: : : ( 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,,

92 .( ) S = a + S = a + d > 0 d < 0 a + d > 0 a + 6 d < 0 a = a + d = a = - d d > d < < d < -. ( ) d < 0 { an }, n, an > 0 an+ < 0, Sn. S = 6 ( a6 + a7 ) > 0, S = a7 < 0, a7 < 0, a6 > 0. S, S,, S S6.. 4.( ) 000 x( ) : 0, 0.0,0.0, x = 0.0 0, lg x = + 0lg.0 =.700, x = (). ( ) y%,, 0 ( + y% ) 0, ( + y% ) 0. 0lg( + y% ) lg, lg( + y% ) , + y%.009, y% : ; 000, 0.9%. 5. ( ) an an - = ( n ) log b a = l og b a ( n - ) log a b ( ) ( n ) { an }. ( ) { an }, 4 l og a b - log a b = 8 log ab - 4 log a b. log a b = x, x - x = x - x, x = 0 () x =, l og a b =, b =. b =, { an }. 6. an = 0 - n 0, n 0. n >, an < 0; n, an > 0. 8

93 a + a + + an = = = a + a + + an a + a + a - a4 - - an n( a + an ) ( a + a + a ) - ( a + a + + an ) - n + 7 n n - 7 n + 48 ( n ) ( n 4 ) 8

94 ,..,..,,.a + bi.,. r( cos+ isin ) r, r = a + b, cos= a r, sin= a r. a + bi r(cos+ isin )..,. ( i - ) ;,.., ; ; n, n (n ). ax + bx + c = 0( b - 4 ac < 0). x = - b - ( b - 4 ac)i a ( b - 4 ac < 0).. i. : ( )i = - ; ( ) i,. i :. i 4 n =, i 4 n+ = i, i 4 n+ = -, i 4 n+ = - i ( n N) 8

95 a + bi ( a b R).a, b. b = 0, ; b 0 ; a = 0, b 0,. a + bi : ( a + bi) ( b = 0 ) ( b0 ) ( a = 0, b 0 ) ( a 0, b 0 ), C, R C.. a b c d R, a + bi = c + di a = c b = d., a + bi = 0 a = b = 0. 4.,,. z = a + bi z = a - bi.. z = a + bi ( a b R). ( ) : z = a + bi Z( a, b), Z a, b,.x, y ( ).( ) C. b' ( ) : z = a + bi O, Z( a, b) OZ ( ). C O.. ( ) : z = a + bi OZ, ' z ( ), a + bi. ( ) : r = a + bi = a + b x, OZ z = a + bi, 0 <,, arg z. b b O b O O y a y a y r a Z : a + bi Z : a + bi ( ) : z = a + bi r(cos+ isin ), r( cos+ isin ), r z, z. Z b x x x 84

96 ( ) : r(cos+ isin ) a + bi, a = rcos, b = rsin. r = a + b cos= a r sin= b r r.. ( ) :,,, ( ) : < ' O ( a + bi) ( c + di) = ( ac) + ( bd)i y Z Z Z = Z + Z x y Z Z = Z , z = a + bi z = c + di OZ OZ, Z = ( a + c) + ( b + d)i, OZ OZ OZ. O Z - Z x, z = a + bi z = c + di z = ( a - c) + ( b - d)i, OZ OZ Z Z, Z Z, OZ.. ( ) :, i -,,, ( a + bi) ( c + di) = ( ac - bd ) + ( bc + ad )i ( ) :, r ( cos + isin ) r ( cos + isin ) = r r [cos( + ) + isin ( + ) ] ( ) : z z, OZ OZ, OZ, r, OZ z z.. ( ) :,,,, 85

97 ( a + bi) ( c + di) = a + bi c + di = ( a + bi) ( c - di) ( c + di) ( c - di) = ac + bd c + d + bc - ad c + d i ( ) :,, r (cos + isin ) r (cos + isin ) = r r 4. ( ). [cos ( - ) + isin( - ) ] [ r(cos+ isin ) ] n = r n [cos n+ isin n] ( n N) ( ) r(cos+ isin ) n n + k r ( cos + isin n. + k ) ( k = 0,,,, n - ) ( n N) n ( ), = - + i, = - - i, = =, = =, = + + = 0, + + = 0. a b R, ( a - 4 a + 5) + i( b - b ) ( ) ( A) ( B) ( C) (D) x = a - 4 a + 5 = ( a - ) + > 0, y = b - b = - ( b - ) - 5 < 0, ( a - 4 a + 5 ) + i( b - b ). D.. : z + z = + i, z ( ) ( A) - ( C) i ( B) 4 - i 4 - i (D) 4 + i z = x + yi, ( x y R), z = x - yi, z = x + y. x + yi + x + y = + i, x + x + y =, y = x = 4 y =, z = 4 + i. 86

98 D.. sin95+ icos95 ( ) ( A) 95 (B) - 5 ( C) 5 ( D) 85 sin95+ icos95= cos (90-95 ) + isin (90-95 ) = cos ( - 5 )+ isin ( - 5 ), - 5. B. tan= cos95 = cot95= tan ( - 5 sin95 ). sin95> 0, cos95< 0,. = - 5. B. 4. z = + 4i, z = - - i, z - z ( ) ( A) 5 4 ( B) 7 4 ( C) 4 z - z = ( + 4i) - ( - - i) = 5 + 5i, z - z = 5-5i, z - z 7 4. ( D) ,. 5. ( + i) 4 ( - i) 5 ( A) + i ( B) - + i ( C) - i (D) - - i ( + i) 4 ( - i) 5 = 4 [ ( + i) ] = 5 ( - i) 5-4 ( - i) ( + i) ( - i) B. = - = B. + - ( - 4 ( + i) 4 = = - + i. i, =, + i) 5 = ( i) ( cos 5 = 5 + isin ) 5-4 ( ) ( cos + isin ) - 4 = - 5 = = = - + i. 6. z, z - i ( ) ( A) ( B) ( C) 5 (D) ( ) z = a + bi ( a b R), a + b = 4. z - i = a + bi - i = a + ( b - )i 87

99 = a + ( b - ) = a + b - b + = 5 - b, a + b = 4, - b., b = -, z - i 5 - ( - ) =. D. ( ) z = ( cos+ isin ), z - i = cos+ isin- i = cos+ ( sin- )i = 4cos + ( sin- ) = 5-4sin. sin= -, z - i 5-4( - ) =. D. ' () Z, Z,, z - i Z i, : zo = - i i, - i - i =., D. O i y - i - 4-5,, ; ;, i,,, 4 ( A) ( - ) - ( + )i ( B) ( - ) + ( - )i ( C) ( + ) - ( + )i (D) ( + ) + ( - )i, z = ( - i) (cos + isin 4 4 ) D. = ( - i) ( + i) = ( + ) + ( - )i. x ( ) 8. z C, z - + z + = 8, z ( A) ( B) ( C) (D) ( ), z - + z + = 8 z Z F ( -, 0) F (, 0) 8, F F, z Z. 88 B. = 6,. z = ( m + 4 m - ) + ( m - 5 m + 6)i ( m R), m =.

100 . z + z = 0, z =.. x 7 + x 5-4 x - 4 x =. 4. z C, z + i =, arg( z + i) =, z =.., z, m + 4 m - = 0 m - 5 m m = - 7 m =, m m, m = - 7, z. : z = x + yi, x y R, x - y + x + y + xy i = 0. x - y + x + y = 0 x y = 0 z = 0 z = i. : z = 0 z = i. ( x + yi) + x + y = 0,, x = 0 y = 0 x = 0 y =.. = ( x + x) ( x 4-4) = x( x + ) ( x - ) ( x + ) = x( x + i) ( x - i) ( x + ) ( x - ) ( x + i) ( x - i). : x( x + i) ( x - i) ( x + ) ( x - ) ( x + i) ( x - i). 4. z + i =, arg( z + i) =,. z + i = (cos + isin ) = + i, z = + ( - )i. : + ( - )i. ( ) ( - i + i ) ( cs c 0- s ec0 ) ( ) ( + 4i) ( - i) ( + i) ( - i) 5i + i ( )i 5 + i 5 + i 40 + i 8 0 ( ) csc0- sec0= = sin0 - cos0 = cos0- sin0 sin0 cos0 4sin(0-0 ) sin0 cos0 = 4 sin0 sin0 = 4. 89

101 = ( - i + i ) 4 = ( - i + i ) 8 = ( - i) 8 =.,,., : ( i) = i. ( ), ( + 4i) ( - i) ( + i) ( - i) 5i = i = - i, + 4i - i + - i + i i - i 5i 5 + i 5 + i = ( 5 ) + =,. :. = = - i, + i - i = i, 5 5 = 5,,,...: z z = z z z z = z z ( ) i 5 + i 5 + i 40 + i 80 = i + i + + =. :. i, :. z = - i 4 n =, i 4 n+ = i, i 4 n+ = -, i 4 n+ = - i i 4 n + i 4 n+ + i 4 n+ + i 4 n + = 0 + i. r = ( - ) + ( ) =, tan= - z Z( - =, 0 = 6, z = (cos isin 6 6 ). ), z - 6 = 5 6 z a + bi ( a br), r = z = a + b, 0 tan 0 = b a ( a 0 ), Z( a, b) z 0,- 0,+ 0, - 0, - i = [ cos (- ) + isin (- 6 6 ) ], - - i = [cos(+ 6 ) + isin( 90

102 + 6 ) ].. z z A B, OA OB 5 4, AB, z = - - i, z. z (cos isin ) = ( - - i) ( cos + isin 4 4 ) z = (cos 4 + isin 4 ) ( cos 5 + isin ) cos + isin = (cos 9 + isin ) = + i.,,, i, 5 + i, +. ( + 5i) ( 5 + i) = 0 + 4i + 5i - 0 = 9i,. + 5i 5 + i,. + =. 5. : ( ) x + x + 5 = 0 ( ) x + x + = 0 ( ) = = - 6 < 0,. x = = - 4i = - i, x = - + i, x = - - i. ( ) = - 4 = - < 0,. x = - - = - i, 6 x = i, x = i. 6. z z 0, z + z = z - z, ( z z z = x + y i, z = x + y i, x x y y R. z + z = z - z, x + x + ( y + y )i = x - x + ( y - y )i, ). ( x + x ) + ( y + y ) = ( x - x ) + ( y - y ), 9

103 x x + y y = 0. z z = x + y i x + y i = ( x + y i) ( x - y i) ( x + y i) ( x - y i) = x x + y y x + y + y x - x y x + y i = x y - x y x + y i. ( z z ) = ( x y - x y x + y ) i = - ( x y - x y x + y ), ( z z + z = z - z, z + z = z - z, ( z + z ) ( z + z ) = ( z - z ) ( z - z ), z z + z z = 0, z ). z z = - z z = - ( z z ). z z, ( z z ). 9. z = a + bi ( a b R, b 0 ), z z z ( ) ( A) z = z z ( B) z = z = z ( C) z z = z (D). + i - i ( ) ( A) ( B) ( C) 7 (D) 7. sin0- icos0 ( ) ( A) 0 ( B) 50 ( C)80 (D) z + z = + i z ( ) ( A) + i ( B) - i ( C)4 - i (D) i 5. m < 0, m ( ) ( A) m(cos0 + isin0) (B) m( cos+ isin) ( C) - m( sin + icos ) (D) - m( cos+ isin) 6. z z - =, z ( ) ( A) ( B) 8 ( C)0 (D) 4 7. z z + = z - +, z ( ) ( A) (B) ( C) (D)

104 8. z - z + z = 0, + z00 0 z 00 0 ( ) ( A) - ( B) - ( C) (D) 9. OZ - + i, OZ 90, OZ, OZ ( A) + i ( B) - + i ( C) - - i (D) - i. ( sin+ icos ) ( + icot ) 5 =. (cot- i) 5. z = a + a - 6 a + + ( a - a - 0 )i ( a R), a.. z z - i, z. 4. (i - ) ( + 4i) ( - i) z = - i, z = z + i(4 z + 6) - z,. ( ). 6. x y ( xi + 4) + ( yi + x) = ( y - i) - ( - xi), x =, y =. 7. z = cos + isin 8 8, z +. z. ( ) ( - + i) ( + i) ( ) ( - i) - ( - + 5i) ( - 4i) ( ) ( + i) 0 (4 ) ( - i) (cos + isin ) ( cos - isin ). x R, y R, z = x - ( x - y)i, z = y + ( 4 x + )i, z i - z = - ( + i), z z i - i, z C, z = z +, arg ( + z ) = 7 4, z. 5. : ( ) x - 4 x + 8 = 0 ( ) x + 6 x + 0 = 0. A. C. D 4. D 5. D 6. D 7. C 8. B 9. C 9

105 , , 7. ( ) i ( ) - 5-0i 94 ( ) i (4 )8 (cos + isin ). x - y + xi - y + ( 4 x + )i = - - i, ( x - y) + (6 x + )i = - - i, x - y = -, 6 x + = - z z. - - i - i = - + i = - i =. ( - - i) ( + i) ( - i) ( + i) tan(- ) = - - =. x = - y = = - - i,, < <,< <, - < - < -, - = z = z + z + z arg( + z ) = 7 4 arg z + z z + z =, - < - < 0 = z + z = 7 4, 7 7 (cos + isin 4 4 ) = - i, + z = - i, z = - + i. 5. =, ( ) = ( - 4 ) = - 4 < 0, x - 4 x + 8 = 0. x = 4-4 = 4 i = i, x = + i, x = - i. ( ) = = 6-40 = - 4 < 0, x + 6 x + 0 = 0. x = = - 6 i = - i,

106 x = - + i, x = - - i. 95

107 ,, ,,.. y x 0. x. y = f( x) x0, y = f ( x) ( x0, f ( x0 ) ),.. c, x m ( m ), e x, ln x x ( ) x, y = f( x) A, x, y = x +, f ( x) A. f ( x) A, lim f ( x) = A, x+ ( ) x x, y = f ( x) A, x, y = x -, f ( x) A. f ( x) A, lim f ( x) = A. x- ( ) x, y = f( x) A, x, y = 96 f ( x) A,

108 x, f( x) A. lim f ( x) = A. x (4 ) x, f( x) = C C, lim C = C. x (5 ) x, y = x 0,. x x0 lim x x = 0. ( ) x x0 ( x x0 ), y = f ( x) A, x x0, f( x) A, lim f ( x) = A, x x0, f ( x) A. xx 0 ( ) x x0, f( x) = C, lim C = C. xx 0 ( ) x x0, f( x) = x x0,. ( ) lim xx0 f ( x) = A, lim xx0 g( x) = B, lim x = x0. x x 0 lim [ f( x) g( x) ] = AB; x x 0 lim [ f( x)g( x) ] = xx 0 f( x) lim xx 0 g( x) = A B ( B 0). AB; :,. C n,, ; lim [ Cf ( x) ] = C xx x lim x0 f ( x), 0 lim x x 0 [ f ( x) ] n x. 4. = [ lim xx0 f ( x) ] n. ( ) y = f ( x) x = x0, f ( x) x = x0.. lim f ( x) = f ( x0 ), x x 0, y = f ( x) x = x0 x = x0 ( ) y = f ( x) ( a, b), y = f( x) 97

109 ( a, b), ( a, b).. ( ) y = f ( x) x = x0, x x = x0 x( ), y = f ( x). y = f ( x0 + x) - f ( x0 ), x 0, y ( ), y = f ( x) x x = x0 (),, y x = x 0, y x = x 0 = lim x 0 f( x0 + x) - f ( x0 ) x ( ) y = f ( x), ( a, b) x, f ( x), y = f ( x), y = f ( x) y = f ( x) ( a, b),, y, y= y f ( x) = lim x0 x = lim x 0 f( x + x) - f ( x) x x0 ( a, b), y = f( x) x = x0 f ( x0 ) y = f ( x) ( a, b) f ( x) x = x0 f ( x0 ). ( ) y = f ( x) x = x0 : y = f ( x) x = x0 f ( x0 ) y = f( x) ( x0, f( x0 ) )., ( x0, f ( x0 ) ) y - f( x0 ) = f ( x0 ) ( x - x0 ). (4 ) y = f ( x) y = f ( x + x) - f ( x) ; y x = f ( x + x) - f( x) x y, y= lim x 0 x ( ).. ( ) ( C)= 0(0 ) ; ( ) ( x m )= mx m - ( m ) ; ( ) ( e x )= e x (e ) ; ( ) ; (4 ) ( ln x)= ( e ). x. ( ) ( ), ( ), ( uv)= u v. ( ),,, 98..

110 ( uv)= u v + uv. ( ),,,, ( u v. y = u )= v - uv ( v 0). v f( x), x x, x > x, f ( x ) > f ( x ), y = f( x) ; x > x, f ( x ) < f ( x ), y = f ( x)., y =. f ( x),, y = f( x), y> 0, y ; y< 0, y.. ( ) y = f ( x) x0, f ( x0 ) x0, f ( x0 ) f( x), y = f ( x0 ) ; f ( x0 ) x0, f( x0 ) f ( x), y = f ( x0 ),. ( ) f ( x) ; f ( x) = 0 ; f ( x),, f ( x) ;, f ( x). : y y ( + - ) ( ) ( - + ) ( ) f ( x) = 0 x = x0, f ( x), f( x) x = x0...y = f( x) [ a, b], y = f( x) ( a, b), y = f ( x) [ a, b], : ( ) y = f ( x) ( a, b) ( ) ; 99

111 . ( ) y = f( x) f ( a), f ( b),,,,.. lim x+ ( ) x = ( ) ( A) 0 ( B) ( C) (D) x, y = ( ) x 0,. lim x lim ( x + ) x = 0. A. x - x + = ( ) ( A) 0 ( B) ( C) (D) 00 x, ( x - ), ( x + ),, x,,. C.. lim x x - x + x + - lim x - x x + = lim x x + x = lim ( - x x ) lim ( + = x x ). = ( ) ( A) ( B)0 ( C) (D) lim x x - x + x + D. 4. lim x4 x - 6 x - 4 = lim x ( x - x + ) lim x ( x + ) = lim x x - lim x x + lim lim x x + lim x x = =. = ( ) ( A) 0 ( B)8 ( C)4 (D) x 4, ( x - 4) 0,, x 4 x = 4, x = 4,,, x - 6 lim x 4 x - 4 = lim x 4 ( x + 4) = lim x4 x + lim x4 4 = 8.

112 B , ( ) y y y y x x x x O O O O ( A) (B) (C) ( D) - 5 -, y = f ( x) x = x0, lim f( x) = f ( x0 ). x x 0,,,, D. D. 6. ( x)= ( ) ( A) x ( B) x ( C) ( x)= ( x )= x - = x- = B. 7. ( x + ) x ( A) x + ( B) x + x x ( x + )= x - ( x + ) = x -. x x x D. x x. (D) ( C) x - (D) x - x x x ( ) 8. y = x - x + 5 ( ) ( A) (B) ( -, 0) ( C) ( 0, + ) (D) (, + ) y = x - x + 5, y= 6 x -. y = x - x + 5, y> 0. y= 6 x - > 0 x >, (, + ) y> 0, y = x - x

113 0 D. y =. f( x), y, y> 0 y< 0, 9. y = x - x + 4 ( ) ( A) x = (B) x = ( C) x = (D) x = 4 y = x - x + 4, y= x -, y= 0 x =. x >, y> 0 ; x <, y< 0. x = y, y = x - x + 4. B.. lim x- x - x - x + x + =.. lim x. lim x =. x x + x - x - x + =. 4. y = x, y x = =. 5. ( x - x + )=. 6. (e x + e x )=. 7. y = x + Q(, ). 8. y = x - x + [ -, ].. lim x- ( x + x + ) = 0., ( x + ), x - x - x - x = -, x + x + x = -,, lim x- : -. x - x - x + x + = lim x -. lim x x = 0, lim x :0. = 0. x ( x - ) ( x + ) ( x + ) ( x + ) = lim x - lim x - x + = x - ( x - ) lim ( x + ) = -. x -. x, ( x + x - ) ( x - x + ),

114 x, ( + x - x ), lim ( + x x - ) = lim x + lim x x x ( - lim x :. x + x ), - lim x = =. x lim ( - x x + ) = = lim x - lim x x x + lim x + x - x - x + = lim x + x - x - x + = x. x =. x 4. y = x, y= x, x = y= =, y x = =. :. 5. ( x - x + )= ( x )+ ( - x)+ ( )= 4 x = 4 x -. :4 x (e x + e x )= (e x )+ ( e x )= e x + e x ( x)= e x + e x. : e x + e x. 7. y = x +, y= 4 x, Q(, ) y x = = 4, y = x + Q(, ) y - = 4 ( x - ), 4 x - y - = 0. :4 x - y - = y = x - x + y= 6 x - x. y= 0 x = 0 x =. > x > 0, y< 0, x < 0, y> 0, x = 0, y =. x >, y> 0,0 < x <, y< 0, x =,. y = x = -, y = - 60; x =, y = 48. [ -, ], - 60, 48. : - 60 x + ( ) lim( x - ) ( ) lim x x- x + ( ) x lim x - x + x + (4 ) lim x - x - 6 x x 0 x - 5 x - x 0

115 ( ) lim x ( x - ) = lim x ( ) lim x - x + x + = lim x- ( ) x lim x - x + x + x - lim = x - = -. ( x + ) ( x - x + ) x + - = lim x x + x + x = = lim x- ( x - x + ) =. lim ( - x x + ) x lim ( + ) x x =. (4 ) lim x 0 x - x - 6 x x - 5 x - x = lim x0 - x - 6 x - 5 x - x =. lim x0 ( - x - 6 x ) lim x0 ( - 5 x - x ) =. ( ) y = x ( ) y = 5 x 4 - x ( ) y = e x + x + ln x ( 4) y = : x - ( ) y= ( x )= ( x- )= - x - - = - x - = - x. ( ) y= (5 x 4 - x )= (5 x 4 )- ( x )= 54x x - = 0 x - 6 x. ( ) y= (e x + x + ln x )= ( e x )+ ( x )+ ( ln x )= e x + 6 x + x ( 4) y= ( x - )= - ( x - ) ( x - ) = - ( - x).. R, h, x, x,?, r, ABO ADO, AO AO = BO DO, r R = h - x, h r = ( h - x ) R. h S = rx = h - x Rx h = Rx ( h - x) h = R h ( hx - x ), S= R h ( h - x),

116 S= 0 x = h. x > h, S< 0, x < h, S> 0, x = h.,. x h, R, S = h ( hx - x ) 4. R ( ),,? r, r = R, r = R h = R - r, V = r h = (R ) R = R ( R ) R = A, V = A V= A4 - - A 4 -, V= 0, = 6 = 0( ). = 6, V,,. = 6,.. lim x- x = ( ) (A )0 ( B) ( C) (D). lim x = ( ) x ( A) ( B) ( C) 0 (D). lim x0 x + x x = ( ) 05

117 ( A)0 ( B) ( C) (D) 4. lim x x + x - = ( ) ( A) 0 ( B) ( C) (D) 5. x = 0 ( ) ( A) y = sin x ( B) y = x ( C) y = e x (D) y = cot x 6. y = x - x ( ) ( A)6 x - ( B) 6 x + x ( C) x + x (D) 6 x - 7. ( xe x + ln x)= ( ) x ( A)e x + xe x + x ( B) ( - x)e x + x 06 ( C) ( + x) e x - x (D) x + e x 8. ( x + x - )= ( ) ( A) x x - ( B) - ( x - ) ( C) + x ( x - ) (D) x - 9. (, - ) y = x - x ( ) ( A) x + 9 y + 6 = 0 ( B) 9 x + y + 6 = 0 ( C)9 + y - 6 = 0 ( D) x - 9 y + 6 = 0 0., ( -, 0) ( ) ( A) y = 4 + x 4 ( B) y = - x ( C) y = + x ( D) y = x +. y = x - x + ( A) x = 0, x = ( B) x = 0, x = ( C) x = ( D) x = 0 -. y = x + x - ( -, ) ( ) ( A) 9, - ( B) - 5, 9 ( C) 0, 9 ( D) -, - 5. lim x x - x x 4 + x + =.. lim x x - 5 x + 6 x - x - 6 =.. lim x ( x + x) =. 4. lim x x - x x - =.

