > ,- , -. , . , , 253 ; ( )qp pq a = , 52 2525 53 3 3 | |= = |\ .. 253 5 23 x = . 25 253 3 = . : 0 a > , , : a =, , , 0 0= . : 23 2 338 8 64 4 = = = 43 4334 43 41 1 127 2727 327= = = = . . .- :1 1 1 1 77 12 3 43 4 3 4 12 + = = = = . 2.4 731.4 49 1 a , : a :

, . 2,-: i) 153`ii) 105 1 iii) 67 5 . ii) 215 15 3 15 3 15 35 333 3 33

. iii)

2210 5 1 10 5 1 10 5 1 5 5 1105 1 25 15 1 5 15 1

. iv)

2 26 7 5 6 7 5 6 7 563 7 57 57 57 5 7 57 5

. 3 : 3 610 5 40 10 . : 1 1 1 1 113 3 63 6 3 2 621 3 1 1 1 1 1 1 1 13 6 6 3 6 2 2 2 2 21 1 112 3 610 5 40 10 5 40 2 5 5 2 52 5 5 2 5 2 2 5 5 52 5 2 5 10 742. 501. 1. :i)100 , 31000 , 410000 , 5100000 . ii)4 , 38 , 416 , 532 . iii)0, 01 , 30, 001 , 40, 0001 , 50, 00001 . 2. i) 24 ii) 220iii) 21 xiv) 24x

3. : 2 22 5 3 5 1 . 4. : 5 3 5 3 8 x x x x. 5. : i) 8 18 50 72 32 14 . ii) 28 7 32 63 32 31 . 6. : i)2 2 2 2 2 2 ii) 3 3 32 3 5 3 5 2 . 7. : i) 3 32 2 2 ii) 5 3 32 2 2 2. 8. : i) 4 3 3 123 3 3 3 ii) 9 6 18 8 5 132 2 2 2 iii) 6 3 4 35 5 5 25 5 . 9. : i) 25 121075

ii) 216 751850

. 2.4 751.4 51 10.-:i) 45 3 ii) 87 5 iii) 7 67 6+

11. i) 162 981650 32+=ii) 12 2011 69 339 27+=+, . 1.i) 3 3 2 25 63 2= +

ii), 0 > ( ) = + +. 2.i) ( )23 2 7 + ( )23 2 7 . ii) : 37 12 7 37 12 7 6 + = . 3.i) 22 33 2| |+ | |\ . . ii) , 21| |+ |\ . . 4. i) 3 545 3 5 3+ = +ii) ( ) ( )2 21 18 32 3 2 3 = +. 5. = = .i) . ii) : + < + . iii) , + s + . ; 762. 2 521. 1 I., , , . .1.( ) = = + = + . 2. 2 = , = . 3. 2 2 2( ) + = + . 4. + 5. . 6. , > < > . 7. 2 > , > . 8.1> , > . 9. > > , 0 > . 10. 1> , 1 > . 11. 0 < < , 2 2 > . 12. 23 > > , 6 > . 13. 23 < < , 6 > . 14. 2 24 20 25 0 + > . 15.( ) ( )2 21 1 0 + + > . 16.( ) ( )2221 1 0 a + + > . 17. ( ) ( )2 20 0 + + = = = . 18. 0 > , + = + . 19. 2 = , = . 20. 2 = . 2.4 771.4 53 21.0 > , ( )2 = . 22. 0 > , = . 23. 0 > , 2 = . 24. 2 2 + = + . 25.0 > , 6 3 = . 26. 4 2 = . 27. 25 55 25 > . 28. 22 1111 22 > . II. . 1.2 5 x < , v . - 416 x = . 416 2 = . 416 2 = , ( ) ( )4 44 416 16 16 = = . 416 x = , 416 2 = 416 2 = . : vx = ,0 > , v v . - 38 x = :( )33 3 3 38 8 8 8 8 2 x x x x x = = = = = = . , 38 2 = : vx = ,0 < , v a . - 44 x = .x 40 x > , .: vx = ,0 < , . 3.2 x = 872.2 x=63 , v vx -= e` , x = , : -, v vx = , x =- , v vx = , 1x = 2x = . 48 0 x x + = ( )4 3338 0 8 00 80 8 2x x x xx xx x+ = + = = = = = = 1. i) 3125 0 x = ii) 5243 0 x = iii) 71 0 x = .2. i) 3125 0 x + = ii) 5243 0 x + = iii) 71 0 x + = . 3. i) 264 0 x = ii) 481 0 x = iii) 664 0 x =4. i) 5 28 0 x x = ii) 40 x x + = iii) 516 0 x x + = . 5. 381m x, x 3x. .6. i)( )31 64 x + = ii) 31 125 0 x + = iii)( ) ( )41 27 1 0 x x = . 3.3 2 2.3 2 20, 0 x x + + = =,- :

20, 0 x x + + = = (1) . , 2012S v t t = + , S -t,v0.- t, :20102t v t S + = , . .: 2 222222 22220 0 [o0 ]2222 4 442 4 x x x x x x x x x x x + + = + + = = + = + = + + = +| | + = |\ . 2 4 = , : 222 4x | |+ = |\ . (2) : - 0 > , : 2 2 2 2 x x + = + = 3.3 2 892.3 2 65 2 2 x x + = =(2), (1), :1 2 2 2 x x + = = 1,22x = . - 0 = , (2) :20 02 2 2=0 =02 22 2 x x x x x x x | | | | | |+ = + + = |||\ . \ . \ . + + = = 2 . - 0 < ,(2),(1), , . 2 4 = , 20, 0 x x + + = = ,- . : 2 4 = 20, 0 x x + + = = 0 > 1,22x = 0 = 2x= 0 < . 903. 66 2. 9 22 3 1 0 x x + = ( )2 3 4 2 1 1 0 = = > , 13 112 2x+= =23 1 12 2 2x= =. 9 24 4 0 x x + = ( )2 4 4 1 4 0 = = ,- ( ) 422 1x = =. : 2 24 4 0 ( 2) 0 2 ( ). x x x x + = = =9 22 3 4 0 x x + =( )2 3 4 2 4 23 0 = = < , . 20, 0 x x + + = = 1 2, x x , : 1 2 22 2 2 x x + + = + = = ( )( ) ( )222 21 2 2 2 24 42 2 4 4 4 x x + = = = = =S 1 2x x + P 1 2x x , : S= P= Vieta. 20 x x + + = ,Vieta,- : ( )2 221 2 1 220 000 x x x x x x x x x xx Sx P+ + = + + = + + = + = 20 x x + + = , .32 23 2 0 x x + =3.3 2 912.3 2 67 1 ( )22 3 1 4 3 0 x x + + = vo ( ) ( ) ( )2 2 2 4 3 1 4 4 3 4 3 2 3 1 4 3 1 (= + = + = ( ( ) ( ) ( )21,22 322 3 1 4 3 1 2 3 2 2 3 12 2x+ + = = = 2, 300m., , i) ;ii) 50 m/sec; g10 m/sec2. i)S t sec : 212S gt = 2300 10secmS m g =, : 2 2 2110 300 5 300 60 60 7, 752t t t t t = = = = , - . 7, 75sec t. ii) 0v ,t sec 201t2S v t = + . 050secmv =0 t > : 2 22110 50 300 5 50 300 0210 60 010 100 4 60 10 18, 434, 22sec.2 2t t t tt tt+ = + = + = + + + = = , 4, 22sec . 923. 68 2. , , , . 2 ,, 2,,- , 2 . 1: 22 3 0 x x. 22x x, : 22 3 0 x x x , 22 3 0 . 1 23 1 . ,0 xt .3 x, 3 3 x x. 2: : 223 1 2 2 11x x xx x x x

. 1 0 xz 20 x xz ,0 x z 1 x z . x: 2 22223 1 2 2 1 3 1 2 2 11 1 11 1 13 1 1 2 2 14 3 0x x x x x xx x x x x xx x x x x x x xx x x x xx x

3.3 2 932.3 2 69 11 x 23 x.,-, 23 x. 3: :

4 22 7 4 0 x x (1) 2x y :

22 7 4 0 y y (2) 22 7 4 0 y y 14 y 212y 20 y xt , 14 y. ,(1) 24 x, 12 x 22 x. :4 20, 0 x x z . 1. : i) 22 5 3 0 x x ii) 26 9 0 x xiii) 23 4 2 0 x x. 2. : i) 21, 69 0 x ii) 20,5 0 x x iii) 23 27 0 x . 3. : i) 22 2 0, 0 x x zii) 20, 0 x x z . 4.\ 22 0, 0 x x z . 943. 70 2. 5. = ,\ ( ) ( )2 2 22 2 0 x x + + + + = . = . 6. 2 i)2. 3 ii)1 12 iii)5 2 6 5 2 6 + . 7. , , i) 2 15 .ii) 9 10. 8. i) ( )25 3 15 0 x x + + =ii) ( )22 1 2 0 x x + = . 9. 2 2 22 x ax + = , , e\ . 10.68cm 26cm. 11. i) 27 12 0 x x + =ii) 22 35 0 x x + = iii) 28 12 0 x x + = . 12. ( )21 4 1 5 0 x x + = . 13. 21 15 6 0 x xx x| | | |+ + + = ||\ . \ .. 14. i) 1 131 6x xx x++ =+ii) 222 2 3 202 2x xx x x x + + = . 15. i) 4 26 40 0 x x + = ii) 4 24 11 3 0 x x + = iii) 4 22 7 3 0 x x + + = . 3.3 2 952.3 2 71 1. 2 2 3 42 1 0, 0 x x z . i) 2 4. ii) 21

21 a

. 2. 25 2 6 3 2 0 x x. i) 2 1 2ii) 32 2. 3.\ 2 22 9 3 4 0 x x . 4. 20 x x ,0 z , 1 20 x x . 5. : i) 1 1, 0 x x z ii), , 0x x z . 6. 22 8 0 x x i) \ . ii) , . 7. . 8. . 4m 3m . d,- . 72 2. 9. . - 12 -. , 8 . . 10. 4 210 0 x x 1. . 2 I. , , . . 1. ( 1) ( 1) x x . 2. H

