: : : ( CIP ) : ( ) /. :, ISBN :. G7. 4 CIP ( 00 ) 005 : : ( ) : : ( 0 : 0004) : : : / 6 : 7 ( ) : 408 () : 00

Transcription

1 () ( ) ( : )

2 : : : ( CIP ) : ( ) /. :, ISBN :. G7. 4 CIP ( 00 ) 005 : : ( ) : : ( 0 : 0004) : : : / 6 : 7 ( ) : 408 () : 000 : ISBN / G89 : (. 00 )

3 00,,, 00 %, + X,,, 6 5,,, 50, 0,,, , ,. 4 %, ,, 70. %, 5. 55,, 00 00,, 00 ( ) ( ) ( ) ( ) 9,,, : :,,,,,, : 00

4 ,,,, 00,, 0, 0 %, ; 55 59,,, ;,,,,,, :,: ; ( ; ; ; ; ) ; ( ) ; (0000 ),,,,,,,, :,,,,,,,,,,!!! 00 7

5 00 () ( ) 0 (0) (0) () () () (5) (6) () (6) (8) (8) (9) (9) (9) (9) (0) () () (4) (5) (5) (6) (7)

6 (50) (55) (59) (59) (59) (59) (59) (60) (6) (6) (67) (68) (70) (70) (70) (70) (7) (7) (7) (78) (80) (8) (8) (8) (8) (8) (84) (85) (9) (9) (94) (94) (94) (94) (96) (97) (98) ( 0) ( 05)

7 ( 08) ( 08) ( 08) ( 08) ( 09) ( 09) ( 0) ( 0) ( 4) ( 5) ( 7) ( 7) ( 7) ( 7) ( 7) ( 8) ( 8) ( ) ( 5) ( 8) ( 8) ( 8) ( 8) ( 9) ( 9) ( 0) ( 0) ( 7) ( 40) ( 4) ( 4) ( 4) ( 4) ( 4) ( 4) ( 44)

8 ( 48) ( 49) ( 5) ( 5) ( 5) ( 5) ( 5) ( 5) ( 5) ( 5) ( ) ( 5) ( 5) ( 54) ( 54) ( 54) ( 54) ( 54) ( 58) ( 59) ( 6) ( 6) ( 6) ( 6) ( 6) ( 64) ( 64) ( 64) ( 64) ( 65) ( 7) ( 74) ( 76) 4 ( 76) ( 77) ( 77) ( 78)

9 ( 78) ( 78) ( 79) ( 80) ( 80) ( 8) ( 8) ( 8) ( 9) ( 97) ( 00) ( 00) ( 00) ( 00) ( 0) ( 0) ( 04) ( 06) ( ) ( 4) ( 7) ( 7) ( 7) ( 7) ( 7) ( 8) ( 8) ( 8) ( 8) ( 8) ( 9) ( 9) ( ) ( 4) ( 6) ( 6) 5

10 ( 6) ( 6) ( 7) ( 8) ( ) ( 7) ( 9) ( 9) ( 9) ( 9) ( 40) ( 40) ( 40) ( 4) ( 46) ( 48) ( 50) ( 50) ( 50) ( 50) ( 5) ( 5) ( 5) ( 5) ( 5) ( 5) ( 5) ( 5) ( 5) ( 5) ( 57) ( 58) ( ) 00 () 6

11 () ( 60) 00 () () ( 6) 00 () () ( 66) 00 () () ( 69) 00 () () ( 7) 00 () () ( 75) 00 () ( 78) 00 () ( 8) 00 () ( 85) 00 () ( 89) 7

12 00 ( ) : 5 ; 5, 75.,. ( ) A = { x - < x < }, B = { x x > }, A B ( A) { x < x < } ( B) { x - < x < } ( C) { x x > } ( D) { x x > - } A.,.,,,, A B = { x < x < }., A.,, , ( ),,. ( ) cos< 0 tan > 0, ( A) ( B) ( C) ( D) C.,, sin cos tan cot., cos, ;, ; tan, ;,.,,, C. sincostancot,, sin cos tan cot. ( ), ( A) y = x ( B) y = x ( C) y = log x ( D) y = sin x

13 B. ( ). y = f ( x), x x, x > x, f ( x ) > f ( x ), f( x) ; x > x, f ( x ) < f( x ), f ( x)., y = f ( x), f( - x) = - f( x), f( x) ; f ( - x) = f ( x), f( x)., B. ().,. (4 ) 0 < a < b, ( A) a < b ( B) a > b ( C) log a > log b ( D) a < b D.,. ( A ) y = x, y = x (0, + ), a >, A. ( B) b y = x, y = x ( 0, + ), a < b, B. ( C) y = log x, log a < log b, C. (D) y = x, a < b, D.,,. (5 ) y = f - ( x) y = f ( x), (, - ) y = f ( x), y = f - ( x) ( A) ( -, ) ( B) (, - ) ( C) ( -, ) ( D) ( -, - ) C.. :,, (, - ) y = f ( x), y = f - ( x) ( -, ), C., x y.. (6 ) y = sin xcos x ( A) ( B) ( C ) (D) 4

14 C..,, y = Asin (x + ) y = Acos (x + ), A ( ),, T = T =. y = sin xcos x y = =, C. 4 sin4 x, (7 ) : x =, : x - x + = 0, ( A) ( B) ( C) ( D) A., A B. A, B, A B, B/ A, A B ; A/ B, B A, A B ; A B, B A, A B ; A/ B, B/ A, A B.,, /,, A.,997 ( ), 998 ( ), 999 ( ), 000 (7 ),00 ( 6),. (8 ), ( A) 0 C. ( B) 5 ( C ) 0 (D) 5 5 P 5 5, P,, P / P 5 5 = 0. (9 ) a = ( 4, x), b = ( 5, - ), a b, x ( A) 0 ( B) - 0 ( C ) 8 5 A. (D) -, () ab = 0 - x = 0, x = 0, A. ab = 0 a b( a b ) 8 5

15 (0) 4,, B. ( A)70 ( B) 6 ( C )08 (D)90,,,,. + 4 = 5, = 6., 6 5, 6, B. () z = + i, i, z ( A) 6 D. ( B) 6 ( C ) (D) 5 arg z,, z = - i, r = - i = + ( - ) =, cos=, sin= -, arg z = 5, D. z arg z 0 arg z <. () x - x - = 0 B. ( A) x + x + = 0 ( B) x + x - = 0 ( C) x - x - = 0 (D) x - x + = 0 x, x - x - = 0, - x - = 0 x x, x + x = x x = -, x x, x + x -, B. x + x x x = = x + x x x x x = - = - = -,, = 0, x + x - = 0.,. 4

16 () x = 4cos ( ) y = sin A. ( A) x = ( B) x = 6 5 ( C) x = 7 6 (D) x = 5 6,, x = a c ( x ) y = a ( y ). c x = 4cos y = sin. x = 4cos cos= x y = sin 4 sin= y, cos + sin =, ( x 4 ) + ( y ) =. x 6 + y 9 =., x, c = 6-9 = 7,, A. x = 6 7 7,, ' x, y.. x = a c (x ) y = a c (y ),. (4) x + y = ( A) ( B) ( C ) (D)4 A. y x + y = x + y =, x - y =, - x + y = x + y = -,,. o x, x + y =, A., x + y =, x, y,, x + y = x + y =, - x + y =, x - y = x + y = -,,. (5) P( 4, 8) x + y - x - 4 y - 0 = 0, 8, 5

17 ( A) x - 4 y + 0 = 0 y = 8 ( B) x - 4 y + 0 = 0 x = 4 ( C) x + 4 y - 44 = 0 x = 4 (D)4 x - y + 8 = 0 x = 4 B. < Ax + By + C = 0( A B 0), x + y - x - 4 y - 0 = 0, ( x - ) + ( y - ) = 5, (, ), 5., E, DQ, EF DQ, DQ = 8, EF + FQ = EQ, EF, EF = A + B + C A + B, FQ = 8 5, A + B + C A + B + 4 = 5, = 4, EQ = ( A + B + C) = 9( A + B ) P(4, 8 ) Ax + By + C = 0, 4 A + 8 B + C = 0 4 B = 0 B = - C = - 4 A A C = 0, A D O F y Q P( 4, 8) E G ( 5) B C A x + By + C = 0 x - 4 y + 0 = 0 x = 4 x - 4 y + 0 = 0 x = 4, B.,,,,,,,,. x : 4, 5, 0,. (6) x 64 - y 6 = x 64 - y 6 = y, a = 64, b = 6, a = 8, b = 6, c = a + b = = 00, c = 0, e = c a = 0 8 = 5 4., 5 4., x, y, a b c c = a + b, e = c a > 0, b > 0). 6, c > a.x y a - x b = ( a

18 (7) f ( x) = 0 x+, f( lg). 0. f ( x) = 0 x+ = 0 x 0, f (lg ) = 0 lg 0 = 0 = 0., 0. a l og a N = N. (8) y = - x +, cos. -. y = - x + k = t an= -, 80> 0, = 0,, -. cos= cos0= -. 0 < 80. (9) R,. 8 9 R. a, R, a + a + a = ( R), a = 4 R, a = 4 R, a = R, a = ( R) = 8 9 R., 8 9 R. R,,.. : 5, 55.. (0) ( ) a b c, b a c, a b c. b a c, a = b + c, a b c, q, b = aq, c = aq ( q 0, q ), a 0. a = aq + aq, q + q - = 0, q = -, q =, q,. : -. () ( ), P L 40, L, A 7

19 B, APO = 60, BPO = 0.A B k m/ h (), 80 km/ h. AB, A BA B O L AB, AB. AB = AO - BO = 40tan60-40tan0 = = 80 ( ),, AB V = 80 / 600 8( km/ h). 000 : A B 8k m/ h, 80 km/ h. - 5 P () ( ) y = x + bx + k( b 0, k 0 ) x MN, MN =, y = kx + b M N.. MN P( - P y = kx + b, k( - ( - b,0 ). b ) + b = 0, k =. MN =, b +, - b - x + bx + k = 0. b + ) ( - b - ) = b 4 - =, b =, b =. : y = x + x + y = x + y = x - x + y = x -. () ( ), S - ABCD S AD S BC, SAB S BC. MN BCAD, S - ABCD, SM BC, S N AD, BC AD.S l BC AD, l S BC S AD.SM l S N l SBC S AD MS N = 90. ABCD a, MN = a. SM = S N, SM = S N = a, SB = a + 4 a = a. A N D S E ( ) l B M C 8

20 SB E A E SB. SA B SBC, CE SB, AE = CE = SMBC S B = a., SAB SB C AEC. AEC, AC = cosaec = AE + CE - AC AECE AEC = 0. a : = -, AEC, : SAB SB C 0. (4) ( ) : ( ) 6 ; (),.. () x 6 + y =, 0 < < 6. PQ OP OQ, O. < OP OQ x +, 0 <.PQ : OP = 6 cos + 6sin, OQ = PQ = OP + OQ = = = = = 6 sin + 6cos, 6 cos + 6sin + 6 sin + 6cos 6 ( + 6) ( cos + 6sin ) ( sin + 6cos ) 6 ( + 6) ( ) sin cos + 6 ( sin 4 + cos 4 ) 6 ( + 6) ( - 6) sin cos ( + 6). ( - 6) sin + 4 (), [0, ] 4 ( + 6 ) 8. ( - 6 ) sin + 4 = 4, 4 ( + 6) ( - 6 ) + 4 8, 4 8,. + 6 d, d = :. Q O y ( 4) 6 -,. P x 9

21 0,.., ; ; ;...,.,..,..,... 4.,. 5.,. 6., ; ;.,..,.. ax + bx + c = 0. = b - 4 ac ;. ; ;.., 0,,, 0.