118 5. y = 6. y = - x. x - x, f ( ) =. 7. y = x - x ( -, - ). 8. y = x - x. 9. y = x - 4 x cm ( ),,.. ( ) lim x x - x - 8 ( ) lim x a ( x - ) x - x + ( ) x lim x +. ( ) y = x - x + 9 x - 4 ( ) y = e x + xln x ( ) y = ( + x) ( - x ). y = x x = x = -,. 4. y = x - 4 x V,,,? ,,, lcm, r,? 7. a ( - 5-5),, - 5-5, x,? A. C. B 4. B 5. D 6. B 7. A 8. B 9. C 0. D. A. B 07

119 ( - x - ( ) lim x x - 8 = lim x ( -, ) (, + ), ) x - ( x - ) ( x + 4 x + 4 ) = lim x ( ) lim x a ( x - ) = lim x a x - lim xa = a -. ( ) x lim x - x + x +. - = lim x x + x + x = x + 4 x + 4 = 6. lim ( - x x + ) x lim ( + ) x x =. ( ) y= ( x - x + 9 x - 4)= ( x )+ ( - x )+ ( 9 x)+ ( - 4)= x - 6 x + 9. ( ) y= ( e x + xln x) = ( e x )+ ( xln x)= e x + ln x + x x = ex + ln x +. ( ) y= [ ( + x) ( - x ) ]= ( + x) ( - x ) + ( + x) ( - x ) = - x - x( + x) = - x - 4 x - x = - 4 x - x.. y = x, y= x, x =, y = 4, y x = x = -, y = 4, y x = - = 4, (, 4) y - 4 = 4 ( x - ), 4 x - y - 4 = 0. = - 4, ( -, 4) y - 4 = - 4( x + ), 4 x + y + 4 = 0. (, 4) k = 4, ( -, 4) k = - 4,, tan= k - k + k k arctan y = x - 4 x - 4, y= x - 4, = 4 - ( - 4 ) - 6 = 8 5, y= 0 x = x = - x >, y> 0; > x > -, y< 0; x < -, y> 0. x = y, y = x = - y, y = r, h, S.

120 V = r h, h = V r. S = r + r h S= 0 r = r =, V, = r + 4r V r = r + 4 V r, S= 4r - 4 V r. V,,, S = V + 4 V = 6 V, V,, 6 V , x, y, S. x = r, y = ( l - r - r)/, x = r, y = ( l - r - 4 r)/.,,. S = r + xy = r + rl - r - 4 r S= l - (+ 8) r, S= 0 r = r = l (+ 8 ). l + 8. = lr - ( + 4 ) r l + 8,,, S = RtABC, AC = x, BAC = 0, BC = xtan0= x, AB = x, a - x, x S = ( a - x) sin60= 4 ( a - x),. V = S x = 4 ( a - x) x = a x 4 - ax + x, V= a 4 - ax + x, 09

121 V= 0 x = a 6 x = a (, ), x =, a 6, V, V = x 4 ( a - x) = 4 a 6 ( a - a 6 ) = a

122 ,.,.,..,,,. ;,..,. ( ), : :. k60+ ( k Z) k+ ( k Z) { = k60+, k Z} { = k+, k Z},, x,,., k< < k+, ( k Z) k60< < k60+ 90( k Z) ; k+ < < ( k + )( k Z) k60+ 90< < k60+ 80( k Z) ;,

123 (k + )< < k+ ( k Z) k60+ 80< < k60+ 70( k Z);, (k + )+ < < ( k + )( k Z) k60+ 70< < k60+ 60( k Z);,..,. 60. = 60, = 60,.,,. = l r, l, r.. 4. = 60= 80= = ( 80 ) 57.0= 57 8 l r ( ) : l = r , P( x, y), r, r = x + y, : sin= y r cos= x r tan= y x cot= x y

124 - - sec= r x csc= r y. ( - - ) sin cos tan cot sin cos 0-0 tan cot 0 0

125 4. - < < <, - ( ) ( A) ( -, 0) ( B) ( -,) ( C ) ( 0, ) (D) ( -, ) - < < - < - < - < < + - < - <, <, - < 0, - < - < 0. A ( ) ( A) ( B) ( C) (D) - 440= , ,. D.., ( ) ( A) ( B) ( C) (D), k< < k+ k< < k+ 4 ( k Z), ( k Z). k, ; k,. D. 4., ( ) ( A) sin > 0, cos < 0 ( B) sin < 0, cos > 0 ( C) tan < 0 (D)t an > 0,

126 + k< < + k( k Z), + k< < + k( k Z). 4 k, ; k,.., sin > 0, cos < 0, tan < 0;, sin < 0, cos > 0, tan < 0. A B D, C. 5., sin- tan ( ) ( A) sin- tan> 0 ( B) sin- tan< 0 ( C) sin- tan= 0 ( D), sin< 0, tan> 0, sin- tan< 0. B. 6. ( A) ( B) ( C), (D),,. A. ( ) ,,,.. R, R,,.. P ( a, - 4 a), a < 0,. 4. tan sec< 0,. 5.= : { = k60-5, k Z},. k =, 45, k = 0,

127 := k60-5( k Z),, 45, , AOB = 60=. A B = R = R. AOB S AO B = R sin = 4 R, OAB S = lr = R R = 6 R, - - : S = 6 R - 4 R = ( 6-4 ) R. : R, ( 6-4 ) R.. r = OP = ( a) + ( - 4 a) = 5 a. a < 0, r = - 5 a. sin= cos= y r x r tan= y x = - 4 a a = - 4 a - 5 a = 4 5, csc= 5 4 ; = a - 5 a = - 5, sec= - 5 ; = - 4, cot= - 4. : sin= 4 5, cos= - 5, tan= - 4, cot= - 4, sec= - 5, csc= :. 5. = - 4, - < < -.. :.. y = x, sin cos tan., y = x P (, ), r = OP = + = 0. sin= y r = 0 = 0, 0 cos= x r = 0 = 0 0, tan= y x = =., y = x P ( -, - ) 6 r = OP = ( - ) + ( - ) = 0.

128 sin= y r = - 0 = - 0 0, cos= x r = - 0 = - 0 0, tan= y x = - - =.. 4 < + <, - < - < -, -. - = m(+ ) + n(- ) = ( m + n)+ ( m - n). m + n = m = m - n = -, n =, - = (+ ) + (- ). < + < 4 6 < - < - < - - < (+ ) <, - 5 < - < ( - 5 6, 6 ). (- ) < -,. cm, 0. = 0=, l = r = = ( cm). 0 S = r + l = + = 6 + (cm). lr = = (cm ), 0( 6 + )cm, cm.. ( ) ( A) { = k, k Z } ( B) { = k+, k Z} ( C) { = k, k Z} ( D) { = k, k Z} 7

129 . - 80< < < 80, - ( ) ( A) - 60< - < 0 ( B) - 80< - < 80 ( C) - 80< - < 0 ( D) - 60< - < 80.R,. R ( ) ( A). ( B). ( C)6.4 (D) P ( - 4 a, a) ( a < 0), 5sin+ cot ( ) ( A) - 7 ( B) - ( C)0 (D) 5., cos = - cos, ( ) ( A) ( B) ( C) (D) 6. sin< 0, tan> 0, ( ) ( A) ( B) ( C) (D) 7.8sin 50cos ( )cot ( - 55 )tan( - 75 ) ( ) ( A) ( B) - ( C) 8. y = sin x sin x + cos x cos x + tan x tan x + cot x cot x ( A) { -, 0, 4} (B) { -,4} ( C) { -, 0,, 4} (D) { - 4, -, 0, 4} (D) - ( ) 9., ( ) ( A) tan cos ( B)cos cot ( C) sin sec (D)cot sin 0., cos= - 5, ( ) ( A) ( B) ( C) (D). ABC, ( ) ( A) sin A ( B)cot A ( C)cos B + C. 50, - 70< < 60,. (D) tan A. y = x( x 0 ),,,.. R,,,. 4.0 < < 4, sin cos cot. 5.a sin80+ b t an765+ ( a - b ) cot5- abcos60=. 6.tan675+ cot765- sin ( - 5 ) + sec( - 6 ) =. 7.sin tan cos cos cos n( n N). 8

130 . sin + cos =, sin+ cos sin 4 + cos 4.. sin+ cos= k, sin + cos < 0, k.. P, P -, P 0,.. D. A. A 4. A 5. C 6. C 7. A 8. A 9. D 0. C. D , - 0, 50. = k- 4 ( k Z),, -. R, R 4. sin< cos< cot 5. a - ab cos < tan< cos < sin < cos n. sin + cos = = sin + cos, sin - sin + cos - cos = 0, sin ( - sin ) + cos ( - cos ) = 0. sin ( - sin ) 0, cos ( - cos ) 0, sin ( - sin ) = 0 cos ( - cos ) = 0 sin= 0 cos= sin= cos= 0 sin+ cos=, sin 4 + cos 4 =.. sin+ cos= k sin(+ ) = k, k [ -, ], 4 sin cos= k - sin + cos < 0, ( sin+ cos ) ( sin - sin cos+ cos ) < 0, k( - k - ) = k( - k ) < 0.. 9

131 , 0 < k - < k < 0 k > - < k <. - < k < 0, - < k < 0.. P ( 0 ) - ( - ) =, sin= y r = 0 = 0 0 cos= - 0 = - 0, sec= - 0 tan= - =, cot=., csc= 0, 0, 0

132 .,., sin csc=, cos sec=, tan cot= tan= sin cos, cot= cos sin sin + cos =, + tan = sec, + cot = csc k60+ ( k Z),, ;. 90,70,,,.,, : sin cos tan cot - - sin cos - tan - cot 90- cos sin cot tan 90+ cos - sin - cot - tan 80- sin - cos - tan - cot sin - cos tan cot

133 sin cos tan cot cos - sin cot tan cos sin - cot - tan sin cos - tan - cot k60+ sin cos tan cot., 0 90, sin( ) = sin cos cos sin, cos ( ) = cos cos sin sin, tan( ) = tan tan tan tan tan sin= sin cos, tan= - tan, cos= cos - sin = cos - = - sin tan - tan tan sin=, cos=, tan= + tan + tan - tan asin bcos= a + b sin( arctan b a ) ( a > 0, b > 0)., sin sec csc - = ( ) ( A) ( B) tan ( C )cot (D) -,, sin sec csc - = sin sec cot. = sin sec ( - cot ) = - sin cos cos sin = -. D.. sin( ) ( A) ( B) - ( C ) ( D) - ( )

134 sin( ) = - sin680= - sin( ) C. = - sin( ) = - ( - sin60 ) =. : ( ) ; ( ) ; ( ) cos (+ ) = - ( A) sin(+ ) = 5 4 5,, sin(+ ) cot (- ), cot( - ) = 4 ( ) ( B) sin (+ ) = - ( C) sin(+ ) = - (D) sin(+ ) = - cos (+ ) = , cot( - ) = - 4, cot( - ) = 4, cot( - ) = , - cos= - 4 5, cos= 4 5. sin(+ ) = - sin= - - cos = - - ( 4 5 ) = - cot(- ) = - cot= - cos sin = - B = , 4., sin 4 + cos 4 = 5 9, sin ( ) ( A) ( B) - ( C) (D) - sin 4 + cos 4 = ( sin + cos ) - sin cos = - sin = 5 9, sin = 8 9., + k< < + k ( k Z) + 4 k< < + 4 k ( k Z). sin= A..

135 sin = x, cos = y x + y = 5 9 x + y = - xy = 4 9, 4 x y = 8 9, sin = sin x - cos x =, sin x = ( ) ( A) 8 9 ( B) 8 9 ( C ) (D) sin x - cos x =, sin x - sin x cos x + cos x = 9, - sin x = 9, sin x = 8 9. A. 6. tan (+ ) = 5 ( A) 8, tan(- 4 ) = 4 ( B) ( C) tan (+ ) = tan[ (+ ) - (- 4 4 ) ] C. = t an(+ ) - t an(- 4 ) + tan(+ ) tan(- = 4 ), tan(+ 4 ) = ( ) (D) =.,,, + 4 (+ ) - (- 4 ) sin(- ) cos- cos (- ) sin= 4 5 ( A) ( B) 5 5 ( C) 5,, cos 5 ( D) 5 sin(- ) cos- cos (- ) sin= sin[ (- ) - ] = sin ( - ) = - sin, - sin= 4 5, sin= , 5 ( )

136 cos= - cos - ( sin ) = - - ( - - = - 5, 4 5 ) = - 5, 8. cos - = B. 5 = cos60 ( ) ( A) sin40 ( B)cos40 ( C)cos0 (D) - cos50 + cos60 = A. [ + (cos 0- ) ] = cos 0 = cos0 = - cos0 = - cos (80-50 ) = cos50= sin40.. sin- cos=, sin - cos.. tan0+ tan40+ tan0 tan40.. sin7+ cos5 sin8 cos7- sin5 sin8. 4. cos0 cos40 cos60 cos80.. sin- cos=, ( sin- cos ) =. sin - sin cos+ cos =, sin cos=., sin - cos = ( sin- cos ) ( sin + sin cos+ cos ) : 4 9. = ( sin- cos ) ( + sin cos ) = ( + ) = ,..., tan0+ tan40+. tan0 t an40 = tan( ) ( - tan0 tan40 ) + tan0 t an40 = ( - tan0 tan40 ) + tan0 tan40=. 5

137 , tan (0+ 40 ) = tan0+ t an40 - tan0 tan40 =. - tan0 40= tan0+ tan40, tan0+ tan40+ tan0 t an40=. :.. sin7= sin (5-8 ) = sin5 cos8- cos5 sin8, cos7= cos( 5-8 ) = cos5 cos8+ sin5 sin8, = sin5 cos8 = tan5= tan(45-0 cos5 cos8 ) = tan45- tan0 + tan45 tan0 = - + = -. : -.,,,.. 4. = sin0 cos0 cos40 cos80 = sin40 cos40 cos80 4 sin0 8 sin0 : 6.. = sin80 cos80 6sin0 = sin60 6 sin0 = 6. ( ) ( sin A + tan Atan A + cos A) sin A cos A ( ) 6 ( + sin+ cos ) ( sin - cos ) + cos ( ) = ( + tan Atan A ( ) = ) sin Acos A cos A ( 70< < 60 ) = ( + sin A - cos A ) sin A = tan A. cos A sin A = ( cos + sin cos ) ( sin - cos ) ( + cos ) cos (cos + sin ) ( sin - cos ) 4cos 70< < 60, 5< < 80,,

138 = cos ( sin - cos ) - cos = cos., : ( ) ( ) ; ( ) ( ) ; ( ) ( ) ; (4 ) ; (5 ) ; ( 6) ( ) ; (7 ) ; (8 ).. cos (- ) - cos (+ ) =, ( + cos ) ( + cos ) =, tan tan. cos (- ) - cos (+ ) = [cos(- ) + cos (+ ) ] [ cos(- ) - cos(+ ) ] = cos cos sin sin = 4sin sin cos cos= ( + cos ) ( + cos ) = cos cos = 4cos cos = tan tan=. 994,.,.,,. tan+ t an. tan- t an = sin(+ ) sin(- ). = = sin cos + sin cos = sin cos - sin cos sin cos+ sin cos cos cos sin cos- sin cos cos cos sin cos+ cos sin sin cos- cos sin = sin(+ ) sin(- ) =..cos(- x) = ( A) 5 6 ( C), x ( -,), x ( ) ( B) 6 (D) cos + tan + sin = -, ( ) + cot 7

139 ( A) ( B) ( C ) ( D).sin+ cos= m, tan+ cot= n, m n ( ) ( A) m = n ( B) m = n + ( C) m = n ( D) n = m 4., sec + tan + tan sec - ( ) ( A) - ( B) ( C) - ( D) 5. ( 0, ), log sin ( ) ( A) sin ( B) - sin ( C) csc ( D) - cos 6. cos=, + tan4 ( ) ( A) 4 6 ( C) 7 ( B) ( D) 8 7. sin4 xcos5 x = - cos4 xsin5 x ( ) ( A) 0 ( B) 0 ( C) 50 ( D) ABC, A B C, ( ) ( A) sin B + C = sin A ( B)cos ( B + C) = cos A ( C) cos ( B + C) = cos A ( D) sin( B + C) = sin A 9.cos xsin ( y - x) + cos ( y - x) sin x ( ) ( A) ( B)cos y ( C) sin y ( D) cos xsin y 0. sin= - ( A) ( C) - 8,70< < 60, sin ( ) ( B) -. sin x = + cos x, tan x ( ) ( D) 8 ( A) ( C) ( B) ( D) 8

140 . sin (+ ) =, sin(- ) =, tan cot ( ) ( A) - 5 ( B) 5 ( C) 5 ( D) 5.cot0+ cot40- cot0 cot40 ( ) ( A) ( B) - ( C) ( D) - 4. ( 0, ), sin(+ ) sin+ sin ( ) ( A) sin(+ ) < sin+ sin ( B) sin (+ ) = sin+ sin ( C) sin(+ ) > sin+ sin (D). tan= t, sin cos t.. sin- cos=,, sin - cos =, sin 6 + cos 6 =..lgtanlgtanlgtanlgtan89=. lgtan+ lgtan+ lgtan+ + lgtan89=. 4.csc0- sec0=. 5. sin+ 5cos= 9,cos+ 5 sin= 5, sin (+ ) = sin- cos. 4 sin x + cos x 7.tan x =, 5sin x - cos x. 8.tan+ cot= 5, tan + sec csc+ cot.. ( ) sin+ cos sec+ csc ( ), tan sec - - csc - cot., ( ) sin68 sin7+ sin58 sin98 ( )8cos cos cos sin cos x - ( + ) x + m = 0, sin - cot + cos - tan. 9

141 4. sin+ cos=, sin- cos sin+ cos. 5. : ( ) tan - cot sin - cos = sec + csc ( ) + tan A - sec A - tan A + sec A = sec A + t an A - sec A + t an A + 0.A.C.B 4.A 5.C 6.A 7.B 8.C 9.C 0.B.B.D.B 4.A t.. + t 6, ( ) = ( ) = , sin sin+ cos cos + = sin+ cos = sin cos. sin+ cos sin sin cos tan - tan., cot cot = tan - tan - - cot cot = 0. ( ) = sin cos8+ ( - cos ) ( - sin8 ) = sin cos8+ cos sin8 ( ) = = sin( + 8 ) = sin0=. = 8sin cos cos cos sin = 9 sin 4 cos sin = 9 sin 8 9 sin =. 9 4sin cos cos sin 9. sin cos x - ( + ) x + m = 0, sin+ cos= +, sin - cot + cos - tan = sin - cos + cos - sin = sin cos sin sin- cos + cos cos- sin

142 = sin+ cos= + 4. sin- cos = k, sin+ cos= sin+ cos sin+ kcos= sin- cos, sin+ cos= sin= + k - k cos= - k - k sin + cos =, ( + k - k ) + ( - k - k ) =, k = - 6, sin- cos sin+ cos = ( ) = = = sin cos - cos sin 4 - cos 4 sin sin - cos = sin cos sin - cos ( sin + cos ) ( sin - cos ) sin cos = sin + cos sin - cos sin cos cos + sin = sec + csc =. ( ) = ( sec A - tan A) + (t an A - sec A) ( sec A - tan A) - (t an A - sec A) = sec A + tan A - sec A + tan A + =... = ( sec A - tan A) ( sec A + tan A - ) ( sec A - tan A) ( sec A + tan A + )

143 ,, ( ).. y =, y = Asin(x + ) y = sin x, Asin (x + )., arcsin x arccos x arctan x

144

145 - -, y = sin x, x [0,] ( 0, 0),,, (, 0),, -, (, 0),,,,,. y = cos x, x [ 0, ]., y = Asin (x + ) ( A > 0,> 0 ). y = sin x y = cos x y = tan x R R { x x R xk+, k Z} y [ -, ] y [ -, ] y R - - [ - + k, + k] ( k Z) [ + k, + k] ( k Z) [ ( k - ), k] ( k Z) [ k, ( k + )] ( k Z) ( - + k, + k ) ( k Z) T, y = f ( x), x, f( x + T ) = f ( x), y = f ( x).,,,. y = Asin(x + ) y = Acos (x + ) ( A, A 0, x R) T =. y = Asin (x + ) y = sin x..y = sin ( x + ) y = sin x (> 0 ) (< 0 ). 4

146 .y = Asin x y = sin x ( A > ) A A < ) A..y = sinx y = sin x ( <, 0 ) ( > ). 4.y = Asin (x + ) y = sin x, A. A. 5.y = Asin (x + ) y = Asin(x + ).. -, - a, sin= a, arcsin a.. 0, - a, cos= a, arccos a, = arccos a.. - < <, tan= a( a R), arct an a, = arctan a.. ( 4, ), sin cos tan ( ) ( A) sin> cos> tan (B )tan> cos> sin ( C) cos> tan> sin (D)t an> sin> cos ( 4, ), sin> 0,0 < cos<. tan= sin, tan> sin. cos cos= sin( - ),> -, sin> cos, tan> sin> cos. D. =, ( 4, ). sin= sin = tan> sin> cos. D., cos= cos =, tan= tan =,,,. 5

147 . y = lgtan x ( ) ( A) ( k, k+ ) ( k Z) ( B) ( k, k+ 4 ) ( k Z) ( C) ( k, k+ ) ( k Z) ( D) tan x > 0, k< x C. k< x < k+ ( k Z ). < k+ ( k Z),. sin x > cos x, x ( ) ( A) { x k- < x < k+ 4 4, k Z} ( B){ x k+ < x < k , k Z} ( C) { x k- < x < k+ 4 4, k Z} (D){ x k+ < x < k+ 4 4, k Z} sin x > cos x, cos x - sin x < 0, cos x < 0. D. k+ < x < k+ ( k Z), k+ < x < k+ ( k Z) y = cos ( x - ) ( ) ( A) [ k- 5, k+ ] ( k Z) ( B) [ k-, k+ 6 ] ( k Z) ( C) [ k+, k+ 6 ] ( k Z) (D) [ k+ 5, k+ 6 ] ( k Z), x k+ 0 x - k+ ( k Z), k+ x k+ 4 k+ x k+ 6 ( k Z), ( k Z).