0 1 2 x x .3. H 0 1 2 x x .4. H 0 1 2 x x .5. 2 x x . 6. 2 x x . 7. 20 x x , . 8. 2, x - . 9. 22 0 x x . 963. 3 3.3 2 972.3 2 73 10. 2 24 4 0 x x + = ,0 = , . 11. 2 22 2 0 x x + = ,0 = ,- . 12. 2 22 3 0 x x + + = . 13. 211 0 x x| | + + = |\ ., 0, 1 = . 14. 23 201x xx += 23 2 0 x x + = . 15. 222 3 151x xx+ += 2 2(2 3 1) 5( 1) x x x + + = . 16.xy-10 S = 16 P = . 17.xy-10 S = 25 P = . 18.xy-2 S = 2 P = . II. : 1. (2 1)( 2) (3 2 )( 2) x x x x + = + : (2 1)( 2) (3 2 )( 2) 2 1 3 2 4 4 1 x x x x x x x x + = + = = = . 2 x = . 2. 2 1 2 x x = : 2 1 2 2 1 2 2 1 2 1 1 x x x x x x x x = = = = = . x . 983. 74 2. 2 ., , . , . 2 2 2, , x px q x px q x px q. 20 x x 1500., CardanoGirard. Descartes Wessel, Argand Gauss - . 21,242 x r

2 20, 0 x x z . 2 . , Sridhara (1025 .. ). :220 x x x x

4 - 2 , . 3.3 2 992.3 2 75 ( )2 22 2 2 2222 24 4 44 4 42 42 4 , 4 0. x x x x x x + = + + = + = + = > : 242 x =: . . Vieta2 20, 0 x x + + = = , x ,-

2x y= (1) : 202 2 y y | | | | + + = ||\ . \ .- : 24y 04 ++ = . 242 y = 24 0 >- y (1) :242 2 2 x y = = 242 x = . :Vieta,- ., 3 20 x x x + + + = , 3x y= - .1003. 76 2. HarriotThomasHarriot(1560-1621)-,2,-ArtisAnalyticalPraxis.- : 1x 2x 20, 0 x x z (1). 1x 2x . 1 20 x x x x ,, 21 2 1 20 x x x x x x (2) (1) 0 z , : 20 x x (3) (2) (3) , . : 1 2x x1 2x x (4) 2 21 2 1 2 1 24 x x x x x x (4) 21 24 x x

r ,[ 24 0 t ] (5) (4) (5) :2142 x

2242 x

: (5). 1x 2x . 44.1 1

3.1 1 :x + > 0 x + < 0 0 x + > 0 x + < , . : 0 x x x + > + > > : -0 > , :

x x x> >> -0 < , :

x x x> , 9 xe, 0 > , 9 , 0 s . : - 4 8 x > : 84 8 24x x x > > > . 3 1024. 78 3. (2, ) x e + - 4 8 x > : 84 8 24x x x > < < . ( , 2) x e . -0 2 x > xe,0 2 x > . i) : ( ) ( ) x x x 2 4 6 12 + + < ( )xx x52 2 16 3+ + > +ii) . i) : ( ) ( ) 2 4 6 12 2 8 6 12 x x x x x x + + < + < 2 12 6 8 + < + x x x 2 10 < x

2 102 2 + + + > +12 10 12 12 + + > + x x x2 > x . 2 x >4.1 1 1033.1 1 79 ii)5 x < 2 x > ,-x 2 5 x s < , | ) 2, 5 x e . -(),- 2 5 x s < - , -. . 1 :2 3 < x . 2 3 < x , 0 0 0x x x x x < < < + : 2 3 2 3 2 31 5x xx < < < + < < x x < < < : 2 3 3 2 3 x x < < . 1044. 80 3. x x x > < > : 2 1 5 2 1 52 1 5 x x x > < >2 42 6 x x < >2 3 x x < > ( ) ( ) , 2 3, xe + . 1. : i) 1 2 32 4 6 ++ x xx iii) 2 1 2 22 5 10 5 + < x x x. 2. x :3 1 5 < + x x 122 2 s +xx . 3. : 112 2 > +xx 113 3 s xx . 4. x e] : 128 >xx x 14 02+ + x ii)1 4 x > iii)2 1 5 x + > . 7. : i)2 6 2 6 x x = ii)3 1 1 3 . x x = 4.1 1 1053.1 1 81 8. : ii) 1 4 152 3 3x x ii) 1 2 12 3 3x x x ! .9. 26 9 5 x x d . 10. 0x x ,- 7, 3. 11. CD FD 9325F C . -41 FD50 FD. CD. 1. x : i)3 4 1 6 x dd ii)4 2 3 2 xdd.2. x : i)2 4 x d dii)2 5 4 x dd . 3.3 5 . i) ; ii)5 3 x xd . iii) . 4.1 7 . i) ; ii) 1 7 6 x x . iii),- 1 x 7 x. 4.2 2 3.2 2 2, 0 + + = x x 2 , , . 20 + + = x x -. 20, + + = x x 12 +=x 22 =x . 2, 0 + + = x x : 2 2| |+ + = + + |\ . x x x x 2 2222 2 2 (| | | |= + + + ( ||\ . \ . ( x x 22242 4 (| |= + + ( |\ . ( x . : x x x 2222 4 (| |+ + = + ( |\ . ( (1). : - 0 > . ( )2 = , : 2222 2x x x (| || | (+ + = + | | | ( \ .\ .

2 2 2 2 x x | || |= + + + | | | |\ .\ .

2 2 x x ((| | | | + = ((|| || ((\ . \ . . : ( )( )x x x x x x21 2+ + = , 1 2, x x . 4.2 2 1073.2 2 83 , 0 > , . - 0 = . (1) :x x x222| |+ + = + |\ .. , 0 = , . - 0 < . = , : x x x 2222 4 (| |+ + = + + ( |\ . ( xe\, , . 2, 0 x x + + = : - 0 > ,: ( )( )21 2x x x x x x + + = , 1 2, x x . - 0 = , : 222x x x| |+ + = + |\ .. - 0 < , : 2222 4x x x (| |+ + = + + ( |\ . ( . : 9 22 3 2 x x + 9 16 25 0 = + = > 112x = 22 x = . :( ) ( )( )212 3 2 2 2 2 1 22x x x x x x| |+ = + = + |\ .. 9 21 932 2x x + + 1 9 9 4 02 2= = 32= .-:1084. 843. ( )221 9 13 32 2 2x x x + + = . 9 22 6 5 x x += 4 0 < . : 223 12 6 5 22 4x x x (| | + = + ( |\ . ( . 2, 0 x x + + = , . - 0 > , , , : ( )( ) ( )21 21 x x x x x x + + = . 1 2x x . ,( ) 1 , . 9 1 2< < x x x (), 10 x x > 20 x x < ,( )( )1 20 x x x x < . ,( ) 1 , . 9 1 2x x x < < (), 10 x x > 20 x x > ,( )( )1 20 x x x x > . ,( ) 1 , . - 0 = , : 222x x x| |+ + = + |\ .. , 2x= , 2x= . 4.2 2 1093.2 2 85 - 0 < , : 2222 4x x x (| |+ + = + + ( |\ . ( . -x . \. : 2, 0 x x + + =: - , 0 > x , .-, x -. - . x2+x+ > 0 x2+x+ < 0 20 x x + + > 20, 0 x x a + + < = , . - . 1

i) 22 3 2 0 x x > (ii) 22 3 2 0 x x < x , 22 3 2 x x (i) (ii). 12 2,2 0 = > , . x 12 2+ ( ) f x+00+1104. 863. : i) 22 3 2 0 x x > xe\ 12x < 2 x > , ( )1, 2,2x| |e + |\ .. . ii) 22 3 2 0 x x (ii) 22 1 0 x x + < 22 1 x x + 0 = , 1 x = .1 = ,, xe 1 x = . 4.2 2 1113.2 2 87 (i)x , 1 x = , (ii) . (i) . 4

21 0 x x + + > 21 x x + + 3 0 = < , 1 = ,,xe\.- . 1 x e\ : 24 5 0 x x < 26 0 x x > . . : 9( ) ( )24 5 0 5 1 0 1 5 x x x x x < + < < < 9( ) ( )26 0 2 3 0 2 3 x x x x x x > + > < > ( ) 3, 5 x e . 2 ( )21 4 0, x x + + + = e\i) . ii) ; iii) ; iv) \ ; i): 1124. 883. ( ) ( )22 1 4 1 4 2 15 = + + = ( . ( ) ( )2 2 4 1 15 64 0 = = > . : 12 852+= = 22 832= = . . 3 5+ +00+ : ii) 0 > , 3 < 5 > . iii) 0 = , 3 = 5 = . iv) 0 < , 3 5 < < . 1. : i) 23 2 x x + ii) 22 3 2 x x . 2. : i) 223 22 3 2x xx x + .ii) 222 8 4249x xx+ iii) 224 12 92 5 3x xx x + +. 3. x e\, : i) 22 15 x x ii) 24 4 1 x x + iii) 24 13 x x + . 4. x e\, : i) 24 3 x x + ii) 29 6 1 x x + iii) 22 2 x x + . 4.2 2 1133.2 2 89 5. :i) 25 20 x x d ii) 23 4 x xd . 6. : i) 22 0 x x ! ii) 22 3 5 0 x x. 7. : i) 24 4 x x! ii) 29 6 x xd . 8. : i) 23 5 0 x x d ii) 22 3 20 0 x x ! . 9. 214 3 04 x x! . 10. x \ : 22 1 4 12 x x . 11.x \ 26 5 0 x x 25 6 0 x x ! . 1.i) : 2 22 2 26 . ii) 2 22 226 . 2. 22 2x x . 3. 22 23 2x x x x x

