22 0208-02-am algebra-b-lyk_lyseis

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Transcript of 22 0208-02-am algebra-b-lyk_lyseis

  1. 1. . . . . . 22-0208-02-001-076.indd 1 31/1/2014 1:19:56
  2. 2. & , - / & / . . 22-0208-02-001-076.indd 2 31/1/2014 1:20:21
  3. 3. : . . , . , . . , , , , . , , . . , , . . , . , , , . . : ) . ) . ) . ) . ) . . : . . . 208.indb 3 16/1/2014 2:09:10
  4. 4. 208.indb 4 16/1/2014 2:09:10
  5. 5. 1.1 5 1 1.1 1. i) x y x y x x y x y = + = = + = = = 4 2 2 6 2 3 1. ( , ).3 1 ii) 2. i) x y x y x y x y x y x y 7 8 45 8 7 45 8 7 0 45 1 2 = + = = + = = + = . ( ) ( ) (2) y x= 45 (1) 8 7 45 0 8 315 7 0 15 315 21x x x x x x = + = = =( ) . y = =45 21 24. ( , ).21 24 ii) x y x y x y x y x y x y = + = = + = = + = 1 3 2 4 4 3 8 4 4 3 6 4 3 8 4 3 2 4 3 8. ( ) ( ) 1 2 (1), (2) 8 6 3 4 x x= = . (1), (2) 6 10 5 3 y y= = . 3 4 5 3 , . y x A(3,-1) O 1 1 x+y=2 x-y=4 208.indb 5 16/1/2014 2:09:10
  6. 6. - 16 3. i) x y x y + + + = + + + = 5 2 2 1 7 2 0 7 5 2 2 1 28 0( ) ( ) + + + = + =7 35 4 2 28 0 7 4 5x y x y . x y x y x y + = + = + + = 6 3 6 2 8 2 6 3 6 48 2 12 3 18 48( ) ( ) = =2 3 48 30 2 3 18x y x y . 7 4 5 2 3 18 1 2 x y x y + = = . ( ) ( ) y 7 4 5 3 2 3 18 4 x y x y + = = ( ) ( ) 21 12 15 8 12 72 x y x y + = = 29 87x = , x= = 87 29 3. x = 3 (1) 7 3 4 5 4 21 5 4 16 + = = + = y y y , y = 4. ( , ).3 4 ii) 2 1 3 4 2 4 4 2 1 12 4 3 2 x y x y = + = +( ) ( ) = + =8 4 48 3 6 8 3 46x y x y . x x y x x y + = + = 3 2 3 3 3 3 3 6 2( ) ( ) + = + =3 9 18 2 2 2 9x x y x y . 8 3 46 2 9 1 2 x y x y + = + = . ( ) ( ) (1) x y= 9 2 8 9 2 3 46 72 16 3 46 13 26 2( ) . + = + = = =y y y y y y (2) y = 2 x x+ = =2 2 9 5. ( , ).5 2 4. i) x y x y x y x y = = = = 3 3 3 2 3 3 3 6. . 208.indb 6 16/1/2014 2:09:10
  7. 7. 1.1 7 ii) 2 2 1 2 1 0 2 2 2 2 0 2 2 2 2 y x x y x y x y x y x y = + + = = + = = = . k k k, , + 2 2 . 5. i) D = = = = 2 1 3 5 2 5 3 1 10 3 13 0( ) . Dx = = = = 7 1 4 5 5 7 4 1 35 4 39( ) . Dy = = = = 2 7 3 4 2 4 3 7 8 21 13. x D D x = = = 39 13 3 y D D y = = = 13 13 1. ( , ).3 1 ii) 3 2 8 3 1 x y x y = + = . D = = + = 3 2 1 3 9 2 11. Dx = = = 8 2 1 3 24 2 22. Dy = = = 3 8 1 1 3 8 11. x D D x = = = 22 11 2 y D D y = = = 11 11 1. ( , ).2 1 6. i) D = = + = 2 5 6 7 14 30 44 0, . ii) D = = + = 2 3 4 6 12 12 0. 2 3 40 4 6 80 2 3 40 2 3 40 x y x y x y x y = = = = . iii) D = = + = 3 1 9 3 9 9 0. 208.indb 7 16/1/2014 2:09:10
  8. 8. - 18 3 11 9 3 2 3 11 3 2 3 x y x y x y x y + = = + = + = . 7. i) D = + = ( ) +( ) = = 3 1 2 1 3 1 3 1 3 1 2 2 2 0. : 3 1 2 2 3 1 1 3 ( ) + = + +( ) = x y x y ( ) + = ( ) + ( ) +( ) = +( ) ( ) ( ) + 3 1 2 2 3 1 3 1 3 1 3 1 3 1 3 1 2 x y x y x y == ( ) + = 2 3 1 2 2x y 3 1 1+( ) +( ) ( ), ,k k k . ii) D = + = +( ) ( ) = = 3 1 4 1 2 3 1 3 1 3 1 2 2 2 0. 3 1 4 7 2 3 1 2 +( ) + = + ( ) = x y x y +( ) + = +( ) + +( ) ( ) = +( ) +( ) + = + 3 1 4 7 3 1 2 3 1 3 1 2 3 1 3 1 4 7 3 1 x y x y x y (( ) + = +( ) x y4 2 3 1 . 8. i) = 3 2 11x y (4) 208.indb 8 16/1/2014 2:09:10
  9. 9. 1.1 9 2 5 2 3 2 11 3 2 5 6 4 22 3x y x y x y x y = + + =( ) = + =4 19 4 19x y x y (5) 5 2 3 2 11 33 5 6 4 22 33x y x y x y x y+ = + + + =( ) + = = x y x y5 11 5 11 (6) (5), (6) 2 x 2 4 19 5 11 x y x y + = = x = 4 y = 3. x y (4) = 5. ( , , ).4 3 5 ii) x y= +3 2 (4) 5 3 2 32 4 15 5 10 32 4( )y y y y + + = + + = = = 14 2 6 7 3y y (5) 3 3 11 2 2 2 9 3 6 2 2 2( )y y y y + + = + + = = 7 4y (6) (5), (6) 2 x 2 7y 3 7y 4 . = = . iii) 2 4 6 3 2 2 10 5 3 2 16 x y x y x y + = + + = + = . y x= +4 2 6 (4) 3 2 4 2 6 2 10 3 8 4 12 2 10x x x x+ + + = + + + =( ) + = =x x10 2 10 2 (5) 5 3 4 2 6 2 16 5 12 6 18 2 16x x x x+ + = + + =( ) + = =x x10 2 10 2 (6) (5), (6) x x = = 10 2 10 2 x k= +10 2, = k k, . (4) y k k k= + + = +4 2 10 2 6 16 2( ) . + 16 2k k k, ), . ( ,10 2k + 208.indb 9 16/1/2014 2:09:11