148 C. 5. : y = sin( x - )cos ( x ) y = sin ( x) y = sin 4 x - cos 4 x y = sin xsin x - cos xcos x ( A) (B) ( C) (D) y = sin( x - )cos( x ) = T = 4 =. y = sin x = ( - cos4 x) = - cos4 x +, T = 4 =. ( ) sin4 x + sin( - ) = sin4 x - 4, y = sin 4 x - cos 4 x = ( sin x + cos x) ( sin x - cos x) = - cos x, T = =. y = sin xsin x - cos xcos x = - cos( x + x) = - cos4 x, T = 4 =. C. 6. y = sin( 5 - x) ( ) ( A) ( B) ( C), (D) y = f( x) = sin( 5 - x) = sin[ + ( - x) ] = sin (- x) = cos x. y = cos x, y = sin ( 5 - x). B. 7. sin x < cos x x ( ) ( A) [ - 4, ] ( B) [ - 4, ] ( C) [ - 4, ] (D) [ 0,] 4 y = sin x y = cos x ( x [ -,] ) ( - - 4), x [ - 4, ], cos x > sin x. 4 A. 8. y = sin( x + 5 ) ( ) ( A) x = - ( B) x = - 4 ( C) x = 8 ( D) x = 5 4 7

149 - - 4 y 0 4 x y = sin( x + 5 ) = sin[+ (+ x) ] = sin (+ x) = cos x, y = cos x x = -. A., y = sin x x = k+ ( k Z) ; y = cos x x = k( k Z). 9. y = Asin (x + ) x = 9-8 ; x = 4 9, ( ) ( A) y = sin( x - 6 ) ( B) y = sin ( x + 6 ) ( C) y = sin( x - 6 ) (D) y = sin ( x + 6 ) y = Asin(x + ), -., A = y = Asin(x + ) T = ( ) =, T = = =. B., A C (0) y = sin x, y = sin ( x - ) ( ) ( A) (B) ( C) (D) 6 6 y = sin x, y = sin ( x - ) 6. C.

150 . y = sin( x + ) ; ; ; 6 ; ; ; ; x.. f ( x) = ax + btan x + csin x + 5, f ( 5) = 0, f( - 5) =.. y = sin x + cos 4 x x, cos x = m - 6 m +. T =, A =, = 6, : yma x =, : ymi n = -. k- x + k+ 6 k - m. ( k Z), k x + ( k Z), 9 9 k - k x k+ x + k+ ( k Z), 6 k + k x + 4 ( k Z), 9 9 ( k Z). k + k x + 4 ( k Z). 9 9 y = 0, sin( x + 6 ) = 0. x + k = k( k Z), x = 6-8 x ( k - 8, 0 ) ( k Z). : ; ( k Z), ; 6 ; ; - ; k - x k ; k + x k ; ( k -, 0) ( k Z ). 8. f( 5) = 0, a5 + btan5 + csin5 + 5 = 0, a5 + btan5 + csin5 = 5. f ( - 5) = a( - 5 ) + btan( - 5 ) + csin ( - 5 ) + 5 f( - 5) = 0. = - [ a5 + btan5 + csin5] + 5 = = 0, 9

151 : 0.. y = sin x + cos 4 x = - cos x + cos 4 x = - cos x( - cos x) = - cos xsin x = - 4 sin x = - 4 ( - cos4 x) = cos4 x,. T = 4 =. : x 6 cos x, m - m +. m - m + m - m + - 0, m > -. m + m - m + m - m + : m. 0, m < - m. m.. y = sin ( x + ), ( ) x x + 0 sin ( x + ) ( ) : T = =, A =, f = T =, =. k- x + k+ k- k- ( k Z), 5 x k+ ( k Z), x k+ ( k Z).

152 - - 5 [ k- 5, k+ ] ( k Z). k+ x + k+ ( k Z), k+ x k+ 7 ( k Z), 6 6 k+ 7 x k+ ( k Z), [ k+ 7, k+ ] ( k Z).. y = a + bcos x, -. b > 0,, -, y = b - sin4 ax, a + b = a - b = -, a = b = y = b - sin4 ax = - sin x,,, -. b < 0,, -,, a - b = a + b = -, a =, b = - y = b - sin4 ax = - - sin x,,, -., b =,, - ; 4

153 b = -,, -.. sin= 5, < <,. < <,0 < - <, sin(- ) = sin= 5,- = arcsin 5, = - arcsin 5. )arcsin a ( a ), -, ; ) -,,,.,. 4. ( ) cos= - ( ) cos=, < <, ;, - < < 0,. ( ),0, = arccos - ( ) - < < 0, 0 < - <, cos ( - ) = cos=,. - = arccos, = - arccos. 5. ( ) tan=, 0 < <, ; ( ) tan= - 5, < <,. ( ) 0 < <, - < <. = arctan. ( ) - < <, - < < < 0, tan(- ) = tan= - 5, - = arct an( - 5), = + arct an( - 5). 4

154 ., ( ) ( A) y = - sin x ( B) y = sin( - x ) ( C) y = sin x ( D) y = xsin x. y = Asin (x + ), x = 7, y =, x =, y = -, ( ) ( A) y = sin( x + ) ( B) y = sin ( x - 6 ) ( C) y = sin ( x + ) ( D) y = sin ( x - 6 ). y = tan x ( A) ( B) ( C) ( D) ( ) 4.y = cos( + x) y = cos (- x), x ( ) ( A) { x k x + k, k Z} ( B){ x k x + k, k Z} ( C) { x - + k x + k, k Z} (D){ x + k x + k, k Z} 5., (0, ), ( A) y = x ( x R) ( B) y = sin x ( x R) ( C) y = cos x ( x R) ( D) y = e sin x ( x R) ( ) 6. y = cos ( sin x) ( ) ( A) x [ -, ] ( B) x [ k-, k+ ] ( k Z) ( C) x [ k, k+ ] ( k Z) ( D) x R 7.sin< cos, ( ) ( A) - < < 4 4 ( C) k< < k+ 4 ( B) k k+ 4 ( k Z) ( k Z) ( D) k- < < k+ 4 4 ( k Z) 8., ( ) ( A)cos0< cos < cos < cos0< cos 4

155 ( B)cos0< cos < cos < cos0< cos ( C) cos0> cos > cos > cos0> cos (D)cos0> cos > cos > cos0> cos 9., ( A) y = cos x [ -,0 ] [, ]. ( B) y = tan x, x [ 4, 4 ], x, [ -, ] ( C) y = cos ( x - ) (D) y = sin x, [,]. ( ) 0. y = sin ( x + 8 ) x = ( ) ( A) - 4 ( B) - 4 ( C) 4 (D).a >, 0 x, f ( x) = - sin x + acos x + ( ) ( A) + a ( B) - a ( C) - a (D) - a. y = sin( x + ), y = sin x ( ) ( A) ( C) 6. y = sin xcos x + cos x - ( A) ( B) ( C) 4 (B) (D) 6 ( ) (D) 4. y = sin( x + 4 ) ( ) ( A) [ -, ] ( B) [ - 4, ] ( C) [ -, 0] (D) [ - 4 4, 4 ] 5. y = cos x + cos x ( ) ( ) 44. y = cos x + sin x ;.. y = log sin x..y = sin( x - ) y = sin ( x + ). 4. sin x - cos x = - m, m. + m

156 5.cos x > 6. y = sin( x - ), x [ 0, ] , x [ 0, ]. x =, y. x =, y.. ( ) y = - cos x 7 sin x 7 ( ) y = atan x a. ( ) y = log0. 5 ( sin x + ) ( ) y = 4 + tan( x + 6 ). x ( ) sin x =, 0 < x < 0 ( ) tan x =, < x < ( )t an x = - 4, - < x < 0 4. f ( x) = sin x + cosx, f ( ) + f ( ) + + f (00). 45

157 .D.A.B 4. A 5. B 6.D 7.D 8.D 9.D 0.C.C.D.A 4.B 5.C. 0, - 8. { x x = k+, k Z}., 4. m - m [ 0, 7 ) ( 4 4, ] 6. x = 5, ; x = 0, - 6 ( ) y = - cos x 7 sin x 7 = t an x 4, 46 T = = 4. 4 ( ) T =. ( ) sin x + > 0, = a. a k- < x < k+ 7 ( k Z), 6 6 { x k- 7 < x < k+ 6 6, k Z}. ( ) { x x R x k+, k Z}.. ( ) 0 < x <, - x, x = arcsin 0. ( ) - < x < 0, - < x <, x = arctan( - 4). ( ) 0 < <, tan =, = arctan. tan(+ ) = tan =. < + <, x = + = + arctan.

158 4. sin x cos x = 4, f ( x) = sin x + cosx 4. f ( ) + f( ) + + f (00) = 500 [ f( ) + f ( ) + f( ) + f (4 ) ] + f (00) + f (00) f ( ) = sin x + cos x = 500[ f ( ) + f ( ) + f( ) + f (4 ) ] + f( ) + f ( ). =, f( ) = sin+ cos= -, f ( ) = sin + cos = -, f ( 4) = sin+ cos=, f ( ) + f ( ) + f( ) + f (4 ) = 0, f ( ) + f ( ) = 0. f ( ) + f ( ) + + f (00) = 0. 47

159 ,.,,.,.,,, , AB C, C = 90, a b c A B C D B, CD A B. ( ) : A + B = 90 ( ) : c = a + b A C ( ) : CB = BDAB, AC = ADAB, CD = ADDB (4 ) : SAB C = ab = AB CD C (5 ) : sin A = cos B = a c b a tan A = cot B = a b A c B sin B = cos A = b c tan B = cot A = b a. ( ) 48

160 ( ca) ( ) B = 90- A ( ) a = csin A ( ) b = ccos A ( 4) SABC = ab = c sin Acos A ( ) b = c - a ( ) sin A = a c,a (c a) ( ) cos B = a c,b (B = 90- A) ( 4) S ABC = ab = a c - a ( aa ab) ( ) B = 90- A A = 90- B ( ) c = a sin A = a cos B ( ) b = acot A = atanb ( 4) S ABC = ab = a cot A = a tan B ( ) c = a + b ( ) tan A = a b, A (a b) ( ) tan B = b a,b ( B = 90- A) ( 4) S ABC = ab. ABC, A B C a b c, R ABC. ( ) : A + B + C = 80 ( ) : a sin A = b sin B = c sin C = R ( ) : a = b + c - bccos A b = c + a - cacos B c = a + b - abcosc cos A = b + c - a bc cos B = c + a - b ca cos C = a + b - c ab (4 ) : SAB C = absin C = bcsin A = acsin B. 49

161 (AB c) ( ) C = 80- ( A + B) ( ) a = csin A sinc, b = csin B sinc ( ) SABC = absinc ( a bc) ( ) c = a + b - abcos C ( ) sin B = b sinc,b c ( ) A = 80- ( B + C) (4 ) S ABC = absinc ( a b c) ( ) cos A = b + c - a bc cos B = c + a - b ca ( ) C = 80- ( A + B), A, B ( ) S ABC = absinc (a ba) ( ) sin B = bsin A, B a ( ) C = 80- ( A + B) ( ) c = asin C sin A (4 ) S ABC = absinc. AB C, C = 90, b =, c =, a sin B ( ) ( A) a =, sin B = ( B) a =, sin B = ( C) a =, sin B = (D) a =, sin B = RtABC, b =, c =, a = c - b = ( ) - =, sin B = b c = =. C , 5 7 ( ) ( A) 0 (B) 60 ( C) 0 50 (D) 60 0 cos= ( 5 7 ) 0 5 =, 50

162 = 60. B.. AB C, a cos A = b cos B = ( A) ( B) ( C) (D) a cos A = a a + c - b ac b, acos B = bcos A, cos B = b b + c - a bc, a = b, a = b. b = c, a = b = c. D. c, ABC ( ) cosc, 4. AB C, ABC =, abc ( ) ( A) ( B) ( C) (D) ABC =, A = x, B = x, C = x, A + B + C = x + x + x = 80, x = 0A = 0, B = 60, C = 90. abc = sin Asin Bsin C = =. C. 5. RtAB C, C = 90, A = 60, a + b =, ABC ( ) ( A) 6-8 ( B) ( C) 8 ( D) 0 RtABC, A = 60 a = csin A, b = ccos A, a + b = csin A + ccos A. a + b =, = csin60+ ccos60, c = ( - ), AB C l = a + b + c = + ( - ) =. B. 6. AB C, a =, b =, C = 50, c ( ) ( A) 49 (B) 7 ( C ) (D), c = 7. c = a + b - abcosc = ( ) + - cos50 B. = ( ) + - ( - ) = 49, 5

163 . AB C, sin Asin Bsin C = ( - ) ( + ) 0,.. AB C, ( a + b + c) ( b + c - a) = bc, A.. AB C, a = 4, b = 5, sin A = 4 5, B. 4. 0m, 45 0,.. abc = sin Asin Bsin C = ( - )( + )0. a - = b + = c 0 = k, a = ( - ) k, b = ( + ) k, c = 0 k. c, C cosc = [ ( - ) k] + [ ( + ) k] - ( 0 k) ( - ) k( + ) k 0 < C < 80, C = 0. : 0.. ( b + c) - a = bc, b + c - a = bc, = -, cos A = b + c - a bc 0 < A < 80, = bc bc =. A = 60. : 60.. a sin A = b, sin B = bsin A sin B a = =, B = b < a, B < A, B = 5 ( ). : , AC = x( m) A RtAB C, ABC = 45, BC = x. CD = BC + BD = x + 0. RtADC, tanadc = AC CD, C B D tan0= x x + 0, = x x + 0, x = 0 ( + ). : 0( + ) m. 5

164 . AB C, a - b = ccos B - ccos A, ABC., a - b = c a + c - b ac - c b + c - a bc ab( a - b) = b( a + c - b ) - a( b + c - a ), a - b - a b + ab - ac + bc = 0, ( a - b) ( a + b - c ) = 0, a = b a + b = c. ABC..,. AB C, ( bcosc + ccos B) - ( acosc + ccos A) = ccos B - ccos A, ( b - a)cosc = 0, a = b C = 90, AB C. : A + B = 0. ( sin A + sin B + sin C) ( sin A + sin B - sin C) = sin Asin B, sin A = a + b - c = ab, a + b - c ab a R, sin B = b R, sin C = c R. 4 R ( a + b + c) ( a + b - c) = =,, 4 R ab, cosc =, C = 60, A + B = , ABC, ABC = 90, CD AB, D A B, CD = 4 AB, A B. ABC, ACB = 90, CD = ADDB. C CD = 4 AB, AB = c, AD = x, AD DB, ( 4 c) = x( c - x), 6 x - 6 cx + c = 0, A D B x = ( ) c 4. 5

165 AD DB, AD = ( - 4 ) c. CD = 4 c, tan75= tan A = CD AD = 4-4 = +. tan45+ tan0 - tan45 tan0 = +, 0< A < 90, A = 75, B = 90-75= 5. A = 75, B = 5..RtABC, C = 90, a = 8, c = 0, tan B = ( ) ( A) 4 ( B) ( C) 4 (D) 54. ABC, A = 90, b B, ( ) ( A) a = bsin B ( B) a = ( C) a = bcos B (D) a = b sin B b cos B.RtABC, C = 90, ( ) ( A) a - b = csin A - B ( C) a + b = csin A - B ( B) a - b = csin A + B (D) a + b = sin A + B 4.ABC, sin A + sin B = sin C, ( ) ( A) ( B) ( C) (D) 5. ABC, C = 90, a = 6, B = 0, c - b ( ) ( A) ( B) - ( C) (D) - 6.ABC, C = 90, tan A =, ABC 60cm, ABC ( ) 5 ( A) 60cm ( B)0cm ( C) 40cm (D)0cm 7.ABC, AB =, BC =, C ( ) ( A) 0 < C 6 ( C) 6 < C < ( B)0 < C < (D) < C

166 8.RtABC, CD = cm, sin A =, SABC = ( ) ( A) cm ( B) cm ( C) cm (D)4 cm. ABC, C = 90, a =. 5, b = 5, c =, A =, B =. AB C, SAB C = 8, AB = 4, AC = 5, BC =.. AB C, AB = 5, BC = 4, AC =, BC AD =. 4. AB C, sin Bsin C = cos A, AB C. 5. AB C, a =, c =, A = 0, b =, cosc =. 6. AB C, C = 90, a = 6, c = 0, AB h.., ( ) A = 5, a = 4, b = 4 + 4, B C ( ) a =, b = 6, c = +, A B C csab C. SABC.. AB C, : a sin B + b sin A = absin C..C.B.A 4.A 5.C 6.D 7.A 8.D. 5, 0, , 0 4., ( ) a sin A = sin B = b sin B 4 sin5 = sin B, B = 45, B = 5 B = 45, C = 80- ( B + A) = 80- (45+ 5 ) = 0. b sin B = c sin C c = 6 + 6, sin45 = c sin0, 55

167 SA BC = ac sin B = 4 ( ) sin45= + 4. B = 5, C = 80- ( B + A) = 80- ( 5+ 5 ) = 0, b sin B = c sin C c = 6 +, sin5 = c sin0, SA BC = ac sin B = 4 ( 6 + ) sin5= ( ) cosc = a + b - c ab cosc = + ( 6 ) - ( + ) C = 75. a sin A = 6 = 6-4 c sin C sin A = + sin75,, sin A =, A = 45, B = 80- ( A + C) = 80- ( ) = 60, SA BC = absin C =. a sin A = = 4 R sin b sin B = 6 sin75= + c sin C = R, Asin Bcos B + 4 R sin Bsin Acos A = 8 R sin Asin B( sin Acos B + sin Bcos A) = 8 R sin Asin Bsin( A + B) = 8 R sin Asin Bsin C = ( Rsin A) ( Rsin B) sin C = absin C =.. 56

168 .,, () , ( ),. ( ) A, B A B.. ( ). (4 ) AB A B, AB.. ( ). ( ). AB, AB.AB, AB. a, b, c,. ( ) AB AB AB, AB. a a.. (4 ), 0.a a, - a. (5 ) a b,, a = b. (6 ),, 57

169 .. ( ) a b( - - ), A, AB = a, BC = b, AC, AC a b ( ), a + b ( ) a b( - - ), A, AB = a, AD = b, AB AD ABCD, AC = a + b. ( ) : a + b = b + a ( a + b) + c = a + ( b + c). a b( - - ), O, OA = a, OB = b, BA a b, a - b, a - b = OA - OB = BA. a - b = a + ( - b) a, a, : ( ) a = a ; - - ( ) > 0, a a ; < 0, a a ; a = 0, a = ( ) (,R) : ( ) a = (a) (+ ) a = a + a ( a + b) = a + b ba,, b = a;, b = a,

170 a b. e e, a,, a = e + e., e e. ( ). a b, OA = a, OB = b, AOB = (0 80 ), a b.,= 0, a b ; = 80, a b. = 90, a b, a b.. a b,, a b cosa b,, ab, ab. ab = a b cos. a b, a b, ab = 0;, ab = 0, a b.. ab ab a b a b cos. 4. ( ) ab = ba ( ) ( a) b = ( ab) ( ) ( a + b)c = ac + bc, R., aa a. e. ( ), x y e e. a e ( x, y) a. a = xe ( ) a = ( x, y ), b = ( x, y ),, R. + ye ab = ( x x, y y ) ; a = ( x, y ) ; ab = x x + y y. 59

171 ( ) a = ( x, y ), a = x + y. (4 ) A( x, y ) B( x, y ), AB = ( x - x, y - y ). a a l, O, P0, OP0 = r0, OP = r( - - 4). r = r0 + ta l., a = ( a P0 ( x0, y0 ) P( x, y),, a ) l, P l x - x0 = y - y0 a a Ax + By + C = 0., F, a = ( h, k) F, F F.. P( x, y) F, F P ( x, y ), a = ( h, k), A( x, y ) B( x, y ) x= x + h y= y + k AB = ( x - x ) + ( y - y ) P( x, y) AB, A B ( x, y ) ( x, y ), P x = x + x, y = y + y 60. a = (, 4 ), b = ( 0, - ), cosa, b ( ) ( A) 4 5 ( B) - cosa, b= 4 5 ( C ) 5 (D) - ab, ab = (,4)(0, - ) = 0 + 4( - ) = - 8, a = a b 5

172 + 4 = 5, b = 0 + ( - ) =, cosa, b= B. 00 (8 ) = A( -, ) B(, ) C( -, + ) ( ) ( A) ( B) ( C) (D) AB = [ - ( - ) ] + ( - ) =, AC = [ - - ( - ) ] + [ - ( + ) ] = ( - ) + ( + ) =, BC = [ - ( - ) ] + [ - ( + ) ] = ( + ) + ( - ) =, AB = AC = BC, AB C, ( C).. A B x y, AB ( -, ), AB = -, ( A) ( - 4, 0 ) (0, ) ( B) ( 4, 0) ( 0, - ) ( C) (0, - 4) (, 0 ) (D) ( 0, 4) ( -, 0) ( ) A B x y, A( x,0 ) B( 0, y). x y =, x = - 4, y =. A( - 4,0 ) B( 0, ), A.. ( a - 4 b) - ( a - b) =.. NQ + QP + MN - MP =.. A( ab, abc), B( ac,0 ), AB =. 4. P x A (5,), P. 5. A(, - ), B( - 4, 5), AB C, AC = AB, C.. = - a + b.. = N P + MN - MP = N P + MN + PM = NM + MN = 0.. AB = ( ab - ac ) + ( abc) = a ( b + c ) = a ( b + c ). 4., P ( a,0 ), AP =, a = 0 a = 0. (0, 0 ) (0, 0). ( a - 5) + =, ( a - 5) = 5, x, y, 6