. 1144. 903. 4. 2 3 5 0, x x + + + = e\ . : i) ii) iii) . 5. e\ 23 0 + + > x x x e\. 6. ( )22 2 3 , 2 x x + + = . i) - 0 < . ii) ( )22 2 3 0, 2 x x + + < = x e\. 7. 3 = . - 5. 8.i) 2 20 + > , e\ , 0 = . ii) 1 = + , 0 = . 4.3 & 3.3 & ( ) ( ) ( ) ( ) ... P x x x x = ,( ) x ,( ) x ,,( ) x + x () 2x x + +().- ( ) P x , . xe\ ( ) ( )( )( )2 21 6 2 1 = + + + P x x x x x x . : 91 0 1 x x > > , 1 x 1 > x , 1 x = 1 x < . 9( )( )26 0 3 2 0 3 2 x x x x x x + > + > s > , 26 x x + 3 x < 2 x > ,3 x = 2 x = 3 2 x < < . 9 22 1 x x + + 1 8 7 0 = = < , xe\. ,,( ) P x , . x3 12+ 1 x ,0+ ,+26 x x + +0 ,0+22 1 x x + + + ,+ ,+ ,+( ) P x0+00+( ) P x 3 1 x < < 2 x > , 3 x < 1 2 x < < .3 x = , 1 x = 2 x = . 1164. 92 3. () () () x x ... x 0 ( 0 ) > < , ( )( )( )2 21 6 2 1 0 x x x x x + + + < xe\( ) ( )( )( )2 21 6 2 1 P x x x x x x = + + + . ( ) P x ( ) ( ) , 3 1, 2 xe . ()() x0 ( 0 ) x > > ( )( )( ) ( )0 0 xx xx < < , ,( ) ( ) 0 x x > ( ) ( ) 0 x x < ( ) x . , ( )( )221 2 106x x xx x + +>+ . ( )( )( )2 21 6 2 1 0 x x x x x + + + > , ( ) 0 P x > , , ( ) P x- ( ) ( ) 3,1 2, xe + . ( )( )0 xx > - x ( ) ( ) 0 x x > ( ) 0 x = . 4.3 & 1173.3 & 93 224 303 4x xx x +>+ . : ( )( )22 224 30 4 3 3 4 03 4x xx x x xx x +> + + >+ 23 4 0 x x + = . 24 3 x x + 13 , 23 4 x x + 1 4 . : ( )( )2 2( ) 4 3 3 4 P x x x x x = + + x4 13 + 24 3 x x + + ,+00+23 4 x x + +00+ ,+( ) P x+ , , ,+ ( ) | ) , 4 3, xe + . 1. ( ) ( )( )( )2 22 3 2 1 P x x x x x x = + . 2. ( ) ( )( )( )2 2 24 3 2 1 P x x x x x x = + + + + . 3. ( )( )( )2 21 2 9 0 x x x + > . 4. ( )( )( )2 23 2 6 3 0 x x x x + + s . 5. ( )( )2 22 2 1 0 x x x x + + s . 6. ( )( ) ( )2 23 2 3 1 2 0 x x x x x + > . 1184. 94 3. 7. : i) 201xx

!

ii) 2 103xx

d

. 8. 22202x xx x d . 1. : i) 2 341xx

!

ii) 243 5xx

d

. 2. 23 102 01x xx d

. 3. : i) 23 5 1xx xd ii) 32 1 2xx xt . 4. 12xx

! . 5..- -x ,- ()-7 x 25 x x .- . 6. -,-. ,t, 220/4t mgr ltt

. 4/ mgr lt , . 4.3 & 119 4 3.3 & 95 3 I. -. 1. 22 0 x x + + > : )1 > )1 = )1 < )1 > . 2. 22 0 x x + > x e\, : )1 )1 s . 3. 2 22 3 0 x x + s x e\, : )0 > )0 ) 1 5 x s s) 1 5 x < < . 5. 1 1 x x = : ) ) 1 x =) ) . II. , , . 1. 2 20 x x + + > ,0 = , x e\. 2. 2 24 5 0 x x + + s , 0 = , x e\. 3. 2( 1) 0 x x > 1 0 x > . 4. 2( 1) 0 x x s 1 0 x s . 5. 2 111xx>+2 1 1 x x > + . 6. ( )2102xx>1 0 x > . 7. ( )2102xx>( ) ( )21 2 0 x x > . 1204. 96 3. 8. 201xx

t

( 2)( 1) 0 x x t . 9. 201xx

( 2)( 1) 0 x x . 10. 1 21 1x xx x

21 1 1 x x x . III. . 1 22 6 4 x x 1 2 x x2 23 2 x x 1 2 x x 3 23 2 x x 2 1 2 x x4 22 6 4 x x 2 1 2 x x IV. : 1. 2 6 1 0 x x ! : 2 6 1 0 2 6 0 1 0 3 1 3 x x x x x x x ! !! ! !! . 0 ,3, . 2. 4xx : 2 244 4 0 2 2 x x x xx . 1, 2 2, . 3. 2( 2) ( 1) 0 x x t : 2( 2) ( 1) 0 1 0 1 x x x x t t t . 2, 1, . 55.1 10000 2%. . - . , 10000 : 1 :10000 + 0,02 10000 = 10000(1 + 0,02) = 10200 . 2 :10000 1,02 + 0,02 ( 10000 1,02) = 10000 1,02 (1+0,02) = 10000 (1,02)2 = 10404 . 10000 : 3 10000 (1,02)3 , 4 10000 (1,02)4 . 10000 (1,02 ) . :: 12 3 ... ... 10000 1,0210000 (1,02)210000 (1,02)3... 10000( 1,02) ... 10000 (1,02). . - 1,2,3,...,,... . 1 1225. 1, 2 2 ... - . , 1 1, 2 2, 3 3, ..., , ... - (). .i) 112, 222, ... 2, ... () 1 = 12, 2=22 . = 2.ii) () = (1) : 1 = 1, 2 = 1, 3= 1,...iii) () - : 12,22,32,...,2,...=2 . .. 20 = 202 = 400, 100 = 1002 = 10000 . . .. (), 1, 1 , , :1 = 1, 2=1, +2 = +1 + :3 = 1 + 1 = 2, 4 = 2 + 1 = 3, 5 = 3 + 2 = 5, 6 = 5 + 3 = 8, .-. () . () +2 = + + . , , :(i) (ii), .: , 5.1 123 . - .. :2, 3, 5, 7,11,13, ...1 20 -: i) = 22 3ii) i) 1 = 2 . 12 3 = 1,2 = 2 . 22 3 = 53 = 2 . 32 3 = 15, 4 = 2 . 42 3 = 2920 = 2 . 202 3 = 797ii) 2 1 = 2 . . 1245. 3 = 3+5. -. +1 = [3 ( + 1) +5] (3 + 5) = 3 + 3 + 5 3 5 = 3 +1 = 3 + . 1 = 3.1 + 5 = 8, :1 = 8 +1 = 3 + ' 1. : i) = 2 + 1ii) = 2 iii) = 2 + iv) v)vi) vii) = |5 - |vii) ix)x)xi) = ( 1) + 12. : i) 1 = 2, ii) 1 = 0,iii) 1 = 3, +1 = 2(- 1)3. : i) = + 5ii) = 2iii) = 2 1iv) = 5 + 34. :i) 1 = 1,+1 = + 2ii) 1 = 3, +1 = 5 1, 3, 5, 7,... , 2. - :+1 = + 2 +1 = 2 () 2. 15, 10, 5, 0, 5, 10,... - 5. :+1 = 5 +1 = 5 , () 5. : , .-., () , :+1 = + +1 = 1 , +1 = + . 1, : - :5.2 1265. 1 = 1 2 = 1+ 3 = 2+ 4 = 3+ ..................................................1 = 2 + = 1 + , = 1 + ( 1). 1 = 1 + ( 1)..3,5,7,9,...,1=3 = 5 3 = 2, = 3 + ( 1) 2. 20 = 3 + 19 2 = 41, 100 = 3 + 99 2 = 201 . , , - , : = = , = ,,,, :2 = + = ,,,. . : , , 5.2 127 1, 2, 3, 4,... - 100 S100 = 1+2+3 +...+ 98+99+100 , : , :S100 = 1+2+3 +...+ 98+99+100S100 = 100+99+98 +...+ 3+2+12S100 = (1+100)+(2+99)+(3+98)+...+ (98+3)+(99+2)+(100+1) 2S100 = 101+101+101 +...+ 101+101+101 2S100 = 100101, , : () *: S = 1+(1+)+(1+2) + ... + [1+(2)]+[1+(1)] S = +()+(2) + ... + [(2)]+[(1)] :2S = (1+)+(1+)+(1+) + ... + (+1)+(+1) 2S = (1+). = 1 + (1), :1285. 1 7+10+13 + + 157 1 = 7, = 157 = 3. , . = 1+( 1) 157 = 7+(1)3 7+(1)3 = 157 7+33 = 157 3 = 153 = 51 2 52, 47, 42,... 90;1 = 52, =47 52 = 5 S = 90. , *,=20. 20 90.3 42 87.100 . = 1+(1) 42 = 1+ 87 = 1+18. 5.2 129 1 1 + 9 = 42 1 + 18 = 87 1 = 3 = 5. ' 1. :i) 7, 10, 13,... ii) 11, 13, 15,... iii) 5, 2, -1,...iv) v) 6, 9, 12,...2. -:i) 15 2, 3, 8...ii) 20 11, 18, 25,...iii) 30 4, 15, 26,... iv) 35 17, 25, 33,...v) 50 vi) 47 3.i) 12 16, .ii) , 5 = 14 12 = 42iii) , 3 = 20 7 = 32.4.i) 5 2. .{1305. ii) 7 = 55 22 = 145, - 18.5.i) 1 = 2 = 5 97;ii) 1 = 80 = 3 - 97;6.i) 10 40.ii) x 5x + 1 11 3x 2.7.10 25, .8. 40 -:i) 7, 9, 11,...ii) 0, 2, 4,....iii) 6, 10, 14,...iv) 7, 2, +3,...9. 80 -: i) 2, 1, 4,...ii) 10. : i)1+5+9+...+197ii)9+12+15+...+90iii) 71013...10911. 180;i) 4, 8, 12,... ii) 5, 10, 15,...12. 15 . 53 . 15 ;5.2 131 ' 1. = 124. - 1 .2. :i) 200 , ii) 300 - iii) 16 380.3. :i) 5 1 199, ii) 3 10 200.4. :i) 30 = 54, ii) 40 = 53.5. 1 200 4 9.6. - 1, 3, 5, 7,... , 4000.7. -,1,,S .8. .- 24/; 9. 33.- 1 S120 10 125 27 1093 12 2102 16 81325. 800 - 4160 . . .10. 38010 . . [ - ].11. :11. , , -:1 20 , 5. 4700. ; 3, 6, 12, 24, ... - 2. : () 2.27,9,3,1,...-. :5.3 5.3 133 , () . : , . . () 1 0, , 0,0*.,() , :+1 = 1 , +1 = - . 1, : :1 = 1 2 = 1 3 = 2