  10. 10. - 110 B 1. i) 1 y x= + . ( , )0 2 ( , )4 0 2 0 0 4 2 4 2 0 2 1 2 = + = + = + = = = 1 1 2 2: .y x= + 2 y x= 1. ii) y x y x = + = 1 2 2 1 , ( , ).2 1 2. x y , x y x y x y + = + = = = 26 2 3 68 10 16. 10 16 . 3. x y x y x y x y + = + = = = 2200 1 5 4 5050 1500 700, . 1500 700 . 4. T = 20 R = 0 4, , 0 4 20 20 0 4, ,= + + = (1) T = 80 R = 0 5, , 0 5 80 80 0 5, ,= + + = (2) 20 0 4 80 0 5 1 600 11 30 + = + = = = , , . R T= + 1 600 11 30 . 5. x m y m , x y+ =100. (1) 50 100 x 208.indb 10 16/1/2014 2:09:11
  11. 11. 1.1 11 80 100 y . 50 100 80 100 68 100 100x y+ = . (2) (1) (2) x y x y x y x y + = + = + = + = 100 50 100 80 100 68 100 100 100 5 8 680. 5 8 100 680 5 800 8 680x x x x+ = + =( ) = = = 5 8 680 800 3 120 40 x x x x y = 60. 40 m 60 m . 6. i) 2 4 3 4 2 3 2 4 3 4 x y y x y x+ = = + = + . 1 1 2 = x y y x y x+ = = + = +2 2 1 2 2 . 2 1 2 = ii) 1 2= , . . iii) 3 4 2 4 6 3 2 . 7. i) x y x y + = + = 2 1. D = = = + 1 1 1 1 12 ( )( ). Dx = = = + + 2 3 21 1 1 1 1( )( ). Dy = = = 2 2 1 1 1( ). D 0 1 1, , x D D x = = + + + = + + + ( )( ) ( )( ) 1 1 1 1 1 1 2 2 208.indb 11 16/1/2014 2:09:11
  12. 12. - 112 y D D y = = + = + ( ) ( )( ) . 1 1 1 1 1, 2 1 1 1 + + + + , . =1, x y x y + = + = 1 1 . = 1, + = = = = x y x y x y x y 1 1 1 1 . ii) x y x y = + = 1. D = = + 1 1 1 02 , . . 8. i) D = + = + = + 1 2 4 1 1 1 4 2 1 82 ( ) ( )( ) ( ) ( ) = + + = + = = + 2 2 2 1 8 9 9 3 3 ( ) ( )( ). Dx = + = + = = + 1 2 2 1 1 1 2 2 1 4 5 ( ) ( ) ( )( ) ( ). Dy = = = + = = + 1 1 4 2 2 1 4 2 2 4 2 2 2 1( ) ( ). D 0, 3 3, x D D x = = + + = + + ( ) ( )( ) ( )( ) 5 3 3 5 3 3 y D D y = = + + = + + 2 1 3 3 2 1 3 3 ( ) ( )( ) ( ) ( )( ) . = 3, 2x 2y 1 2x 2y 1 4x 4y 2 2x 2y 1, . = = = = = 3, 4x 2y 1 4x 2y 1 4x 2y 2 4x 2y 2, . = + = + = + = 208.indb 12 16/1/2014 2:09:11
  13. 13. 1.1 13 ii) D = + = + = = = + 2 5 1 2 2 2 5 4 5 9 3 32 2 ( )( ) ( )( ). Dx = + = + = + = = 5 5 5 2 5 2 25 5 10 25 5 15 5 3 ( ) ( ). Dy = = = = = 2 5 1 5 5 2 5 5 10 5 5 15 5 3( ) ( ). D 0, 3 , x D D x = = + = + 5 3 3 3 5 3 ( ) ( )( ) y D D y = = + = + 5 3 3 3 5 3 ( ) ( )( ) . = 3, x y x y + = + = 5 5 5 5, ( , ),5 5 k k k - . = 3, 5x 5y 5 x y 1 x y 5 x y 5, . + = = = = 9. R1 , R2 R3 1 , 2 3 , R R R R R R 1 2 2 3 1 3 6 1 7 2 5 3 + = + = + = ( ) ( ) ( ) . : 2 18 91 2 3 1 2 3( )R R R R R R+ + = + + = (4) (4) (1), (2) (3), R R R R R R1 2 3 1 2 39 6 3+ + = = . R R R R R R1 2 3 2 3 19 7 2+ + = = . R R R R R R1 2 3 1 3 29 5 4+ + = = . 2 cm, 4 cm 3 cm. 10. . = = x, = = y = = z. 208.indb 13 16/1/2014 2:09:11
  14. 14. - 114 x y y z z x + = + = + = ( ) ( ) ( ) 1 2 3 2 2 ( )x y z x y z+ + = + + + + = + + (4) (4) (1) + = + + = + z z 2 2 . (4) (2) x x+ = + + = + 2 2 . (4) (3) y y+ = + + = + 2 2 . : + + = 2 , x = + = = 2 2 2 y = , z = . 11. x, y, z lt , x y z x y z x z x y z + + = + + = = + + = 52 50 100 10 100 30 100 32 100 52 2 52 (11 50 10 30 1664 2 2 3 ) ( ) ( ) x y z x z + + = = (1) (3) y z+ =3 52, y z= 52 3 (2) 50 2 10 52 3 30 1664 + + =z z z( ) + + = = = 100 520 30 30 1664 100 1144 11 44 z z z z z , , z lt 11 44, x lt= 22 88, y lt=17 68, . 12. 1 , f(x) yy 3, f( ) ,0 3= = 3, f x x x( ) .= + + 2 3 f(x) ( , )2 1 = = = = = = 2 2 2 1 4 2 1 4 1 f f ( ) . f x x x( ) .= +2 4 3 208.indb 14 16/1/2014 2:09:12