173 ( a, 0) (0, b). 5. AC = AB, B AC ( ). C ( x, y ), x = - 4, y = 5, x =, y = -. + x - + y = - 4 = 5 C ( - 9, )., x = - 9 y =. a = e - e, b = - e + e, a b. b = - ( e - e ), b = - a, a b.. a = (, ), b = (, - 4), a + b, a - b, a + b. a + b = (4, - ) ; a - b = ( -, 6 ) ; a + b = (, 4) + (, - 4) = ( 5, 0) ( ) A B C ( -, ) ( -, ) (,4 ), D A C, D. AB = (, ).D( x, y), DC = ( - x,4 - y), AB = DC, (, ) = ( - x,4 - y), x =, y =. D (, ). 4. a = (4, ), b = ( 5, y), a b, y. a b, 4 = 5, = y. a = b, (4, ) = (5, y ), y = 5 4.., a = ( x, y ), b = ( x, y ), a b, x y - y x = 0; 5. P ( -, ), P (, ), P P. M( x, y ), N ( x, y ). P P = (, ), P M = P P, ( x +, y - ) = ( - ( - ), - ), x = -, y = 5, 6

174 M ( -, 5 ). P N = P P, N (0, 7 ). 6. a b = 5, a = 4, b =, ab. ab = a b cos= 4 cos5= a = (5, - 7), b = ( 6, 4), ab. ab = ( - 7 ) 4 =. 8. a =, b =, a b 0, ( a + b) ( a - b). = a - ab - 6 b = a - a b cos0-6 b = - ( - ) - 4 = a =, b = 4, a + kb a - kb, k. ( a + kb)( a - kb) = 0, a - k b = 0, a = 4, b = 6, 4-6 k = 0, k =. 0. ( ) A(, - ) a = ( 5, ), A ; ( ) B(4, - 4) a B(, ), a. ( ) A ( x, y ). x= + 5 = 7, y= - + = -. A( 7, - ). ( ) = a( h, k), = 4 + h, = k. h = -, k = 6. a = ( -,6 ).. y = x - F a = ( 0, - ), F, F. P F, P ( x, y), F P( x0, y0 ), x = x0 + 0 y = y0 -, x0 = x y0 = y +. P( x0, y0 ) y = x -, y + = x -, y = x - 5. F... ABC x y,, - - 7, A B (0, b), ( a,0 ), C ( 0, 0). 6

175 D A B, D ( a, b). AD = (0 - a) + ( b - b) = a + b, BD = ( a - a) + (0 - b) = a + b,. DC = ( a - 0 ) + ( b - 0 ) = a + b, AD = BD = DC.,,. A B (0, b) ( a, 0), ( 0, b) ( a,0 ). : A(, ) B( -, 5) AC = AB, C ( ) 64 ( A) ( 0, ) (B) (, - 4 ) ( C) (, - ) (D) (0,6 ). A( acos a, asin a) B( asin a, - acos a), a ( A) - < a < ( B) a > a < - ( C) - a (D) a a - ( ). A( a, b) B( c, d) C ( ) ( A) ( c + a, d + b) ( B) ( c - a, d - b) ( C) ( c + a, b + d) (D) ( c - a, d - b) 4. a = (, ), b = (, ), c = (, 4), ( ab)c ( ) ( A) ( 6, 4 ) (B) (4, ) ( C) (9, 4) (D) 4 5. a = (, - ), (, - ) ( ) ( A) x + y + = 0 ( B) x + y - = 0 ( C) x - y - = 0 (D) x - y - = 0. AB + BC = ;. AB - AC = ;. A A + A A + A A + A A4 = ; 4. ( a + b) - ( a - b) + a = ; 5. ( x - y) ( a + b) - ( x - y) ( a - b) = ; 6. a = ( -, 4 ), b = ( 5, ), a - b = ; 7. A( -, 4 ) B( 6, 8), AB, BA.

176 8., BC = a, AB = c, CA = b, ab + bc + ca = ; 9. A( x,5 ), B( -, y), C(, ), C A B, x =, y = ; 0. A( tan, cot ), B( sec, csc ), AB =.. A( -, - ), B(, ), C(, 4), D( - 7, - 4 ), AB CD?. a =, b = 4, a b = 50, ab, ( a + b)... a =, b = 9, ab = - 54, a b. 4. a = (5, - 6), b = (, 4), ab. 5. A(, ) B(, )C( -, 5 ), AB A C. 6. a (, ) (, 4),? 7. y = x F, a = ( -, ) F, F. 8. y = x + 4 x + 7. ( ) ; ( ). 9. a = (, - 4), A(, - ). 0. A( -, - ) B(, 4 ) C( - 5,0 ), : ABC. A(, - 7 ) B( 5, ) C( -,0 ), BC.. A( x, y) x y.. A. C. B 4. B 5. A. AC. CB. A A4 4. a + 5 b 5. ( x - y) b 6. ( -,0 ) 7. ( 9, 4), ( - 9, - 4) AB = ( 4, 4), CD = ( - 8, - 8 ), AB = - AB CD. 9. 4, - CD.. ab = a b cos50= 4 - = - 6. ( a + b) = a + b + ab = ( - 6 ) =

177 . 9cos= - 54, cos= , = ab = 5 + ( - 6) 4 = AB = (, ), AC = ( -, ).. ABAC = ( - ) + = 0. AB AC. 6. a = ( h, k), = + h 4 = + k, h = k =. ( x, y ), (0, 0 ), (, ). x= 0 + y= 0 +, x= y=. 7. P F, P ( x, y), F ( x0, y0 ), x = x0 - y = y0 +, x0 = x + y0 = y -. P( x0, y0 ) y = x, y - = ( x + ), y = x + 4 x + 7. F. 8. ( ), y = ( x + ) +, A(, ). ( ) ( ) AO = (, ) ( O ). P( x, y), P ( x, y ), x= x + y= y -, x = x- y = y+. y = x + 4 x + 7 y+ = ( x- ) + 4( x- ) + 7,. y= x y= x : y = x. 9. x - = y + - 4, x + y + = AB = ( - - ) + ( - - 4) = 5, 66 BC = ( + 5) + ( 4-0 ) = 5, AB = BC, ABC.. BC D ( x, y),

178 x = 5 + ( - ) =, y = + 0 =., D (, ). AD = ( - ) + ( ) = 65.. A x ( x, - y), y ( - x, y), ( - x, - y).. 67

179 ,.., 0 80 ( 80 ),,... ;,... 4.,. 5.. ( ),.,, ( )...,...,.,..., ( ).. (),... ;. 4. ;. 5., y x,. 6.,.. 7.,,. 68

180 . x. x 0,, 0 < ,,k, k = tan. 0< < 90, k > 0; 90< < 80, k < 0; = 0, k = 0; = 90, k.. P ( x, y ) P ( x, y ) k = y - y x - x ( x x ) x = x, P P y y, = 90,. y = y, P P x x, = 0, k = 0. ( x 0, y 0 ),k y - y 0 = k( x - x 0 ) y y b, k y = kx + b y ( x, y ) ( x, y ),x x, y y y - y y - y = x - x x - x x y a b,a 0, b 0 x a + y b = AB A x + By + C = 0 :. x y = b( b 0 ) ;. x y = 0 ;. y x = a( a 0 ) ; 69

181 4. y x = 0 ; 5. y = x ; y = - x. l : y = k x + b l : A x + B y + C = 0 l : y = k x + b l : A x + B y + C = 0 k = k b b A = B C A B C k = k b = b A A = B B = C C k k A A B B k k = - A A + B B = 0 l : A x + B y + C = 0 A x + B y + C = 0 A x + B y + C = 0 l : A x + B y + C = 0, ;, ;,.,. P( x0, y0 ) Ax + By + C = 0 d, d = Ax0 + By0 + C A + B,, 90,. tan= k - k + k k,. tan= A B - A B A A + B B 70

182 . A(, ) B( 5, )C(4, ), ( ) ( A) ( B) ( C) (D) ka B = = -, kbc = ka B = kbc = kac. A BC. A. AB = ( - 5) + ( - ) =, BC = (5-4 ) + ( - ) =, AC = ( - 4) + ( - ) =, AB = AC + BC, A BC. A. = -, kac = = -,. A(, ) B( -, ) O( 0, 0), C ( A) ( -, 5 ) ( B) ( 5, ) ( C) (4, 0 ) (D) ( 0, 4), AB OC. C ( x, y), AB ( - x + 0 y + 0 = - = 5 A., x = - y = 5., 5 ),. ( ). - - l l l k k k, ( ) ' y ( A) k < k < k (B) k < k < k l ( C) k < k < k (D) k < k < k k < 0, k > 0, k > 0. k > k, k < k < k. D. o l ax + y + = 0 x - y - = 0, a = ( ) ( A) - ( B) - 6 ( C ) - B. (D), a =, a = l x

183 7 : a = -, a -, a = - 6. B. ax + y + = 0 x - y - = 0 y ( a + 6 ) x - = 0,, a + 6 = 0, a = - 6. B. 5. x - 4 y + 5 = 0 x ( ) ( A) x + 4 y - 5 = 0 (B) x + 4 y + 5 = 0 ( C) - x + 4 y - 5 = 0 (D) - x + 4 y + 5 = 0 x - 4 y + 5 = 0 k= 4, k = - 4. x - 4 y + 5 = 0 x - 5, ( - y = - x + 4 y + 5 = 0. B. 4 ( x + 5 ), 5,0 ). P( x, y), P x P ( x, - y) x - 4 y + 5 = 0, x - 4( - y) + 5 = 0, x + 4 y + 5 = 0. B.,,. 6., ( ) ( A) x + y + = 0 x + y - = 0 ( B) x + y + = 0 x + y - = 0 ( C) x - y + = 0 x - y - = 0 (D) x - y + = 0 x - y - = 0 y = x + b, x - y + b = 0. d = b = x - y = 0. C., b =, b =,

184 997,. 7. (, ) x - y + = 0 ( ) ( A) y + x - = 0 ( B) y - x - = 0 ( C) y + x + = 0 (D) y + x - = 0 ( ) x - y + = 0 k=, k = -, y - = - ( x - ), x + y - = 0. D. ( ) x - y + = 0 k=, k = -. x + y + m = 0, (, ), + + m = 0, m = -. x + y - = (),,. 8. (, 4 ) y = - x + 6 ( ). ( A) - ( B) + ( C) + x + y - 6 = 0, (D) - d = A. = -.,. 9. l l : x + y - = 0 x, l l, l y ( A) - 4 ( B) - x + y - = 0 x ( 4, 0), 8 l x (4,0 ), x + y - = 0 - ( C) 4 (D) 8 l, l y = ( x - 4 ),, ( ) x - y - 8 = 0, x = 0 y = - 8, 7

185 l y - B l l 6 x + x - = 0, l l ( ) ( A) 5 (B) 0 ( C) 45 (D) 60 6 x + x - = 0, -. tan= = 45. C. k - k + k k = - ( - ) + ( - ) =,. ( x, y) ( a, b) N, ( x, y) M ( m, n), M.. AB C(, - 5)D(0, - 9 ), AB.. l : x + y - = 0 l : 5 x + y + = 0 l : x - 5 y + 6 = 0 l. 4. m, ( m - ) x + ( m + ) y - ( m - ) = y P A (, 5), P. 6. A(4,6 ) B( - 4, 0 ) C( -, - 4), C AB. 7. A(, 5 ), B(, ).. N ( xn, y N ), a = x + x N b = y + y N, x N = a - x yn = b - y. N ( a - x, b - y). M ( x M, y M ), xm = x + m y M = y + n M x + m, y + n : ( a - x, b - y) ; ( x + m.., y + n ).. CD, tan= 4. 74

186 AB k = tan= 4 tan - tan = - ( 4 = - 4 ) 7 : x + y - = 0 5 x + y + = 0, x = - y = l l ( -, ). l l, l 5 x + y + c = 0, ( -, ) l, 5( - ) + + c = 0, c = -, l 5 x + y - = 0. : 5 x + y - = m = 0, x - y - = 0, m = -, x =, x - y - = 0 x = (, - ). (, - ) ( m - ) + ( m + ) ( - ) - ( m - ) = 0. (, - ). m( x + y - ) - ( x - y - ) = 0. x + y - = 0 x - y - = 0, x = y = -. (, - ). : (, - ). 5. P ( 0, y). (0 - ) + ( y - 5 ) =, y = 0, y = 0, P ( 0, 0) (0, 0). : ( 0, 0) ( 0, 0 ). 6. kab = = 4, C A B, y - ( - 4 ) = 4 [ x - ( - ) ], x - 4 y - = 0, C AB 75

187 y - ( - 4 ) = - 4 [ x - ( - ) ], 4 x + y + 6 = 0. : x - 4 y - = 0; 4 x + y + 6 = : y - 5 = k( x - ) kx - y - k + 5 = 0 B(, ), k - - k + 5 k + k = 4, =, y - 5 = 4 ( x - ), x - 4 y + = 0. x - = 0 A(,5 ), B(, ), x - = 0. : x - 4 y + = 0 x - = 0. : x - 4 y + = 0 x - = 0.. P(, ),,. ( ) x - 4 y + = 0 ; ( ) x - y + 0 = 0 x - y - 8 = 0, P. ( ) x - 4 y + = 0, tan= 4. tan= tan - tan = 4 - ( = 8 4 ) 5, y - = 8 5 ( x - ), 8 x - 5 y + 6 = 0. ( ) x - y + 0 = 0, x - y - 8 = 0 A( x, y ) B( x, y ). x - y + 0 = 0 x - y - 8 = 0 x + x = 76 y + y = x y, x - y + 0 = 0 x - y = 0, x = y = 4. y = x - -, x + y - 8 = 0.. A( -, 5 ) l: x - 4 y + 4 = 0.

188 A( -, 5) l: x - 4 y + 4 = 0 A ( x, y), AA M ( x - ( x -, y + 5 ) l. ) - 4( y + 5 ) + 4 = 0. x - 4 y - = 0 AA l, y - 5 x + 4 = -. 4 x + y - = 0 x - 4 y - = 0 4 x + y - = 0, x = y = -. (, - ). A( -, 5) l A ( x, y), AA l, AA kaa= - 4, AA y - 5 = - 4 x + y - = 0. 4 x + y - = 0 x - 4 y + 4 = 0 AA l M ( 0, ). 4 ( x + ), x = 0 y =, M A A, A (, - ). x = 0 - ( - ) =, y = - 5 = -. ABC, BC x - y + = 0, A y = 0, B (, ), A C. x - y + = 0 y = 0 AB kab = A( -,0 ), ( - ) =, x A, AC -, AC y = - ( x + ) BC x - y + = 0, BC -. BC y - = - ( x - ) x = 5 y = - 6, C ( 5, - 6), ( - - ). A y B(, ) o - - C x 77

189 .AB, A, AB = 6, B ( ) ( A) - 4 ( B) ( C) ( + ) ( - ) (D) + -. l A B C, A BC, : AB = AC, BC = AC, AB - AC = 0, AB + AC = 0, ( A) ( B) ( C) (D)4 ( ). ( a, b) ( - b, a) ( 0, 0) ( ab, a0 ), 78 ( A) ( a - b, a + b) (B) ( a + b, b - a) ( C) ( a, 0) (D) (0, a) 4.m np, A( m + n, p), B( n + p, m), C( p + m, n) ( A) (B) ( C) (D) ( ) ( ) 5.( a, b) x + y = 0 ( ) ( A) ( - a, - b) ( B) ( - b, - a) ( C) ( b, a) (D) ( a, b) 6., x + y + = 0 ( ) ( A) 6 ( B) ( C) (D) l A ( m, n) B( n, m), m n, ( ) ( A) l x (B) l y ( C) l (D) l 4 8. (, ) 4 5 ( ) ( A) 4 x - y + = 0 (B) 4 x + y - 6 = 0 ( C) x - 4 y + 6 = 0 (D) y = 4 ( x - ) + 9. (, ), ( ) ( A) x + y = 5 (B) x - y = 0 ( C) x + y = 5 x - y = 0 (D) 4 x - y = 5 0. l: ax + by + c = 0, ab < 0, bc < 0, l ( ) ( A) ( B) ( C) (D). ( m + ) x + ( - m) y = m x, m ( ) ( A) 6 5 ( B) ( C)6 (D) - 6

190 . a, ( a + ) x + ( a - ) y + 7 = 0 ( ) ( A) (0, 0 ) ( B) ( -, ) ( C) ( -, ) (D) ( -, - ). mx + y - n = 0 x + my + = 0 ( ) ( A) m =, n = (B) m = -, n = - ( C) m =, n - m = -, n (D) m =, n l 4. - x = - y ( ) ( A) ( B) ( C) (D) 5. (, ), l : x + y - cos+ b = 0, l : xsin+ y + cos- a = 0, l ( A) ( B) ( C) (D) ( ) 6. x - y - 4 = 0 x 4, ( ) ( A) x - y - = 0 ( B) y = - x + 6 ( C) y = x + 6 (D) y = x , (, cos ) xsin+ ycos= 4, ( A) 6 ( B) 4 ( C) (D) 5 ( ) 8. ( 4, a) 4 x - y =, a ( ) ( A) (0, 0) (B) [, ] ( C) [0, 0] (D) ( -, 0] [,0] 9. l : x - y + = 0 l : x - = 0 ( ) ( A) - arct an ( C) - arctan (B) arctan (D) + arctan 0. l : y = ax + b( a 0), y = x l ( ) ( A) y = a x - b a (B) y = - a x + ( C) y = a x - b (D) y = ax + b. Ax + By + C = 0( A B C ), AB C ( A) AB C > 0 (B) A B C ( C) A B < 0 (D) C A > 0 b a ( ). - -, l : y = m x + n, l : y = nx + m, 79 ( )

191 ' o y l l x o y l l x l o y y l x o y l l x (A) (B) - - ( C) (D). Ax + By + C = 0 Ax + By + C = 0 ( ) ( A) ( C) C + C A + B (B) C - C C - C A + B A + B (D) 4. y = ax - a +, x [ -, ], y, a ( ) ( A) a > ( C) a < (B) < a < a > (D) a <. P (5, 0 ) P (, ) P ( 4, 7), P P P.. P (5cos, 5sin ) P (5cos, 5sin ), - < < - < < -, P P =.. l x - y - = 0, P(, ), l. 4. C( -, 4) M( -, - ) N(, ). 5. A(, ), P(, ) Q(4, - 5),. 6. x + 4 y - = 0,. 7.l: y = x +, A( t, 4) l, l A 60,. 8.x + y - = 0 x - y - 7 = 0 ; x + y - 5 = 0. 9.y = kx + y = k x - 5 y = x, k =. 0. ax + y + = 0 x + a y - = 0, a.. l x y x - y - 6 = 0 y x, l.. a b a + b = 5. 80, A( a,0 ) B( 0, b) C, C

192 . l x l y, 6, l.. l : x + y + = 0 l : x - y + 5 = 0, l : 6 x - y + 5 = 0 l.. l (0, 6 ), 4, l.. C. C. A 4. A 5. B 6. D 7. D 8. D 9. C 0. D. D. C. C 4. B 5. B 6. B 7. A 8. C 9. C 0. A. B. C. B 4. B -.. 5sin. x = 4. 5 x - y + 7 = 0 5. x + y - 7 = 0 4 x + y - 6 = 0 6. x + 4 y + = 0 x + 4 y - 7 = 0 7. x + y - 7 = 0 y = 4 8. x - y - 0 = x - y + 6 = 0. ( 5, 5 )., l x a + y a =, a = 6, a = 6, l x 6 + y 6 = x y - 6 =, x + y - 6 = 0 x + y + 6 = 0.. x + y + = 0 x - y + 5 = 0 l l ( -, ). l l, l x + 6 y + c = 0. l l l ( -, ), ( - ) c = 0. c = - 4. x + 6 y - 4 = 0, x + y - = 0.. l y - 6 = kx, y = kx + 6. x = 0 y = 6, y = 0 x = k = 4, 6 k. k = 4 8

193 k = 4, y = 4 x + 6, 4 x - y + 8 = 0 4 x + y - 8 = 0. 8

194 ,..,,.., ;,,..,,.....,, ( ).. ;..,,..,,... 4.,,,.,,..,... a b p, ;, ; ;...,,...,, ;,,. 8

195 ., x y,,.. ( h, k) ( h0 k0 ),.,. :., C f ( x, y) = 0 ( ). ( ). ;.. ( ) :. ( ) : ( x, y). ( ) :, x y. (4 ) :..,., f( x, y) = 0,. : ( ) f ( x, y) = 0, y = 0, x, x. f ( x, y) = 0, x = 0, y, y. ( ) - y f ( x, y) = 0 y, x. - x f ( x, y) = 0 x, y. - x, - y f ( x, y) = 0 x, y,. ( ) f ( x, y) = 0 y = ( x) x = ( y), x y. 4. F( x, y) = 0 F( x, y) = 0 G( x, y) = 0, G( x, y) = 0.,,,. 84

196 ,.AB, A B A, B.. A, B, A B, A B.. B, A, B A, A B.. A B, B, A B, B A, A B,...,.. ( a, b), r ( x - a) + ( y - b) = r.,, r x + y = r.. ( - : x + y + Dx + Ey + F = 0 ( D + E - 4 F > 0 ), D, - E ), r = 4. D + E - 4 F. Ax + By + C = 0, ( x - a) + ( y - b) = r. d =, d < r ; d = r ; d > r. 5. Aa + Bb + C Ax + By + C = 0, A + B ( x - a) + ( y - b) = r x + y = r P( x0, y0 ) x0 x + y0 y = r.. F F ( F F ).,.. x a + y b = ( a > b > 0) y a + x b = ( a > b > 0 ) 85