...............................................1 = 2 = 1 - , = 11 1 = 1 1..3,6,12,24,...1=3, = 3 (2)1. 5 = 3(2)4 = 48, 10 = 3 (2)9 = 1536 .1345. , , , : ,,, 02=, =, , , . . : , , , 2 = 1, 3, 9, 27,... 1 = 1 = 3, S7 7 . S7 = 1+3+9+27+81+243+729(1),- : (1) =3 3S7 = 3+9+27+81+243+729+2187(2) (2) (1) :3S7 S7 = 218712S7 = 2186 S7 = 1093 , : () 1 5.3 135S = 1 + 1 + 12 + + 12 + 11(1) (1) S = 1 + 12 + 13 + + 11 + 1(2) (2) (1) :SS = 11 (1)S = 1(1), 1, ::=1, S = 1, 1.1 1. : 1365. , = 11, 2 , . = 11 : 1 = 8 = 9. : ' 1. : i) 3, 6, 12, ...ii), 2, 6,...iii) 9, 27, 81, ...iv)v) 16', 8, 4, ...vi) 18, 6, 2, ...vii) 1,0,4,0,16, ... vii) 2, 4, 8, .... ix) 3, 9, 27, ...5.3 1372. -: i) 9

ii) 7 2, 6, 18, ...iii) 8 729, 243, ... iv) 10 1 2, 4, ...v) 9 3.i) , 2.ii) , 4.i) 12 96.ii) , 5. :i) 14 4 = 125 10 = ii) 21 13 = 23 = 6. 3, 6, 12,.... 768.7.i) 4, 8, 16,... 2000.ii) 128, 64, 32,..., 0,25.8.i) 5 20, ii) x x4, x+1, x19 .1385. 9. 10 i) 1, 2, 4,... ii) 3, 9, 27,... iii) 4, 8, 16,...10. :i) 2+8+32 + ... + 8192 ii) 4+2+1 + ... + iii) 1+(2)+4 + ... + 256.11. . 3, 12 ;12. 60 - . 4 . ' 1. . - 1 .2. - ;3. :i) ii) k, .4. , - .5.3 1395. , 2 + 6 = 34 3 + 7 = 68.6. 90 2%. , , ().-10; [ ].7. 10%, . , , , (I).- , 10 ;[ ].8. C'261z C" . C' C" 11 , C' C" 13 . : i) , ii) .9. 40 lt . 4 lt . 4 lt ... D , , :i) (D).ii) , 7 . [ ].1405. 10. . : 1, 2 2 , 3 4 , 5 8 . , 1 g 20000 .11. -. . . .i) - (S) .ii) - (U) , 1. , - .. %. . - , .( ). 1 1 2 1,2,3,..., ., , 5.4 - 1425. ,, = (1+) .10000 2%. 10 . = (1+), 10 10 = 10000 (1 + 0,02)10 = 10000 (1,02)10 = 10000 1,218994 = 12189,94 .. (1,02)10 . . %. ; ( ), , (1+), . 1 (1+)1 . 1 (1+). 5.4 - 143 = (1+)+(1+)1 + ... + (1+) = (1+)+(1+)2 + ... + (1+) = (1+)[1+(1+)+(1+)2 + ... + (1+)1]

.10000 2%. 10 -; , 10 - 1445. ' 1. 5000 5%. 5 ;2. 3%1050.000 ;3. , 10.000 , - , 5 12.762 ;4. 5 5.000 3%. 5 ;6 6.1 4.1 ,-,. ,- , .1.5000 %, 5000100. , .,3 , 150 , 5 , 250 .2.Skm- 2h, km/h, 2 S . -,-S.,60 , 120 S, 70 , 140 S, .3. 2 .-, . 1 , , 2 , 4 . - . :9 .41466. 98 4. 9(..-).-, . . : () . f. f,g,h. . f , x y , :y f x y f x. f x f x. o x,f, ,y, x, . , ( ) f x x , - f f . :: ( )fx f xoo .. f, - , :>: 0, fx xf oo\ : 1 f .6.1 147 4.1 99 , ^ 1, 2, 3, 4, 5, 6, 7}, ^ `0 0 0 0 0() 9 , 11 , 12 , 13 , 15 f : f o .x .x f (.. 180).x (.. 3 7 13). 2 ={, , } ={1, 2, 3, 4, 5}, (). : 9(),- .9(), .9(), - .9(). .1486. 100 4.

,f, :- - -( ) f x xe,, : f , _ \ _ \ ,,,- . f ( ) f x ...f, ( ) 1 4 f x x = ,,( ) 1 4 f x x = ,, 1 4 y x = . :-f \ ( ) f x .- \ .( ) 1 4 f x x = 1 ,4| (=

(\ , 1 4 0 x > , \. 6.1 1494.1 101 , :( )21, 01, 0x xf xx x + . f 1, 0 1 : 91 0 x = < , ( )21 f x x = + , :( ) ( )21 1 1 1 1 2 f = + = + = . 9 0 x = , ( ) 1 f x x = , : ( ) 0 0 1 1 f = = . 9, 1 0 x = > , ( ) 1 f x x = , :( ) 1 1 1 0 f = = . , , f - x ,. ( ) ( ) ( )2 2 24 7, 4 7 4 7 f x x x gt t t hs s s = + = + = + .x . , ( ) ( ) ( )24 7, f = + .( ) 2 f 2 , :( ) ( ) ( )22 2 4 2 74 8 7 19f = += + + = , ( ) ( ) ( )223 3 4 3 79 12 7f x x xx x= += + -. 1506. 102 4. ( )212s t gt = , 212s gt = ,s- s(t). -, -,,. , t , , s(t) . ( )112f x xx= + f x 2 0 x = 1 0 x >, , 2 x = 1 x > f | ) ( ) 1, 2 2, = + *() 1. : i)( )451f xx= +ii)( )22164xf xx x= iii)( )211f xx=+ iv)( )1f xx x=+ 6.1 1514.1 103 2. : i) ( ) 1 2 f x x x = + ii)( )24 f x x = iii)( )24 3 f x x x = + iv)( )11f xx= 3. ( )3,02 3,0x xf xx x ( ) 5 f ,( ) 0 f( ) 6 f . 4. f : ,1, 4 . i) f 0 x, 1 x = ,2 x =3 x = . ; ii) x ( ) 36 f x = , ( ) 49 f x = , ( ) 100 f x = ( ) 144 f x = . 5. : i)( )451f xx= +,ii) ( )22164xg xx x= iii)( )211h xx=+. x : i)( ) 7 f x =ii)( ) 2 g x = iii)1( )5h x = . 4.2 - , -.,-, :' x x ' y y . ' x x x,' y y - y., ( , ) ,( , ) -,, : , . -.- ( , ) , , ( , ) . , xy ,- . , xy .: ,,-6.2 6.2 1534.2 105 ,-. Oxy . :x ' x x -,' y y x , lxOy , l' yOx ,l' ' x Oy l' y Ox -1,2,34,,-. . x, - , , : 9 ' x x , , (. ). 9 ' y y , B , (. ). 9 , , (. ).913 ' , (. ).

1546. 1064. Oxy 1 1, x y 2 2, x y . : 2 22 1 2 1 x x y y: + : 22 22 22 1 2 12 22 1 2 1( ) ( ) ( ) x x y yx x y y : 2 22 1 2 1 x x y y . ' x x( ) ' y y( ). , (3,1) ,(3, 5) (-1,1) - , : 2 2 2( ) (3-3) (5 1) 4 4 2 2 2( ) (-1-3) (1 1) 4 4 2 2 2 2( ) (-1- 3) (1 5) 4 4 4 2 . ,,( ) ( ) ,- 2 2 2( ) ( ) 32 ( ) , -. 6.2 1554.2 107 C o O . , x y C, 2 2 2x y , xy C , . 2 2 x y , : 2 2 2 2 2 x y x y , xy , C , -

2 2 2x y (1) (1), , C , - . , 1 2 21 x y . . fOxy - . ( , ) Mxy ( ) y f x,( , ( )) Mx f x ,A x ,-f fC .,-,( ) y f x fC . -,( ) y f xf. , fC f , , , ( ) y f x. x A y , f. f (. ). , - (. ). 1566. 1084. f,, f, f x x c -f ( , ( )) M x f x c-( , ( )) M x f x f x x c . -f g , .i) f : 3,2,1,0,12 ii) :( ) 0 f x,( ) 2 f x &( ) ( ) f x g x. iii) :( ) 0 f x ! ( ) ( ) f x g x ! . i):3 2 f ,2 0 f ,1 1 f,0 1 f ,1 0 f 2 2 f. ii)0 f x f ' x x , 12 x 21 x. 6.2 1574.2 109 ( ) 2 f x = f 2, 13 x = 22 x = . ( ) ( ) f x g x = f g , 11 x = , 20 x = 32 x = . iii) ( ) 0 f x > - f ' x x , ( , 2) (1, ) x e + . ( ) ( ) f x g x > f - g , ( , 1) (0, 2) x e . 1. : ( ) 1, 2 ,( ) 3, 4 ,( ) 0, 0 ,( ) 3, 0 ,( ) 0, 5 ( ) 2, 3 . 2. ( ) , x y . , x y ; 3. ( ) 1, 3 , i) ' x xii) ' y yiii) l x yiv) O . 4. : i)( ) 0, 0 ( ) 4, 2 ,ii)( ) 1,1 ( ) 3, 4 , iii)( ) 3, 1 ( ) 1, 1 ,iv)( ) 1, 1 ( ) 1, 4 . 1586. 1104. 5. : i)1, 2 ,4,-2 3, 5 . ii)1, 1 ,1,1 4, 2 . 6. : 2, 5 ,5,1 ,2, 3 ,1,1 . 7.k . i) 2f x x k , 2, 6 ii) 3g x kx, 2, 8 iii)1 h x k x , 3, 8 . 8., . i)4 f x x ii) 2 3 g x x x iii) 2( 1) h x xiv) 21 q x x x v)1 x x x vi) 24 x x x . 9. 21 f x x . : i) fC . ii) fC -' x x . 10. 25 4 f x x x 2 6 g x x . : i) fC gC . ii) fC gC .