22 .. ; (,, ).. ( ) :. :, p q ( p q, q0 ),..,. :. : = ;= ( ) :.: x, ;,.. ( ) :,..,,. (4 ) :.. (5 ) : a a, ; ;. a = a 0 - a ( a > 0) ( a = 0) ( a < 0), a a.

23 (6 ),,., ;,.. ( ) :,. ( ),,,,,. ( ) :,,,.,.. ( ) :,,.,,.. :,. :,,,... :,,,..,.. :,.: aa a n = a n,, a, n, a n n a, a n.n, a n a. ;, ; 0. : x n = a( n ), x a n, an, a n,, a, n.,,,,.,,. (4 ) : a b c. a + b = b + a ab = ba ( a + b) + c = a + ( b + c) ( ab) c = a( bc) a( b + c) = ab + ac.,.,,.

24 . ( ) :,, x y - 4 x ;, 9 y - 6 x y + 4 y x + y ;.. ( ) :,...,,,, :,, ;,,..,,,.,, a( x + y + z) = ax + ay + az,, ( a + b) ( c + d) = ac + ad + bc + bd.,,,.,.,, 0,. ( ) :,,,.,,,. (4 ) : (5 ) : a m a n = a m+ n a m a n = a m - n ( a 0, m > n) ( a m ) n = a mn ( ab) n = a n b n ( ab) = a ab + b ( a + b) ( a - b) = a - b ( ab) ( a ab + b ) = a b ( ab) = a a b + ab b

25 (6 ) :. : ; ; ; ;.. ( ) :.. ( ) : ( ) : 4. a b = am bm, a b = am b m a b c d a b c d = ac bd ( m ) = ad bd bc bd a b c d = a b d c = ad bc ( a b ) n = an b n = ad bc bd ( ) : a a.. a( a 0).,,.,,. ( ) : ( a) = a ( a 0 ) ( a ) = a = a ( a 0) - a ( a < 0) :,. : ab = ab ( a 0, b0 ) a b = a b ( a 0, b > 0) ( ) :,. :,,,.. (4 ) n : x n = a( n N n > ), x a n., ; ;, ; ;,. 4 (5 ) : a n a n. n a.. (6 ) :. n a, ( ) ( n a ) n = a;

26 ( ) n, n a n = a; n, n a n = a = a ( a 0 ) - a ( a < 0 )...,.,. ( ) : () ( ),. (),. ( ) : ax + b = 0 ( a 0 ). ax + b = 0, a 0, x = - a = 0, b 0, ; b a ; x = - a = 0, b = 0,. b a. ( ) : ax + bx + c = 0( a 0 ),. : x = - b b - 4 ac a : = b - 4 ac > 0, ; = 0, ; < 0,. : x x ax + bx + c = 0 ( a 0 ), x + x = - x x = c a x + x = p,, x - px + q = 0 x x. x x = q. ( ) :,. b a a x + b y = c a x + b y = c. () :,. 5

27 a x + b y + c a x + b y + c z = d z = d a x + b y + c z = d :,. ( ) ax + bx y + cy + dx + ey + f = 0.,,., ;. 6. ( A) (B ) ( C) (D), ( ), A B C ; D,,, D. D.. 4 a m - b 6 5 a b m - 6, ( ) ( A) m =, n = ( B) m =, n = ( C) m =, n = ( D) m =, n = 0 4 a m - b 6 5 a n - 6, D. m - = n - 6 =, m = n =.., ( ) ( A) x = x = ( B) ( x - ) ( x - ) = 0 x = ( C) - y - = 5 - y - = (D) 5 x - 5 = x + x = - x = x =, A, ( x - ) ( x - ) = 0 x = x =, B ; C, - C ; D, 5 x - 5 y - = y = 4, 6 - y - = y =, = x + x = - 6 5, D. 6 5

28 D. 4. x + ( m + ) x + m + = 0 7, m ( ) ( A) - ( B) ( C ) (D) - x x + x = - + ( m + ) x + m + = 0 x x, m + x x = m + - x + x = m + - m + m - 0 m - 9 = 0, m =, m = -. = ( m + ) m m = -. D. = 7-8 ( m + ) 0, - m - 0, m - m, 00 (),. 5. a b ab = 0, ( ) ( A) (B) a 0 b = 0 ( C) a = 0 b 0 (D) a b (A ) (B) ( C ),. (D). ab = 0 a = 0 b = 0, a b. D. 6. a, ( ) ( A) a = a (B) a = - a ( C) a a (D) a a a 0, a = a. a < 0, a > a. : a R, a a. D. ( ) a = 5, a = 5, B. a = - 5, a = 5, A C. D < m < 0, ( m + ) - m ( ) ( A) m + (B) ( C ) - m + (D) - m - - < m < 0 m + > 0, m < 0 = m + - m = m + - ( - m) = m +. 7

29 A. :, a b, a + b - a - 4b + 8 ( ) ( A) (B) 0 ( C) (D) : ( a - ) + ( b - ) +. ( a - ) 0, ( b - ) 0, ( a - ) + ( b - ) +. C. 9. ( a - b) - ( a < b) ( ) a - b ( A) b - a ( B) a - b ( C) - b - a (D) - a - b a - b < 0, b - a > 0. ( a - b) - C. a - b = - ( b - a) - a - b = - - a - b ( b - a) = - b - a < x <, - x + x + 4 x + 4 ( ) ( A) 0 ( B)4 ( C) x ( D) 4 + x 0 < x <, - x = - x, x + 4 x + 4 = ( x + ) = x +, = - x + x + = 4. B.. x = -, x - x + ( ) ( A) + ( B) ( C) ( D) x = - = +, x - x + = ( x - ) = ( + - ) =. C.. ( ) ( A) x + y = ( x + y) ( x + xy + y ) ( B) + x = ( + x) ( C) x + 8 y = ( x + y) ( x - xy + 4 y ) ( D) y - x = ( y - x) ( y + x y + x ) x + y = ( x + y) ( x - xy + y ), A.

30 + x = ( + x) ( - x + x ), B. x + 8 y = ( x + y) ( x - xy + 4 y ), C, D.D.. a5 x 5 + a4 x 4 + a x + a x + a x + a0 - ( x - ) 5 = 0, a0 + a + a + a + a4 + a5 ( A)0 (B ) ( C) ( D) 6 a5 5 + a4 4 + a + a + a + a0 = a0 + a + a + a + a4 + a5 x =, a0 + a + a + a + a4 + a5 =. B. ( ) 4. x x + px + q = 0 p q, p q ( ) ( A) p = -, q = - ( B) p =, q = - p = 0, q = 0 ( C) p =, q = 0 (D) p = 0, q = - p =, q = 0, p + q = - p pq = q q = 0 p =, q = 0 p = 0, p = q = -, p =, q = - p = 0, q = 0. B. 996,. 5. x - x - 6 = 0 ( ) ( A) 6 x + x - = 0 (B) 6 x - x - 8 = 0 ( C) x - x - = 0 (D) 8 x + 9 x + = 0 x - x - 6 = 0 x x, x + x x x x + x =, x x = - = x + x = x x x x = = - x + 6 x - = 0, 6 x + x - = 0. A. - = - 6,, 9

31 0. x - + y ( z + ) = 0, x + y + z =.. a + b - 4 a - b + 5 = 0, a + b. b - a. - x x. x x - x - y -,. 5. x + mx + 0 = 0, m =. 6. x + y = x y, x + y =. 7. 5,. 8. x =, x - x - 0 x - 4 ( x + 5 x - ) x + 7 x + 0 x - 5 x x - = 0, y - 7 = 0, z + = 0. x =, y = 7, z = -, x + y + z = ( - ) = 5. : 5.. ( a - ) + ( b - ) = 0, a = b =. a + b b - a : +. = + - = + - = +. - x 0. x x ; x 4. x x - 4. : x x , ( x - ) ( x - y - ) = x - xy - x - x + y + = x - xy - x + y +. : x - xy - x + y x + mx + 0 = 0, = ( m) = 0, : 0. m = x + y = x + y, x + y = x y, x y x + y =. :. 7. x =, x = 5. x + x = 8, x x = 5,, x - 8 x + 5 = 0.

32 : x - 8 x + 5 = x - x - 0 x - 4 = ( x + 5 x - ) x + 7 x + 0 x - 5 x + 6 ( x - 6) ( x + 5) ( x + ) ( x - ) ( x - x + 5 ) ( x + ) ( x + 5 ) ( x - ) ( x - ) = x - 6 x -, x = : 5., = x - 6 x - = - 6 = -,,.. : 5. ( ) ( x + y) - 4 ( x + y - ) ( ) x 6 - y 6 ( ) a 4-4 a + 4 a -. ( ) = ( x + y) - 4 ( x + y) + 4 = ( x + y - ).. : ( ) ( ) = ( x + y ) ( x - y ) = ( x + y) ( x - xy + y ) ( x - y) ( x + xy + y ). ( ) = ( a 4-4 a + 4 a ) - = ( a - a) -. = ( a - a + ) ( a - a - ) = ( a - ) ( a - a - ) b a - b + b ab + b. a - a b + ab b - a = = = b a - b + b ( a + b) ( a - b) a( a - ab + b ) b( a + b) b a - b + - b a( a - b) ab - b a( a - b) = b a.,,.,. ( ) a = 0.5, b = - = [ ab - ( a b - 4 ab -, ab - [ a b - ( 4 ab + ab) ] - 4 ab + a b. ab) - 4 ab ] + a b = ab - a b + 4 ab + ab - 4 ab + a b = ab. a = 0.5, b = -, = 0.5 ( - ) = - 4.,. ( ) ( x - x + 8 x - 4) + (6 x + 9 x ) - (5 x - x - x ). = x - x + 8 x x + 9 x - 5 x + x + x = x + x + 7 x - 4.