197 A ( - a,0), A ( a,0 ) B ( 0, - b), B (0, b) A (0, - a), A (0, a) B ( - b,0 ), B ( b,0) F ( - c,0), F ( c,0 ) F (0, - c), F ( 0, c) F F = c( c > 0) c = a - b : x y, a, b, x : x y, a, b, y e = c a (0 < e < ) x = a c y = a c. F F ( F F ),,.. x a - y b = ( a > 0, b > 0) y a - x b = ( a > 0, b > 0 ) A ( - a,0 ), A ( a,0) A ( 0, - a), A (0, a) F ( - c,0 ), F ( c,0) F (0, - c), F (0, c) 86

198 x a - y b = ( a > 0, b > 0) y a - x b = ( a > 0, b > 0 ) F F = c c = a + b : x, y, a, b,x : x, y, a, b, y e = c a ( e > ) x = a c y = a c y = b a x y = a b x.. x - y = a y - x = a.. F l, F, l.. y = px ( p > 0 ) y = - px ( p > 0) x = py ( p > 0 ) x = - py ( p > 0 ) O( 0,0 ) x y F( p,0) F( - p,0) F(0, p ) F( 0, - p ) x = - p x = p e = y = - p y = p.,,,. 87

199 . O O ( h, k), x = x+ h y = y+ k, ( x, y), ( x, y ).,.., x y t x = f ( t) y = ( t) t, M( x, y),, x y t,.. ( ) P0 ( x0, y0 ), x = x0 y = y0 + tcos, t, + tsin t P( x, y) P0 ( x0, y0 ). ( ) C( a, b), r x = a + rcos,. y = b + rsin ( ), : x a + y b = ( a > b > 0) x = acos,. y = bsin 88 x b + y a = ( a > b > 0) x = bcos,. y = asin (4 ), : x a - y a - y b x b = ( a > 0, b > 0) x = asec,. y = btan = ( a > 0, b > 0) x = bcot,. y = acsc (5 ) y = px( p > 0)

200 x = pt y = pt, t.. : ( ). ( ). ( ). (4 ).. t, x = f( t),, y = y( t), : x = f ( t) y = y( t) t.. a = bax + by = ( ) ( A) ( B) ( C) (D) a = b = -, - x - y =,, a = b ax + by = ; ax + by =, a = b, a = b a x + by =. B..,,, ( A) ( B) ( ) ( C) (D),,, /,, /,, /, /.. A.. M(5, ) x + y - x + 6 y + 9 = 0 ( ) ; ; ( A) 5 (B ) ( C )5 (D) ( x - ) + ( y + ) =, C(, - ), r =, M(5, ) C(, - ) MC = (5 - ) + [ - ( - ) ] =, 89

201 d = MC - r = ( ) - = 5. A. 4. x + ky = y, k ( ) ( A) (0, + ) ( B) (0, ) ( C) (, + ) (D) (0, ) x + ky = x + y k =., k > 0, k > 0, y, k >, k <. 0 < k <. D. x + ky =, k > 0. y, k <, 0 < k <. D. x b + y a = ( a > b > 0), a x + b y = a b ( a > b > 0 ), x - y = ( ) ( A) y = x ( B) y = x - C. x ( C) y = x (D) y = x. y =, y = b a x = x x - y = 0, y = x, y = x. C.,, (), y + x = 0 ( ) ( A) F(,0 ), x = ( B) F( -, 0), x = ( C) F( 6, 0 ), x = - 6 y = - p = 4, p = 8, F( - D. ( D) F( - 4 x. 6,0 ), x = 6. 6, 0 ), x = 6,,. 7. x a - y 5 = x 5 + y 6 =, a > 0, a ( )

202 ( A) ( B) 4 ( C) 46 ( D) 6 a + 5 = 5-6, a =. a > 0, a =. A. 995, a b c. 8. A(, - ), x ( ) ( A) ( x - ) = ( y + ) ( B) ( x - ) = - 4 ( y + ) ( C) ( x + ) = ( y - ) (D) ( x + ) = 4 ( y - ) A(, - ) x O y O,, x = x+ y = y-, x O y, x = - py ( p > 0 ). p = =, x = - 4 y, ( x - ) = - 4 ( y + ). B. : p p = ;. 9. x - x + = 0, ( ) ( A) ( B) ( C) (D) x - x + = 0 x =, x =. C. e =, 0 < e <, e >. 0. x = - y = - t t ( t, t 0) ( A) ( x - ) ( y - ) = ( B) y = ( C) y = x = - ( - x) - (D) y = y = - B. t x, t = = x( x - ) ( - x) ( - x) x( x - ) ( - x) x - x + - x y = - t ( ) t =, ( 0, 0), A D; t =, (, - ), C, B.. 9

203 x = + t y = 4 + t ( t ), y ( ) ( A) 5 ( B) - 5 ( C) 5 (D) - t x - y + 5 = 0. x = 0, y = 5, y 5. C. x = 0, t = - C. 5, y = 4 + t = 4 - = ,,,,. x = - + tsin 6. l y = - tcos, l ( ) 6 ( A) 6 ( B) ( C ) 5 6 (D) l 6.. y - x + = 9 - tcos 6 tsin = - cot 6. 6 tan= - cot = -, = 6. D.. x = + cos y = - + 5sin ( ) ( A) ( -, 5 ), ( -, - ) (B) (, ), (, - 5 ) ( C) (, ), ( - 7, ) (D) (7, - ), ( -, - ) x = + cos y = - + 5sin x - y + 5 = cos, = sin, ( x - ) x - = x x = x+ y + = y y = y-, 9 + ( y + ) 5 x 9 + y = ( 0, 4), ( 0, - 4), 5 =, (, - ).

204 ( x - ) 9 B. + ( y + ) 5 = (, ) (, - 5 ). 4. x = + 8sec ( ) ( ) y = + 6tan ( A) ( B) ( C) (D) D. x = + 8sec y = + 6t an ( x - ) = sec 8 ( y - ) = tan 6 D. x - = 8sec y - = 6tan,, ( x - ) - 8 ( y - ) 6 =. 5. x = 4 + cos y = + 5 sin ( ) ( A) (B ) ( C) 9 (D) 9 x = 4 + cos y = + 5sin, ( x - 4 ) ( x - 4 ) = cos ( y -, ) = sin 5 + ( y - ) 5 =. a = 5, b =, c = 5 - =, c =. B. 6. l x = - t ( t ), l ( ) y = t ( A) x - y - = 0 (B) x + y - = 0 ( C) x + y - = 0 (D) x - y - = 0 t = y x = - t x + y - = 0, x + y - = 0. C.. 4 x - y + 4 = 0 y, x,,.... y = - x + y = 4 x A B, AB. 4. x + 4 y + m = 0 x + y = 4, m. 9

205 5. x 5 + y 4. = F F, B, BF F 6. x + y - 6 x - 7 = 0 y = px ( p > 0 ), p =. 7.,. 8. x = + 4cost ( t ), t. y = sint 9. x = - t,. y = - + t 0. x 5 - k + y 6 - k = x, k.. x = + t ( t ), y. y = 4 + t. x = 0, y =, y. y = 0, x = -, x -. - y y,, x. y = 4 x + 4. y 0, 4 x + 4 0, x -. x = -. : ; - ; x; x = -.. P( x, y). P( x, y) y x =, xy =. : xy =.. y = - x +, y = 4 x x = + y = - - x = -, y = - + A( +, - - ), B( -, - + ), AB = [ ( + ) - ( - ) ] + [ ( - - ) - ( - + )] = 8. y = - x +, y = 4 x y x - 6 x + = 0, x + x = 6, x x =, x - x = ( x + x ) - 4 x x = 6-4 = 4, 94 : 8. AB = + k x - x = + 4 = 8.

206 :, ; k A B, : AB = + k ( x + x ) - 4 x x,,. 4. d = m = m, + 4 5, d < r, m 5-0 < m < 0. : - 0 < m < a = 5, b =, c =. <, BF + BF = a = 5, F F = c = =, BF F l = BF + BF + F F = + 5. a = 5, b =, c =. F ( -, 0), F (, 0 ), B( 0, ). BF = ( - ) + ( ) = 5, BF = + () = 5, F F =, BF F l = = 5 +. : ,,.. 6. ( x - ) + y = 4, C(,0 ), r = 4. y = px x = - p =. :. p, - ( - p ) = 4,,, 7. : e = ;= x = + 4cost y = sint sin t + cos t =, ( x - 4 ( x - ) 6 ) + ( y + 4 ) =, 5 + ( y + 4) 5 =. cos t = x - 4 sint = y

207 : ( x - ) 6 + ( y + 4 ) 5 =. 9. x = - t ( t ), t, y = - + t x + y = 0. k = - = tan () = + arctan ( - ) = ( 0 < ). 4 : 4, x 5 - k + y 6 - k = x, 5 - k > 0, 6 < k < k < 0 : 6 < k < 5.. x = + t, t y = 4 + t, x = 0, y = 5. x - y + 5 = 0. : , ( x - ) + ( y - ) = P(, ),.. k, y - = k( x - ), kx - y + - k = 0, d = k k k +, d = r. k - k + =, k = 4. = k - k +, y - = 4 ( x - ), x - 4 y + 6 = 0. ' y o C P - - P(, ),,, x =, P x - 4 y + 6 = 0, x =. k,, x 96

208 . x + y b =,, P, P,. - -, x + y b =, x, 0 < b <, c = - b. y = 4cx. x b x + 4cx - b = 0, P x P, xp > 0, xp = - c + 4c + b 4 b = e. a =, e = c a = c + 4cx b =, - c + - b b. ' = c, xp = - e + + e - e = - e + e. xp =, - e + e = e =. e =. o y ,,,. '. y = px - -,, y = x, 5. y = px, A ( p y = x, p). y y = - = px AB = (8 p - x, B (8 p, - 4 p), p ) + ( - 4 p - p) = (5 ),, o y A - - P B x x p =, p = 9 ( p = - 9 ), y = x a - y b x. = F x - 4 y - 5 = 0 ( ), M, M 5, a b. 97

209 x - 4 y - 5 = 0 x ( 5, 0), F(5, 0 ). M ( x0, y0 ), x 0 + y 0 = 5 x0-4 y0 = 5. x0 = y0 = a = b = 4 a =, b = 4., ( - a = 49 b = ) a - a + b = 5 ( ), ( ) b =,.. ' M o y P(, ) y = 4 x A B,. A( x, y ) B( x, y ), A B y = 4 x, F x y y = 4 x, = 4 x y - y = 4 ( x - x ), ( y - y ) ( y + y ) = 4( x - x ). A B P (, ), y + y = 4, y x - y - x = y 4 + y = 4 4 = = kab. AB y - = ( x - ), x - y - = P(, ) y = 4 x A B, AB. AB AB y ( + tsin ) = 4 ( + tcos ), x = + tcos y = + tsin ( t ), = 4 x t sin + 4( sin- cos ) t - 8 = 0 P(, ) AB, t : t t t + t = 0 sin- cos= 0, t an=. 0 < <, = 4. t = 6, t = 4, t = - 4, AB = t - t = 4 - ( - 4 ) = 8. AB 8.,,,. 98 t, : ( ), t t, l = t - t.

210 ( ) P0 ( x0, y0 ) M, M t M = t + t = y = - 4 x, l: x + y - = 0 A(, - ). ( x - a) + ( y - b) = r, b = - 4 a ( - a) + ( - - b) = r, a + b - = r a = b = - 4 r = ( x - ) + ( y + 4 ) = 8... ( ) ( A) y = x ( B) x - y = 0 ( C) y = - x (D) y = x. x - xy - y = 8 ( ) ( A) x ( B) y ( C) ( D). : 0 < x < 5; : x - <, ( ) ( A) ( B) ( C) ( D) 4. : l l, : l l, ( ) ( A) ( B) ( C) ( D) 5. : ; :, ( A) ( B) ( C) ( D). ( ) 6. x + y + Dx + Ey + F = 0 x, ( ) ( A) D 0, E 0, F = 0 ( B) D 0, E = F = 0 ( C) D = F = 0, E 0 ( D) D = E = 0, F 0 7. x + y + (- ) x + y + = 0, ( ) ( A)> 0 ( B) 5 ( C)> < 5 (D)R 8.( x - ) + y = ( ) ( A) ( B) ( C) (D) 99

211 9.F ( -,0 ) F (, 0),, F, AB F ( A) 4 ( B) ( C) 6 (D) AB ( ) 0. 6 ABC, B C ( -, 0) (,0 ), A ( ) ( A) x 5 + y 9 = ( B) x 5 + y 6 = 00 ( C) x 5 + y 6 = ( y 0) ( D) x 9 + y 5 = ( y 0)., 6, ( A) 4 x + y = 6 ( B) x + 4 y = 6 ( C) 4 x + y = 9 x + 4 y = 9 ( D) 4 x + y = 6 x + 4 y = 6. x 6 + y 9 ( ) = (4, ), ( ) ( A) x - y = 0 ( B) x + y - 4 = 0 ( C) x + y - 4 = 0 ( D) x + y - 8 = 0. x + y 4 b b ( A) = P b, P 6 b ( B) b ( C) b (D) b ( ) 4. P( tan, sec ), ( ) ( A) x - y = 6 ( B) x - y = 8 ( C) y - x = 8 ( D) x - y = 8 y - x = 8 5. y = 44 ( A) y 5 - x 44 ( C), x 5 y = 0, = ( B) x 5 - y 44 = x 44 - y 5 = ( D) y 44 - x 5 = ( ) 6. mx - my = F(0, ), m ( ) ( A) ( B) - ( C) - (D) - 7. x 9 + y = x k k - y 0 =, k ( ) ( A) k > ( B) < k < ( C) 0 < k < (D) k = 8. x - 4 y = 4, (, 5 ) ( )

212 ( A) x 4 - y 6 x = ( B) 6 - y 4 y = ( C) 4 - x 4 = (D) y 4 - x 6 = 9. x 9 - y = F F, A, AF = 5, AF ( A) ( B)5 + 0 ( C) (D)8 0. y = 9 x x - y - 8 = 0 MN, MN ( A) ( 8, 7 ) ( B) ( - 4 8, 7 4 ) ( C) ( 8, ) (D) ( - 8, ) ( ) ( )., x, x - 4 y - = 0, ( A) y = - 6 x ( B) y = x ( C) y = 6 x (D) y = - x ( ). A(,), F y = x, P, PA + PF, P ( ) ( A) (0, 0 ) ( B) (, ) ( C) (, ) (D) (, )., O (, - 4 ), (, - ) ( ) ( A) (6, - 6) ( B) ( -, 4) ( C) (0, - ) (D) ( 0, ) 4. ( y + ) = 4 ( x + ) ( ) ( A) (0, - ) ( B) (, 4) ( C) (, - ) (D) (, ) 5. ( x - ) 4 + ( y - ) m = x = 5, m ( ) ( A) ( B) - ( C) (D) - 6.r > 0, xcos+ ysin= r x = rcos ( ) y = rsin ( ) ( A) ( B) ( C ) ( D) r 7. xy = ( t ) ( ) ( A) x = y = t t ( B) x = sin t y = csc t ( C ) x = cos t y = sec t ( D) x = tan t y = cot t 8. x = cos x = cos t ( ) y = sin y = + ( t ) ( ) sin t ( A) 0 ( B) ( C ) ( D) 4 9. x = t - t + ( t ) ( ) y = t - (A) x = y - y + (B) x = y - y - (C) x = y - y + (D) y = x - x - 0

213 x = ( - cos 0. ) (, - 0) ( ) y = sin ( A) ( B) ( C ) 4 ( D). x = - + t ( t ) ( ) y = + t ( A)- arcsin( - ( C)- arccos( - 5 ) ( B) arcsin( - 5 ) 5 ) ( D)- arccos( - 5 ). x = pcos- y = qsin+ ( p > q > 0 ) ( ) ( A) q p ( B). x = + t y y = t p - q p ( C ) p + q p ( D) p p - q = 4 x A B, AB ( ) ( A) ( B) 5 ( C ) ( D) 5 4. x = t + ( 0 t 5 ) ( ) y = t - ( A) ( B) ( C ) ( D) 5. x = 4 + 6cos ( ) ( ) y = + 0sin ( A) 8 ( B)6 ( C ) 4 ( D) 4 4., ( x - ) + ( y + ) = 0 ; x - 7 x + 0 = 0.. A(, m) x - xy + y + = 0, m =.. ABC, BC ( -, 0 ) (, 0 ), AD, A. 4. x y ( x - ) + y =, y x. 5. x - y + = 0, x + y = P(, 4) ( x - ) + ( y - ) =,. 7. x 00 + y 6. = P :, P 8., e =, 6, P x 45 + y 0 =, F F, PF PF, P

214 x + 6 y = 400,.. x 5 - y 9. =, F F, P F, P F. (, - ),.. C y = 4 x - y = x, C. 4.,, y 6,. 5.,, A(, - 4). 6. ( x + ). 7. l: x = - + ( y - ) 4 5 t = ; ; y = t y A, l B, AB =. 8. x = + t y = t P(, - 5 ). ( t ) x - y - = 0, 9. x = + 5cos,. y = + sin 0.P x = cos =, O, OP. y = sin. x a + y b =.. x = sin y = + cos.. l :. x = + tcos y = + tsin ( t ), l P(, ) l, l x = + 5 t 4. y = - ( t ). t. P ( - 5, 0 ) P ( 5, 0), M P P, M. 0

215 . x 5 + y 6 =,.. y = x + m x 4 + y = A B, m, ( ) AB, ( ) OA B ( O ). 4. A(, ) l, A, l. 5. l P (, - 5 ), =. ( ) l. ( ) l, l x + y = 6 AB P. 6. y = x + ( m - ) x + m( m - ). : m,. 04.B.C.B 4.D 5.B 6.C 7.C 8.C 9.C 0.C.C.D.D 4.C 5.D 6.C 7.D 8.D 9.C 0.A.C.C.D 4.A 5.A 6. B 7. D 8. A 9. B 0. C. D. B. B 4. A 5. B. (, - ), x = 5 x = x + y = 9 ( y 0 ) x - y + 5 = 0, x - y - 5 = 0 6. x = 4 x - y + 4 = , (, 4) ( -, 4) x 9 + y 5 = x 5 + y 9 = y 9 - x 6 = x 5 + y 5 =. x = 4 y - 4. x = 6 y 5. y = 8 x, x = - y 6. ( -,) ( -,), ( -,), y = F ( -, ), F ( 6, ) ; x = - 7 4, x = ab.x + ( y - ) =. x = - tsin y = + tcos ( t ) 4.- arctan 5

216 . M ( x, y), P = { M MP = MP. MP MP = }, ( x + 5) + y = ( x - 5 ) + y,, x + y - 50 x + 75 = > 6, x, x, x. a = 5, b = 4, (5, 0), (, 0). (, 0 ), (5, 0 ), x - a y b = ( a > 0, b > 0), a =, c = 5, b = c - a = 5-9 = 4,, x 9 - y 6 =.. y = x + m x + 4 y = 4, y, 5 x + 8 mx + 4( m - ) = 0., A B x x, AB = [ ( x + x ) - 4 x x ] = [ 64 m - 80 ( m - ) 5 = m. h, h = m, ] SOA B = 5 m ( 5 - m ). ( ) m = 0, AB, ( ) m ( 5 - m ) m + (5 - m ) m = 5 - m, m = 0 SOA B. = 5.., OA B, 4. l y - = k( x - ), y = k( x - ) +. y = k( x - ) + x 5 + y 4 = 4 x + 9( kx - k + ) = 6, ( 9 k + 4 ) x + 8 k( - k) x + 9 k - 8 k - 7 = 0. x x, x + x = - 8 k( - k) 9 k + 4, 05

217 x x l x 9 + y 4 = x + x = 9 k( - k) 9 k + 4 l y - = - =, k = ( x - ), 4 x + 9 y - = 0. l x 9 + y 4 = B( x, y ) C( x, y ), 06 ( x + x ) ( x - x ) - 9 y - y x - x = - x 9 + y 4 = x 4 9 x + x y + y 9 + y 4 =. + ( y + y ) ( y - y ) 9 = 0, A B C, x + x =, y + y =, l k = - l y - = ( x - ), 4 x + 9 y - = ( ) - - 5, l P(, - 5), =, l x = + tcos y = tsin, x = + t y = t ( t ). ( ) l ( ) x + y = 6, ( + t) + ( t) = 6, t + ( - 5 ) t + 0 = 0. t t = 0, t, PA PB = 0,, l x + y = 6 A B P ( x, y), x = - m - y = m 4, ( m ), O y B 4 9, x A P(, - 5) - - 5

218 x = - m - y = m 4. m, 4 x - 4 y - = 0, m,. 07

219 ....., ,., 45, ;, ( ). b D C B B A B A A ,,,,, AC(4 - - ). 08

220 .,.,.,.,.,.,..., (4 - -, )

221 . 4 ( ).,,., ()., ( ).,

222 ,.,.,,.,.,.,.,.,.,.

223 ,,..,.,. : ( ), ; ( ), ; ( ).,,.,,.. :.

224 ,.,..,..,.. ( )..,,.

225 .,,.,.,.,,.,.., ( ) ( A), ( B), ( C) A,, l, A l (D) A ;,, B ; C ;, D. D. 4

226 . : = m, l = A, l, ( ) ( A) m A (B) m A ( C) l m (D) l A = l, A l A. l, A, A = m. A.,,.. : ; a b, a, b ; a b, a, b ;., ( ) ( A), ( B), ( C), (D),, ;,,, ;, b, a b, a b,, a b,. A. 4. AB CD - A B C D, AB BC ( ) ( A) 0 (B) 45 ( C) 60 (D) 90 AB C D, AD BC, B AD. AB D, B AD= 60. C. :,.,. 5. ( ) ( A) ( B) ( C) (D),,,,,,,,. C. 6. SA SB SC, O S A BC, O ABC ( A) ( B) ( C) (D) SA SB SC, 5 ( )

227 SA SBC, SA BC. SO ABC, AO BC. BO AC, CO AB, O ABC. B. 7. S - ABC, AB SC, AC SB, BCAS ( ) ( A) 0 (B) 45 ( C) 60 (D) 90 SO ABC. AB SC, AC SB, AB OC, AC OB. O ABC. AO BC, SA BC. D.,,. 8. l, m, : l m l m l m l m ( A) ( B) ( C) (D) ( ). ( ),,,,. m l m l m l m l = CD, P, PA A, PB B, PA =, PB =, AB = 7, - CD - ( ) 6 ( A) 50 ( B)0 ( C) 90 (D) 60 PA PB, CD O, AO BO, AOB. PA =, PB =, AB = 7, cosap B = = -, APB = 0. AOB = 80- AP B = 80-0= 60. D.. a b, c b, c a. a, c a, c.