  15. 15. 1.1 15 2 , g(x) xx 1, g( ) , =1 0 + = 0. (2) g(x) ( , ),1 4 = = = = = + + = 2 1 2 4 2 1 4 2 3 4 g g( ) ( ) . (( )4 , (3), (2) (4) 3 0 4 3 3 4 3 1 + = + = = = = = = 1, = 2 = 3, g x x x( ) .= + +2 2 3 2os : g(x) 1 1= . 2 , 1 2+ = . , xk xk = 2 xk =1, = + = + = = 2 1 2 1 1 2 1 31 2 2 2 . 1 1= 2 3= , g x x x x x( ) ( )( ) ( )( ).= = + 1 2 1 3 , ( , ),1 4 g( ) ,1 4= ( )( ) .1 1 1 3 4 1+ = = g x x x x x( ) ( )( ) .= + = + +1 1 3 2 32 3 , h(x) xx 2 4 yy 4, h h h ( ) ( ) ( ) 2 0 4 0 0 4 4 2 0 16 4 0 4 4 2= = = + + = + + = = + = + = = + = + = = = 4 16 4 4 4 2 2 4 1 4 2 2 4 2 2 == = = = = 1 4 3 0 5 4 , h x x x( ) , .= +0 5 3 42 208.indb 15 16/1/2014 2:09:12
  16. 16. - 116 3os : h(x) 1 2= 2 4= . h x x x( ) ( )( ).= 2 4 , ( , ),0 4 h( ) ,0 4= ( )( ) , .0 2 0 4 4 0 5 = = , h x x x x x( ) , ( )( ) , .= = +0 5 2 4 0 5 3 42 1.2 1. y x= 1 (1) , , x x x x x x x x x2 2 2 2 2 1 1 3 1 2 3+ + = + + + =( ) ( ) =x x2 2 0. (2) (2) x1 1= x2 2= , (1) y x1 11 1 1 2= = + = y x2 21 1 2 1= = = . , ( , )1 2 ( , ).2 1 2. i) , , 12 3 3 4 9 12 4 0 12 2 x x x x = + =( ) . ( ) (1) , x = 2 3 , y = 4 3 . , 2 3 4 3 , . , , y x= 3 2 12 3 4x y = . , 2 3 4 3 , . y xO M 1 1 y=3x 12x-3y=4 2 208.indb 16 16/1/2014 2:09:12
  17. 17. 171.2 MH ii) x y y x 2 2 9 1 2 + = = ( ) ( ) (1), (2), x x x2 2 2 9 2 9+ = = x1 3 2 3 2 2 = = x2 3 2 3 2 2 = = , y x1 1 3 2 2 = = y x2 2 3 2 2 = = . , 3 2 2 3 2 2 , 3 2 2 3 2 2 , . , , x y2 2 9+ = O( , )0 0 3 y x= . , A 3 2 2 3 2 2 , B 3 2 2 3 2 2 , . iii) - x 0, y 0 y x = 2 . x x 2 2 4 5+ = + =x x4 2 4 5 + =x x4 2 5 4 0. (1) x2 = (2), (1) 2 5 4 0 + = . (3) 1 1= 2 4= , (2) x2 1= x2 4= . O A B y y=x 3 x x2 2 +y =9 O B B y x x2 2 y 5' ' 5 2 y x = 5 =+ 208.indb 17 16/1/2014 2:09:12
  18. 18. - 118 x1 1= , x2 1= x3 2= , x4 2= , y y x 1 1 2 2= = , y x 2 2 2 2= = y3 2 2 1= = , y4 2 2 1= = . , ( , ), ( , ), ( , ) 1 2 1 2 2 1 ( , ).2 1 , x y2 2 5+ = O( , )0 0 5, y x = 2 . , ( , ), ( , ), ( , ) 1 2 1 2 2 1 ( , ).2 1 3. v v t= +0 v v t =0 , = v v t 0 . S v t t v t v v t t v t v v t v t vt v t = + = + = + = + 0 2 0 0 2 0 0 0 01 2 1 2 2 2 2 ( ) . S v v t= + 0 2 . 1. 2 10 252 y y+ + = , - , y y2 2 15 0+ = , 3 5. y = 3 x2 16= , x = 4 x = 4. y = 5 x2 0= , x = 0. ( , ), ( , ), ( , ).4 3 4 3 0 5 y x= 1 2 52 x y2 2 2 5+ = . B A y xO 2 2 2 x y 5+ = 208.indb 18 16/1/2014 2:09:13
  19. 19. 191.2 MH 2. y x y y( )2 5 0 0 = = 2 5 0x y = , y y x x = = + 0 4 32 (1) 2 5 0 4 32 x y y x x = = + (2) (1) y = 0, x x2 4 3 0 + = . x1 1= x2 3= , (1) , ( , )1 0 ( , ).3 0 (2) y x= 2 5, (3) 2 5 4 3 6 8 02 2 x x x x x = + + = . x3 2= x4 4= , (3) y3 2 2 5 1= = y4 2 4 5 3= = . (2) , ( , )2 1 ( , ).4 3 , ( , ),1 0 ( , ),3 0 ( , )2 1 ( , ).4 3 3. x, y , xy =120 (1) ( )( )x y+ =3 2 120 (2) (2) xy y x+ =3 2 6 120 (1) 120 3 2 6 120 3 2 6 2 6 3 + = = = + y x y x y x , (3) (1) x x x x x x 2 6 3 120 2 6 360 3 180 02 2+ = + = + = . x1 12= x2 15= . x cm=12 , , (1), y x cm= = = 120 120 12 10 . 4. , y x k= +2 y x= 2 y x k y x = + = 2 2 (1) y x= 2 , = +x x k2 2 x x k2 2 0+ + = . (2) , (1) , (2) . , = >4 4 0k , k 0, > 1 2 . (1) , , . = 0, = 1 2 . (1) , , . < 0, < 1 2 . (1) , , . , . y xO 1 21 y x 2 = y x , 0,5= + > y x , 0,5= + < y x 0,5= 208.indb 20 16/1/2014 2:09:13