4.3 : ( ) f x x Oxy x x c . x , (1), x xc . c x x , c x x0 D. 0 180 d D D. -x xc . . ,-,,, . 90D, -x xc , . ( ) f x x ( ) 0, 5 1 f x x .- , f -0, 5 1 y x(). (1) x y, 900. 6.3 :(x) = x + 1606. 112 4. : 9' x x (-2,0),0 y 2 x , ' y y (0,1), 0 x -1 y 9 : () 10, 5() 2 , , 0, 5 1 y x x.,, ( ) fx x ,y x , y (0,) . - : x0 ! , 0 90 D D x0 , 90 180 D D x0 , 0 D. 0 ,( ) fx , x. 1 1( , ) x y 2 2( , ) x y y x . 6.3 f(x) = x+1614.3 f(x)=x+113 : 1 1y x 2 2y x , : 2 1 2 1 2 1( ) ( ) ( ) y y x x x x. : 2 12 1y yx x

,( 1,3) A(3, 6) B 6 30, 753 ( 1)

., c x x 0, 75 , 36,87D . () f x x 0 ,f( ) f x x,-y x.-: 91 y x. , xx, 1 ,45 . y x xOy xO y . 91 y x. , xx, 1 ,135 .y x- yOx y O x . 12 1 1y x 2 2y x - xx 1 2 .x 1 2 , 1 2 , 1 2 1 2 . : 1626. 114 4. 9 1 2 1 2 z ,(.), 9 1 2 1 2 , . x 1 2 z , 1 2 z , 1 2 z 1 2 . (. ) : x1 y x , \, :1 y x ,1 y x, 2 1 y x ., , 1 -' y y , y x , ' y y . x2 y x , \, :2 y x,2 1 y x , 2 3 y x ., , =2, y x , , . 6.3 f(x) = x+163 4.3 f(x)=x+115 ( )f x x = :( ), 0, 0x xf x xx x ( ) f x x = : 9, 0 y x x = s 9, 0 y x x = > ' x Oy xOy. -f .i) -- .ii) ( ) 0, 5 1 f x x + > . i) y x = + ( ) 2, 0( ) 0,1 : 0 2 = + 1 0 = + , : 0, 5 = 1 = : 0, 5 1 y x = + . 1646. 116 4. ,( ) 2, 2 -, ( ) 2 0, 5 2 1 = + , . ii)( ) 0, 5 1 f x x > + f -0, 5 1 y x = + ,., ( ) ( ) 2, 0 2, x e + . 1. ' x x : i)2 y x = +ii)3 1 y x = iii)1 y x = +iv)3 2 y x = + . 2. : i)(1, 2) A(2, 3) B ii)(1, 2) A(2,1) Biii)(2,1) A( 1,1) B iv)(1, 3) A(2,1) B . 3. : i) 1 = ' y y B(0, 2) . ii)' x x 45 = ' y y (0,1) B . iii)2 3 y x = -(1,1) A . 6.3 f(x) = x+1654.3 f(x)=x+117 4. : i)(1, 2) A(2, 3) B ii)(1, 2) A(2,1) Biii)(2,1) A( 1,1) Biv)(1, 3) A(2,1) B . 5. C Celsius F -Fahrenheit 5( 32)9C F = 0oC32F100oC 212F. ; 6. : 2, 0( ) 2, 0 11, 1x xfx xx x' < 1111= _ @6, 5. i) f [ 6, 5] x . ii) : ( ) 0, ( ) 1 ( ) 1 f x f x f xiii) ( ) 0, 5 f x x d . 2. 1 y x - ' x x . . 3.600.-2000. 100 - : i),t, :) ) . ii) . 4. . x ( ) f x +.-= ( ) E f x . 6.3 f(x) = x+1674.3 f(x)=x+119 5. 1 2 ,20cm , 3, 4. 1 2 , t,,- 1k 2k . i) 1( ) h h t 2( ) h h t,- t, 1 2. ii) 2 1 . iii) . ; 6.4 - 4.4 ) ( ) 1 f x x = + . ( )1, 01, 0x xf xx x + , -( ) 1 f x x = + ,- 91, 0 y x x = + s91, 0 y x x = + > , 1 ' y y - ' x Oy xOy,, ( ) x x =().,( ) x x = -(1)1,- ( ) 1 f x x = + . , , , : ( ) ( ) 1 f x x = + , xe\, xe\( ) f x 1 ( ) x . : f , : ( ) ( ) , 0 f x x c c = + > , c ( ) (1) ' y y . 6.4 - 1694.4 121 ) ( ) 1 f x x = . ( )1, 01, 0x xf xx x , ( ) 1 f x x = , 91, 0 y x x = s91, 0 y x x = > , 1 ' y y - ' x Oy xOy ( ) x x =().,( ) x x = - 1 , -( ) 1 f x x = .,,, : ( ) ( ) 1 f x x = , xe\, xe\( ) f x 1 ( ) x . : f , : ( ) ( ) , 0 f x x c c = > , c ( ) 1706. 1224. ) ( ) 1 f x x = . ( )1, 11, 1x xf xx x + , ( ) 1 f x x = , 91, 1 y x x = + s91, 1 y x x = > , 1 ' x x - ' x Oy xOy ( ) x x =(). ,( ) x x = -(2) 1 , -( ) 1 f x x = .,,, ( ) ( ) 1 f x x = , xe\, ( ) 1 f x x = x ( ) x x = 1 x . : (2) ' x x . 6.4 - 1714.4 123 f: ( ) ( ), 0 f x x c c = > , c ( ). ( ) ( ), f x x c = f x x c ,c x. , f c - ( ). ) ( ) 1 f x x = + . ( )1, 11, 1x xf xx x < =+ > , ( ) 1 f x x = + , 91, 1 y x x = s 91, 1 y x x = + > , 1 ' x x - ' x Oy xOy ( ) x x =(). ,( ) x x = - 1 , -1726. 1244. 1 f x x . , , , 1 f x x , x\, 1 f x x x x x 1 x.: f , : , 0 f x x c c ! , c ( ). , f x x c f x x c,c- x. , f c - ( ). ( ) 3 2 f x x. 3 y x , -y x3.-3 2 y x,-6.4 - 1734.4 125 3 y x 2 - .,- ( ) 3 2 fx x --y x, 3- 2 (). : , - : ( ) ( ) fx x c dr r ,, 0 c d !,- . A 1.-: x x, 2 f x x 2 g x x . 2. : x x, 2 h x x 2 q x x . 3. : x x,2 1 F x x 2 1 G x x. 1746. 1264. 4. 1 (0, 0) O(2, 0) A . -: i)( ) ( ) 2 fx x( ) ( ) 2 g x xii)( ) ( 3) h x x ( ) ( 3) q x x iii)( ) ( 3) 2 F x x ( ) ( 3) 2 G x x. 5. 2( ) 2 1 x x . f - : i) 2 1 . ii) 3 2 . iii) 2 1 . iv) 3 2 . 6.5 -- 4.5 -- T f t-t 0 t- 24 t. ) > @4,16 - . 1766. 128 4. ,,- , | |1 2, 4,16 t t e 1 2t t ( ) T ft = | |16, 24 . : f- , 1 2, x x e 1 2x x < : ( ) ( )1 2f x f x >f f ,( ) 2 5 f x x = + \. 1 2 1 2, , x x x x e < \ . : ( ) ( )1 2 1 21 21 22 22 5 2 5x x x xx xf x f x< > + > + > : ( ) f x x = + , 0 = , | |0, 24 t e( ) T f t = 4 t = -, ( ) 4 3 f = . : f, , 0 x e() :( ) ( )0f x f x > , xe 0 x e , ( )0f x f ( ) min f x . , ( )43 1 f x x = + .

40 x > , xe\,

43 0 x > , xe\,

43 1 1 x + > , xe\. :( ) ( ) 0 f x f > , xe\ , f 00 x = , ( ) 0 1 f = ) 216 t = , ( ) 16 11 T = . : ( ) ( ) 16 11 f t f s = , | |0, 24 t e( ) T f t = 16 t =, ( ) 16 11 f = . : f,, 0 x e() ( ) ( )0f x f x s , x e6.5 - - 179 4.5 131 0 x , 0f x - f max f x . , 43 1 f x x.

40 x t , x\,

43 0 xd , x\, 43 1 1 x d , x\. :( ) 0 f x f d , x\ , f 00 x, 0 1 f. () () . : (.) (.)(.) (. ).

1806. 132 4. )- fC f \. fC ' y y , fC ' y y fC . ,,( , ) Mxy fC ' y y '( , ) M xy ( , ) Mxy '( , ) M xy fC ,y f xy f x , : f x f x f . : : f, , , x: xf x f x yy, 4 22 1 f x x x, \ x\ : 4 24 22 1 2 1 f x x x x x f x, ' yy . )- fC f \. fC ,- fC - fC . 6.5 - - 1814.5 133 ,,( , ) M x y fC '( , ) M x y ( , ) M x y '( , ) M x y fC ,y f x y f x, : f x f x f . : : f,,, x : xf x f x . , 32 f x x x , - \ x\ : 332 2 f x x x x x f x, . : 2y x, 4y x, 6y x.,, ' y y ,,-y x, 3y x, 5y x.,-,, . -f [ 6, 6]. f : 1826. 134 4. ) f : i) ,ii) iii) . ) f , - . f , ' y y ., ' y y f , f , (). :) f : i) [0,2][5,6] , ii)[ 2, 0] [ 6, 5] , [0,2][5,6] f . iii)[ 5, 2] [2,5] . 6.5 - - 1834.5 135 )f 4x 6 6. : max ( ) ( 6) (6) 4 fx f f f 0 x 0. : min ( ) (0) 0 fx f . 1)- : ) ) .