228 a, c, c a. a, c, c. a b, b, a.. AB CD, E F A B CD, BD AC, BD = AC, EF BD.. a, c a, c. 4. a A BCD - A B C D, BD CC DD. 5. ABCD, BA D = 60, AB = 0cm, PA A BCD P A = 5cm, P DC ; P BD. 6. A - BC - D 60, AB = AC =, BD = CD = 0, BC = 4, AD.. : ; c ; ; ;.,,,,.. AD G, BC H, EG GF FH HE, EGF H. AD BC, AD = BC, EGF H. EG BD, GE F. EGF H, GE F = 45. : 45.. :. 4. CD, BD C BD CC DD. RtBCD, BC = a, CD = a, BD = a, sinbd C = BC BD = a a =. :. :,,,. 5. ABCD A CD AE = 0sin60= 5, P DC PE = PA + AE = 5 + (5 ) = 0 (cm ) ; AB CD A BD AO = 0 cos0= 5, P BD PO = PA + AO = 5 + ( 5 ) = 0. : 0; BC O, AO DO, AOD = 60. RtABO, AB =, BO =, AO = - = 5. RtBOD, BD = 0, BO =, DO = 0 - = 6. 7

229 RtAOD, AD = AO + OD - AO OD cosaod AD = 0. : 0 = cos60= 0, : ; ;..,,, , ABCD - A B C D, : A C C BD.! AC, AC A C BD. D C AC BD, A C BD. B C, B C A C BC B C BC, A C BC.. BD BC C BD, BD BC = B, A C C BD. A A D , :,..... S - ABC S AC ABC, ACB = 90, SA = AC = SC = BC, SA B S A C, cos. 8 SC = a. SA C BAC, ACB = 90, BC SA C, BC SC. SA = AC = SC = BC = a, AB = SB = a. D SA ( ), BD SA, CD SA, BCD SAB SAC. = BDC. RtBCD, CD = a, BD = AB - AD = ( ) - ( a) = 7 a, cos= cosbdc = CD BD = a 7 a = 7! A D S B B ,,. B C C

230 ,,,.,... ABC, P Q R, : P QR , A B ABC, AB ABC. P AB, P ABC. Q ABC, R AB C. PQ R AB C. PQ R, P Q R A BC Q, P Q R. A B P AB O, PA O, C O, :PAC PBC ( ). C, AB O, BC AC. PA O, BC O, BC PA. PA AC = A, BC PAC. A BC PCB, PBC PAC. : > >. b P Ȯ C ) ) ëë äðä ÄÒ Ì Ì ¾Ò ¾Ò äðä C ABC BC, A, ABC =, AB C, AB. 6 b A AD,D, BD( ), ABD AB, ABD =. D BD DE, E, AE, : AED ABC. AED = 6. RtADB, sin= AD AB ; RtADE, sin 6 = AD A E ; RtAEB, sin = AE AB. B 0 ««Í Í Ê Ê Ð ««Í Í Í««Í Ð E C A D R B sin= sin sin 6 = 4, = arcsin 4. 9

231 99,.,.., ( ) ( A) ( B) ( C) (D). ( A) ( B) ( C) (D) ( )., ( ) ( A) ( B) ( C) (D) 4., ( A) ( B) ( C) (D) ( ) 5.a b, c d a be F GH, c d ( A) ( B) ( C ) ( D) ( ) 6.a b, a c, b c ( ) ( A) ( B) ( C) ( D) 7.E FGH A BCD AB BC CD DA, BD =, AC = 4, EG + HF ( A) 5 ( B)0 ( C ) ( D) ( ) 8. S - ABC, E F SCAB, EF S A ( A) 90 ( B)60 ( C )45 ( D) 0 ( ) 9.a b, a, b ( ) ( A) b ( B) b ( C ) b ( D) b b 0. - a - 60, A, A A ( ) 0 ( A) ( B) ( C ) ( D). m n, ( ) ( A) m n, m, n ( B) m n, = m, n ( C) m n, n, m ( D) m n, m, n

232 ., ( A) ( B) ( C) ( D) ( ).,, ( ) ( A) 0 ( B)45 ( C )60 ( D) a, a ( ) ( A) a ( B) a ( C) a a ( D) a 5.ABCD AC, AB CD ( ) ( A) 0 ( B)45 ( C )60 ( D) 90. AB CD, AB =, BC = 9, D A BCD PD = 8, P B..ABCD - A B C D, AA C C BB D D C C ; BA C AC.. O AB, PA O, C A B, AC BC, BC PC. 4.AB CD, AB CD, AE CF, AC = 5cm, EF = 4cm, AB CD. 5.ABCD Q, QA = QB = QC = QD, ABCD. 6., ( ) 0, 60 00,. 7. 0,. 8.60P, P cm cm, P... :,. : = CD, EA, EB, : CD AB..,,.. 4. :, 5. RtABC P C 4cm, 6 0cm, : ( ) P ABC ;

233 , ( ) PC , SA A BCD A C, AC BC O, SC = 5, AB = ( ) : BD SC. ( ) : SB C SA B. ( ) SC AB. (4 ) SA B S AC. 7. ABCD, A B E BC F CD B GDA H EH FG BD,. S A O C D.D.C.B 4.C 5.D 6.D 7.B 8.C 9.D 0.A.C.D.C 4.C 5.C.7.,. 4.cm arctan 8.4cm. : a b, a, b, = c, : c a b. a b, b ( ). a. a, = c, a c, : c a b.. EA, CD, 4 - -, CD EA. EB, CD, CD EB, CD EA B. AB EA B, CD AB. a A c b C D. E. B , ABC, P, PBA = PB C, PQ, Q. : QB A = QB C. PR AB, PS BC RS, PRB = PS B = 90. PB = PB, PBR = PB S, RtPR B RtPSB, PR = PS.

234 Q P, QR = QS. QR AB, QS BC, ABQ = CBQ , a b c O, a b, bc, ca, a b, bc, c a. :,,. c b, c a, a b = O, a, b, c. c, c,,, , a b c A B C, CO AO, CO BO, AOB - c -. AO BO, AOB = 90,.,. ±á ÞÞ B , PO ABC, PD AC, PE BC, OD E, ODOCOE. PD = PE, OD = OE, DCEO. PO = xcm, OD = acm, OC = acm. PD = 6 0cm, PC = 4cm, x + a = ( 6 0 ) x + ( a) = 4 x =. PO = cm. sinpco = PO P C = 4 =, PCO = 0. P A BC cm, PC ( ) SA AC, AC S C ( ) BD AC, BD SC() ( ) SA AC, SA BC, BC AB BC SAB ( ), S A A R S P Q A C C c a D O b D O P C BC SBC, O SBC SAB( ). ( ) AB DC, SCD SC AB. A AB SAD, AB DC, DC SAD, DC SD. DC =, SC = 5, cosscd = 5, SCD = arccos 5 (4 ) AB SA, AB SA B, AC SA, AC SA C,. E B B B C

235 SA B SAC = SA, CA B C - SA - B. ABCD, CA B = 45, SA B S AC 45. =C 4C (@( û ïéïîà «ii{ <B îî 7. ( ) , EH BD, A EH BD = M. M EH, EH M. M BD, BD BCD. M BCD. M BCD FG. EH FG BD. ( ) , EH BD, EH FG. EH BD FG. B E E H D G F A H C M B D G F C 4

236 ., , ( ).. ( ) a b, A, AB = a, BC = b, AC, AC a b ( ), a + b. ( ) a b, A, AB = a, AD = b, ABAD ABCD, AC = a + b. ( ) a + b = b + a ( a + b) + c = a + ( b + c). a b, O, OA = a, OB = b, BA a b, a - b, a - b = OA - OB = BA. a - b = a + ( - b).. a, a, : ( ) a = a ; ( ) > 0, a a ; < 0, a a ; a = 0, a = 0. ( ) : ( ) a = (a) (+ ) a = a + a ( R) ( a + b) = a + b 5

237 i j k, a, ( a, a, a ), a = a i + a j + a k ( * ) ( i, j, k).. ( i, j, k),.. ( a, a, a ) a, ( * ) a {i, j, k}. a = a i + a j + a k, b = b i + b j + b k, a + b = ( a + b, a + b, a + b ) ; ab = a b + a b + a b a = a + a + a a b a b + a b + a b = 0.,,.. b a,, b = a;, b = a, a b OP 0 = r0, OP = r, r = r0 + ta. l a, a l, t (4 - - ). a b, O, OA = a, OB = b, AOB( 0 AOB 80 ) a b, a, b, a, b= b, a.a, b= 90, a b a b, a b ( ), ab, a b cosa, b ab = a b cosa, b. ( ) ab = 0 a b( a b ) ; ( ) a = a. 6

238 .. ABCD - A B C D, P B BC C, AP = AB + x AD + y A A, x y ( ) ( A), (B), ( C), (D), AP = AB + BC= AB + ( BC + BB ) = AB + AD + AA. A.. OA BC, MN OA BC, OA = a, OB = b, OC = c, MN = ( ). ( A) a + b + c ( B) ( a + b + c) ( C) - a + b + c ( C) - a + b + c MN = ON - OM = ( OB + OC) - OA = b + c - a. C , ABCD - A B C D, BA = a, BC = b, BB = c, BD ( ) ( A) a - b - c ( B) a - b + c ( C) a + b + c (D) a + b - c BD = BB + B D, B D = BD = BA + BC = a + b, BD = a + b + c, C. 4. a = ( -, ), b = (, 5), a + b = ( ) ( A) (5, 4) (B) ( - 5,4) ( C) (7,4 ) (D) (5,9 ) a = ( -, ), a = ( - 6, 9) ; b = (, 5) ; a + b = ( - 6 +, 9 + 5) = ( - 5, 4 ). B. A A D D C B {i, j, k}, a = i + j, b = - i + j - k, ab =. ab = ( i + j)( - i + j - k) = - ii + jj = - i + j = 0. :0.. {i, j, k}, a = i + j, b = j + k, a b. a = aa = ( i + j)( i + j) =, a =, B 7 C

239 b = bb = ( j + k)( j + k) =, b =, ab = ( i + j) ( j + k) =, cosa, b= ab a b =. : , ABCD, AB = a, BC = b, CD = c, D DA = a, E F A C BD, EF = , BC M, EMMF. EM AB, EM = AB = a. MF CD, MF = CD = c. EF = EM + MF = a + c. A F C M E B : a + c. 4. {i, j, k}, a = i + x j, b = j + k, a b =, x. ab = = ( i + x j ) ( j + k) = x j = x :. x =. x.. AB CD - A B C D, CD DC O, AO CD. AOCD= 0. CC= a, CD = c, CB = b, CD= a + c, OA = OC + CA = - = - CD+ b + c ( a + c) + b + c = b + c - a, CDOA = ( a + c) ( b + c - a) a b, b c, a c ab = bc = ac = 0 CDOA = - a = c = ab + ac - a + cb + c - a + c = - a + c ca.

240 CDOA = 0 OA CD, AO CD.. ABCD - A B C D, BA A= DA A= 60, BAD = 90, ( ), AC. AB = a, AD = b, AA= c. CC= AA= c, AC= a + b + c, AC = ( a + b + c), AC = a + b + c + ( ab + ac + bc). a = a =, b = b =, c = c =. a b, ab = ac = cos60=, bc = cos60=. AC = (0 + + ) = 5, AC= 5.. AB = BC = 4 ABCD A C 0, B D. ( ) ( ), BE AC E, DF AC F. AC 0, ( ), BD., AC = 5, AE = FC = 9 5, EF = 7 5 BE, FD= 60, BD = ( BE + EF + FD)( BE + EF + FD ), BE = DF = 5. = BE + EF + FD + ( BEEF + BEFD + EFFD) = ( 5 ) + ( 7 5 ) + ( 5 ) + 5 cos60= BD =

241 4. OA BC, MN OA BC.OA = a, OB = b, OC = c( ). ( ) MN { a, b, c} ; ( ) MN ; ( ) : MN OA, MN BC. ( ) MN = ON - OM = ( b + c) - a = - a + b + c; ( ) MN = ( - a + b + c) ( - a + b + c) = 4 ( a + b + c - ab - ac + bc). a = b = c =, ab = bc = ca = cos60=, MN = 4 ( - ) =, MN =. ( ) MN OA = ( - a + b + c)a = ( ) = 0, MNBC = ( - a + b + c)( c - b) = ( ) = 0, MN OA, MN BC.. O - AB C, OA = a, OB = b, OC = c, M ABC A D, OM { a, b, c} ( ) ( A) a + b + c ( B) 4 a + 4 b + 4 c ( C) 4 a + 4 b + 4 c ( D) a + 4 b + 4 c. OA BC, MN OA BC, G M N, OG = ( ) 0 ( A) ( B) 6 4 ( C) ( D). a A BCD - A B C D, A BCB ( ) ( A) a ( B) - a ( C) a ( D) a 4. AB CD - A B C D, ACBD= ( )

242 ( A) ( B)0 ( C) ( D) 5. AB CDA B C D, E A C, AE = AA + x AB + y AD ( x y R), x y ( ) ( A) x =, y = ( B) x =, y = ( C) x =, y = ( D) x =, y = ABCD, M GN BC CD BD, AB + ( BC + BD) = ( ) ( A) AN ( B) AG ( C) AM ( D) MN , ABC O, MN OA BC, G M N, MG = GN, OG = ( ) ( A) OA + OB + OC ( B) OA + OB + OC ( C) 6 OA + OB + OC ( D) OA + OB + OC. O A B, OP = x OA + y OB, P AB.. O A BC.OP = x OA + y OB + z OC, P A BC.. {i, j, k}, a = i + j + k, b = - i + j + k, c = j + k, a + b + c. 4. {i, j, k}, a = i + j + k, b = i + j, cosa, b=. 5. OABC, MN OA BC, OA = a, OB = b, OC = c, MN =. 6. AB CDA B C D, AC BD , OA BC, OB = OC, AOB = AOC =. : OA BC , ABCD - A B C D, BD CB.. : a b, a + b a - b. 4. OA + OC = OB + OD, : AB CD , AB, AC, BD AB, 0, AB =, AC = BD = 4, C D.

243 A B ' N M G C 4 -O - 8 D M A G C B N D. B. B 4. B 5. C 6. B 7. C. x + y =. x + y + z = ( b + c - a) OABC = OA( OC - OB ) = OAOC - OAOB = OA OC cos- OA OB cos, 6 OB = OC, OABC = 0. OA BC.

244 ..BA = a, BC = b, BB= c, BD= a + b + c, CB= c - b, BDCB= ( a + b + c) ( c - b) = ac - ab - b + c. ac = ab = 0, b = c =, BD CB, BD CB90.. ( a + b)( a - b) = a - b, a = b, a = a, b = b, ( a + b)( a - b) = 0, a + b a - b. 4., AB CD. OA - OB = OD - OC, OA - OB = BA = - AB OD - OC = CD, - AB = CD, AB = - CD, , D DD D, BD, DBD= 0. CA, CA DD, CABD= 0, CD = ( CD) = ( CA + AB + BD) CD = 5. = CA + AB + BD + ( CAAB + ACBD + ABBD) = cos0= 5,

245 .,..,..,. 4.,.. ( ) :,,,. :. :. :. :. :. :. :. ( ) :,... ( ) : c, h, S = ch (4 ) : S h. V = Sh. S h. a. 4. ( ) :,,

246 ..,, ( ) :,,,. ;. ( ) : c, h, S = ch (4 ) : S, h, V = Sh (5 ) :,,.. ( ) :. ( ) :. (). (). ( ) : r,c, l, S = cl = rl (4 ) : r, S, h,. V = Sh = r h () : (). 5

247 ( ) :... ( ) : r,c, l, S = cl = rl (4 ) : r, S, h, V = Sh = r h. ( ) :,. ( ) :... d R r : r = R - d ( ) : 4, S = 4R (4 ) : R, V = 4 R. P = {}, Q = {}, R = {}, ( ) ( A) R Q P ( B) P Q R ( C ) R P Q (D) P R Q, P Q;, Q R, P Q R. 6 B.. 4,, ( ) ( A) 88 (B) 66 ( C) 48 (D) 44 x x x, ( x) + ( x) + x = 4, 4 x x =. = 4 4, 6 4, S = ( ab + bc + ca) = ( ) = 88. A.. AB C - A B C a, A AB = A AC = 6,

248 ( ) ( A) a ( B) a ( C ) a ( D) a A ABB, SA AB B SA AC C = a. = a sin 6 = a. A AB = A AC, B BCC, SB BCC = a, ABC - A B C a + a + a = a. C. 4.,, ( ) ( A) ( B) ( C) (D),,. C. 5. cm, 60, ( ) ( A) cm ( B) cm ( C)4 cm (D) cm cos60=,, csc60= = 6, 6, S = ch= 6 6 =, S = 6 4 a = 6 4 ( 6 ) =. + = ( cm ). D. 6. S, ( ) ( A) S ( B)4S ( C )S ( D) S r, l, S = rl, S = cl = rl = S. C. 7., ( ) ( A) 45 (B) 60 ( C) 90 (D) 0 r, l,, 7

249 (rl)(r ) =, l r =, r l =. sin= r l =, = 45, = 90. C ,, ( ) ( A) 0 ( B)5 ( C) 50 (D)00,,,, d = = 50, S = 4r = d = 50. C.,,. 9. ABCD - A B C D, D B CA ( A) (B) ( C) (D) ( ) a, a, D B CA. ( aa) = 6 a, D B CA a a = a. D B C A. B. 0. 5cm, 60, ( ) ( A) 0cm ( B) 75 7 cm ( C) 50 7 cm (D) 5 7 cm r, l, h, rl + r r l = 5 60= 60, rl + r = 5, l = 6 r r = 5 7 l = 6 r, h = l - r = ( 6 r) - r = 5 r = = 5, V = r h = 5 7 D. 5 = 5 7 (cm )., 8

250 ,.. a,.7cm, cm.. cm, 4cm.. 48cm, 7cm, 6cm,. 4.,., 5. h, 60, S = S =. 6. R,. 7. 4, 8 5cm, , 4,... x, x = a, x = a, S = 6 x = 6 ( a) = a. y, 6 y = 7, y =. l = y = = 6. : a, 6.. cm, 4cm, h = - ( ) =, V = Sh = 4 = 6 (cm ). : 6 cm.. xcm, 7 48 = ( x - 6 ), x x = 4( cm). : 4cm. 4. :,. 5. htan60= h. r, h = r, r = h, S = rh = h h = h, 9

251 S = S+ S = h + r = h + ( h) = h + h. : h, h + h. 6. x, l = x = R, x = R. S = 6 x = 6 ( R) = 8 R. : 8 R. 7. r, h, l = h + r. r l = r = 4 h + r, rh = r = 4 h rh = 8 5, r = 4 h = 5. V = Sh = r h = 4 5 = 5. : ,,. 8. R, r. 00, 4R = 00, R = 5, V = 4 R. V = 4 V, 4 r = 4 4 R, r = 4 R, r = R 4 = 5 4. : ,,,.. cm, 80cm,. hcm, acm. 6 ah = 80 h + ( a) =, h = a = 5, h = 5 a = 6. 40

252 a, V = a h. a = 5, h =, V = ( 5 ) = 5 (cm ) ; a = 6, h = 5, V = 6 5 = 70 (cm ). 5 cm 70 cm , S - ABCD, SD A BCD, SD = AD = a, A - SB - C. b RtSAB, A AE SB E, CE AC, AEC A - SB - C. SD ABCD, SABSBDSCB. SD = AD = a, SA = a, SB = a. RtSAB, AE = SAAB SB = aa a = 6 a, A S D E B C CE = 6 a, AC = a. AEC, cosaec = AEC = 0. ( 6 a) + ( A - SB - C 0. 6 a) - ( a) 6 a6 a. SABCD acm, bcm, , SE BC, SOC, S SO = b - ( a ), SO = 4 b - a. SOE, SE = SO + OE = 4 b - a 4 + a 4 A = -, D O B E C = 4 b - a. S = 4 a V = a 4 b - a = a 4 b - a ( cm ), 4 b - a = 6 a 4 b - a (cm ). 4

253 .M = { }, N = {}, P = { }, Q = {}, ( A) P N M Q ( B) Q M N P ( C) P M N Q ( D) Q N M P ( ). ( ) ( A) ( B) ( C) ( D).a b c, ( ) ( A) ( C) a + b + c ( B) a + b + c ( D) a + b + c ab + bc + ca 4.9cm 5cm, 5cm, ( A) 6cm ( B) 6 cm ( C) 8cm ( D) 8 cm ( ) 5.ABC - A B C, AB = AC = 0cm, BC = cm, A AB C cm, ( ) ( A) ( ) cm ( B) ( )cm ( C) 96cm ( D) 49cm 6. ( ) ( A) ( B) ( C) ( D) 7.,, ( A) ( B) ( C) ( D) ( ) 8.a, 60,, 0, 4 ( A) 4 a (B) a ( C) 8 a (D) a ( ) 9. 0cm, cm, ( ) ( A) h = cm ( B) l = cm ( C) S = 60 cm ( D) S = 0 94cm 0., a, ( ) ( A) + a (B) 4 a ( C) + 4 a (D) a

254 ., 4, ( ) ( A) (B) 4 ( C) 6 (D) 8., ( ) ( A) (B) 4 ( C) 4 (D).8,, ( ) ( A) (B) ( C) (D) 5 4.ABCD, AD, AC = 8cm, AC A B 0, ( A) 4 cm (B) 8 cm ( C) 6 cm (D) cm ( ) 5.,, ( A) (B) ( C) (D) ( ) 6. a, ( ) ( A) a (B) 4 a ( C) a (D) 7.0cm 45, / 4, ( A) 00cm (B) 00cm ( C) 00 cm (D) 00 cm ( ) 8.R, ( ) ( A) R (B) R ( C) R (D) R 9.60, A B R( R ), AB ( ) ( A) R (B) R ( C) R (D) R 0., ( A) 65 (B) 54 ( C) 4 (D) ( ).cm, 6cm, ( ) ( A) 4cm (B) 7 cm ( C) 4cm 7 cm (D) 8cm.S, a, ( ) ( A) Sa (B) Sa ( C) Sa (D)., ( A) 4 (B) 7 ( C) (D) 8 ( ) 4. 6, 5, ( ) 4