33 ,. (4 ) ( + x x + ) - x + x - ( 6 x + x - x + + ) = x + x + - x - ( x - ) x + 4 x + = x + x + - x - x + 4 x + =. : ( ) ( y - ) = ( x + ) ( x + ) - x + x + 4 x + ( )9 ( x - ) = 4( x + ) = x + 6 x + x + 4 x + ( ) () ( y - ) =, y - =, y = +, y = -. () ( y - ) =, ( y - ) - ( ) = 0, ( y - + ) ( y - - ) = 0, y = +, y = -. () y - 4 y + = 0 y = - b b - 4 ac a = 4 ( - 4) - 4 y = +, y = -. ( ) ( x - ) = ( x + ), ( x - ) = ( x + ), x = 0. ( x - ) = - ( x + ), =, x = 5. x = 0, x = x - px + q = 0 x - rx + s = 0, r 0, sp r. x x x - px + q = 0, x 0, x 0. x x x - rx + s = 0 s = x x, r = + = x x x + x x x x + x = p, r = sp. = s( x + x ),

34 sp r =. 995,.,. 5. x = + -, y = - +,. ( ) x y + y x ( ) y + x x y ( ) x + y = = ( + ) + ( - ) ( - ) ( - ) ( ) xy = =, x y + y x = x + y x y = ( x + y) - xy x y = 6 - = ( ) + - = 4. = 6, y + x = y + x = ( x + y) ( x - x y + y ) = ( x + y) [ ( x + y) - xy ] x y x y ( xy ) ( xy ) = 6 (6 - ) = x - y - = 0 4 x + y - = 0 y = x - 4 x + ( x - ) - = 0, 0 x - 0 = 0, x =, y = -. x = y = x - 0 = 0, x =, x = y = -, x = y = -.. a + b = 0, a b ( ) ( A) ( B) ( C) (D). A B a b, a - b - ( b - a) ( ) ( A) b - a ( B) a - b ( C) a (D) 0. a - a ( )

35 4 ( A) ( B) ( C)0 (D) 4. x < -, - + x ( ) ( A) - - x ( B) + x ( C) x (D) - x 5. n < 0, m n ( ) ( A) - mn n ( B) mn n ( C) - mn n (D) - - mn n 6. x, ( ) ( A) x < x - (B) x = x - ( C) x > x - (D) x x - 7. a = +, b = ( - ) -, a b ( ) ( A) a b (B) a b ( C) a b (D) a b 8. : xy z ; x - xy + y ; 4 x ; - x + x ; x - x + y ( ) ( A) (B) ( C) (D) 9. m n, x ( ) ( A) mx n ( B) m + x ( C) m + n nx m + n (D) mx m + n 0. ( x - ) = - x ( ) ( A) x = ( B) x = ( C) x = 4 (D) x = x =. x x - ax - a = 0 6, ( ) ( A) ( B) - 6 ( C)6 - (D) -.,, ( ) ( A) x + x + = 0 (B) x - x + = 0 ( C) x - x + = 0 (D) 7 x - x - 7 = 0. a b c, a c, x + ax + b = 0 x + cx - b = 0, a b c ( ) ( A) a + b = c (B) a + c = b ( C) a = b + c (D) a + b + c = 0 4. ( x - ) = 4 x + kx + 9, k ( ) ( A) ( B) - ( C)6 (D) x + ( m + ) x + m + 5 = 0, m ( A) - 4 ( B) - 5 ( C) - (D) - ( ) 6. x + y = 0 ( ) ( A) 4 ( B) ( C) (D) 7. x = y, x y, ( x + x ) ( y - y ) ( )

36 ( A) x + y ( B) y - x ( C) x (D) y 8. a =, a + a a - a + a - a a + a ( ) ( A) 6 + ( B) + (D) 4 + (D) 4 -. ( x - ) + y + = 0, x y =.. x -. ( x x + ) - = x + 4 -, x =. + ( x - 5) 0 x. 4. a - < 0, a - a =. 5. x m x - ( m - ) x + 9 m - = 0, m. 6. x y, x + ( y - ), x + y =. 7. a b - + ( c - 6) = 0, ab c = x x. 9. y + 6 y + 8 y. 0. A, A( x - xy + y ) = x + y, A =.. : ( ) [ (9 x - 4 y ) ( x - y) ] ( 9 x - 6 xy + 4 y ) ( ) [ ( x + y) - x y] [ ( x - y) + x y] ( x + y) ( x - y) ( ) a b ( - 4 a b) ( - a) (4 ) x y, x + 4 y - x + 4 y + = 0, 4 x + y.. : ( ) x + y =, x y = a + 4, x + y = 6, a. ( ) x a - b = y b - c = z, x + y + z. c - a ( ) x > 0, y > 0, x( x + y) = y( x + 5 y), x + xy + y x + xy - y. (4 ) x y, x + 4 y - x + 4 y + = 0, 4 x + y.. : 5

37 ( ) ( x - ) ( x - ) = (4 x + ) ( x - ) ( ) x + x x + = 0 x - ( ) x + - x - x + = ( x + ) ( ) x - x x + 8 x - = 5 4. : ( ) x + y = 5 x - x y - y = 0 ( ) x + y 4 = x + 5 y - = x + y + 5 ( ) ( 4) x + y = 5 xy = 6 x - y = x + y = 8 5. ( x + a) ( x + b) + ( x + b) ( x + c) + ( x + c) ( x + a) = 0, a b c, : ( ) ; ( ), a = b = c. 6. x + 5 x - = 0,,.. C. D. B 4. A 5. A 6. A 7. B 8. D 9. D 0. D. D. C. C 4. D 5. A 6. D 7. B 8. C x - a 5. m 5, m x + y., x , 0 9. y( y + ) ( y + 4) ( )7 x + 8 y ( ) x 6-64 y 6 ( ) - 8 a 7 b 4. ( ) - 7 ( ) 0 ( ) ( 4). ( ) x = x = - ( ) x = 9 ( ) x = x = (4 ) x = + 9 x = - 9 6

38 4. ( ) ( ) x = y = - x = y = - x = - y = ( ) (4 ) x = 4 y = 9 x = + y = - + x = 9 y = 4 5. x + ( a + b + c) x + ab + bc + ca = 0, x = - y = - - = 4 ( a + b + c) - 4 ( ab + bc + ca ) = 4( a + b + c - ab - bc - ca). ( ) 4( a + b + c - ab - bc - ca) = [ ( a - b) + ( b - c) + ( c - a) ], a b c R, ( a - b) 0, ( b - c) 0, ( c - a) 0, [ ( a - b) + ( b - c) + ( c - a) ] ( ), = [ ( a - b) + ( b - c) + ( c - a) ] = 0, ( a - b) + ( b - c) + ( c - a) = 0. a b c R, ( a - b) 0, ( b - c) 0, ( c - a) 0,, a - b = 0, b - c = 0, c - a = 0. a = b = c. 6. x + 5 x - = 0 x x,, x - x -, x + x = - x x = - ( x - ) + ( x - ) = ( x + x ) - x x - = ( - ( x - ) ( x - ) = x x - ( x + x ) - = ( x x ) - [ ( x + x ) - x x ] - = ( - ) - [ ( - 5 ) - ( - y - 4 y - 8 = 0. 5, 5 ) - ( - ) ] - = - 8, ) - = 4, 7

39 .,.,,,..,,..,,, (),.... =,,.., x y,.,.,,,..,..,,.. x y y = kx, y = k x, x y y = ax + b., y = ax + bx + c( a 0) y = ax ( a0) ;...,..,, y = ax + bx + c( a 0) y = ax ( a 0 ). 8., x, y,. 4..,.,.

40 ,,.,,..,, a > 0 a,, a, a > 0 < a <,..,, loga N = b a b = N. a > 0 a... :.A, B, C,. :.a, b, c,. a A: a A, a A. a A: a A, a A..( ) :. :. :. :... :, N. 0 N. :, Z. :. Q(Q +, Q - ). :, R(R +, R - ). :, C. :,, :{a, b, c}. :,. { x x - x - 0}, { 00 }. : - - A.. 9

41 A B, B A, B A, B A A B. A, A. : A B, B C, A C. : B A, A B, B A, B A A B( - - ). : AB, A B, B A, A B, A = B.. A B, A B, A B( - - ). : A A = A, A =.. AB, AB, A B A B A B. : A A = A, A = A. 4. :,,, U. : U, A U, U A , A U, CU A( ). A A, CU A. : A CU A = U, A CU A =.., x y, x - - 5,, y, y x, x, y = f ( x) ( f ). x,, x y,.. 0

42 .. ( ) :.. ( ) :. ( ) :.. ( ) :, x x x, x < x, f ( x ) < f ( x ), f( x) ; x x x, x < x, f ( x ) > f( x ), f( x). y = f ( x), f ( x), f ( x). ( ) : y = f( x) x, f ( - x) = - f ( x), f( x) ; y = f ( x) x f ( - x) = f( x), y = f ( x)., y.,. 4. y = f ( x) y0, x x 0 y0, y, x, y = f ( x), : x = f - ( y), x, y, y = f ( x) y = f - ( x). y = f ( x) y = f - ( x). y = f ( x) y = f - ( x) y = x.. ( ) : y = kx ( k 0 ). ( ) : (0, 0 ) (, k) ( - - 6)

43 k > 0,, ; k < 0,,. k, x ; k, x ( ).. ( ) : y = k x ( k 0). ( ) : k > 0,, ; k < 0,,. x y. k, ( - - 7) ( ) : y = kx + b( k 0). ( ) : (0, b) y = kx. k > 0, k < 0. k, (0, b) x ; k, ( 0, b) x ( )

44 y = ax + bx + c( a b c, a 0).. y = ax ( ) y = ax,, y. ( ) a > 0, y = ax x (),, ; a < 0, y = ax. x (),, ( ) a,, a,.( - - 9) y = ax + bx + c y = ax + bx + c = a( x + b a x + c a ) = a[ ( x + b a ) - = a( x + b a ) + b 4 a + c a ] 4 ac - b 4 a, y = ax + bx + c y = ax,, y = ax. b a > 0, y = ax b a. b a < 0, y = ax b a. 4 ac - b 4 a > 0, y = ax 4 ac - b 4 a. x = - 4 ac - b 4 a < 0, y = ax 4 ac - b 4 a., y = ax + bx + c, y b a, ( - y = ax b, 4 ac - b a 4 a ). + bx + c.