  20. 21. 21 2 2.1 MONOTONIA - AK - 2.1 - - 1. f ( , ] 1 [ , ).1 + g ( , ], 0 [ , ]0 2 [ , ).2 + h ( , ], 1 [ , ],1 0 [ , ]0 1 [ , ).1 + 2. f x =1, f ( )1 1= . g . h x = 1 x =1 h h( ) ( ) , = = 1 1 2 . 3. i) f x f( ) ( ). 3 f x f x x x( ) ( ) ( ) , + + 3 6 10 3 6 3 10 3 02 2 2 . ii) g(x) g(1). g x g x x x x x( ) ( ) ( ) , + + + 1 2 1 2 1 1 1 2 1 0 12 2 2 2 . 4. i) f1 x f x x x x x1 2 4 2 4 3 5 3 5( ) ( ) ( ) , = + = + f1 . ii) f2 x f x x x2 3 1 3 1( ) , = + = + f2 . iii) f3 x f x x3 1( ) , = + , , f f3 31 1( ) ( ). iv) f4 x f x x x x x f x4 3 5 3 5 43 3( ) ( ) ( ) ( ) ( ), = = = f4 . v) f5 ( , ) ( , ) +1 1 0. , f5 , . f x x x x x 5 2 2 1 1 ( ) ( ) , = = , . vi) f6 x f x x x x x x x f x6 2 2 2 6 2 1 2 1 2 1 ( ) ( ) ( ), = + = + = + = f6 . 208.indb 21 16/1/2014 2:09:13
  21. 22. 22 - 2 5. i) f1 *={x x 0} x * f x x x f x1 1 1 1 ( ) ( ). = = = f1 . ii) f2 [ , )2 + . , . iii) f3 x f x x x x x f x3 31 1 1 1( ) ( ). = + = + = f3 . iv) f4 * , f x x x x x 4 2 2 1 1 1 ( ) .= + + = , i), : v) f5 , f x f x5 5( ) ( ), = x . vi) f6 [ , ]1 1 , f x f x6 6( ) ( ), = x [ , ].1 1 6. i) Cf O( , ).0 0 f . ii) Cg yy. g . iii) Ch yy, O( , ).0 0 h . 7. i) f . ii) g . iii) h . 8. ) C1 , C2 C3 yy. y y y x x x O O O y f (x)= y g(x)= y h(x)= 208.indb 22 16/1/2014 2:09:13
  22. 23. 232.2 - ) C1 , C2 C3 . 2.2 1. 4.3, ( ) ,x x= xOy x 'Oy. f x x( ) = + 2 y x= , 2 , f x x( ) = 2 y x= , 2 (). 2. h x x( ) = + 2 y x= , 2 , q x x( ) = 2 y x= , 2 (). y y y O O Oxx x y=f(x) y=g(x) y=h(x) y y y O O Oxx x y=f(x) y=g(x) y=h(x) y x Cf C Cg 1 2 2 O x y Ch C Cq 12 1 2O 208.indb 23 16/1/2014 2:09:14
  23. 24. 24 - 2 3. y x= + 2 , , , y x= 2 . y x= + +2 1,, , y x= + 2 1 . , F x x( ) ,= + +2 1 y x= , 2 1 (). , G x x( ) ,= 2 1 y x= , 2 1 (). 4. i) f x x x x x x( ) ( ) ( ) ( ) .= + = + + = +2 2 5 2 2 1 2 5 2 1 32 2 2 2 , f g x x( ) ,= 2 2 1 3 . ii) f x x x x x x( ) ( ) ( ) ( ) .= = + + = 2 4 9 2 2 2 2 8 9 2 2 12 2 2 2 , f g x x( ) ,= 2 2 2 1 . 5. i) x y C CF CG 1 1 O y x Cf C Cg O A 2 2 208.indb 24 16/1/2014 2:09:14
  24. 25. 252.2 - ii) iii) 6. i) f x x x( ) ( ) ( ) .= + = 2 2 1 1 2 22 2 ii) f x x x( ) ( ) ( ) .= = 2 3 1 2 2 3 32 2 iii) f x x x( ) ( ) ( ) .= + + = +2 2 1 1 2 22 2 iv) f x x x( ) ( ) ( ) .= + = + 2 3 1 2 2 3 32 2 y y y x x xO O O Ch C CF Cq CG C C 3 1 1 1 1 1 1 2 3 5 208.indb 25 16/1/2014 2:09:14
  25. 26. 26 - 3 3 3.1 1. 30 6 = x , x = = =6 30 6 1 2 3 . = = = x 3 3 3 1, = 45 . , = x y , 45 3 = y , y = = = = = 3 45 3 2 2 6 2 6 2 2 3 2 . 2. + = 90 = 90 . 30 2 = ( ) , ( ) = = =2 30 2 1 2 1 60 2 = ( ) , ( ) . = = =2 60 2 3 2 3 3. i) S = 6 1= , = 6rad. ii) S = 6 2= , = 3rad. iii) S = 6 3= , = 2rad. 4. = 180 i) = 30, = = 30 180 6 . 30 6 = rad. ii) =120, = = 120 180 2 3 . 120 2 3 = rad. iii) =1260, = = 1260 180 7 . 1260 7 = rad. iv) =1485, = = 1485 180 33 4 . = 1485 33 4 rad. 208.indb 26 16/1/2014 2:09:14
  26. 27. 3.1 27 5. = 180 i) 10 180 18= = , 10 18rad = . ii) 5 6 180 150 = = , 5 6 150 rad = . iii) 91 3 180 5460 = = , 91 3 5460 rad = . iv) 100 180 18000 = = , 100 18000 rad = . 6. i) 1830 5 360 30 = + , 1830 30 1 2 = = , 1830 30 3 2 = = 1830 30 3 3 = = , 1830 30 3 = = . ii) 2940 8 360 60 = + , 2940 60 3 2 = = , 2940 60 1 2 = = 2940 60 3 = = , 2940 60 3 3 = = . iii) 1980 5 360 180 = + , 1980 180 0 = = , 1980 180 1 = = 1980 180 0 = = 1980 . iv) 3600 10 360 0 = + , 3600 0 0 = = , 3600 0 1 = = 3600 0 0 = = 3600 . 208.indb 27 16/1/2014 2:09:15
  27. 28. 28 - 3 B 1. = h ( ) , ( ) . = h (1) 70 = h ( ) , ( ) . = h 70 (2) ( ) ( ) ( ), = + (1) (2), h h h h + = + = 70 1000 70 1000 70 + = = + h h( ) . 70 1000 70 1000 70 70 (3) i) = 30 , , (3), h = + 1000 30 70 70 30 478 = 45 , h = + 1000 45 70 70 45 733 = 60 , h = + 1000 60 70 70 60 1062 . ii) h =1000, , (3), 1000 1000 70 70 1 70 70 45 = + = + = + = = 70 70 70 1 70 70 70 1 1 ( ) ,, .5723 58 . 2. i) 45 = ( ) ( ). = : 45 2 = = ( ) ( ) ( ) , ( ) = = =2 45 2 2 2 2 ( ) ( ) = ( ) . = 2 208.indb 28 16/1/2014 2:09:15