255 ( A) 9 (B) 9 ( C) 7 (D) 9 5.cm 4cm,, ( A) cm (B) 6cm ( C) 48 5 cm (D) 0cm ( ) 6.S, T, ( ) ( A)T S (B)S T ( C) 7. 4cm, 60, ( ) ( A) 4 cm (B) 64 cm ( C) 48 cm T S (D) S T (D). 8.,,, ( ) ( A) (B) ( C) (D) 9.R, ( ) ( A) R (B) 8 R ( C) 8 9 R (D) R.4cm, 8cm,.. a, h, ; ; ; ;.. AB C - A B C a, A B C. 4. 0cm, cm, ; ;. 5. 0, 4cm, 60,. 6. 8cm, 40, ;. 7.b,, a, 4,. 8. a, b, ;. 9.5cm A B C, AB = 6.4cm, BC = 4.8cm, CA = 8cm, ABC. 0.a, ;.., a b c, V V. 44.Q Q Q,.. 6, 7,

256 . 4. h,, 60,. 5. 5, 60,. 6. 6cm, 60,,. 7..5cm,.5cm,. 8.ab,,.. :.. S - ABC SO = h, SM = l, SO A B C.. R, H, x. ( ) ; ( ) x,?.b.c.b 4.C 5.D 6.A 7.D 8.C 9.D 0.C.B.C.C 4.C 5.A 6.B 7.C 8.C 9.D 0.D.C.A.B 4.A 5.C 6.C 7.C 8.A 9.C.cm. a + 9 h, 6 a + 6 h, 6 a,. 7 4 a 4.0, 94, cm 6.44cm, 6 5cm 7. ab 8. b a, a 4 4b a, a.v V. Q Q Q h 4 a 4 a + 6 h, a 4 a + 6 h + 4 a cm, 4cm 45

257 7.5cm 8. b a , AC, B D. : B D = AB + BC + BB., BD. B B BD, B D = BD + BB. BD = AB + AD = AB + BC, B D = AB + BC + BB , OM OA, RtSOM, OM = l - h SABC, O A BC. AB = AM = OMtan60= l - h, SAB C = 4 AB = 4 4 ( l - h ) = ( l - h ),, SAB SAB C= 4 ( l - h ). S AB C C = ( h h ) = 4, A A D b D B ( ) ( ), r, x, S = rx. r R = H - x H, r = R - R R x, S = Rx - H H x. ( ) S x,. x = - R - R H = H.,. A B B S C C A C O B C O M H x r R

258 ..,,...,..,...,.., , n, m, m,, n m n, N = m + m + + mn.., n, m, m,, n mn, N = m m mn 47

259 .. n, m( m n),, n m, m = n,.nm( m n), n m, P m n.. P m n = n( n - ) ( n - )( n - m + ) = n! ( n - m)! ( m n N m n) n! n, n, 0! =., m = n, P n n = n! = n( n - ).. n, m( m n), n m.n m( m n), n m, C m n.. C m n = n( n - ) ( n - )( n - m + ) m! C 0 n =... C m n = n! m!( n - m)! ( m n N, m n) = C n n - m C m n + = C m n + Cn ( a + b) n = C 0 n a n + C n a n - b + + C r n a n - r b r + + C n nb n n +, C r n ( r = 0,,, n).. r + Tr+ = C r na n - r b r.. ( ),. ( ), ;,. 48 ( ), m - C 0 n + C n + C n + + C n n = n

260 (4 ),, C 0 n + C n + C 4 n + = C n + C n + C 5 n + = n , k b, y = kx + b, ( A) 6 (B) 8 ( C) (D)4 y = kx + b k b,. P 4 = 4 =, C. ( ). 8, ( ) ( A) 56 ( B)56 ( C )6 (D)5,. C 8 = = 56, A..,,,.. 5,,,, ( ) ( A) 6 ( B)8 ( C) 0 (D) : 5 C 5 : 4, = 5 4 = 0 (),, D. 995,,,,. 4. 5, 4, ( ) ( A) P 5 P 4 (B) P 5 P 4 P 5 5 ( C) C 5 + C 4 + P 5 5 (D) C 5 C 4 P 5 5 A,, B,,, C, D. D ( ) ( A) 0 ( B)0 ( C )00 (D) 0 ( ), 0,, P 5,, 5, P 5. 49

261 , C. P 5 P 5 = = 00 (). ( ) 0,, P 6 = 0, 0 P 5, C. P 6 - P 5 = 00 ().,.( ) :,.( ) :,,. 6. C x - x 6 = C 5 x x ( ) ( A),, 5, 7 ( B), ( C),, 5 (D),5 C m n = C n n - m x - x = 5 x - 5 x - x = 6 - ( 5 x - 5). x - x = 5 x - 5 x =, x = 5, x - x = 6 - ( 5 x - 5) x = - 7, x =, x = 5 x = - 7. B. 7. a b c d e 4, 4,, b, ( ) ( A) 4 ( B)6 ( C) 0 (D) 96 b, P 4,, 4, P 4 50 D.. 8. ( x -., P 4 P 4 = 4 4 = 96( ). x ) 6 ( x 0) ( ) ( A) C 6 ( B) C 6 ( C) - C 6 ( D) - C 6, 6 - r = 0, r = 4, Tr+ = C r 6 x 6 - r ( T5 = T4 + = C 4 6 = C 6 = 6 5 = 5. B. - x ) r = ( - ) r C r 6 x 6-998,, r.

262 . 9. ( x + ) 5, ( ) ( A) C 7 5 x 7 (B) C 8 5 x 4 ( C) C 7 5 x 4 C 8 5 x 7 (D) C 7 5 x 7 C 8 5 x = 6,, 8 9,.T8 = C 7 5 ( x) 8 = C 7 5 x 4, T9 = C 8 5 ( x) 7 = C 8 5 x 7. C. 0. ( a x - x ) 9 x 9 4 ( A) ( B)4 ( C) 6 (D)8, Tr+ = C r 9 ( a x ) 9 - r ( -, a ( ) x ) r = ( - ) - r a 9 - r C r 9 x r- 9. r - 9 =, r = 8, ( - ) - 8 ac 8 9 = 9 4,, a = 4. B.. ( + x) + ( + x) + ( + x) + + ( + x) n x ( ) ( A) C n+ ( B) C n+ ( C ) C n+ ( D) C n+ ( + x) + ( + x) + ( + x) + + ( + x) n x C + C + C C n, B. C + C + C C n = C + C + C C n = = C n+. ( + x) + ( + x ) + + ( + x) n = ( + x) [ - ( + x) n ] - ( + x). P P 6 6 7! + 6!. ( x4 - = ( + x) n+ - ( + x) x. ( + x) n+ x. ( + x) n+ x C n +, B.. x ) 6, x 0.. ( x - y) ( + x) n, 4 8,,..,, 5

263 P P 6 6 7! + 6! : = ! + 6! = (7 - ) 6!(7 + ). Tr+ = C r 6 ( x4 ) 6 - r ( - x ) r = 5 8 = 5 6. = C r 6 ( - ) r ( ) 6 - r r x 4 ( 6 - r) x - r = C r 6 ( - ) r r- 6 r x 4-4 r - r = C r 6 ( - ) r r - 6 x 4-7 r. 4-7 r = 0, r =. x 0 C 6 ( - ) ( ) - = 5. : 5.. ( x - y) 4 = [ x + ( - y) ] 4 = C 0 4 x 4 + C 4 x ( - y) + C 4 x ( - y) + C 4 x( - y) + C 4 4 ( - y) 4 = x 4-4 x y + x y - 8 xy + 4 y 4. : x 4-4 x y + x y - 8 x y + 4 y ( - x) n, 4 C n, 8 C 7 n. C n = C 7 n C n - n = C 7 n n - = 7( n - n - 7) n = 0. ( + x) n = ( + x) 0,. 6, C 5 0 = 5. : 6, ,,,,,? 6 C 6, 4 C 4, 5 5 P 5 5,, C 6 C 4 P 5 5 = : ,,,,. 5

264 . ( x - ( x - x ) 6 x ) 6. - r = 0, r = 4. Tr+ = C r 6 ( x ) 6 - r (, T5 = ( - ) 4 C 4 6 = , - 60 x. - x ) r = ( - ) r 6 - r C r 6 x - r T4 = ( - ) C 6 x = - 60 x,, Tr+ r + r, :. : ( ) P m n + mp m - n = P m n+ ; ( ) C m+ n + C m n + C m - n = C m+ n+. ( ) P m n + mp m - n = P m n + mp m - n = P m n+. T4 = ( - ) C 4 6 x 0 = 60. n! ( n - m)! + m n! [ n - ( m - ) ]! = n!( n - m + ) ( n - m + )! + mn! ( n - m + )! = ( n + )! [ ( n + ) - m]! = Pm n+, = n!( n - m + + m) ( n - m + )! ( ) C m+ n + = C m + n+ + C m n + = C m+ n + C m n + C m n + C m - n = C m+ n + C m n + C m - n. C m+ n + C m n + C m - n = C m + n+. ( ) a, a,, an+ n + m P m n +,, a, a.a a, a,, an+ n m - a, mp m - n ; a a, a,, an+ n m, P m n,, P m n + mp m - n = P m n+. ( ) a, a,, an + n + m + C m + n +.,, a a ; a a ; a a ; a a.a a C m n ; a a C m n ; a a C n m - ; a a C n m+ 4. n ( n 4). C m + n + C m n + C m - n = C m+ n+.., ( n - ), n, n( n - )., 5

265 ,., n ( n 4) n( n - ). n an, n +, an +, an + = an + ( n - ) + = an + n - ( n 4 ). n = 4, 5,, k, a5 = a4 + a6 = a5 + 4 ak = ak - + ak - ak = a4 + ( k - ) = k - = ( k - ) ( k - ) - = k( k - ). an = n( n - ) ( n 4 )..P 6 - P 5 ( A) 00 ( B)60 ( C) 60 (D)40 ( ). P m = 0, m ( ) ( A) 5 ( B)4 ( C) (D).( n - 7 ) ( n - 6 ) ( n - 5 ) ( n - 4 ) ( n - ) ( ) ( A) P 5 n - 7 ( B) P 5 n - ( C) P n n (D) P n n ( A) 56 ( B)46 ( C) 8 (D)0 ( ) 5.C + C + C 4 + C 5 + C 6 + C 7 + C 8 + C 9 + C 0 ( ) ( A) 990 ( B)65 ( C) 0 (D) ,, ( ) 54 ( A) P 4 6 P ( B) P P 5 5

266 ( C) P P 4 4 P 5 (D) P ,,,, 4, 5 ( ) ( A) 00 ( B)04 ( C) 80 (D) ,,, ( ) ( A) C 6 C 4 C ( B) C 6 C 4 C C ( C) P 6 P 4 P (D) C 6 C 4 C / P 9. ( x + x ) 6 ( ) ( A) 0 ( B)0 ( C) 5 (D)0 0. ( x - ) ( x + ) 8, x 5 ( ) ( A) C C 4 8 ( B) C C 5 8 ( C) C C 5 8 (D) C C 6 8. ( x + x ) n 5, ( ) ( A) 56 x ( B)84 x ( C) 56 x 4 (D)84 x 4. ( + x) 9 ( ) ( A) 6 x 5 ( B)6 x 6 ( C) 6 x 5 6 x 6 (D)6 x 4 6 x 5. ( - x) 9 = a0 + a x + a x + + a8 x 8 + a9 x 9, a + a + + a8 + a9 = ( A) - ( B) - ( C) 0 (D).C 00 = ; C n+ C n+ =..C 6 + C 6 + C 6 + C C C 6 6 =..( ) 7,,,. ( ) 7,,. ( ) 4.0,, 5,. 5. ( a + b) n, r + r (. x + 5 x ) n, 04, 7. ( - x) 9 = a0 + a x + a x + + a8 x 8 + a9 x 9, a + a + + a8 + a9 =. 8. ( + x) 6 ( - x) 6 x 6. 55

267 . 0, 5. ( )? ( ) A? ( ) A B?. 9,, 9 5, 5,?. 4,? 4. f ( x) = ( x + x - ) 9 ( x + ) 4, : ( ) f ( x) ; ( ) f ( x). 56. B. A. B 4. D 5. B 6. C 7.D 8. A 9. B 0. B. B. D. B n + 6 n - n C C ( r + )( n - r) 6. T6 = 46 x - 4, T7 = 46 x ( ) C 5 0 P 5 5 = 040( ). ( ) A C 4 9, P 5 5,, A C 4 9 P 5 5 = 50 ( ). ( ) B, B, 9, 5? C 4 8 P 5 5 = 8400 ().. 5, : C C 4 9, 5, : C C 9 C C C C 9 = 6.., C 4 = 6., P 4 = 4., :, C 4 P 4 = 6 4 = 44( ). 4. f ( x) = ( x + x - ) 9 ( x + ) 4 = a0 + a x + a x + + a x.

268 x =, f ( ) = a0 + a + a + + a = 9 4 = 8, x = -, f ( - ) = a0 - a + a - + a = ( - - ) 9 ( - + ) 4 = -,, ( a + a + a5 + + a ) = 8, a + a + a5 + + a = 4. f ( x), 8, 4. 57

269 .....,..,..., ,..... n k.... n k.,.....,.....,....,. 58.

270 ,, ;, ;,.., A m n ( n, m A ),, A, P( A).,0 P( A),, 0..,.., n,, n., A( ) m, P( A) = m n..,. A, A,, An, A, A.,, A n. A, A,, An, A + A + + An (A, A,, An ). P( A + A + + An ) = P( A ) + P( A ) + + P( An ),, A A., A + A, P( A + A) =. P( A) + P( A) = P( A + A) =. A(B) B(A),.. A B, P( AB),, A, A P( AB) = P( A)P( B),, A n, P( A A An ) = P( A )P( A )P( An ) 59

271 p, n, k Pn ( k) = C k n p k ( - p) n - k,,,,.. x, x,, xn n [ ( x, S.., x, - x) + ( x - x) + + ( xn - x) ],...,,.. ( ) x, x,, xn x i ( i =,,, n) P(= x i ) = pi, x x x n P p p pn,. ( ), ( ). 60. E( ) = x p + x p + + xn pn

272 X Y, ( x, y ) ( x, y ) ( xn, yn ),, xi yi ( i =,,, n),., x y y = a + b x, Y X, a, b.,,, a = Lx y L x x, b = y - b x Lx x = n ( x i - x) = n x i - ( xi ), Lx y = n ( x i - x) ( yi - y) = n x i y i - ( xi ) ( y i ).,., X = x0, Y = y0 : y0 = a + b x , ( ) ( A) 4 ( B)4 ( C ) (D) C 9 = 84, C 4 = 4, =. C. 00 (7 ),.., 5 7, ( A) 5 7 ( B) 5 ( C ) 7 (D) 5 ( ),,.7, 7. C.,., 5 7, 6

273 D, = 5.. 6, ( ) ( A) 5 ( B) 0 ( C) 60 6,., 90, 6 90 = 5. A. C 4 C = 4 = 6()., 4.,. 4., ( ) ( A) 0 ( B) 0 ( C) 00 ( D) (D) 0000, 0 4,. 0000,. D , ( : ) : ,., x = ( ) = 47, 0 S = 0 [ ( ) + ( 00-47) + + ( ) ] = 68. : 47, P

274 ., : 89. E( ) = = ,95,5,, , C 5 ; 00 C 00., A, P( A) = C 5 C 00 = ,,5,0,, : ( ) ; ( ). A, A, A. ( ) P( A ) = P( A ) = P( A ) = , = , = ( ) P( A + A + A ) = P( A ) + P( A ) + P( A ) = = ( ) ; ( ) ,,?,. 00, A, A. P( A) = C 5 C 00 = 6 70, P( A) = - P( A) = ,. 4., ,.., A ;, B, P( AB) = P( A) P( B) = = %, 4 ( ). 6

275 . P4 ( ) = C ( ) ,, ,. x = 8 ( ) = 0, S = 8 [ ( ) + ( ) + + ( 9.7-0) ] = , : x i ( ) y i () ( ) y x ; ( ) 8,? z = x, : x i z i = xi y i z i = x i y i zi y i zi =.40, yi =.5, z i =.466, y i = 87.49, zi y i = 6.. ( ) y z. y ^b = zi i - n zi yi = z i - n ( zi ) ^a = y - ^bz = = 0.96, y z y = z. z = x, = 9.56,

276 y x ( ) 8,.6. y = x y = =.6,. 00, 95, 5., ( A) 495 ( B) 00 ( C) (D) 4 99 ( )., ( ) ( A) ( B) 4 ( C) (D) 6. A B, ( ) ( A) P( A + B) = P( A) + P( B) ( B) P( A) = - P( B) ( C) P( AB) = P( A)P( B) (D) P( A) = , ( ) ( A) 0 ( B) 4 ( C) 0. (D)0. 5., ( ) ( A) 6 ( B) 4 6 ( C) 8 6 (D) ,, ( A)0. 6 ( B) ( C) (D) ( ) 7., ( Q) ( ) ( A) 5 ( B) 4 ( C) 7 5 (D) 4. 0.,.. 5,.. 0, : x =

277 - 0 P E( ) =..,, 0. 4, 0.8,.., 0.9, 4,??., 0.04, 4, 4. x y : x i y i ( ) ( xi, yi ). ( ) y x.. C. D. C 4. C 5. D 6. B 7. B A ;B;C, A + B C, 7 5 P( C) = - P( A + B) = - P( A) - P( B) = 0...,,,4 A, A, A, A4. P( A ) = = 0... P( A A A A4 ) = = P4 ( ) = C 4 ( 0.04 ) ( ) 4 - = ( ) ( xi, yi ) ( ) : x i y i

278 x i y i xi y i xi =, yi = - 8, x i = 9, y i = 46, xi y i = zi y i - b = n zi yi = z i - n ( zi ) = -.9, - 8 a = y - b x = ( -.9 ) 7 = 6.7. Y X y = a + b x = x, ( - 8) O - y x y = x

279 () 00 ( ) ( ) () ( ), 50, 0. (, 75 ) :.,,..,,,,,..,. 4., tan, cot. : 5, 5, 75,,.. M = { x x - 4}, N = { x x < 6}, M N ( ) ( A)R ( B) { x - 4 x < 6} ( C ) (D){ x - 4 < x < 6}., k60- ( k Z) ( ) ( A) ( B) ( C) ( D).,, ( ) ( A) y = - x - ( B) y = log x ( C) y = ( ) x ( D) y = log0. x 4. x - - < 0 - < x < 4, a ( ) a - x > 0 ( A) a - 4 ( B) a - 4 ( C ) a 8 (D) a 8 5. f ( x) = ax + b x + c f - ( x) = x + 5 x -, ( ) ( A) a =, b = 5, c = - ( B) a =, b = -, c = 5 ( C) a = -, b = - 5, c = ( D) a =, b = 5, c = - 68

280 6. y = sin x + 4cos x ( ) ( A) ( B) ( C )5 (D)6 7. : C f ( x, y) = 0 ; : f( x, y) = 0 C, ( ) ( A) ( B) ( C) ( D) 8. 7,, ( ) ( A) 7 ( B) 6 7 ( C ) 7 (D) a = (5, 8 ), b = (, ), c = (, - ), ( ab) c ( ) ( A) ( 4, - 68) ( B) 4 ( C ) - 4 (D) 0. x - y + 8 x - 4 y + 47 = 0 ( ) ( A) ( B) ( C ) (D). 68 ( ) ( A) x - 6 x + 7 = 0 ( B) x + 6 x + 8 = 0 ( C) x + 6 x - 8 = 0 ( D) x - 6 x - 7 = 0. z = + 4i, z = - - i, z - z ( ) ( A) 5 4 ( B) 7 4 ( C ) 4 (D) - 4. y = x - 4 x + 4 ( ) ( A) ( -, - ) ( B) (, + ) ( C) [ -, ] ( D) ( -, - ) (, + ) 4. y = log ( x + ) ( ) ) y y y y - O x O x x - O O x (A ) ( B) ( C ) ( D) 5., ( -,0 ), 5 x - y = 0 ( A) x 5 - y 4 ( C ) y - x = ( B) x 4 - y 5 = = ( D) x - y = ( ) 69

281 ( 75 ) :.... : 4, 5, 0,. 6. A n, A. 7. x - y - 4 = 0 x 4,. 8. z + =, arg ( z + ) =, z =. 9. x + y + 8 x - 6 y + 4 = 0 y. : 5, 55,. 0. ( ) ABC, C c B b, C B. ( ) ABC ; ( ),?. ( ) f ( x) = x - e x.. ( ) P - AB C, O ABC, PA = a, PB = b, PC = c. ( ) PO { a, b, c} ; ( ) PO.. ( ) { an }, n Sn, an Sn. ( ) ; ( ). 4. ( ) x + y - = 0 x + y + x - 6 y + m = 0 A B, O, m, OB OA? 70

282 00 ( ) ( ) : 5 ; 5, A B D C A D D D A C D B D C B : 4, 5, 0,. 6. n - 7. x + y - 6 = i - i 9. ( x - 4) + ( y - ) = : 5, ( ) c = b, Rsin C = Rsin B, sin C = sin B. B = C -, sin C = sin( C - ) = sin Ccos - cos Csin, sin C = sin C - cosc, cos C = 0. C, C =, ABC. ( ) ABC c = 4. ( ) C =, B = C - = 6, A =, a = 4sin =, b = 4 sin 6 =. ABC =.. ( -, + ) f ( x) = ( x - e x )= x- (e x )= - e x f ( x) = 0, x = 0. : x ( -,0 ) 0 (0, + ) y y - f ( x) = x - e x x = 0 ymax = -.( -,0 ), (0, + ). 7

283 !. ( ), O A BC, x y PO = = ( - x - y) a + xb + yc, PA + x A B + y A C PO ABC, PO AB, PO AC, PO AB = 0, PO AC = 0. [ ( - x - y) a + xb + yc]( b - a) = 0 [ ( - x - y) a + xb + yc]( c - a) = 0, x + y = x + y =, x = y =, A P O B C PO = a + b + c. ( ) PO = a + b + c, PA PB PC j k.,, PA PB PC i PO = ( ) + ( ) + ( ) =.. ( ) an + = Sn. n =, a + = S, S = a, a + = a, a =. n =, a + = S, S = a + a = + a, ( + a ) = a +. a > 0, a = 6. n =, a + = S, S = a + a + a = a = 8 + a, a > 0, a = 0. a + = ( a + 8). a =, a = 6, a = 0. ( ) an + Sn + = 8 ( an+ + ), = Sn ( n N + ), Sn = 8 ( an + ). an+ = Sn+ - Sn = 8 [ ( an+ + ) - ( an + ) ]. 7