45 a > 0 a < 0 ( - b, 4 ac - b ) a 4 a x = - b a x < - x > - b, a b, a x = - y = b a 4 ac - b 4 a x < - x > - b a, b a, x = - y = b a 4 ac - b 4 a. y = x n ( n ).. x n (n, ). ( ) n, x n R. ( ) n, n = p q ( p q, q > ), xn = x p q = q x p. q, x n R; q, x n [0, + ). ( ) n, n = - k, x n = x k, x n { x x R, x 0}. (4 ) n, n = - p q ( p q, q > ), xn = x p q = q x p. q, x n { x x R, x 0}; q, x n [0, + ).., n,, n > 0, n < 0, n > 0 : 4

46 ( ) ( 0, 0), (, ) ( ), x. n < 0 : ( ) (, ). ( ), x. ( ), y, x.. (, m n N). ( ) : a n = aaaa ( n N, n > ) a = a ( ) : a 0 = ( a 0 ) n ( ) : a - n = a n ( a 0, n N) (4 ) : a n m = m a n a < 0, m,. n a < 0, m, a m ( a > 0, m n m > 0 ). n m > 0,0 n m = 0, n m 0, 0 n m.. a m a n = a m+ n ( a > 0, m n R) ( a m ) n = a mn ( a > 0, m n R) ( ab) m = a m b m ( a > 0, b > 0, m R) 5

47 . a b, N. ln N. = N ( a > 0, a ), b a N, loga N = b, a, 0, lg N; e,. loga ( MN ) = loga M + loga N ( M > 0, N > 0) loga M N = loga M - loga N ( M > 0, N > 0 ) loga M n = nloga M ( M > 0 ) loga n M = n loga M ( M > 0 ). ( ) ; ( ) 0, loga = 0; ( ), loga a = ; (4 ) a log a N = N; (5 ),, 0 ; 0,, : loga b = 5. loga N = logb N logb a logb a ( ) : 0, lg N. ( ) :, : lg0 n = n( n ) ;,. ( ) : N, N a0 n ( a < 0, n ), lg N = lg( a0 n ) = n + lg a, n N, lg a (), N,. N, N ; 0 < N <,, (). 6 :

48 y = a x ( a > 0, a ) y = log a x ( a > 0, a ) ( -, + ) (0, + ) y > 0 (x ) x > 0 (y ) a 0 = ((0,) ) log a = 0 ( (,0 ) ) a > > ( x > 0) a x = ( x = 0) < ( x < 0) 0 < a < < ( x > 0) a x = ( x = 0) > ( x < 0) a > > 0 ( x > ) log a x = 0 ( x = ) < 0 ( x < ) 0 < a < < 0 ( x > ) log a x = 0 ( x = ) > 0 ( x < ) 4 a >, a x 0 < a <, a x a >, log a x 0 < a <, log a x y = a x y = loga x.. M = {,,, 4, 5}, N = {, 4, 6}, T = {4, 5, 6}, ( M T ) N = ( ) ( A) {4, 5, 6} ( B){, 4, 5, 6} ( C ){,,, 4, 5, 6} ( D) {, 4, 6} M = {,,, 4, 5}, T = {4, 5, 6} M T = {,,, 4, 5} {4, 5, 6} = {4, 5}.N = {, 4, 6}, ( M T ) N = {4, 5} {,4,6} = {, 4, 5, 6}. B. : ( M T ) N = ( M N ) ( T N), : ( M T) N = ( M N) ( T N ) = ( {,,, 4, 5} {, 4, 6} ) ({4, 5, 6} {, 4, 6} ) = {,,,4,5,6} {,4,5,6} = {,4,5,6}. B. 00 ( ),.. M = { x 0 x < }, N = { x x - x - < 0}, M N = ( A) { x 0 x < } ( B){ x 0 x < } 7 ( )

49 ( C) { x 0 x } (D){ x 0 x } x - x - = ( x + ) ( x - ) N = { x - < x < } M N, M N = M. B. M, ( D) ( ) - ( ) - < 0 N, M M N, ( A) ( C). B.. U = {,,, 4, 5}, A = {, 4}, CU A ( ) ( A) ( B)6 ( C) 7 (D)8 CU A = {,,5},CU A : {} {} {5} {, } {, 5} {5, } {,, 5}. D. 998,,,.,, CU A.,. 4. ( ) ( A) {( x, y) x = 0 y = 0} ( B){ ( x, 0), ( 0, y) x y R} ( C) {( x, y) x = 0, y R y = 0, x R} (D){ ( x, y) xy = 0, x y R} ( x, 0) ( 0, y), x y R, x y = 0, x y R,, D. 5. U = {,, 5, 7, 8}, M = {,,7}, N = {, 7, 8}, CU ( M N) = ( A) {, 5, 8} ( B){,, 5, 7, 8} ( C) {,, 5, 7} (D){, 5, 7, 8} M = {,, 7}, N = {, 7, 8} M N = {, 7},CU ( M N ) = {, 5, 8} A. ( ) 6. U, MN U, M N = N, ( ) ( A)CU M CU N (B) M CU N ( C)CU M CU N (D) M CU N, C. () U = {,,}, M = {,}, N = {}, CU N = {,}, B D. CU M = {} CU M CU N. 8

50 , C.,,,,,,. 7. X = {( n + ), n Z}, Y = {( 4 k ), k Z} ( ) ( A) X Y (B ) X Y ( C) X = Y (D) X Y, X Y, C., ( n + ), (4 k), X Y x, C.,,, 4, C. 8. A = {0, }, B = {0,, 4}, C = {,, }, ( B C) A = ( ) ( A) {0,,,, 4} ( B) ( C) {0, } (D){0} B C = {0,,,, 4}, ( B C) A = {0, }. C ( ) ( A) 5 4 > > ( B)5 4 > > ( C) > 5 4 > (D) > > 5 4 a =, b =, c = 5 4 a = ( ) b = ( ) = 6 = 64, = 4 = 8, c = ( 5 4 ) = 5 = 5, a < b < c, a < b < c, < < 5 4. A. 0. a = 4 4, b =, c = 6, a b c ( ) ( A) a > b > c ( B) b < c < a ( C) b > c > a ( D) a < b < c a = 4 4 = 4 = ( 4 ) = ( 6 8 ), b = = 4 = ( 4 ) = ( 6 ), c = 6 = 6 6 = (6 6 ) = ( 6 7 ). 8 < < 7, a < b < c. D.. ( x + y) - ( x - + y - ) ( ) ( A) x - + x - y - + y - ( B) x - + y - ( C) x - y - ( D) = x - y - x + y ( x + y ) = x + y x + y x y = x y = x- y -. 9

51 C.. y = log ( 4 x - ) ( A) 4 < x ( B) x ( C) x > 4 ( D) x 4 y = log ( 4 x - ) 0 < 4 x -, 4 < x. A. 00 ( 4).,,.. y = x 4 5 ( ) ( A) f ( x), (0, + ) ( B) f( x), ( -,0 ) ( C) f ( x), (0, + ) (D) f( x), ( -, 0), f ( x), ( -, 0 ). B. 4. f ( x) = - - x ( - x 0 ), y = f - ( x) ( ) y = x f( x) = - - x ( - x 0 ) ( A) b ' y = y f - ( x) B. y y y - O x O x O x O x - - (A) (B) - - (C) (D) y = f - ( x),. 40 y = y = - - x ( - x 0), ( - y) = - x, x = - ( - y), x = - - ( - y), f ( x) = - - ( - x) (0 x ). f - ( x) B. f( x) :, ; y = f( x) x = f - ( y) ; x y y = f - ( x),. 5. y = x - x + y = x ( )

52 ( A), ( B), ( C), (D), y = x - x + y = ( x - ) + y = x, y = x C. - x y = ax + bx + c - -, OA OB ( ) ( A) ( C) a c c a - c a y = 0, ax x ( B) - (D) c a b - 4 ac a + bx + c = 0, x x x = x x = OA OB, x x = c a < 0, x x = c a = - c OA OB = - a. B. c a, - -, y = x n, n,, C C C C4 n ( ) ( ( A) -, - ( C) -,, (B),, -, -, -,, (D),, -, - : B. 8. y = a x ( a > 0, a ), - 4 ), a ( ) ( A) ( B) ( C)9 (D)8 - - (, - 4 ), ( - 4, ). a - 4 = a = 9. C. 9. f ( x + ), f ( x) ( ) 4

53 ( A) x = - (B) x = ( C) x = f( x + ), y ( x = 0 ). (D) x = - f( x + ) = f[ ( x + ) ], f( x) f( x + ),, x =. C. ( ) f( x + ) = x = t - x, x + = t,, f ( t) = ( t - ). t x, f ( x) = ( x - ), f( x) = ( x - ) = ( x - ). f( x) x =. C. 0. f ( x) = log 9 x + 5, f ( ) ( ) ( A) ( B)log 7 ( C ) - ( D) - log 7 f ( ) = f A. = log = log =.. y = f ( x) [0, + ) - - 4,, ( -,0 ), f ( x) = ( ) ( A) x + ( B) x - ( C) - x + ( D) x - y = f( x), f ( - ) = 0, D. f (0 ) = -, A x 0, x - = - x -, - x + = - x -, B C - x 0,., x < -, x - = - x -, - x + = x +, B., f( x) = - x +. C. A B C D - - 5, 4

54 f ( x) = - x +. f( x) = x ( x ) f ( x) = - x - ( x 0) x - (0 x ) y = f ( x), x ( -, 0 ] ( x, y), y = f( x), ( - x, y) y = f ( x), x [ 0, + ), y = - - x - = - x +. f( x) = C. - x - ( x 0 ) - x + ( x < 0 ),. ( a > 0, a, x > y > 0) ( ) ( A)loga ( x - y) = loga x - loga y ( B) loga ( xy) = loga xloga y ( C) (loga x ) = loga x ( D) loga x - loga y = loga x = 8, y = 4, a =, loga x = log 8 =, loga y = log 4 =, loga ( x y) = log 8 4 = 5, loga ( x - y) = log (8-4) =, loga x y = 8 log 4 =, loga ( x - y) loga x - loga y, loga ( xy) loga xloga y, ( loga x ) loga x, loga x - loga y = loga D. x y... lg x - lg y =, 0 lg x y ( ) ( A) 0 (B) 00 ( C ) lg x - lg y = lg x y =, 0 l g x y = 0 = 000, D. 000 (D) log 5 5 = m, log5 = ( ) ( A) m log5 = log5 C. ( B) + m ( C) - m (D) m = log log5 5 = - m x y 4

55 994,. 5. n = logb (logb a) logba, a n ( ) ( A) ( B)6 ( C)logab (D)logb a, n = loga (logb a)., a n = logba. D. nlogb a = logb(logb a) logb a n = logb (logb a) a n = logb a. D.. ( = ) : ( ) {5} ( ) 5 {5} ( ){, 5} {5, } ( 4) {0,5} {5} (5 )0 {,, } ( 6) 0 (7 ) A B A B ( 8) A A B. f ( x) = 4 x + x+, f - ( ).. R f( x), - < x, f ( x) = x +, f ( 0. 5 ) =. 4. f ( x) x [, 4 ], f (log 8 ) f ( - ). 5. y = f( x), x > 0, f ( x) = x( - x).x < 0, f ( x). 44 x 6. a x = +, a + a - x =. a x + a - x 7. lg( ) =. 8.. a = 000, 0.0 b = 000, a - b =. 9. log( x - ) ( x - 8 x + 7) =, x =. 0. log ( + ) + log ( - ) =.. x y, y = ( - x ) - ( x - ) x +. ( ) ( ) ( ) = (4 ) ( 5) ( 6) (7 ) (8 ). y = 4 x + x +, y + = ( x + ). x = y + -, x = log ( y + - ), f - ( x) = log ( x + - ), f - ( ) = log ( + - ) = 0., lg( x + y) =.