2) , . 3) : i) 2( ) 6 10 fx x x 3 x. ii) 22( )1xg xx

1 x. 4) : i) 2 413 5 f x x x ii) 23 1 f x x iii) 31 f x x iv) 3 543 f x x x v) 251xf xx

vi)6 221xf xx

. 1846. 136 4. 5) : i) 11f xx ii) 22 f x x iii) 31 1 f x x xiv) 4 211xxf xx

v)5f x xvi) 26( ) 1 f x x . 6) . 7) 8) ) ) . 6.5 - - 185 6 4.5 137 4 I), , . 1. ( ) 1, 2 ( ) 1, 3 . 2. 22 y x = 1 y x = +. 3.f ,f . 4. . 5. ( ) 1, 2 ,( ) 2,1 ( ) 3, 3 . 6. f 1, (0) 0 f < . 7. f -( ) 1, 2 ( ) 2, 5 , f . 8. f 1, ( ) 2 f x = . 9. | |: -1,2 f \( )23 f x x = . 10. , . 11. f , f - . 12. f , f . II) f. f, -( )43 x x = , 1 - 2 , : ) ( )43( 1) 2 f x x = +) ( )43( 1) 2 f x x = , ) ( )43( 1) 2 f x x = + +) ( )43( 1) 2 f x x = + 1866. 138 4. -,ReneDes-cartes (1596-1650) Pierre de Fermat (1601-1665). Descartes () La Haye( ) Touraine.10 LaFleche,. . , . ,1637 Le Geometrie, - . .- , . Fermat,Toulouse,- , 17 . , 1629 , 1679. Fermat :2 ! ,, a Fermat. Fermat : .Fermat1994-.Wiles,350- . 7 ,-,- 21( ) f x x, 32( ) f x x, 3( )f xx 24( ) f x x x . - : 1. . 2. . 3.- ( .). 4., ,- . ,f , -y y c , , . , x A ,0 x t -.- y y c -.,,2 4, .5 7.1 :f(x) = x2140 5. 5.1 : ( )2f x x = ( )2g x x =( )2g x x = . ,\,xe\ : ( ) ( ) ( )22g x x x g x = = =,g ' yy .,,- g | ) 0, + . : -: | )1 2, 0, x x e + 1 2x x < . 2 21 2x x < ,( ) ( )1 2g x g x < .( )2g x x = | ) 0, + .-: | ) 0, xe +: ( ) ( )20 0 g x x g = > = . g 00 x =, ( ) 0 0 g = . -gx: g x : x10102010501010010100010+ ( )2g x x =201040101001020010200010+,x , +, 2x --+. g -,x - +. 7.1 f(x)=x21895.1 f(x)=x2 141 gx ,- | ) 0, + . ' y y ,- 2( ) g x x = ,- : ( )2g x x = : - ( |, 0 | ) 0, + - 0 x = , (0) 0 g = . - , x , +. ( )2h x x = 2( ) h x x = . xe\ ( ) ( ) h x g x = ,4.2,-( )2h x x = ( )2g x x = ' x x . ( )2h x x = : - ( |, 0 | ) 0, + . - 0 x = , ( ) 0 0 h =- , x +. ( )2f x x = : -0 > , ( )2g x x = . : 1907. 142 5. x 0+ 2( )0f x x=> -( )2f x x =0, 5 = , 1 = 2 = . -0 < , ( )2h x x = . : x 0+ 2( )0f x x=< -( )2f x x =0, 5 = ,1 = ,2 = . 7.1 f(x)=x21915.1 f(x)=x2 143 ( )2, 0 f x x = = ,- ' y y . : 9 , , , . 9 ,,- ' y y . ( )3h x x = . ( )3, 0 h x x = = , , : 3 3( ) ( ) ( ) h x x x h x = = = , -| ) 0, + - . ( )2f x x = ,- : ( )3, 0 h x x = = : -0 > , 9 \. 9- , x + - x .-0 < , 9 \ 1927. 144 5. 9- , x f - x f . 1. - . 2.-:i) 20, 5 x x, 20, 5 2 f x x 20, 5 3 g x xii) 20, 5 x x , 20, 5 2 h x x 20, 5 3 q x x. 3. :i) 20, 5 x x,20, 5 2 f x x 20, 5 2 g x xii) 20, 5 x x , 20, 5 2 h x x 20, 5 2 q x x. 4.i)- 2( ) fx x ( ) 1 g x : 21 x d 21 x ! . ii) . 1. : f x x x. 7.1 f(x)=x21935.1 f(x)=x2 145 2. : 2,0( ),0x xfxx x < => f. 3. -: ( ) fx x = , 2( ) g x x = , 3( ) h x x = ( ) x x =| ) 0, + , /Y. i) 2 3, , x x x x , , f g h : ) 0 1 x < < ) 1 x > . ii) . 4.OAB+ .- . 7.2 :5.2 :( )f xx=

( )1g xx=( )1g xx= ., ( , 0) (0, )-= + \ , x-e\ : ( ) ( )1g x g xx = = , . ( ) 0, + . : -: 1 2, (0, ) x x e + 1 2x x < . 1 21 1x x> ,( ) ( )1 2g x g x > .( )1g xx= (0, ) + .-g:(0, + ) xe 1( ) 0 gxx= > . , (0, ) + g - x.-gx:- g x : x1010 2010 5010 10010 100010. 0 ( )1g xx=10102010501010010100010 . +,x 0,,0, 1x +.,x -0,g -7.2 f(x)=/x1955.2 f(x)=/x147 Oy .' yy - g . - g x: - g x : x10102010501010010100010 . +( )1g xx=1010 2010 5010 10010 100010. 0 ,x +, 1x0., x +, g Ox .' xx -g . g x , (0, ) + . - ,- ( )1g xx= -\ , : ( )1g xx= : - ( , 0) (0, ) + . - : 9,13-,9 , 9y x = y x = ,- 1967. 148 5. 9' x x - ' y y .

( )1h xx= ( )1h xx= . xe\ ( ) ( ) h x g x = . , ( )1h xx= -( )1g xx= ' x x , , ( )1h xx= : -( , 0) (0, ) + . - : 9,24-,9 , 9y x = y x = ,- 9' x x - ' y y . ( )f xx= : -0 > , ( )1g xx= . ( )f xx= 0, 5 = ,1 =2 = . 7.2 f(x)=/x1975.2 f(x)=/x149 x0 , 1h xx . f xx 0, 5 ,1 2 . , 0f x x z ,- ' x x' y y . 1-, 2..- . xy ,2, 2 xy , 0 x y ! , : 2, 0 y xx ! 2yx 1 . 1987. 150 5. 1. . 2.-:i) 1 xx ,12 f xx 13 g xx ii) 1 xx, 12 h xx 13 q xx . 3. :i) 1 xx ,12f xx

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3.2 - . ( )24 3 f x x x = + ( )24 3 f x x x = +( )1 0, 2 2 12 4 2 f f = > = = = = | | |\ ., :x2+ 2( ) 4 3 f x x x = + 7.3 f(x)=x2+x+2035.3 f(x)=x2+x+155 f,9 @ , 2 f >2, f , 9 2 x , 2 1 f . , f : 9 2 x 9' xx 13,- 24 3 x x ,' y y - 3. 1.i) 2( ) 2 4 5 f x x x 2( ) ( ) f x x p q 2( ) 2 gx x f. ii) 2( ) 2 8 9 f x x x ,- g 2( ) 2 gx x .2. :) 22 6 3 f x x x ) 23 5 2 g x x x . 2047. 156 5. 3. ) 22 4 1 f x x x) 22 8 9 g x x x . 4. , 2y x x . .

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\ 2y x- yx . 4. H 1yx y x. 2067. 158 5. II. . 1. 22 f x x x 11 x 23 x, : 5 f0 ,1 f 0 ,5 f 0 , 0 4. 2. 2f x x x 13 x 21 x, : 5 f0 , 2 f0 ,5 f 0 , 0 , 2. III. 2f x x x ,0 z . :1.2 f 1, 3, ) 22 1 3 f x x ) 22 1 3 f x x ) 22 1 3 f x x ) 22 1 3 f x x. 2.1 0 f, 3 0 f !5 0 f, ) 0 0 !) 0 0 ! !) 0 0 !. 3. 1, 20 ! , :) 0 !) 0) 0)0 . 4. 1, 0 , ) 0 ) 0 ) 0 !) 0. IV. C1, C2, C3 C4 - 21 1( ) 4 f x x x , 22 2( ) 2 8 f x x x , 23 3( ) 4 f x x x 24 4( ) 2 8 f x x x ,. . f1f2f3f4