284 ( an+ + an ) ( an + - an - 4) = 0, an+ + an > 0, an+ - an - 4 = 0, an+ - an = 4, { an } 4. ( ) a =, an = + ( n - )4 = 4 n -. ' y 4. A B A ( x, y ) B( x, y ). x = - y, ( - y) + y + - y - 6 y + m = 0, 5 y - 0 y + + m = 0. y + y = 4 y y = + m 5 x x = ( - y ) ( - y ) A O B 4 x = 9-6 ( y + y ) + 4 y y = 4 m OA OB koa kob y y x x. = -, y + m 4 m - 7 = -, m =. m =, OB OA. x y x = -. 7

285 00 ( ) ( ) () ( ), 50, 0 (, 75 ) :.,..,,,,,..,. : 5, 5, 75.,.. : M = { x x > 4}, N = { x x < }, ( ) ( A) M N = { x x > 4} ( B) M N = { x < x < } ( C) M N = { x x < - } ( D) M N = R.,,, ( ) ( A) ( B) ( C) ( D). P x + y =, 5 4 F F, F PF = 0, PF F ( ) ( A) 6 ( B)6( - ) ( C) 6 ( + ) ( D) 6 4. y = sin x sin x - ( ) ( A) ( B) ( C) ( D) 5. + itan5 - itan5 ( ) ( A) 6 ( B) ( C) 4 ( D) 5 74

286 6. y = x 4 ( x ( - 5, 5] ) y = sin x ( x R) y = ln( - x x + ) y = sin x [ -, ] [, 5 ], ( ) ( A) ( B) ( C) ( D) 7. l x - y - = 0, (, - 4 ) ( A) x + y - 8 = 0 ( B) x - y - 8 = 0 ( C) x + y + 8 = 0 (D) x - y + 8 = 0 ( ) 8.x + px + q < 0 { x - < x < }, ( ) ( A) p = -, q = 6 ( B) p =, q = 6 ( C) p = -, q = - 6 (D) p =, q = a = 0, b = ( -, 4 ) a b, a = ( ) ( A) ( 6, 8) ( B) ( 6, - 8) ( C) ( - 6,8 ) ( D) (, 4 ) 0. y = x + 5 x ( ) ( A) x = ( C) ( -, -. x = + t y = 4 + t ( B) x = - ( A)5 ( B) - 5 ( C) ) (D) ( , + ) ( t ), y ( D) - ( ). 4 5 ( ) ( A)5 ( B)8 ( C) 0 ( D). loga <, a ( ) 5 ( A)0 < a < ( B) a > ( C) < a < ( D) 0 < a < a > 4.{ an }, a + a + a + a4 + a5 = 5, a ( ) ( A) ( B)4 ( C) 5 ( D) 6 5. f( x), x (0, ), f( x) = lg( x + ), x ( -, 0), f ( x) ( ) ( A) - lg( x + ) ( B) - lg( - x) ( C )lg( - x) ( D) lg ( x + ) 75

287 (, 75 ) :.... : 4 ; 5, 0,. 6. a = (, ), b = (, - ), a b. 7. ( - x) 9 = a0 + a x + a x + + a9 x 9, a + a + a + + a9 =. 8.p, q,. 9.( + i) 0 - ( - i) 0. : 5, 55,. 0.(0 ) : cos0 cos40 cos60 cos80..(0 ) f( x) = xln x [ 4, ]..( ) z z - z =.( ) PQ y Q. - i, u = z, u. = x OP OQ, O, P ( ) : PQ x. ( ) OPQ. 4.( ) AB, AB 45, 0, = l, AC l, BD l, C D, : ( ) CD ; ( ) AB CD ; ( ) ABD ABC. A C B D l 4 76

288 00 ( ) () : 5 ; 5, D D B C A B B D C A C D D A B : 4, 5, 0, : 5, 55. q p = sin0 cos0 cos40 cos80 = sin40 cos40 cos80 4 sin0 8sin0 = sin80 cos80 8 sin0 = sin60 6 sin0 =. f ( x) = xln x f ( x) = sin0 6sin0 = 6. x ln x + x x = x (ln x + ) f ( x) = 0, ln x + = 0, x = e -. f ( 4 ) = 4 ln 4 = - ln4, f ( ) = ln = 0, f (e - ) = e - lne - = - f (e - ) = - e e f ( x) ; f ( ) = 0 f ( x).. z = x + yi( x y R) x + y - x - yi = - i, x + y - x - yi = + i., x + y - x = - y =, x = 0 y = -, 77

289 z = - i = cos + isin. u = z, u = cos k = 0, u k =, u u - + k + k + isin ( k = 0, ) = cos + isin 4 4 = - + i. = cos isin 4 4 = - i + i - i.. ( ) OP : y = kx ( k > 0 ), OQ: y = - y = kx y = x, k x x = k y = k, P( k, k ). y = - k x y = x, x = k y = - k, Q( k, - k), PQ y + k = y = 0 x =, k =, PQ x =, PQ R (, 0 ). - k - k k - k ( x - k ). ( ) SPO Q = SPO R + SQO R = OR ( yp - yq ) = ( k + k ), k =, POQ,. b A l C D B 4 ( ) 78

290 4. ( ), BD l, BD, BAD A B, BAD = 45., AC l, AC, ABC A B, ABC = 0 RtABD, AB =, BAD = 45, AD =. RtABC, AB =, AB C = 0, AC =. RtACD, CD = AD - AC = - = ( ), B Cl BD E, AE, CE l, AB BE A B CD. EC l, l ACE, BE l, BE ACE, BE AE. RtAB E, AB =, BE =, ABE = 60. AB CD 60. ( ), AC l, AC. A G AC ABC, l C D ABC, ABC = BC. H B, D D H BC H, D H 4 () ABC, ABC, H H G AB G, DG,, DG AB, DG H A BC A BD. RtBCD, CD =, BD =, BC =. DH BC D H = CDBD BC = = 6. RtABD, AD = BD =, DG AB, DG =. RtDG H, sindg H = D H DG = 6. ABD AB C 6. 79

291 00 ( ) ( ) () ( ), 50, 0. (, 75 ) :.,..,,,,,..,. : 5, 5, 75.,.. M = { a, b}, N = { b, c}, P M N P ( ). ( A)6 ( B)7 ( C) 8 (D) 9.: ; : 60. ( ) ( A) ( B) ( C) (D). x 5 + y m = e = ( A) ( B) 5 0 5, m ( ) ( C) 5 (D) M(, 0 ) x + y - 8 x - y + 0 = 0, M ( A) x + y - = 0 ( B) x - y - = 0 ( ) ( C) x - y - 6 = 0 (D) x + y - 6 = 0 5. AB C, sin A = 5, cos B = 5, cosc = ( ) ( A) 6 65 ( B) ( C) (D)

292 6. y = x - x - ( x R, x ) ( ) ( A) y = x - x - ( x R, x ) ( B) y = x - ( x R, x ) x - ( C) y = x + x - ( x R, x ) (D) y = x - ( x R, x - ) x + 7.( 6 a - a - ) x + ( a - 5 a + ) y + ( a - ) = 0 y, a ( ) ( A) ( B) ( C) (D) ' 8. y = ax + bx + c, OA OB y ( A) ( C) a c c a - c a ( B) - (D) c a b - 4 ac a ( ) A O B 8 9. z, z - + i ( ) ( A) ( B) + ( C) - (D) 0., y, P( m, - ) 5, ( A) x = 4 y ( B) x = - 4 y ( C) x = - 8 y (D) x = 8 y x ( ). l, M(, 7 ) l ( ) 6 ( A) ( -, 5 ) ( B) ( -, - 5 ) ( C) ( -, - ) (D) ( -, ).6,, 4,, ( ) ( A) C P 4 5 ( B) C C 4 P 4 4 ( C) C 5 P 4 4 (D) C P 4.a br +, a b,, ( ) ( A) ab < ( C) a + b a + b < ab < < a + b a + b ( B) a + b (D) ab < a + b < ab < a + b < a + b 4. { an } n Sn = 5 n - n, a6 + a7 + a8 + a9 + a 0 ( A)70 ( B)70 ( C) 50 (D) 490 ( ) 5.,, 4,, ( ) ( A) 4 ( B) ( C) (D) 4 8

293 : (, 75 ).... : 4, 5, 0,. 6. x - x y = x + x <. + 5 P(, 9 ). 8.( x + x - ). 9.X. X 0 P X E( X) =. : 5, 55,. 0.(0 ) CD RtAB C A B, ACDCBDABC, B..(0 ),,, 6,,. ƒ.( ) : P - ABC, 4cm, PA ABC, PA = 6cm. ( ) P - ABC ; ( ) PB C A BC..( ) ABC B( -, 0) C(, 0),, ( ) A ; B C ( ) O, y = x + b ( ) MN, MN O b. 4.( ) x, x, C( x) = 8 x + x, R( x) = 6 x - x - 4 x,? P A 8

294 00 ( ) () : 5, 5, B C B B A A D B B C A B D A D SAB C, : 4, 5, 0,. 6.{ x - < x < } 7.5 x - 4 y + 8 = : 5, , ACD CBD ABC. SAC D SCB D = SCB D AC BC = BC AB. tan B = AC BC, cos B = BC A B. AC BC = BC AB B. t an B = cos B. tan B = cos B, sin B + sin B - = 0. sin B = - 5 B = arcsin 5 -. ( ). C A D B 0. a - d, a, a + d, ( a + d) a - d + ( a + d) = 6 a, a + ( a + d) = a = 4 d = 4, d = - 6. a = 9 0, 4, 8, 6 5, 9,,. x, y, - y, 6 - x. a. 8

295 x + ( - y) = y y( 6 - x) = ( - y), x = 0 y = 4, x = 5 y = 9. 0,4,8,6 5,9,,.. ( ) PA ABC, PA P - ABC, ƒ P V P - AB C = PASAB C = 64 = ( ) 8 ( cm ). ABC, A AD BC D, B D C PD, PD BC., PDA P BC AB C. ABC, AB = 4, AD =. tanpd A = PA AD = 6 =, PD A = 60. PB C A BC 60. PA ABC, ABC, AB = AC, PB = AC. BC D, AD PD, PD BC, AD BC, PD A. ABC, AB = 4, AD = tanpd A = PA AD = 6 =, PD A = 60. PB C A BC 60.. ( ) B( -, 0 ), C(, 0), ABC, AB + AC = 8 A( x, y), A B C, 8. x a c =, a = 8, a = 4, b = a - c =. + y b = ( a > b > 0 ). A 0)). x 6 + y = ( ( - 4,0) (4, 84

296 x ( ) 6 + y = y = x + b 7 x + 8 bx + 4 b - 48 = 0. M( x, y )N ( x, y ), x + x = - 8 b 7 x x = 4 b MN = + k x - x = O M N d = b, 8 - b. SMO N = MN d = b = 7 b ( 8 - b ). + (8 - b ) = 8, 8 - b b b = 8 - b, b = 4, SMO N. 4. L( x) = R( x) - C( x) = ( 6 x - x - 4 x ) - ( 8 x + x ) = 8 x - x - 4 x. L ( x) = 8 - x - 4 x = 8-6 x - x, L ( x) = 0, 8-6 x - x = 0, x =, x = - ( ) x = L( ) = =. 85

297 00 ( ) : () ( )., 6, 50, 0. ( 75 ) :.,,..,,,,,..,. 4., tan, cot. 86 : 5 ; 5, 75.,. ( ) 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} ( ) P ( - 5,), cot+ sin ( A) ( ) y = e x ( B) - 7 ( A), (0, + ) ( B), ( -, 0) ( C), ( -, 0) (D), ( -, + ) ( C) (D) -

298 (4 ) y = log (4 x - ) ( A) 4 < x ( B) x ( C ) x > 4 ( D) x 4 (5 ) cos= 5 ( < < ), tan 4 ( A) - ( B) - ( C ) (6 ) : y = b - x, : b = 0, ( A) ( B) ( C) (D) (7 ) 5 4, ( A) 4 ( B)4 ( C ) (8 ) a = (,4 ), b = ( 0, - ), cosa, b ( A) 4 5 ( B) ( C) 5 (9 ),, ( D) ( D) ( D) - ( A) 44 ( B)7 ( C )48 ( D) 6 (0) z = ( sin + icos ), i, arg z ( A ) () 0 < a <, ( B) ( C ) 4 ( A )loga ( - a) > ( B)cos ( + a) < cos ( - a) ( C) a - < ( ) - ( D) ( - a) 0 < a 0 () x = + cos ( ) y = sin 6 5 ( D) 5 ( A ) (, - 5 ), (B) ( -, 5 ), 4 ( C) (, - 5 ), 4 ( D) ( -, 5 ), () x + ( m + ) x + m + = 0 7, m ( A ) - ( B) ( C ) ( D) - (4) x + y + x - 8 y + 8 = 0, P(, 0), ( A )7 x + 4 y - 4 = 0 y = ( B) 7 x + 4 y - 4 = 0 x = ( C)7 x + 4 y + 4 = 0 x = ( D) 7 x - 4 y - 4 = 0 x = (5) f( x) ( 0, + ), f ( - ) = 0, x f ( x) < 0 87

299 ( A ) ( B) ( -, 0 ) ( C) ( 0, ) ( D) ( -, 0 ) (0, ) 88

300 ( 75 ) :. 4, : 4 ; 5, 0.. (6) y = cos x + cos x +. (7) f( t - ) = t - t +, f( x) =. (8), M( -,. 5 ) N (,0 ), (9),. : 5, 55.. ( 0 ) ( ) B,. 8 km. C, A A B = 6. km, AC =. 85km, BA C = 0. B ( ). ( ) ( ) x + bx - = 0 x - x + c = 0, y = x + bx - M, y = x - x + c N, MN. 89

301 ( ) ( ) : ABCD - A B C D, AB =, DB= 5. DA = a, DC = b, DD= c, E CC, CE = CC. ; ( i) DA B E a b c ( ii) DA BE. ( ) ( ) ( ) an+ = an + bn { an } { bn } a =, b = 0,, n =,,,. bn+ = an + bn ( i), { an + bn }. ( ii) { an } { bn }. ( 4 ) ( ) x a + y b =, 0 < b < a, P, F y A B, = PA B, a b,. 90

302 00 () :.,,,..,,,, ;,.., , 75. ( ) B ( ) C ( ) C (4 ) A (5 )B ( 6)D (7 ) C (8 )B ( 9) B (0) D () B () A ()D ( 4 )B (5) D..5, 0. (6) -. ( 7 ) 4 ( x - x + 5 ) ( 8 ) x 4 - y = ( 9 )6 (0),.. : ABC, AB = 6.km, AC =.85km, BAC = 0, BC = cos ( km) : B 4km, ().. : x + bx - = 0 = b + 4 > 0, x x., b = - 4, c = - x + x = - b = - ( - ), x x = - = c y = x - 4 x -, y = x - x -, M(, - 5) N(, - 5 ), MN =

303 (),.. : (i), DA= DD+ D A= c + a, BE = BC + CE = - a + c (ii), DB = AB + BC + CC, 45 = CC CC= a c, ac = 0, DABE = ( c + a) ( - a + c) = - aa + cc = - a + c = = 0. DA BE (),,.. ( ) : (i) cn = an + bn,. {cn }, q 0 cn + = an+ + bn+ = q( an + bn ). an+ + bn+ = an + bn + an + bn = ( + ) an + ( + ) bn, q( an + bn ) = ( + ) an + ( + ) bn, ( + - q) an + ( + - q) bn = 0, n =,, a =, b = 0 a =, b = + - q = 0, + - q = 0, ( + ) = +, = , an+ + bn+ = ( + ) an + ( + ) bn = ( + ) ( an + bn ), a + b = 0, { an + bn } +. { an - bn } -. =. (ii) (i) an + bn = ( + ) n -, an - bn = ( - ) n -, an = [ ( + ) n - + ( - ) n - ], bn = 6 [ ( + ) n - - ( - ) n - ]

304 (4),,,.. : A. F( a - b, 0), a - b ya = b a. a + y b =, A tan= a - a - b b a = a( a - a - b ) b t = b a, 0 < b < a, 0 < t < tan= a a + a - b = + - t < t <, < + - t <, < tan<. arctan < <

305 00 ( ) : () ( )., 6, 50, 0. ( 75 ) :.,,..,,,,,..,. 4., tan, cot. : 5 ; 5, 75.,. ( ) A = { x - < x < }, B = { x x > }, A B ( A) { x < x < } ( B) { x - < x < } ( C) { x x > } ( D) { x x > - } ( ) cos< 0 tan > 0, ( A) ( B) ( C) ( D) ( ), ( A) y = x ( B) y = x ( C) y = log x ( D) y = sin x (4 ) 0 < a < b, ( A) a < b ( B) a > b 94 ( C) log > log b ( D) a < b (5 ) y = f - ( x) y = f ( x), (, - ) y = f ( x), y = f - ( x) ( A) ( -, ) ( B) (, - )

306 ( C) ( -, ) ( D) ( -, - ) (6 ) y = sin xcos x ( A) ( B) ( C) (7 ) : x =, : x - x + = 0, ( A) ( B) ( C) (D) ( D) 4 (8 ), ( A) 0 ( B) 5 ( C) 0 ( D) 5 (9 ) a = (4, x), b = (5, - ), a b, x ( A) 0 ( B) - 0 ( C) 8 5 ( D) - (0) 4,, ( A )70 ( B)6 ( C) 08 ( D) 90 () z = + i, i, z ( A ) 6 ( B) 6 ( C) 8 5 ( D) 5 () x - x - = 0 ( A ) x + x + = 0 (B) x + x - = 0 ( C) x - x - = 0 (D) x - x + = 0 () x = 4cos ( ) y = sin ( A ) x = ( B) x = 6 5 (4) x + y = ( C) x = 7 6 ( A ) (B) ( C) ( D) 4 (D) x = (5) P( 4, 8) x + y - x - 4 y - 0 = 0, 8, ( 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 95

307 ( 75 ) :. 4, : 4 ; 5, 0.. (6) x 64 - y 6 =. (7) f( x) = 0 x +, f (lg). (8) y = - x +, cos. (9) R,. : 5, 55.. ( 0 ) ( ) a b c, b a c, a b c.. ( ) ( ), P L 40, L, A B, APO = 60, BPO = 0.A B km/ h( ), 80km/ h. 96

308 A B O L ( ) ( ) - 5 P y = x + bx + k( b0, k 0) x MN, MN =, y = kx + b M N..! ( ) ( ), S - ABCD S AD S BC, SA B S BC. ( ) ( 4 ) ( ) : ( ) 6 ; (),.. 97

309 00 () :.,,,..,,,, ;,.., , 75. ( ) A ( ) C ( ) B (4 )D ( 5) C ( 6) C ( 7) A (8 ) C ( 9) A ( 0 )B () D () B ( ) A ( 4 ) A ( 5 )B : 4, 5, 0,. (6) 5 4 ( 7 )0 ( 8 ) - ( 9 ) 8 9 R : 5, 55.. (0). : b a c, a = b + c. a b c, q, b = aq, c = aq ( q 0, q ), a 0. 5 a = aq + aq, q + q - = 0, 8 q = -, q =, q,. -. ().. : AB, A BA B. AB = AO - BO = 40t an60-40tan0 = = 80 ( ). 8 98

310 AB V = 80 / ( km/ h ). A B 8km/ h, 80km/ h. ().. : MN P ( - k( - b ( - b + ) ( - b b, 0), P y = kx + b, ) + b = 0, k =. MN =, b +, - b - x + bx + k = 0. - ) = 8 b 4 - =, b =, b =. y = x + x + y = x + y = x - x + y = x -. (),.. : MN BC AD, S - ABCD, SM BC, S N AD, BC AD.S l BC AD, ls BC SA D.SM l, S N l, SBC SAD MSN = 90. A AB CD a, MN = a. SM = S N, SM = S N = a, SB = a + 4 a = a. N D S E ( ) SB E AE SB. SA B SBC, CE SB, AE = CE = SMBC S B = a. 8, SA B S BC AEC. AE C, AC = cosaec = AE + CE - AC AECE AE C = 0. a : = -, AEC, SA B S BC 0. l B M C (4).. : () x 6 + y = ( 0 < < 6 ). 99

311 PQ OP OQ, O. < OP OQ x +, 0 <.P Q OP = 6 sin + 6cos, 6 cos + 6 sin, OQ = PQ = OP + OQ 6 sin + 6cos = = = = = 6 cos + 6sin 6 ( + 6 ) ( cos + 6sin ) ( sin + 6cos ) 6 ( + 6) ( 4 + 6) sin cos + 6 ( sin 4 + cos 4 ) 6 ( + 6 ) ( - 6 ) sin cos Q O y ( 4) 4 ( + 6). 8 ( - 6 ) sin + 4 (), [ 0, ] 4 ( + 6 ) 8. ( - 6 ) sin + 4 = 4, 4 ( + 6 ) ( - 6 ) + 4 8, 4 8,. + 6 P x d, d = 6 -,. 00

312 P6 ( ) 5 P P P7 5 5 P56 ( 8) 5 6 P0 ( ) 5 7 P76 ( ) % 9 P P94 (4 ) 5 P8 ( 9) 5 P P P7 ( 7 ) 5 7 P57 ( ) 5 8 P % 9 P4 (6 ) 5 P7 ( 4 ) P6 4 4 P79 60 % : 00 50,, 75. %

313 () 0,,..... :.,,.: :,,. :,,. :,.. : ; ;. :, ;, ;,. :, ; ;. : ;,

314 ,. ().,..,..,. 4. ; ; (:, ). ().. a 0 ( ar) a + b ab ( a b R) a + b ab( a b 0)..,,,,..., ax + b c ax + b c ().,..,.. ().., =,....,.. 4.,, 5., y = ax + bx + c( a 0) y = ax ( a 0) ;. 0

315 ,,. ()..., n.., n. ()..., ()...,..,. 4.,. 5. n k. 6.,. 7.,. ().,..,.., ().,..,...

316 .. ().,.,. ().,, ( ).... y = Asin x y = sin( x + ) y = sinx y = Asin( x + ) y = sin x,, y = Asin( x + ). 4., arcsin x arccos x arctan x. ().,..,,. ().,, , ().,.., ().,...., 05

317 4.,,. 5.,. 6.. ()......, () ().,..,..,. 4.,..50, 0... ;,. 06 () 50%

318 () ( ) () 5% 0% 5% 50% 0% 40% 0% 50% 0% 07