56 : f - ( ) = y, (, y) y = f - ( x), ( y, ) y = f ( x), 4 y + y + =, y + y - = 0, ( y + ) ( y - ) = 0. y + 0, y - = 0 y = 0, f - ( ) = 0. : 0.. f (0.5) = f( ) = f (0.5 ) = (0.5 ) + =.5. : f ( x) x [, 4 ], f ( x) x [ - 4, - ]. - log 8 > - - 4, f (log 8 ) > f ( - ). : f( log 8) > f( - ). 5. x < 0, - x > 0, f ( x) = - f( - x) = - ( - x) [ - ( - x) ] = x( + x). : x( + x). 6. = ( ax + a - x = + + : -. ) ( a x - a x a - x + a - x ) a x + a - x = a x 7. x = , + a - x = = -. x = ( + 5 ) ( - 5 ) = 0, x = 0 x = - 0 ( ). = lg 0 = lg0 =. :. 8.. a = 000, alg. = lg000 = a = lg. 0.0 b = 000 blg0.0 = lg000 = b = lg0.0 a - b = lg. - lg0.0 = :. = ( lg. - lg0.0 ) lg. 0.0 = lg000 = =. 9. x - 8 x + 7 = x -, x - 9 x + 0 = 0, x = 4, x = 5, x = 5. : 5. 45

57 0. = log ( + ) ( - ) = log [ - ( : - 995,.. x y, - x 0 x - 0, x + 0 x =, x = y = 0, lg( x + y) = lg( + 0 ) = lg = 0. : 0. ) ] = log 4 = -.. U = R, A = { x x - 5 x - 6 0}, B = { x x + x - > 0}, AB CU A CU B CU ( A B) A CU B. x - 5 x - 6 0, - x 6. A = { x - x 6}, CU A = { x x > 6 x < - }. x + x - > 0, x < - x >. B = { x x < - x > }, CU B = { x - x }, A B = { x x < - x - }, CU ( A B) = { x - x < - }, A CU B = { x - x }.. x - px + 5 = 0 A, x - 5 x + q = 0 B, A B = {}, A B. A B = {}, A B. x - px + 5 = 0, p = 8, x - 5 x + q = 0, q = 6, x - 8 x + 5 = 0 x - 5 x + 6 = 0. x - 8 x + 5 = 0, 5, x - 5 x + 6 = 0,, A = {, 5}, B = {, }..,.,,. 46. U = { x 0 < x < 5}, A = { x x - < x, x N}, CU A.

58 x x N, - < A = {,}, - < x - < x <. x <, CU A = { x 0 < x < } { x < x < } { x < x < 5}. 4. : ( ) f ( x) = x - 4 x + x - ( ) f ( x) = lg x + ( ) f ( x) = xlog ( x - ) (4 ) f ( x) = x + x x + x - ( x < 0) ( x = 0) ( x > 0) ( ) f ( - x) = ( - x) - 4 ( - x) + ( - x) - = - ( x - 4 x + x - ) = - f ( x), f ( x). ( ) f( - x) = lg ( - x) + = lg x + = f ( x) f( x). ( ) f( - x) f ( x) f ( - x) - f ( x), f( x). (4 ) f ( x) R f ( x) = f ( - x) = x + x x + x - x - x x - x - f( - x) = - f ( x), f ( x). ( x < 0 ) ( x = 0 ), ( x > 0 ) ( x > 0 ) ( x = 0 ) ( x < 0 ). 5. f ( x) = x (0, + ). x x 0 < x < x < +, f ( x ) = x, f( x ) =, x f( x ) - f ( x ) = x - x = x - x x x. x > 0, x > 0, x x > 0. x < x, x - x > 0, f( x ) - f ( x ) = x - x x x > 0, f( x ) > f ( x ). 47

59 : f ( x) = x (0, + ). : ( ) x x, x < x ; ( ) f ( x ) - f ( x ), ; ( ) f ( x ) - f ( x ),. 6. f ( x) = - f( x) = - - m x + m x + f ( - x) = - f ( x) - m =. m - x + = - ( - m x + ), m x + x - m( x + ) x +, x R, m., x R, m x + = 0, =, 7. y = f ( x) = x - x -,. y = f( x) = x - x - R. f ( - x) = ( - x) - - x - = x - x - = f( x), f ( x), y. y = x - x - y, y, y y = x - x -, : ( ) ; ( ) () ; ( ) () ; (4 ) f ( x) = (e x - e - x ). ( ) f ( x) ; ( ) f ( x) ; ( ) f ( x). ( ) f ( - x) = [ e- x - e - ( - x) ] = - (e x - e - x ) = - f ( x), f ( x) = ( ex - e - x ). 48

60 ( ) x x R, x < x, f ( x ) - f ( x ) = ( ex - e - x ) - ( ex - e - x ). e >, x > x, - x < - x, e x < e x, e - x < e - x, e x - e x < 0, e - x - e - x < 0, f( x ) < f ( x ), f( x) = (e x - e - x ). = [ (ex - e x ) + ( e - x - e - x ) ] ( ) y = (e x - e - x ). e x - e - x - y = 0, e x = y + y + e x = y - y + ( ), x = ln( y + y + ). f( x) y = ln( x + x + ). 9. f ( x) = x + bx + c f ( ) = f( 5), x, f ( x) > c - 8. f ( ) = f (5 ), + b + c = 5 + 5b + c, b = - 6, f ( x) = x - 6 x + c. f( x) > c - 8, x - 6 x + c > c - 8, x - 6 x + 8 > 0, x < x > 4., f( x) ( -, + ), f ( x + ) + f ( x - ) > 0, x. f( x + ) + f ( x - ) > 0 f( x + ) > - f ( x - ).. : ( ) ( - f( x), - f( x - ) = f [ - ( x - ) ] = f ( - x + ), f( x + ) > f( - x + ). f( x), x + < - x +. x < 0. ( ) ( log6 ) + ) - a a - - a log6 8 log 6 + a + a + a - a + ( ) lg(lg + ) + + lg - lg + 49

61 ( ) = ( - a ) ( + a + a + a ) ( - a + a - a ) + = ( - a ) ( + a) - 4 a + = ( - a ) ( a - a + ) + = - a. ( ) = (log6 ) + log6 8log6 = ( log6 ) + log6 ( ) log6 = (log6 ) + (log6 + log6 )log6 = (log6 ) + log6 log6 + (log6 ) = (log6 + log6 ) =. ( ) = (lg + ) + (lg - ) = (lg + ) - (lg - ) =.. x - 0 x + = 0 (> ), - + log8 -., + = 0 = (- ) = (+ ) - 4= ( 0 ) - 4 =, >, - =. = log8 (+ ) - - = log 8 ( 0 ) - = log8 4 =. 50. ( A) {0,, } {0,, 4} ( B){,, } {4, 5, 6} ( C) { x x 0, x < } (D){ ( x, y) y = x, y = x} ( ). Z {, } Z {,,, 4, 5}, Z ( ) ( A) 7 ( B) 8 ( C )9 (D)0.U = {}, A = {}, B = {}, ( A)CU A = B ( B)CU B A ( C )CU B A (D) A B = U ( ) 4. f ( x) = lg( x - x + ) F, g( x) = lg( x - ) + lg( x - ) G, ( ) ( A) F G = ( B) F = G ( C) F G ( D) F G 5. A = {,, 5, a}, B = {,, 4, b}, A B = {,,}, a b ( A) a =, b = ( B) a =, b = ( )

62 ( C) a =.b = ( D) a =, b = 5 6. ( ) ( A) {( x, y) x y 0, x y R} ( C) {( x, y) y 0, x y R} ( B) {( x, y) x 0, x y R} ( D) {( x, y) x y 0} 7. U = {,,, 4, 5, 6}, A = {,,,4}, B = {,4,5,6}, CU ( A B) = ( A) {, 4} ( B) {,, 5, 6} ( C) {,,, 4, 5, 6} ( D) 8. A = { x }, ( ) x - x - 0}, B = { x ( x - ) ( x - ) 0}, C = { x ( x - ) ( x - ) ( A) A = B = C ( B) A B C ( C ) A B C ( D) A B = C ( ) 9.a =, b =, c = 6 0, a b c ( ) ( A) a > c > b ( B) b > a > c ( C) b > c > a ( D) c > b > a 0. lg( x - y) + lg ( x + y) = lg + lg x + lg y x : y ( ) ( A) - ( B) ( C) ( D) -. a > 0 a, x y 0, ( ) ( A)loga x loga y = 4loga xloga y ( B)loga x loga y = ( loga x loga y) ( C) loga x loga y = ( loga x loga y ) (D)loga x loga y = 4loga x loga y.m = lg5 - lg, 0 m ( ) ( A) 5 ( B) ( C) 0 ( D). lg x = lg y, ( ) ( A) x = y ( B) x = y ( C) x = y x 0, y 0 (D) x + y = 0 4.log = a, log6 4 = ( ) ( A) + a ( + a) ( B) + a + a ( C) + a + a ( D) a + a( + a) 5. lg m = b + lg n, m ( ) ( A) nb ( B) bn ( C) b + n ( D) 0 b n 6.y = x ( ) ( A) y = x (B) y = x x ( C) y = a l og a x ( a > 0, a ) (D) y = loga a x ( a > 0, a ) 7. y = ( x - ) 0 + log( x - ) ( x + x) ( ) ( A) { x x > 0} (B) { x x < 0} 5