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= 1, 2,..., 100. - P(0).22. -,.P(A')0,28kai P(B')0,71.i)P(A)1,01P(A)ii) A. 1 1.1A 1. ii)1 , 2. 1 , 3. i) 4.000 ii)9.999 iii)3 , 4.ii)4 , 5.ii)1 , 7. 7 2 B 1. i)1 ii) 21++,2. i) 2( 1) ii)1 ,3. i) 2 2x y ii)xyx y , 4.1 1.2A 1. i) ii) , 2. ,3. i)2, 1 ii)1, 2 ,4. i)9, 810, ii)0,9 0, 7 iii) 4554 4653iv)48,3450,32 ,5. i)10, 216, 2 ii)6,38 15, 68 , 6. , 7.5 0 x < B 1. i) ii) , 2. ,3. ,4. i) 2 ii) 2 1.3 1. i)3 ,ii)4 iii)1 iv)0 ,2.1 , 3. i) 1 ii)1 ,4.1 ,5.202 ,6. i) ( ) 2,37, 0, 005 d D s , ii)2,365 2, 375 B 1. , 3. i)0 x y = = ii)0 0 x y = = ,4. i)1 < . 4. i)4 iii)1 7 x s s . 3.2 1. i)( )( ) 1 2 x x ii)( )( ) 2 1 2 x x + . - 215 3.2 3.34o 4.1 4.2216 - 213 2. i) 12 1xx+ii) ( ) 2 37xx iii) 2 31xx . 3. i) 22 15 0 x x > , ( ) ( ) , 3 5, x e +ii) ( )224 4 1 2 1 x x x + = iii) 24 3 0x x + > x e\ .4. i) 24 3 0x x + > ( ) 1,3 xeii)( )229 6 1 3 1 x x x + = iii) 22 2 0x x + < x e\ . 5. i) | | 0, 4 x e ii)| | 4,1 x e . 6. i) ( ) ( ) , 1 2, x e +ii) 51,2x| |e |\ . 7. i) ,x 2 x e = \ii)3 x = . 8. i) ii) x e\ .9.( ) 1, 3 x e . 10.( ) ( ) 4, 1 3, 4 x e . 11.( ) ( ) 1, 2 3,5 x e. B 1. i)( ) ( ) 2 , + ( ) ( 2 ) 3 + ii),3 3 =2 = . 2.( )( ) 2x x + . 3.,2x x +x =2 x = . 4. i) 4ii)0 iii)0 4 < < . 5. 409 < < . 6. i) 2 8 24 , = 3 < 0 >ii)3 < . 7. .8. ii) 0 >, , 0 x e\ .4. i) 24 3 0x x + > ( ) 1,3 xeii)( )229 6 1 3 1 x x x + = iii) 22 2 0x x + < x e\ . 5. i) | | 0, 4 x e ii)| | 4,1 x e . 6. i) ( ) ( ) , 1 2, x e +ii) 51,2x| |e |\ . 7. i) ,x 2 x e = \ii)3 x = . 8. i) ii) x e\ .9.( ) 1, 3 x e . 10.( ) ( ) 4, 1 3, 4 x e . 11.( ) ( ) 1, 2 3,5 x e. B 1. i)( ) ( ) 2 , + ( ) ( 2 ) 3 + ii),3 3 =2 = . 2.( )( ) 2x x + . 3.,2x x +x =2 x = . 4. i) 4ii)0 iii)0 4 < < . 5. 409 < < . 6. i) 2 8 24 , = 3 < 0 >ii)3 < . 7. .8. ii) 0 >, , 0 . 7. i)1 ,12 ,0 ,1 . ii) ( ) { } ,1 1 x e ,| | | ) 2, 0 1, x e +8. i)| | 1,1 x e ,( ) ( ) , 1 1, x e + . B 1. i)( ) 6 1 f = ,( )152f = ,( ) 4 0 f = , ( )132f = ,( ) 2 1 f = ,( ) 1 0 f = , ( ) 0 1 f = ,( ) 1 1 f = ,( ) 2 1 f = , ( ) 3 0 f = ,( ) 4 1 f = , ( ) 5 2 f = ii) ( ) 0 f x = : 4, 1, 3 ( ) 1 f x = : 2 , 4 ( ) 1 f x = :| | { } 0, 2 6 x e iii)0, 5 y x = ,| | { } 2, 5 2 x e 2.1 y x = ,1 x > .3. i)( ) 2000 100 t t = ,0 20 t s s , ( ) 600 100 t t = + ,0 20 t s s ,ii) t=7min 4.( ) 8 f x x = + ,0 4 x s s . 5. i)( )120203h t t = + , 0 3 t s s( )25 20 h t t = + ,0 4 t s s ii)2, 4 h iii)2, 4 h . 4.4 A 5. i)( )22 2 x ii)( )22 3 3 x iii)( )22 2 x +iv) .( )22 3 3 x + 4.5 A 1.f ( | ,1 ,f| ) 1, + ,g ( | , 0 ,g | | 0, 2 , g | ) 2, + ,h ( | , 1 , h | | 1, 0 , h | | 0,1 , h | ) 1, + .2.(1) 1 f = , g , ( ) 1 2 h = ,( ) 1 2 h = o . 3. i) ( ) ( ) 3 f x f > ii) ( ) ( ) 1 g x g s4. i) ii) iii) iv) v) vi) 5. i) ii) iii) iv) v) vi) 6. i) ii) iii) ,7. i) ii) iii) . 5 5.1 A 1. 22 y x = .4. 21 1 1 x x s s s , 21 1 1 x x x > < > . 2.f ( | , 0 ,f| ) 0, + , ( ) 0 0 f = , . 3. i) ) 3 2x x x x < < < ) 3 2x x x x > > > . 4.3 . 5.2 1. 2yx= . 4. 11 0 1 x xxs < > , 11 0 1 xx> < < , 5. 210 1 x x xxs < > 214 5. i) = ii)( ) ( ) ( )2 2 2 = + . 6.( ) ( ) ( ) ( ) 5 = = = = . 7. i) 2 ii)1 iii)4 . 8. i)( ) 4, 0 ,( ) 0, 4 ii)( ) 2, 0 ,( ) 3, 0 , ( ) 0, 6 iii)( ) 1, 0 ,( ) 0,1iv)( ) 0,1v)( ) 1, 0vi)( ) 2, 0 ,( ) 2, 0 . 9. i)( ) ( ) ( ) 0, 1 , 1, 0 , 1, 0 ii)1 1 x x < >10. i)( ) 2, 2 ,( ) 5, 4 ii) 2 5 x < < . 4.3 A 1. i)45Dii)60Diii)135Div)120D. 2. i)1ii)1 iii)0iv)2 . 3. i)2 y x = +ii)1 y x = +iii) 2 1 y x = . 4. i)1 y x = + ii)3 y x = + iii)1 y = . iv)2 5 y x = + .5. 40C D.6. - 2 y x = + , 0 x s , . 2 y = ,0 1 x s s 1 y x = + ,1 x > . 7. i)1 ,12 ,0 ,1 . ii) ( ) { } ,1 1 x e ,| | | ) 2, 0 1, x e +8. i)| | 1,1 x e ,( ) ( ) , 1 1, x e + . B 1. i)( ) 6 1 f = ,( )152f = ,( ) 4 0 f = , ( )132f = ,( ) 2 1 f = ,( ) 1 0 f = , ( ) 0 1 f = ,( ) 1 1 f = ,( ) 2 1 f = , ( ) 3 0 f = ,( ) 4 1 f = , ( ) 5 2 f = ii) ( ) 0 f x = : 4, 1, 3 ( ) 1 f x = : 2 , 4 ( ) 1 f x = :| | { } 0, 2 6 x e iii)0, 5 y x = ,| | { } 2, 5 2 x e 2.1 y x = ,1 x > .3. i)( ) 2000 100 t t = ,0 20 t s s , ( ) 600 100 t t = + ,0 20 t s s ,ii) t=7min 4.( ) 8 f x x = + ,0 4 x s s . 5. i)( )120203h t t = + , 0 3 t s s( )25 20 h t t = + ,0 4 t s s ii)2, 4 h iii)2, 4 h . 4.4 A 5. i)( )22 2 x ii)( )22 3 3 x iii)( )22 2 x +iv) .( )22 3 3 x + 4.5 A 1.f ( | ,1 ,f| ) 1, + ,g ( | , 0 ,g | | 0, 2 , g | ) 2, + ,h ( | , 1 , h | | 1, 0 , h | | 0,1 , h | ) 1, + .2.(1) 1 f = , g , ( ) 1 2 h = ,( ) 1 2 h = o . 3. i) ( ) ( ) 3 f x f > ii) ( ) ( ) 1 g x g s4. i) ii) iii) iv) v) vi) 5. i) ii) iii) iv) v) vi) 6. i) ii) iii) ,7. i) ii) iii) . 5 5.1 A 1. 22 y x = .4. 21 1 1 x x s s s , 21 1 1 x x x > < > . 2.f ( | , 0 ,f| ) 0, + , ( ) 0 0 f = , . 3. i) ) 3 2x x x x < < < ) 3 2x x x x > > > . 4.3 . 5.2 1. 2yx= . 4. 11 0 1 x xxs < > , 11 0 1 xx> < < , 5. 210 1 x x xxs < > 6.3214 5. i) = ii)( ) ( ) ( )2 2 2 = + . 6.( ) ( ) ( ) ( ) 5 = = = = . 7. i) 2 ii)1 iii)4 . 8. i)( ) 4, 0 ,( ) 0, 4 ii)( ) 2, 0 ,( ) 3, 0 , ( ) 0, 6 iii)( ) 1, 0 ,( ) 0,1iv)( ) 0,1v)( ) 1, 0vi)( ) 2, 0 ,( ) 2, 0 . 9. i)( ) ( ) ( ) 0, 1 , 1, 0 , 1, 0 ii)1 1 x x < >10. i)( ) 2, 2 ,( ) 5, 4 ii) 2 5 x < < . 4.3 A 1. i)45Dii)60Diii)135Div)120D. 2. i)1ii)1 iii)0iv)2 . 3. i)2 y x = +ii)1 y x = +iii) 2 1 y x = . 4. i)1 y x = + ii)3 y x = + iii)1 y = . iv)2 5 y x = + .5. 40C D.6. - 2 y x = + , 0 x s , . 2 y = ,0 1 x s s 1 y x = + ,1 x > . 7. i)1 ,12 ,0 ,1 . ii) ( ) { } ,1 1 x e ,| | | ) 2, 0 1, x e +8. i)| | 1,1 x e ,( ) ( ) , 1 1, x e + . B 1. i)( ) 6 1 f = ,( )152f = ,( ) 4 0 f = , ( )132f = ,( ) 2 1 f = ,( ) 1 0 f = , ( ) 0 1 f = ,( ) 1 1 f = ,( ) 2 1 f = , ( ) 3 0 f = ,( ) 4 1 f = , ( ) 5 2 f = ii) ( ) 0 f x = : 4, 1, 3 ( ) 1 f x = : 2 , 4 ( ) 1 f x = :| | { } 0, 2 6 x e iii)0, 5 y x = ,| | { } 2, 5 2 x e 2.1 y x = ,1 x > .3. i)( ) 2000 100 t t = ,0 20 t s s , ( ) 600 100 t t = + ,0 20 t s s ,ii) t=7min 4.( ) 8 f x x = + ,0 4 x s s . 5. i)( )120203h t t = + , 0 3 t s s( )25 20 h t t = + ,0 4 t s s ii)2, 4 h iii)2, 4 h . 4.4 A 5. i)( )22 2 x ii)( )22 3 3 x iii)( )22 2 x +iv) .( )22 3 3 x + 4.5 A 1.f ( | ,1 ,f| ) 1, + ,g ( | , 0 ,g | | 0, 2 , g | ) 2, + ,h ( | , 1 , h | | 1, 0 , h | | 0,1 , h | ) 1, + .2.(1) 1 f = , g , ( ) 1 2 h = ,( ) 1 2 h = o . 3. i) ( ) ( ) 3 f x f > ii) ( ) ( ) 1 g x g s4. i) ii) iii) iv) v) vi) 5. i) ii) iii) iv) v) vi) 6. i) ii) iii) ,7. i) ii) iii) . 5 5.1 A 1. 22 y x = .4. 21 1 1 x x s s s , 21 1 1 x x x > < > . 2.f ( | , 0 ,f| ) 0, + , ( ) 0 0 f = , . 3. i) ) 3 2x x x x < < < ) 3 2x x x x > > > . 4.3 . 5.2 1. 2yx= . 4. 11 0 1 x xxs < > , 11 0 1 xx> < < , 5. 210 1 x x xxs < > 6.4 6.5 - 219214 5. i) = ii)( ) ( ) ( )2 2 2 = + . 6.( ) ( ) ( ) ( ) 5 = = = = . 7. i) 2 ii)1 iii)4 . 8. i)( ) 4, 0 ,( ) 0, 4 ii)( ) 2, 0 ,( ) 3, 0 , ( ) 0, 6 iii)( ) 1, 0 ,( ) 0,1iv)( ) 0,1v)( ) 1, 0vi)( ) 2, 0 ,( ) 2, 0 . 9. i)( ) ( ) ( ) 0, 1 , 1, 0 , 1, 0 ii)1 1 x x < >10. i)( ) 2, 2 ,( ) 5, 4 ii) 2 5 x < < . 4.3 A 1. i)45Dii)60Diii)135Div)120D. 2. i)1ii)1 iii)0iv)2 . 3. i)2 y x = +ii)1 y x = +iii) 2 1 y x = . 4. i)1 y x = + ii)3 y x = + iii)1 y = . iv)2 5 y x = + .5. 40C D.6. - 2 y x = + , 0 x s , . 2 y = ,0 1 x s s 1 y x = + ,1 x > . 7. i)1 ,12 ,0 ,1 . ii) ( ) { } ,1 1 x e ,| | | ) 2, 0 1, x e +8. i)| | 1,1 x e ,( ) ( ) , 1 1, x e + . B 1. i)( ) 6 1 f = ,( )152f = ,( ) 4 0 f = , ( )132f = ,( ) 2 1 f = ,( ) 1 0 f = , ( ) 0 1 f = ,( ) 1 1 f = ,( ) 2 1 f = , ( ) 3 0 f = ,( ) 4 1 f = , ( ) 5 2 f = ii) ( ) 0 f x = : 4, 1, 3 ( ) 1 f x = : 2 , 4 ( ) 1 f x = :| | { } 0, 2 6 x e iii)0, 5 y x = ,| | { } 2, 5 2 x e 2.1 y x = ,1 x > .3. i)( ) 2000 100 t t = ,0 20 t s s , ( ) 600 100 t t = + ,0 20 t s s ,ii) t=7min 4.( ) 8 f x x = + ,0 4 x s s . 5. i)( )120203h t t = + , 0 3 t s s( )25 20 h t t = + ,0 4 t s s ii)2, 4 h iii)2, 4 h . 4.4 A 5. i)( )22 2 x ii)( )22 3 3 x iii)( )22 2 x +iv) .( )22 3 3 x + 4.5 A 1.f ( | ,1 ,f| ) 1, + ,g ( | , 0 ,g | | 0, 2 , g | ) 2, + ,h ( | , 1 , h | | 1, 0 , h | | 0,1 , h | ) 1, + .2.(1) 1 f = , g , ( ) 1 2 h = ,( ) 1 2 h = o . 3. i) ( ) ( ) 3 f x f > ii) ( ) ( ) 1 g x g s4. i) ii) iii) iv) v) vi) 5. i) ii) iii) iv) v) vi) 6. i) ii) iii) ,7. i) ii) iii) . 5 5.1 A 1. 22 y x = .4. 21 1 1 x x s s s , 21 1 1 x x x > < > . 2.f ( | , 0 ,f| ) 0, + , ( ) 0 0 f = , . 3. i) ) 3 2x x x x < < < ) 3 2x x x x > > > . 4.3 . 5.2 1. 2yx= . 4. 11 0 1 x xxs < > , 11 0 1 xx> < < , 5. 210 1 x x xxs < > 7.27o 7.1 215