  28. 29. 293.1 T ii) 22 5 2 , ( ) ( ) ( ) . = = ( ) ( ). = ( ) ( ) , . = =2 4 22 5 iii) ( ) ( ) . = = 2 ( ) ( ) ( ) . = = 2 2 iv) () ( ) ( ) ( ) . 2 2 2 2 2 2 2 2= + = ( ) + ( ) = 2 2 2. v) 22 5 2 2 2 4 2 2 2 , ( ) ( ) ( ) . = = = = vi) 22 5 2 22 5 4 , , , ..., ... 3. 30 6 1 2 6 12 = = = ( ) ( ) ( ) . 30 . = 30 30 6 6 30 6 3 3 = = = = ( ) ( ) ( ) ( ) . = 2 3. 60 12 3 2 12 = = ( ) ( ) . ( ) . = 6 3 ( ) ( ) ( ) . = = =6 3 2 3 4 3 ( ) ( ) . = = 4 3 = + + = +12 4 3 4 3 12 8 3. = = = 1 2 1 2 4 3 6 12 3( ) ( ) . 4. - 1 3600 . 2 rad 3600 sec. 208.indb 29 16/1/2014 2:09:15
  29. 30. 30 - 3 1 sec 2 rad. 3600 , S = , 1 sec 2 3600 . 1 mm 2 3600 1 3600 2 573 = =mm mm mm . 3.2 1. 2 2 1x x+ = x 3 5 - 3 5 1 9 25 1 16 25 2 2 2 2 + = + = = x x x = = x 16 25 4 5 x x x = = 3 4 x x x = = 4 3 . 2. 2 2 1x x+ = x 2 3 2 2 22 3 1 4 9 1x x+ = + = =2 5 9 x = = x 5 9 5 3 x = 5 2 x = 2 5 5 . 3. x x = = = 1 3 3 3. 208.indb 30 16/1/2014 2:09:16
  30. 31. 313.2 x x x x x= = = 3 3 3 3 3 3 (1) 2 2 1x x+ = , (1), 1 3 1 3 3 4 3 3 4 2 2 2 2 2 2 x x x x x x+ = + = = = =x 3 2 (1) x = = = 3 3 3 2 3 3 2 1 2 . 4. x x = = = 1 5 2 5 5 2 . x x x x x= = = 2 5 5 2 5 5 2 5 5 (1) 2 2 1x x+ = , (1), 2 2 2 2 24 5 1 5 4 5 9 5x x x x x+ = + = = = = 2 5 9 5 3 x x 0 x 2 x 0. < < > (1) x = = 2 5 5 5 3 2 3 . 5. x x x x x= = = 2 2 2 . 2 2 1x x+ = , (1), 2 2 2 2 4 1 5 1 1 5 x x x x+ = = = = = x 1 5 5 5 3 x 2 2 x 0. < < < (1) x = =2 5 5 2 5 5 . 208.indb 31 16/1/2014 2:09:16
  31. 32. 32 - 3 2 1 x x x+ 2 5 5 2 5 5 1 2 5 5 4 5 5 2 5 5 4 5 2 5 4 5 2 5 5 2 5 5 + = / + / = + = + ( ) ( )( 22 5 8 5 20 5) .= 6. 2 2 1x x+ = , i) x = 0 x = 0, 0 0 12 2 + = , 0 = 1, . ii) x =1 x =1, 1 1 12 2 + = , 2 = 1, . iii) x = 3 5 x = 4 5 3 5 4 5 1 2 2 + = . x. 7. (x,y) (0,0) 3. ( ) ( ) ( ) = + = + = +x y2 2 2 2 2 2 3 3 9 9 = + = =9 9 32 2 ( ) . 8. 9 4 9 2 4 3 9 4 4 92 2 2 2 2 2 x y+ = + = + ( ) ( ) = + = + = =36 36 36 36 1 362 2 2 2 ( ) . 9. x y z r r r2 2 2 2 2 2 2 2 2 2 2 + + = + + = + + = + = + = r r r r r 2 2 2 2 2 2 2 2 2 2 2 2 2 ( ) ( ) rr2 . 10. i) 1 0+ 0, : 1 1 1 12 + = = + ( )( ) = 2 2 1 . 1 0+ 1 0 , 1 1 1 1 1 1 2 + = + = ( ) ( )( ) ( ) = = ( ) . 1 1 2 208.indb 32 16/1/2014 2:09:17
  32. 33. 333.2 ii) 4 4 2 2 2 2 2 2 2 2 = = + ( ) ( ) ( )( ) = = = 2 2 2 2 2 1 2 1( ) . 11. i) 1 1 1 1 2 2 + + + = + + + = ( ) ( ) 2 2 1 2 1 2 2 1 2 1+ + + + = + + = + ( ) ( ) ( ) ( ) . 1 2 + = ii) x x x x x x x x x x1 1 1 1 1 1 + + = + + + = ( ) ( ) ( )( ) 22 1 2 x x = = 2 2 2 x x x . 12. i) + + = + + = + + = 1 1 1 1 . ii) 2 2 2 2 2 2 2 2 2 = = = = = = 2 2 2 2 2 2 2 2 2 1( ) 2 . 13. i) x x x x x x x x x x 1 1 1 1 + = + = + = = + 2 2 2 2 x x x x x x x x x x x x( )( x x x x x x = + ) . ii) ( ) ( )1 1 1 1 1 1 2 + = + = x x x x x x x = = = 2 x x x x x x x. 208.indb 33 16/1/2014 2:09:17
  33. 34. 34 - 3 iii) 1 1 1 2 2 2 x x x x x x x x x x x x x+ = + = + = + 2 1 x x x= . iv) 1 1 1 12 2 x x x x x x x x = = = 2 2 x x x x x x. B 1. i) x x+ = ( ) x x+ =2 2 2 2 2 2x x x x+ + = 1 2 2 + = x x x x = 2 1 2 . (1) ii) 1 1 1 2 2 12 2 x x x x x x + = + = = . [ (1)] iii) x x x x x x x x x x x x + = + = + = 2 2 1 = = 1 1 2 2 12 2 . iv) 3 3 3 3+ = + +( ) ( ), 3 3 3 3x x x x x x x x+ = + +( ) ( ) = 3 2 3 1 2 2 1 x x x x 2 + = = = = = 3 3 3 2 3 3 2 3 2 3 2 ( ) . 208.indb 34 16/1/2014 2:09:18