63 ( C) { x x > x } (D) { x x > 0 x, x } 8.f( e x ) = x, f ( )f (e) + f (e ) ( ) ( A) ( B) ( C) e + e (D) + ln ( + e) 9. f [ f ( x) ] = x 4-6 x + 6, f( x) ( ) ( A) f ( x) = x - (B) f ( x) = x + 6 ( C) f ( x) = x - (D) f ( x) = x , (0, + ) ( ) ( A) y = - x (B) y = x - ( C) y = ( ) x (D) y = log. f( x), x (0, ), f ( x) = lg( x + ), x ( -, 0), f ( x) ( A) - lg( x + ) (B) - lg( - x) ( C) lg( - x) (D) lg( x + ) x ( )., ( ) ( A) y = - x (B) y = - x - ( C ) y = x - (D) y = x. y = ( ) x, ( ) ( A), ( -, 0) ( B), ( -, 0) ( C), (0, + ) (D), (0, + ) 4. y = f( x) ( x R), f ( ) >, f ( ) = a, ( A) a > ( B) a < - ( C) a > (D) a < - ( ) 5.f( x) = x + a f - ( x) = bx - 5, ( a, b) ( A) x + y = 7 (B) x + y = 7 ( C) x - y = (D) x - y = ( ) 6. y = x - x - ( x ), y = f( x + ) C, C y = x C, C C, C ( ) 5 ( A) y = - x + x + ( x - ) (B) y = - x + x + ( x - ) ( C) y = - x + x + ( x - ) (D) y = x - x - ( x - ) 7. f( x) = x + bx + c, t, f( + t) = f ( - t), ( )

64 ( A) f ( ) < f ( ) < f (4 ) (B) f ( ) < f ( ) < f (4 ) ( C) f ( ) < f (4 ) < f ( ) (D) f (4 ) < f ( ) < f ( ) 8. y = f( x) ( ) ( A) y = - f ( x) (B) y = f ( - x) ( C) y = - f ( - x) (D) y = f( x) 9., y = f ( x) ( ) ( A) y = f ( x + ) (B) y = f ( x - ) ( C) y = f ( x) + (D) y = f ( x) < x <, F( x) = x, G( x) = x, H ( x) = x - ( ) ( A) H( x) < G( x) < F( x) (B) H( x) < F( x) < G( x) ( C) G( x) < H( x) < F( x) (D) F( x) < G( x) < H( x).f( x) f ( ab) = f ( a) + f( b), f( ) = p, f ( 5) = q, f( 00) ( ) ( A) p + q ( B) p + q ( C ) p + q (D) p q. ( = ) ( ) {, } ( ) a { b, c, d} ( ) {} {, } 4. {0, } (5 ) N Z Q R (6 ) A = { x x < 6, x Z} { x x < 6, x N} (7 ) { a, b, c, d} { b, c, a, d} (8 ) B = { x x + < 0}. 64 x = 4, x = ; = x, x =.. x = + a -, x - a - x + a - 4 =. 4. lg x + ( lg5 - lg7)lg x - lg5lg7 = 0, =. 5. ( x - ) + ( y + ) = 0, x - - y =. 6. ( 4 ) y = ( 4 ) x +, y. 7. loga x =, logb x =, logc x = 9 ( a b c x a b c ), logabc x =. 8.4 x = 5, x + - x =. x + - x 9.f (log x) = x ( x > 0), f ( ) =. 0.y = f( x), [ 0, 4], f ( - ) f (log. 8 ). f( x) = x + mx + nx, g( x) = x + nx + m x - = 0, m, n =..f( x),, : 5

65 f ( ) =. f ( x) = - x ( 0 x ) x ( - x 0). f( x) (0, ], f ( x ). 4. f( x) g( x) = ( 4 ) x y = x, f ( x - x ). 5. f( x) = x 5 + ax + bx - 8, f ( - ) = 0, f ( ) =. 6. f ( x) = + f ( )log x, f ( ) =. x 7.f( x) = 4 x - x+ ( x ), f - ( 0) =.. U = R, A = { x x > 4}, B = { x x > }, A BA B CU A B A CU B.. {0,, }.. A B, A C, B = {,,,5}, C = {0,,4,8}, A. 4. A = { x x < 6}, B = { x x + 0}. ( ) U = N, A B; ( ) U = Z, CU A CU B ; ( ) U = R +, CU A CU B ; (4 ) U = R, CU ( A B) ; (5 ) U = R, CU ( A B) ; (6 ) U = R, CU (CU A B). 5. : ( ) y = lg ( x - 0 ) ( ) y = x + x - + x : ( ), log8 7, log9 5 ( ) ( - ) - 5, ( -.5) : ( )log ( ) ( ) ( log + log4 9 + log8 7 )log9 ( )lg 5 + lg (lg + lg5 ) (4 ) ( 7 9 ) ( - ) - - ( ) - 54 (5 )7 lg0 ( ) lg a + b = c ( a b c cb ), : 9. log8 9 = a, log 5 = b, lg. 0. lg = 0.00, : log( c+ b) a + log( c - b) a = log( c+ b) alog( c - b) a.

66 ( )5 0? ( ) ( 0. ) 0 ( )?. f ( x) = - x + R.. : f ( x) = lg + x - x ( ) f ( x) ; ( ) ; ( ) f ( x) > 0 x.. f ( x) ( 0, + ), f ( xy ) = f ( x) + f( y), f( ) =. ( ) f ( ) f ( 4) ; ( ) f ( - x) + f ( - x) -, x. 4., P Q( ), x( ) : P = 5 x, Q = 5 x,,,??. B. A. C 4. D 5. C 6. A 7. B 8. D 9. D 0. B. D. A. B 4. A 5. D 6. D 7. C 8. A 9. C 0. B. B. A. D 4. B 5. B 6. A 7. A 8. C 9. A 0. D. B. ( ) ( ) ( ) (4 ). - ( 5) ( 6) (7 ) = (8 ), f ( - ) > f (log ).m = 0, n = [ -, 0 ) (0, ] 4.( 0, ) A = { x x < - x > }, A B = { x x > }, A B = A = { x x > 4}. CU A = { x x 4} = { x - x },CU B = { x x }, 55

67 CU A B =, A CU B = R = U.. : ; {0}; {}; {}; {0, }; {0, }; {, }; {0,, }; : ; {0}; {}; {}; {0, }; {0, }; {, }.. A = {} A =. 4. ( ){,,, 4, 5}; ( ){ x x - 6, x Z}; ( ){ x x 6, x R}; (4 ){ x x < - x 6, x R}; (5 ){ x x - 6, x R}; (6 ){ x - 6 < x < -, x R}. 5. ( ) x > log 0 ( ) x 6. ( )log9 5 < < log8 7 ( ) ( - ) - 5 < ( -.5) ( ) x = x = ( ) + ( 6-4 ) - ( ) ( 6-4 ) = - 4 = 8. x > 0, x =. = log = log ( ) =. ( ) = (log + log + log )log 5 = (log + log + log ) 5 log = 5 log log = 5. ( ) = lg 5 + lg + lglg5 = lg 5 + lglg5 + lg (4 ) = = (lg5 + lg ) = (lg0) =. = ( ) = = (5 ) x = 7 lg0 ( ) lg0. 7,, - lg x = lg[ 7 lg0 ( ) lg0. 7 ] = lg7 lg0 + lg( )l g0.7 = lg 0lg 7 + lg 0. 7lg = ( + lg ) lg 7 + ( - + lg 7) ( - lg ) 56 = lg 7 + lg 7lg + lg - lg 7lg = lg 4 x = 4, = log( c+ b) a + log( c- b) a = loga ( c + b) + loga ( c - b)

68 = a + b = c, c - b = a. = log( c+ b) a + log( c- b) a = loga ( c - b) + loga ( c + b) loga ( c + b)loga ( c - b) loga ( c - b ) loga ( c + b)loga ( c - b). logaa loga ( c + b)loga ( c - b) = log( c+ b) alog( c- b) a, log( c+ b) a + log( c- b) a = log( c+ b) alog( c- b) a. 9. log8 9 = a log = a log = a log = a log = a. log 5 = b, lg = log log 0 = log log + log 5 = 0. ( ) lg5 0 = 0lg5 = 0lg a a + b = ab +. = 0 (lg0 - lg ) = 6.99, ( ) lg (0. ) 0 = 0lg0. = 0( lg - lg0) = 0( lg - ) = -.98 = 4.0. ( 0. ) 0. x x R, x < x, f( x ) - x < x, 4. f ( x ) = ( - x + ) - ( - x + ) = x = ( x - x ) ( x + x x + x ) = ( x - x ) [ ( x + x ) + 4 x ]. x - x > 0, ( x + x ) + 4 x > 0, - x f( x ) - f ( x ) > 0, f( x ) > f ( x ), f( x) = - x. ( ) + x - x + R. > 0 ( + x) ( - x) > 0, ( x + ) ( x - ) < 0, - < x <, ( -, ). ( ) f ( - x) = lg + ( - x) - ( - x) f ( - x) = - ( ) lg + x - x x x - = lg - x + x = lg( + x - x ) - f( x), f( x). > 0, lg + x - x > lg, + x - x >. < 0, x( x - ) < 0, 0 < x <. = - lg + x - x, 57

69 x (0, ), f( x) > 0.. ( ) f( ) = f ( ) = f ( ) + f( ) f ( ) = 0, f( ) + f ( ) = f ( ) = f ( ) = 0 f ( ) = - f( ) = -, f (4 ) = f ( ) = -. ( ) - x > 0, - x > 0, f ( - x) + f( - x) = f ( x - x) -, f( x - x) f (4 ). - x > 0 f( x) (0, + ) - x > 0, x - x 4 x [ -, 0 ) 4. x, y, ( - x)., P = 5 x, Q = 5 x, P Q, y = 5 x x( 0 x ). t = - x, x = - t, y = 5 ( - t ) + 5 t = - 5 ( t - ) + 0. t =, ymax = 0 =.05( ), t =, x = 4 = 0.75 ( ), - x =.5 ( ).,, ,

70 . a 0 ( a R) a + b ab ( a b R) a + b ab ( a b 0)..,.... a + b ab ( a b R) a + b ab ( a b R, a 0, b 0). 4. a 0 ( a R) a + b ab ( a br) a + b ab ( a b R, a 0, b 0 ).,,,., ax + b c ax + b c. a > b, b < a; a < b, b > a. a > b, b > c, a > c. a > b, a + c > b + c. a > b, c > 0, ac > bc ; a > b, c < 0, ac < bc. a > b, c > d, a + c > b + d. a > b > 0, c > d > 0, ac > bd. a > b > 0, a n > b n,( n N, n > ). a > b > 0, n a > n b, ( n N, n > )..,,.,. :. :. a R, a 0 ( a = 0 = ) 59