210 1 x xx> < < . 6. 4yx= . 5.3 1. i)( )22 1 3 y x = + . ii)( )22 2 1 y x = . 2. ) 3 32 2f| |= |\ . . ) 5 496 12g| | = |\ . . 1. i)1 ii)1 iii)3 ,5 .2. i)0 < ii) 0 >iii)1 = ,5 = . 3. i)( )210 f x x x = +ii)( ) 5 25 f = . 4. i) ( )23E 6 182x x = +ii) =5.30 ,40 . 6 6.1 A 1.( ) 3, 1 2. i)( ) 21, 24 ii) 3 5,4 3| | |\ ..3. i)( ) 3, 4 ii)( ) 5, 2 . 4. i) ii) : 2,2+ | | |\ ., e\ . 5. i)( ) 3,1 ii)( ) 2, 1 . 6. i) ii) iii) . 7. i) ( )( )( )3 1 1 , + + , e\ ii) . 8. i)( ) 4, 3, 5 ii) iii)( ) 10 2, 16 2, , . + + e\ 1. i) 11:22 y x = + , 2:1 y x = ii) 2,1. 2.10 ,16 . 3.1500,700. 4. 1 11600 30R T = + . 5.40 ml ,60 ml . 6. i) 112 = , 212 = . ii) iii) 32 = . 7. i) 1 = , - , 21,1 1 | | + + |+ +\ ., 1 = , , 1 = , . ii) e\. 8. i) 3 = , ,3 = , , 3 = ,ii) 3 = , 3 = , 3 = . 9. 2 cm ,4 cm ,3 cm . 10.x = ,y = ,z = . 11. 22,88 lt ,17, 68 lt ,11, 44 lt . 12. ( )24 3 f x x x = + , ( )22 3 g x x x = + + , ( )20,5 3 4 h x x x = + . 6.2 1.( ) 1, 2 , ( ) 2, 1 . 2. i) 2 4,3 3| | |\ . ii)3 2 3 2,2 2| | | |\ .,3 2 3 2,2 2| | | |\ .. iii)( ) 1, 2 , ( ) 1, 2 , ( ) 2, 1 ,( ) 2,1 . 1.( ) 4, 3 ,( ) 4, 3 ,( ) 0, 5 . 2.( ) 1, 0 ,( ) 3, 0 ,( ) 2, 1 ,( ) 4,3 . 3.12 cm ,10 cm 4. 1 < . 7 7.1 A 1.3 x = ,3 2 y = , 45 =D. 2. 1 = , 3 = . 3. i)6 rad ii)3 rad iii)2 rad 4. i) 6radii) 23rad iii)7rad iv) 334rad . 7.3216 5. i)18D ii)150Diii)5460D iv) 18000D. 6. i) 1 3 3, , , 32 2 3ii) 3 1 3, , 3,2 2 3 iii)0, 1, 0, iv)0, 1, 0, .

1. i)478, 733,1062 ii)58D .2. iii)2 2 v) 2 22. 3.12 8 3 + ,12 3 . 4.573 mm. 7.2 A 1. 45x = , 34x = , 43x = . 2. 53x = , 52x = , 2 55x = . 3.3 x = , 12x = , 32x = . 4. 52x = , 53x = , 23x = .5. 8 5 205. 6. i) ,ii) ,iii) . 1.i) 212 ii) 221 iii) 221 iv) ( )23-2 . 7.3 A 1. i) 312002 =D, 112002 = D, 1200 3 = D,312003 = D. ii) ( )128502 =D, ( )328502 =D,( )328503 =D,( )2850 3 =D. 2. i) 187 16 2 = , 187 36 2 = ,

187 36 3 = ,18736 = . ii) 21 24 2 = , 21 24 2 = , 21 2114 4 = = . 3. ( ) 180 + + =D, 902 2| |++ = | |\ .D.4. . 6.1 . 1.0 3.23 . 2.ii)345 8610 51213 212029 163034 15817 4. ii)2 3 < < . 5.iii)3 1 = = . 6.A) i)t 6 =ii)1t 2 = , 2t 10 = . 7.E 8.. = . 8.2 x < . 9.) 0 < , , 0 = , , 0 3 < . 10. iii) 2 = , 0 2 2 0 < < < < , , 1 = , 2 2 < >. 11.1 x = .12.iii)f : 2,g : 0, 2,15. .16. i) ( )5 , 0 2010 100, 20 405 100, 40 60x xf x x xx xs s = s s+ s s iii)22 x = .17. ii)5 1 x = . 18. ii) 2, E 1,5. x = = . 19. i)4, 0ii)( ) E 4 x x = 21. P(0) + P(1) +...+ P(100) = 122.i) P(A') = 1 P(A) . ii) .

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