  34. 35. 35 2. i) 2, 7.2. ii) 3 3 3 3+ = + +( ) ( ), 6 6 2 3 2 3 x x x x+ = +( ) ( ) = + + = ( ) ( ) 2 2 1 3 2 2 2 2 1 3 1 3 x x x x x x 2 2 x x. iii) 2 36 6 4 4 ( ) ( ) x x x x+ + = = + 2 1 3 3 1 2 2 6 3 6 2 2 2 2 2 2 2 2 ( ) ( ) x x x x x x x x == 1. 3. 1 1 1 1 1 1 1 12 2 + = + + + = + = + x x x x x x x x ( )( ) ( )( ) ( ) xx x = +1 x x , x > 0, < < 2 2 x . 1 1 1 + = x x x x . 1 1 1 1 1 1+ + = + x x x x x x x x = = 2 2 x x x. 4. 1 1 1 1 + + + x x x x = + + ( ) + ( ) + + ( ) = + + 1 1 1 1 1 1 1 1 2 x x x x x x x x x x x x x x + + + = + = + 2 1 1 1 1 2 2 1 2 22 ( )( ) ( ) ( ) 22 2 2 x x = + = +1 1 x x x x 0 x x 0 2 < = + = = ( )( ) ( ) ( ) ( 1 1 1 1 1 1 2 2 x x x x x x x x x x x x) .= 1 3.2 208.indb 35 16/1/2014 2:09:18
  35. 36. 36 - 3 3.3 1 1. i) 1200 360 3 120. 1200 3 360 120 = + 1200 120 180 60 60 3 2 = = = =( ) 1200 120 180 60 60 1 2 = = = = ( ) 1200 3 2 1 2 3 = = 1200 1 2 3 2 1 3 3 3 = = = . ii) 2850 7 360 330 = + ( ) ( ) = = = 2850 2850 330 360 30 = = = ( )30 30 1 2 ( ) ( ) = = = 2850 2850 330 360 30 = = = ( )30 30 3 2 ( ) = =2850 1 2 3 2 3 3 ( ) . = =2850 3 2 1 2 3 2. i) 187 6 187 12 2 = . 187 12 15 7. 187 6 187 12 2 15 7 12 2 15 2 7 6 = = + = + 187 6 15 2 7 6 7 6 6 6 1 2 = + = = + = = 187 6 7 6 6 6 3 2 = = + = = 208.indb 36 16/1/2014 2:09:19
  36. 37. 37 187 6 1 2 3 2 1 3 3 3 = = = 187 6 3 2 1 2 3= = . ii) 21 4 21 8 2 = . 21 8 2 5. 21 4 21 8 2 2 5 8 2 2 2 5 4 = = + = + 21 4 5 4 4 4 2 2 = = + = = 21 4 5 4 4 4 2 2 = = + = = 21 4 2 2 2 2 1= = 21 4 2 2 2 2 1= = . 3. + + =180 = +180 ( ) 2 90 2 = + . i) = + = +( ( )) ( ).180 ii) = + = +( ( )) ( ).180 + + =( ) .0 iii) 2 90 2 2 = + = + iv) 2 90 2 2 = + = + . 4. ( ) , = ( ) ,180 + = ( ) = ( ) ( ( )) ( ) ,90 90 + = = = ( ) ( ) ( ) ( ) ( ) ( ) + + = 180 90 = . 3.3 AN 1 208.indb 37 16/1/2014 2:09:19
  37. 38. 38 - 3 5. ( ) , = x x ( )2 + =x x 9 2 2 2 2 2 2 + = + + = + = x x x x( ) = = ( ) .x x ( ) ( ) ( ) ,13 6 2+ = + + = + = x x x x ( ) =x x 21 2 5 2 2 2 = + = =x x x x. ( ) ( ) ( ) ( ) + + + x x x x x x 2 9 2 13 21 2 = = ( ) ( ) ( ) . x x x x x x 1 6. ( ) , =x x ( ) = x x ( ) ( )2 = =x x x 2 =x x, 2 2 2 2 2 ( ) ( ) ( ) + + x x x x = + = + = 2 2 2 2 2 1x x x x x x . 1. 495 360 135 135 180 45 45 2 2 = + = = = =( ) ( ) 120 180 60 60 1 2 = = = ( ) 495 360 135 135 180 45 45 2 2 = + = = = = ( ) ( ) ( ) = = 120 120 1 2 ( ) ( ) ( ) = = = =120 120 180 60 60 3 495 360 135 135 180 45 45 1 = + = = = = ( ) ( ) . 2 2 1 2 2 2 1 2 3 1 2 4 2 4 3 1 0 + + = + = ( ) . 2. ( ) ( ) ( )5 4+ = + + = + = ( ) ( ) ( )7 6 = + = = 208.indb 38 16/1/2014 2:09:20
  38. 39. 393.3 AN 1 5 2 2 2 2 = + = = 7 2 4 2 2 2 + = + = + = = ( ) ( ) ( )5 4+ = + + = + = ( ) ( ) ( )7 6 = + = = 5 2 2 2 2 = + = = 7 2 4 2 2 2 + = + = + = = ( ) ( ) ( ) = = 2 2 2 1= . 3. 2 2 2 2+ = + ( ) , 2 2 3 6 + + x x = + + + 3 6 2 3 6 2 x x x x = + = + 5 2 3 6 25 2 3 2 6 2 x x x x = = =25 2 3 3 25 2 23 x x . 4. 0 1 0 1< + + + < < + < ( ) ( ) x x x x x x < + < < + < < + < < < 0 1 1 0 1 1 0 1 1 0 2 2 2 2 x x x x x x x x x 22 1x + . , x = 0, , , x. 208.indb 39 16/1/2014 2:09:21
  39. 40. 40 - 3 6 3 2 2 3 y xO 1 2 y y y y 2 x x 2 x 0,5 x = = = = 2 3 5 y xO 1 y y y x 2x 0,5x = = = 3 22 2 y x O y 1+ x= y 1+ x= 3 2 1 2 2 y x= x22 y 3x y O 1 3 2 = y x= 3.4 1. i) : x 0 2 x 0 1 0 1 0 0,5 x 0 0,5 0 0,5 0 2x 0 2 0 2 0 2 x 0 2 0 2 0 - , - . ii) : x 0 2 x 1 0 1 0 1 0,5 x 0,5 0 0,5 0 0,5 2x 2 2 2 0 2 2 x 2 0 2 0 2 - , - . 2. g(x) = 1 + x - f(x) = x 1 , f(x) = 1 + x 1 . 3. f(x) = 3x - 2 . 3 : x 0 3x 0 1 0 1 0 g, . 2 3 2 2 3 2 22-0208-02-001-076.indd 40 16/1/2014 3:40:28