71 . a br, a + b ab( a = b = ). a br +., a + b ab ( a = b = ),.,.,..,,. ax > b ax < b ( a 0 ). :,,,, ax > b ax < b( a 0 ),,. ax > b( a > 0 ) { x x > b a } ax < b( a > 0 ) { x x < b a } a < 0,..,.,. : ( a > b) x > a x > b x > a x < a x < b x < b x > a x < b x < a x > b b < x < a 60

72 . 4. ( ) ( ax + b) ( cx + d) > 0 ax + b c x + d > 0. : ax + b > 0 cx + d > 0 ( ax + b) ( cx + d) > 0 ax + b c x + d ax + b < 0 cx + d < 0 ( ) ( ax + b) ( cx + d) < 0 ax + b cx + d < 0. : ax + b > 0 cx + d < 0, ( ax + b) ( cx + d) < 0 ax + b cx + d 5. > 0,. ax + b < 0 cx + d > 0 < 0,,,. : ax + bx + c > 0 ( a > 0) ax + bx + c < 0 ( a > 0), ax y = ax + bx + c ( a 0 ),. = b - 4 ac > 0 = 0 < 0 + bx + c = 0 y = ax + bx + c ( a > 0) ax + bx + c = 0 ( a 0) x, = - b b - 4 ac a ( x < x ) x = x = - b a ax + bx + c > 0 ( a > 0 ) ax + bx + c < 0 ( a > 0 ) x < x x > x x b a x < x < x 6. ( ) :,,. 6

73 ( ) : ab = a b : a + b = a + b ab 0 a - b = a + b ab 0 a b = a b ( b 0 ) a + b = a - b ab 0 a - b = a - b ab 0 ( ) : a - b ab a + b,. x > a( a > 0 ) { x x > a x < - a} x < a( a > 0 ) { x - a < x < a} ax + b c ax + b c. a b, a < b, :. a < x < bx { x a < x < b},, ( a, b).. a x bx { x a x b},, [ a, b].. a x < b( a < x b) x { x a x < b} ( { x a < x b}),, [ a, b) ( ( a, b] )., R ( -, + )., x a, x > a, x b, x < b x { x x a}, { x x > a}, { x x b}, { x x < b}, [ a, + ), ( a, + ), ( -, b], ( -, b). 6,,.. a < b < 0, ( ) ( A) a > b ( B) lg( - a) > lg( - b) ( C) a < b a < b < 0, - a > - b > 0, ( D) a > a - b - a > - b, a > b, A ;

74 a < b < 0, - a > - b > 0, lg ( - a) > lg( - b), B ; a < b < 0, ab > 0, a ab < b ab, b < a, C ; a - a - b = C. - b a( a - b) > 0, a >, D. a - b,,, < a < 0, p = + a, q = - a, r = ( A) s < p < q < r ( B) p < s < r < q ( C) s < q < p < r (D) r < q < p < s, a = - A B D. C. + a, s = - a, ( ), p = 5 4, q = 4, r =, s =,,,,. - 5 A B D, C. < a < 0, a = -. a b c R, a > b > c, ( ) ( A) a > b > c ( B) ab > bc ( C) a + b > b + c (D) a - c > a - b.a =, b = 0, c = -, A B C. D. 4. x - ( m - ) x + - m = 0, m ( A) m - - m - + ( B) < m < ( C) m - ( D) - + m < x x, x + x = m - > 0 x x = - m > 0 = ( m - ) m > m < - 4( - m) 0 m - + m - - ( ) { x - + x < }. 6

75 D. 5. a b, a > b, ( ) ( A) a > b ( B) b a < ( C) lg( a - b) > 0 (D) ( ) a > ( ) b. y = ( ) x, a b R, a > b, y = ( ) x x R, a > b, ( ) a < ( ) b. D.,, A B C,,. 6. a = - 5, b = 5 -, c = 5-5, ( ) ( A) a < b < c ( B) a < c < b ( C) b < a < c (D) c < a < b a < 0, b > 0, c > 0. b - c = 5-7 < 0, b < c, a < b < c. A. a < 0, b > 0, c > 0. c = 5-5 = 5 ( 5 - ) = 5 b > b, c > b, a < b < c. A. 7. x - 0 ( ) - x ( A) ( x - ) ( - x) 0 ( B)lg( x - ) 0 ( C) - x 0 (D) ( x - ) ( - x) > 0 x - x - - x x x - x > 0 - x < 0, < x. A x, B < x, C x <, D < x <. B. 8. x - 5 x + < 0 ( ) ( A)R ( B) ( C) { x < x < } (D){ x x > x < } 64 x - 5 x + = ( x - ) ( x - ),

76 ( x - ) ( x - ) < 0 < x <. C. x - > 0 x - < 0 < x - < 0 x - > 0,. 5 - x - > x - 4 x +.. ( ) x - 8 > - x. 4. a > 0, b > 0, - b < x < a x - > 0 x - 5 > x - 5 > x - 5 < - x > x <. : { x x > x < } x - 4 x + x - x - x - - x x 0. : { x x x 0}. 998, ( ) x - 8 > - x ( ) x - 8 > ( ) x x - 8 < x x - x - 8 < 0 - < x < 4. : { x - < x < 4}. 4. > - b x > 0 x < - x b, x < a x > a, x < 0. a > 0, b > 0, { x x < - : { x x < - b } { x x > a }. b } { x x > a }. f ( x) = ( k + ) x - ( k - ) x - ( k - ) x, ( -,0 ), k. f ( x) x ( -,0 ), k + < 0 f( - ) > 0 k + > 0 f( - ) < 0, 65

77 k + < 0 k + k > 0 k + > 0 k + k < 0, k < - - < k < 0., k k < - - < k < ,.. x 0, : ( x + ) > x 4 + x +. ( x + ) - ( x 4 + x + ) = x 4 + x + - x 4 - x - = x, x 0, x > 0, ( x + ) - ( x 4 + x + ) > 0, ( x + ) > x 4 + x +., : ; ;..,,,.. a b c, : a + b + c + a + b + c 6. a + a a a =, b + b b b =,, c + c c c =, a = b = c =,. a + b + c + a + b + c 6.,,,.. 4. : + 5 < < 4, ( + 5 ) < 4, < 6; < 6, 5 < 4; 5 < 4, 5 < 6. 5 < 6 5 < 6 5 < 4 5 < < 6 ( + 5 ) < < 4.,, a b R, a > 0, b > 0, a + b a b + ab,? a + b - ( a b + ab ) = a - a b + b - ab = a ( a - b) + b ( b - a) = a ( a - b) - b ( a - b)

78 = ( a - b) ( a - b ) = ( a - b) ( a - b) ( a + b) = ( a - b) ( a + b). a > 0, b > 0, ( a - b) 0, a + b > 0, ( a - b) ( a + b) 0, a + b - ( a b + ab ) 0, a + b a b + ab. a = b, a + b - ( a b + ab ) = ( a - b) ( a + b) = 0, a = b,..b > a > 0, ( ) ( A)lg a b ( C) > 0 ( B) ab a + b a + a < + a + a ( D) b a < b + a +. x y R +, x + y = 5, lg x + lg y ( ) ( A)lg5 ( B) (lg5 - lg) ( C) ( - ) (D). x + 0 ( ) x - ( A) { x x - } (B ){ x x -, x } ( C) { x x > } { x x - } (D){ x x } { x x - } 4.,, ( ) ( A) ab > 0, a + b > a + b ( B) ab > 0, a + b = a + b ( C) ab < 0, a + b = a + b (D) ab < 0, a + b > a - b 5. a b c R, a > b > c, ( ) ( A) a > b > c (B ) ab > bc ( C) a + b > b + c (D) a - c > a - b 6.a > b > 0, ( A) ab a + b < a + b ( C) a + b > ab > ab a + b < ab (B ) a + b ab ab a + b (D) ab < ab a + b < a + b ( ) 7.x - 6 x + 9 > 0 ( ) ( A) (B ) ( C) (D) x < - x > 8.a =, b = 7 -, c = 6 -, a b c ( ) 67

79 ( A) a > b > c (B ) a > c > b ( C) b > a > c (D) b > c > a.( x - ) > x 0. - x. x - >. 4. x ax + bx + c < 0 { x x < - x > - ax - bx + c > 0. }, x 5. y = x + x ( x > 0 ), x =. 6. f ( x) = x - ax +, f( ) <, a.. ( )8 + x < 6( x + ) ( ) - x < 5.,. ( ) x - x > - ( x - ) < ( x - ) ( ) x + x ( x x ) x 6. a b c, : a( b + c ) + b( c + a ) + c( a + b ) 6 abc. 4. a b R +, : ( a + b) ( a + b ) 4..C.B.C 4.B 5.D 6.C 7.C 8.B.R.{ x.{ x x > x < 0} 4.{ x 5.8, 4 6. < a <. ( ) x - 6 x + < 0. < x 4 } < x < } 68 x - 6 x + = 0 x = -, x = +,

80 { x - ( ) - x - x < 5 < x < + }. x 5 x, - < x < 4, { x - < x 5 x < 4}..,. ( ) ( ) x - x > - ( x - ) < ( x - ) x > - 6, x > 0, { x x > 0}. x + x x ( x ) x 6 9 x -, x 4, { x - 9 x 4}.. b + c bc, a > 0, a( b + c ) abc., c + a ca, b > 0, b( c + a ) abc. a + b ab, c > 0, c( a + b ) abc. a( b + c ) + b( c + a ) + c( a + b ) 6 abc. 4. a + b ab, a + b ab,, ( a + b) ( a + b ) 4. 69

81 .., n,.. ;,.,..,., n..,,,,.. an = a + ( n - ) d, a, n, d, an ; an, d = an+ n, a - an,.. n S n = n( a + an ), Sn = na + n( n - ) d,, an, Sn n, a, d, Sn ; n ;. 4., A = a + b., n..,,,,.. an = a q n -, a, n, q, an ; an, q = an+ an.. n Sn = a ( - qn ) - q Sn = a - anq ( q ), - a, q, n, Sn a, an, q, Sn ; n ; , G = ab..