  40. 41. 413.4 O 4. g(x) = 3x 2 . 3 : x 0 3x 1 0 1 0 1 g . x y O 1 2 y x 3x 3 2 = 2 =y 6 3 2 2 3 5. (x) = x 2 1, 1 f(x) = 2 x 2 2 2. f(x) = 2 x 2 2 1 2 4 = . f, . y y x 2 = = 2 x y = 2 x x y O 1 2 3 4 6. , f x x ( ) = 2 2 2, - 2. 2 ... - g(x) = x 2 , f(x) = 2 2 x , : 2 1 2 4 = . : f(x) = 2 2 x . x 0 2 3 2 0 2 0 2 x 2 x 0 2 3 4 2 0 2 0 22 2 x 208.indb 41 16/1/2014 2:09:22
  41. 42. 42 - 3 y O 2 3 5 7 4 3 2 222 2 y 2= y x= x y x 2= x 7. g(x) = 1 + x f(x) = x 1 , h(x) = 1 + x . 8. f(x) = 2x , 2x - , , x . 2 f(x) = 2x . 2 - f(x) = 2x. x 0 2x 1 0 1 4 6 8 12 12 8 6 4 3 3 3 3 3 3 O x y 2 4 4 2 (9) y x= y 2x= 2 2 (8) y x y x= y 1 y x x = + = 1 1 1 + 208.indb 42 16/1/2014 2:09:22
  42. 43. 433.4 O 9. f(x) = x , - , .x (0,). , f(x) = x, f(x) = x, (0,) - x = 0 x = . (0,) . 1. i) y = x. : y = x. 4. 2 = 4, = 1 2 . 1. y = x 2 . 2 . 3 2 2 3 = , = 3. 1. y = 3x. ii) : y = x y = 3 x y = 0,5 x y = 2,5 x. y x O 2 y x= 208.indb 43 16/1/2014 2:09:23
  43. 44. 44 - 3 2. i) 3 m : t 6 1= , 3 m t 6 1= . 6 m. ii) f(x) = xt. 2 2 6 12 = = . : t 0 3 6 9 12 3 0 3 0 3 0 - . 3. i) 1 1 3 4 3 + =m m, 1 1 3 2 3 =m m. 4 3 2 3 2 3 =m m. ii) 2 ... 2 . 3 iii) - . t 0 1 1 4. i) 0,1 m. 6 3 2 2 3 4 3 2 3 4 3 1 1 3 3+ t () ( ) y t 1 O 6 93 12 3 O 2 2 4 3 1 y 1 3 3 = + t 6 208.indb 44 16/1/2014 2:09:23
  44. 45. 453.5 BA ii) - 2/3 sec. - - . - x(t)=0,15 - [0, 2] /18, 5/18, 13/18, 17/18, 25/18 29/18. 3.5 1. i) x 2k x 0 x 0 ,k x 2k = = = = + Z x 2k x (2k 1) = = + Z Z ii) x 2k 4 2 x x 2 4 x 2k 4 = + = + Z x 2k 4 3 x 2k 4 = + = + Z iii) x x x k k= = = 0 2 2 2 , = + x 2 , 0 0,1 0,2 3 3 3 2 4 3 5 2 y x 208.indb 45 16/1/2014 2:09:24
  45. 46. 46 - 3 iv) x x x k k= = = 2 2 4 2 4 , 2. i) x x x= = = 1 2 6 6 x 2k x 2k 6 6 7 x 2kx 2k 66 = + = = += + ii) x x= = 1 2 iii) x x x= = = 2 2 4 4 = = x x k k 3 4 2 3 4 , iv) x x x k k= = = 1 2 , = + x 2 , . 3. i) x x x k k= = = 0 0 , ii) x x x k k= = = + 3 3 6 6 , iii) x x x k k= = = + 1 4 4 , iv) x x x k k= = = + 3 6 6 , 208.indb 46 16/1/2014 2:09:24
  46. 47. 47 4. i) x x x= = = 3 3 6 6 = x k k 6 , ii) x x x= = = 3 3 3 3 = x k k 3 , . 5. i) 1 2 3 0 1 0( ) ( )= = x x x 2 3 0x = =x 1 x x= = 3 2 2 x = 3 x 2k 2 ,k x 2k 2 = + = + Z x 2k 3 ,k x 2k 3 = + = + Z = +x k2 2 x k= +2 3 x k k= + 2 2 3 , ii) 2 2 1 0 2 2 0 x x x+( ) ( ) = + = 1 0 =x = x 2 2 x =1 = x 4 x = 0 = x k2 4 x k= +2 5 4 x k k= 2 , . 6. i) 3 1 0 3+( ) ( ) = = x x x x =1 = x 3 x = 4 = x k 3 x k k= + 4 , ii) ( )( )2 1 3 0 1 2 2 x x x x+ = = 2 3x = x = 0 3.5 BA 208.indb 47 16/1/2014 2:09:25
  47. 48. 48 - 3 1 x x 3 x 3 x 0 2 2 x x x x 3 3 3 2 2 x 2k x k x k x k ,k . 3 3 3 2 = = = = = = = = = = + = = + Z x k k= + 2 , x x k k= + 2 , . 7. i) 0 951 72 2 5 , ,= = : x = 0,951 = x 2 5 2 x 2k 5 ,k 2 x 2k 5 = + = + Z 2 x 2k 5 ,k 3 x 2k 5 = + = + Z ii) 0 809 36 5 , ,= = : x = 0,809 = x 5 = = x x 5 4 5 = x k k2 4 5 , . iii) 28 636 88 22 45 , ,= = : x x= =28 636, 22 45 = + x k k 22 45 , . 208.indb 48 16/1/2014 2:09:25
  48. 49. 49 8. i) 2 3 3 3 3 2 3 3 x x x= = = 6k 3x 2k x 3 9 ,k ,k . 6k 2 3x 2k x 3 9 + = + = + = + = Z Z ii) x x x 5 1 0 5 1 5 + = = = = = + = + x k k x k k x k k 5 2 5 2 10 5 , , , . iii) 3 2 7 3 0 2 7 3 3 2 7 6 x x x = = = = + = + = + 2 7 6 12 42 7 42 7 12 x k k x k k x k k , , , 9. i) x x+ = + = 3 1 3 2 + = = = x k k x k k x k k 3 2 2 2 2 3 2 5 6 , , , ii) 2 3 4 1 3 4 1 2 3 4 3 x x x = = = 3.5 BA 208.indb 49 16/1/2014 2:09:26
  49. 50. 50 - 3 3x 2k 4 3 ,k 3x 2k 4 3 36x 3 24k 4 ,k 36x 3 24k 4 24k 7 x 36 ,k 24k x 36 = = + = + = = Z Z Z iii) 4 5 3 4 5 3 = =x x = + = + = 4 5 3 3 60 12 4 12 60 x k k x k k x k k , , , 10. i) = t, : 2 1 0 1 3 4 12 t t t t+ = = = t = 1 2 : t = 1 : = = = 1 2 2 2 k k, t = 1 2 : 2k 6 1 ,k 2 6 5 2k 6 = + = = = Z 208.indb 50 16/1/2014 2:09:26
  50. 51. 51 : = 2 2 k = +2 6 k = 2 6 k k, ii) x = t, : 2 3 2 0 3 5 4 22 t t t t+ = = = t = 1 2 : t = 2 : x = 2 , 1 1x t = 1 2 : x x x k k= = = 1 2 3 2 3 , : x k= +2 3 x k k= 2 3 , iii) t = , : 3 3 2 3 3 2 3 3 0 2 3 4 3 6 2 2 = + = = = 3 = 3 3 : = 3, : t t t k k= = = + 3 3 3 , = 3 3 , : t t t= = = 3 3 6 6 = t k k 6 , . 3.5 BA 208.indb 51 16/1/2014 2:09:26
  51. 52. 52 - 3 11. i) : 2 2 2 2 2 2 5 4 1 5 4 4 3 3 4 x x x x x x + = + = = = =x 3 2 x = 3 2 . : x x x k k= = = 3 2 3 2 3 , x x x= = = 3 2 3 3 = = x x 2 3 2 2 3 , : x 2k ,k 3 2 x 2 , . 3 = = Z Z ii) x 2x : x 0 2 0x (1) , : x x x x x x = = =2 1 2 1 2 = + = 2x k x k x k k , , 2 0x . . 12. i) f x x( ) = 3 2 x = 2 1 x = 2 1. x x x k k = = = + 2 1 2 2 2 2 2 , = + x k k2 , =x , 0 2
  52. 53. 53 x x x k k = = = 2 1 2 2 2 2 2 , = x k k2 , =x 0, 0 2
  53. 54. 54 - 3 t 2k 6 6 t , 6 6 t 2k 6 6 = + = k = + Z t 12k 1 ,k t 1 t 5 1 t 12 t 12k 5 = + = = = + Z , . ii) To S t 6 - t 6 1= . : t t t k k 6 1 6 2 6 2 2 = = = + , t 12k 3,k t 3, 1 t 12 = + = Z . B 1. i) : 3 x x x x 4 4 3 x x x x 2 4 4 x 2k x ,k 4 x 2k x ,k 4 2x 2k ,k 4 0x = = + = + = = + = + = 5 2k ,k ( ) 4 x k ,k 8 = + = 208.indb 54 16/1/2014 2:09:28
  54. 55. 55 ii) 2x 3 3+ x 2 0x 3 3 0+ x . : 2x 3x 0 2x 3x 3 3 2x 3x 2x 3x 2 3 6 2x k 3x,k 5x=k+ ,k 6 6 k x ,k 5 30 + = = + = + = = + = + . Z Z 2. i) x x 0. : ( ) ( ) ( ) ( ) ( )( ) x x 1 x x x x x x 1 0 x x 1 x 1 0 x 1 x 1 0 x 1 x 1 ( , x 0) x x k ,k . 4 4 + = + = = = = = = = + , - x 0. ii) , x 0. - : 1 2 4 1 2 4 2 3 02 2 2 x x x x x x = + = = 2 4 x x 1 x 3. 2 = = = : x x x x k k= = = = 1 4 4 4 , x x x x k ko = = = = + 3 72 2 5 2 5 , : k k x 0. 3. : x x x k k= = = + 1 4 4 , 3.5 BA 208.indb 55 16/1/2014 2:09:29
  55. 56. 56 - 3 : x x k k( ) < < < + < 3 4 3 4 3 4 4 , , < + < < < < < = 12 4 16 11 4 15 11 4 15 4 3 k k k k k k k , , , x = + =3 4 13 4 . 4. : 1 1 12 2 + = + = + = x x x x x x ( ) ( ) 2 2 2 1 x x 1 x x 1 1 x x 2 x 2 x 0 1 x x 2 x x 1 0 1 x x x 0 x 1 x 1 x 0 x 0 x 1 x x 2 + = + + = + = + = + = + = + = = = = = = = = = 5. x 0 3 0+ x x x x x x x= + = + = 3 2 3 6 = + = + = + x k x k x k k x k k 6 2 6 6 12 1 , , , ( ) : 0 2 0 6 12 2 < + < x k k , 208.indb 56 16/1/2014 2:09:29
  56. 57. 57 0 6k 24 ,k 6k 23 ,k 1 23 k ,k 6 6 k 0 + < < < [0, 2) 7 13 12 12 12 19 . 12 ( ). y x /12 3.5 BA 208.indb 57 16/1/2014 2:09:29
  57. 58. 58 - 3 3.6 1. i) 12 4 12 4 12 4 3 = + = = 1 2 ii) 170 50 170 50 170 50 120 + = ( )= = = 60 1 2 iii) 110 70 110 70 110 70 110 70 = = +( )= = 110 70 180 1 iv) 7 12 12 7 12 12 7 12 12 2 + = = = 0 2. i) ( ) ( ) ( )( )3x 2x 3x 2x 3x 2x = + = x ii) x x x x x x+ + + = + = 4 4 4 4 = 2 2 3. i) x x+ + = 4 4 x x x x 4 4 4 4 2 2 x 2 x 4 2 = + + = = = 2x ii) 2 2 4 4 x x + = = + = x x x x x 4 4 4 4 4 2 2 4 4 4 2 2 2 2 2 x x x x x= = 4. i) 17 18 4 9 17 18 4 9 17 18 4 9 2 = = = 1 22-0208-02-001-076.indd 58 16/1/2014 3:41:16
  58. 59. 593.6 T ii) 70 20 70 20 70 20 90 + = +( )= = 1 iii) 7 12 4 1 7 12 4 7 12 4 3 = = = 3 iv) 165 15 1 165 15 165 15 180 + = +( )= = 0 5. i) ( )2x x 2x x 2x x + = + = 3x ii) x x x x x x+ + = + = = 6 6 6 6 1 2 iii) ( ) ( ) x 2x x 2x x x . iv) . 3 2 6 1 3 2 6 3 + + + = x x ++ + 2 6 x x x 2 = + = x 6. i) x x+ + = 3 3 ii) +( ) +( ) = + + + = +( )+ +( ) = +( )+ ( ) 7. 105 60 45 60 45 60 45 = +( )= + = + = ( )3 2 2 2 1 2 2 2 2 1+ 3 4 105 60 45 60 45 60 45 = +( )= = = ( )1 2 2 2 3 2 2 2 2 1 3 4 105 1 3 1 3 = + = 2 3 105 1 3 1 3 = + = 2 + 3 208.indb 59 16/1/2014 2:09:31