82 .,,,, n,.. a, a, a,, an, n n, an, { an }.,.. { an } n an n,.,. + an. ( ). ( ),.. n a nan, n, Sn = a + a + a + an S n an = S ( n = ) Sn - Sn - ( n, n N)., a, a + d, a + d, ( d ) a n = a + ( n - ) d n S n = n( a + a n ), S n = na + a b A = a + b n( n - ) d,, a, a q, a q, ( q, a 0, q 0, q ) an = a q n - n Sn = a ( - qn ) - q, Sn = a - anq - q ( q ) a b G = ab, 7

83 . { an }, a + a4 + a5 + a6 + a7 + a8 = 0, 0 S 0 = ( ) ( A) 0 (B) 40 ( C) 50 (D) 60 a + a8 = a4 + a7 = a5 + a6 = a + a0 = 0 = 0, S0 =, C. ( a + a 0 ) 0 a + a4 + a5 + a6 + a7 + a8 = 0 0 = 50. = ( a + d) + ( a + d) + ( a + 4 d) + ( a + 5 d) + ( a + 6 d) + ( a + 7 d) = 6 a + 7 d = 0, a + 9 d = 0, S0 = 0 a +, C. 0 9 d = 0 a + 45 d = 5( a + 9 d) = 5 0 = ,,,,., ( ) ( A) ( B) ( C) (D) - d,,+ d. (- d) + + (+ d) = 80,= 60,, , B = 60, A + C = 80- B = 80-60= 0, B = A + C,.,, 60., C.. n Sn = n + 7 n, a0 0 = ( ) ( A) 0700 ( B)004 ( C )604 (D) 596 a00 = S0 0 - S99 = ( ) - ( ) = 604. C.

84 n Sn, an =. 4., - 0 ( ) S ( n = ) Sn - Sn - ( n ),,, - 4,, ( - ) n+ n,, ( A) - ( B) ( C) - 0 (D) 0 an = ( - ) n+ n, n = 0 0 :. a0 = ( - ) = - 0. C. ( - ) n+. -, - 5. S = n ( ) ( A) - n ( B) - n ( C ) - n+ ( D) - n+ a =, q =., S = a ( - qn+ ) - q B. = [ - ( ) n+ ] - = - S n +, n, n,,. 6. { an } m 0, m 00, m ( ) n. ( A) 0 ( B)70 ( C) 0 (D)60 m A, m + m B, m + m C,, A B C. A = 0, B = 00-0 = 70, C = B - A = 70-0 = 0, m S m = A + B + C = = 0. C. Sm = 0, S m = 00 Sn = na + n( n - ) a = 0 m + 0 m, d = 40 m. d, 7

85 S m = ma +, C. m( m - ) d = m( 0 m + 0 m ) + m( m - ) 40 m = 0. 7., 0 (),, ( A) 5 (B) 5 ( C) 0 (D)04 9, a a0 = a. q 0 - = a. q 9 = 9 = 5., B., ( ) =, q = = 56,, 8. { an } n S n, S S =, q ( ) ( A) ( B) - S S =, a ( - q ) - q a ( - q ) - q q = q = - q = -, B. = - q - q =,.. ( C) - 9. a b c, y = ax (D) - + bx + c x ( A) 0 (B) ( C) (D) a b c, b = a + c. = 4 b - 4 ac = ( a + c) - 4 ac = ( a - c) 0, y = ax, D. + bx + c x. ( ) 0. Sn = ( - ) + ( - ) + ( - ) + + ( n - n), S 0 ( ) ( A) ( C) ( B) (D) S0 = ( - ) + ( - ) + ( - ) + + ( 0-0 ) = ( ) - ( ) = ( - 0 ) - - ( + 0) 0

86 = - A ,,.. { an }, a 0 < 0, a > 0, a > a 0, Sn, ( ) ( A) S S S0 0, S S 0 ( B) S S S5 0, S6 S7 0 ( C) S S S0 0, S S 0 (D) S S S9 S9 = S0 = 0, S0 S 0 9 ( a + a 9 ) 0 ( a0 + a ) = 9 a0 = 0 ( a0 + a ), = 9 a0 < 0, a0 < 0, a > 0,, a > a 0, a0 + a > 0. S0 > 0. a < a < < a0 < 0 < a < a <, S S S9 D.. a =. 0, S0 S , b = +, A =. G = -. n Sn = n + n +, an =.., 4, 5 8, 7, n a a a a4 a5, a4 a ( a + a ) a4 = 8, ( a + a ) a5 =. 5. { an } { bn } { cn }, a = 5, b = 0, c = 5, a5 0 + b50 + c50 = 00, { an + bn + cn } 50.. a b A = ( ) =, a b G = =. :,.. n =, a = S = + + = n, an = Sn - Sn - = ( n + n + ) - [ ( n - ) + ( n - ) + ] = n an = ( n = ) n ( n ). 75

87 : an = ( n = ) n ( n ). Sn = [ ( n - ) + n ]. = [ ( n - ) ] + ( n ) = [ ( n - ) + ] n + ( - ) n - = n + - n. : n + - n. 4. q, a4 a a q = 8, a ( a + a ) a4 ( a + a ) a5 : 0. = = q = 8, q =. ( a + a q) a q ( a + a q ) a q 4 = + q ( + q ) q = + ( + ) = ,,,,. 5. a + a50 = a + a4 9 = = a 5 + a6, b + b50 = b + b49 = = b5 + b 6, c + c50 = c + c49 = = c5 + c6. a + a + + a5 0 = 5 ( a + a50 ), { an + bn + cn } 50 b + b + + b50 = 5( b + b5 0 ), c + c + + c5 0 = 5 ( c + c50 ). 5 ( a + b + c + a5 0 + b50 + c50 ) = 5 ( ) = 50.. { an }, Sn n, an > 0, a = 4, S4 - a = 8, an+ { an } q. a = 4 S4 - a = 8 a q = 4 a q ( + q) = 4 a q = 4 a + a + a4 = a q + a q + a q = 8, an > 0, a = q =, an. 76 an+ an = q = = , n.

88 . { an },, Sn = a + a + a + + an, m n am 5 Sn, lg am lg9 Sn, m n. a m + Sn = 0 lg am + lg Sn = lg9, a m + Sn = 0, am Sn = 8 am = Sn = 7 am = 7 Sn = ( ). am = + ( m - ) =, m = 5, Sn = 7 n + n( n - ) n = 9 n = - ( ), m = 5, n = 9. = 7, 998,,,,.., 5,, 4, 9,,. a - d, a, a + d, ( a - d) + a + ( a + d) = 5, ( a + 4) = ( a - d + ) ( a + d + 9 ) a = 5, d = d = -,, 5, 8, 6, 5, - 6. a, a + d, a + d a, b, c,. a - d, a, a + d; a q, a, aq. 4. { an }, n S n, n, an Sn ( ) { an } ; ( ) { an } ; ( ) bn = ( an+ an + an an + ( ), an + n =, a + n =, a + n =, a + ), n N, b + b + b + + bn - n. = Sn ( an > 0 ). = S, S = a, a =. = S, S = a + a, a = 6. = S, S = a + a + a, a = 0. 77

89 ,6,0. ( ) a n + = Sn ( n N), Sn = 8 ( an + ), Sn + = 8 ( an+ + ), an+ = Sn+ - Sn = 8 [ ( an+ + ) - ( an + ) ], ( an+ + an ) ( an+ - an - 4 ) = 0. an+ + an 0, an+ - an = 4. { an } a =, d = 4, an = a + ( n - ) d = + 4 ( n - ) = 4 n -. ( ) cn = bn -, cn = ( an+ an + an an+ - ), cn = [ ( n + n - - ) + ( n - n + - ) ] = n - - n +, b + b + b + + bn - n = c + c + c + + cn = ( - = - ) + ( - 5 ) + ( 5-7 ) + + ( n - - n + ) n + = n n +.,,.., ( ).. 0, -, - 7, n + ( ) 78 ( A) - 7 n ( B) - 7 ( n + ) ( C) - 7 n + (D) - 7 ( n - ). ac = b a b c ( ) ( A) (B) ( C) (D). { an }, S0 = 0, a + a 0 ( ) ( A) ( B)4 ( C)6 (D)48 4., d =, an =, Sn = 5, a ( ) ( A) 5 7 ( B) 5 ( C)7 - (D) - 5.lg lg( x - ) lg( x + ), x ( ) ( A) 0 ( B)lg 5 ( C) (D)0

90 6.{ an }, { bn }, a = 5, b = 75, a00 + b0 0 = 00, { an + bn } 00 ( A) 0 ( B)00 ( C)0000 (D) ( ) 7. { an }, S4 =, S8 = 4, a7 + a8 + a9 + a0 ( ) ( A) 7 ( B)8 ( C)9 (D)0 8. { an }, S7 = 48, S4 = 60, S = ( ) ( A) 80 ( B)08 ( C)75 (D)6 9. { an }, an > 0, log a + log a + + log a0 = 0, a5 a6 = ( ) ( A) 79 ( B)80 ( C)8 (D)8 0., +, + +,, n -, ( ) ( A) n - - ( B) n - ( C) - n - (D) - n. { an }, m n, n m, m + n ( ) ( A) mn ( B) m + n ( C) m - n (D)0. { an }, d =, an =, Sn = 5, a =, n =.. { an } n Sn = n + n -, { an }.. { an }, a =, an+ - an = 0, an =, a6 =. 4. a4 a8 = 0, a a9 =. 5., lg(00 sin ), lg( 00sin ),, lg (00sinn ), { an }, a0 + a40 + a60 + a80 = 00, a0 + a50 + a9 0 =. 7.ABC, a b c, A - C = 90, a: b: c =. 8. an = n ( n N),. n n S n = n - n. ( ) ; ( )..,,, 7, 6,..n S n. a =, S > 0, S < 0. ( ) d ; ( ) S, S,, S, , ( ) %, 000? ( ) 000,? 79

91 (lg.0 = , lg.4859 = 0.700, lg. = , lg.009 = ) 5. { an }: log a b, 4 log a b,8 log a b,, ( n ) log a b, ( a b, a ) ( ) : { an } ; ( ) { an }, b? 6. { an } an = 0 - n, a + a + + an. 80. A. B. B 4. D 5. B 6. C 7. C 8. D 9. C 0. B. D.a = -.an = 6 n -, n = 0 a =, n =.an = ( )n -, a6 = 4 ( n ) ( n = ) , 8-9 lg ( 7 + )7( 7 - ) 8.a a.( ) n, an = Sn - Sn - = ( n - n) - [ ( n - ) - ( n - ) ] = 4 n - ( n ), n =, a = S = - = = 4 -, an = 4 n - ( n N). ( ) S0 - S5 = ( 0-0 ) - ( 5-5 ) = 45.. a - d a a + d, ( a + d) a a = 6 d = 4 ( a - d) + ( a + d) a a + ( a + d) = 6 a = 8 4 d = -, = 7,,