math e book release2-1.1

1. 2Math E-BookRelease 2.1 http://math.boxchart.com Release 2.0 13 2548Release 2.1 28 2548 ( Release 2.0) 2548 O-NET & A-NET SCIENCE CENTER () 159 ( 15% 135 ) 3/1 . 10200 .. . 0-2225-7160, 0-2221-5884 7-Eleven

2. O-NET/A-NET 3 .+++ + ..2544 4 ( .4 .6) () 14 (..41 ..48) (2532 2548, ) (O-NET / A-NET) :]Math E-Book Release 2.1 ( ) 3. O-NET/A-NET 4 (1) () :]() ( !)(2) () .. 2 ..- . . () - - .- . () . . Science Center - - ( ) , , , - 3 !- Thaiware.com, Boxchart.com, f0nt.com ... [email protected] http://math.boxchart.com :] Math E-Book Release 2.1 ( ) 4. O-NET/A-NET 5ae(eoo O-NET/A-NET) 2549 (Central University Admissions System) 4 1. GPAX . [10%]2. GPA 4-5 [20%]3. O-NET (Ordinary National Educational Test) [35%-40%] 5 ( 2 ) ... O-NET .64. A-NET (Advanced National Educational Test) [30%-35%] ( 3 ) O-NET ( 2 3 ) ... A-NET 3 (1) O-NET A-NET 1 (2) (Short Answer) (3) 1 (O-NET) 2 (A-NET)- | GPA 4% | O-NET 7% | A-NET 20%- | GPA 4% | O-NET 8% | A-NET 10%- | GPA 5% | O-NET 7% | A-NET 10%- | GPA 4% | O-NET 7% | A-NET 10%- | GPA 5% () | O-NET 20%- | GPA 5% | O-NET 14%- | GPA 5% | O-NET 8%- | GPA 4% | O-NET 8%- | GPA 4% | O-NET 7%- | GPA | O-NET 7%- | GPA 5% () | O-NET 7-10% | A-NET (NIETS)http://www.ntthailand.comMath E-Book Release 2.1 ( ) 5. O-NET/A-NET 6 ( O-NET) 1 () 2 ( 2.2 2.5) 3 ( 3.5) 5 ( 5.2 5.5) 7 ( 7.9) 8 ( 8.1) 13 ( 13.1 13.4 ) 16 ( 16.1 16.6) 17 ( 17.5 17.6 ) ( A-NET) 2 13 16 ( 16.4) 17 Math E-Book Release 2.1 ( ) 6. O-NET/A-NET 7a 1 111.1 121.2 - 151.3 21 2 312.1 322.2 362.3 392.4 442.5 48 58 3 593.1 603.2 633.3 653.4 673.5 69 82 4 834.1 : 844.2 : 864.3 : 924.4 : 944.5 : 964.6 : 994.7 : 102 5 1195.1 1205.2 1215.3 124Math E-Book Release 2.1 ( ) 7. O-NET/A-NET 8 5.4 1275.5 131 fog 146 6 147 7 1577.1 1587.2 1607.3 1627.4 1657.5 1667.6 1697.7 1717.8 1727.9 173 8 1878.1 1878.2 1918.3 1928.4 195 () 204 9 2059.1 2069.2 2089.3 2119.4 2159.5 216 10 22710.1 22810.2 23010.3 23110.4 23310.5 23510.6 23710.7 240 : 250Math E-Book Release 2.1 ( ) 8. O-NET/A-NET 9 11 25111.1 25211.2 25411.3 25611.4 259 268 12 26912.1 27012.2 27212.3 274 13 27913.1 28013.2 28213.3 28413.4 285 14 29514.1 29614.2 29814.3 300 306 15 30715.1 30715.2 30915.3 31215.4 31715.5 319 332 16 33316.1 33316.2 33516.3 33716.4 33916.5 34116.6 345 358Math E-Book Release 2.1 ( ) 9. O-NET/A-NET 10 17 35917.1 36017.2 36317.3 37417.4 37817.5 38317.6 388 1 (14 ) 403 | 2541 408 | 2542 417 | 2542 426 | 2543 435 | 2543 444 | 2544 453 | 2544 462 | 2545 471 | 2545 481 | 2546 492 | 2546 502 | 2547 512 | 2547 523 | 2548 532 1 541 (17 )() 1 | 2532 2541 542 2 | 2541 2548 573 : 1 ( 2 ) 588 2 599 : Math E-Book 604 645Math E-Book Release 2.1 ( ) 10. O-NET/A-NET 11{s,e,t}1 e (Set) , 7, 360 , (Element Member) A, B, C { } A , B 7, C 360 , D 7, E 3 33 A {= , , , , , , } (comma)B { 2, 1, 0, 1, 2}= B {0, 1, 1, 2, 2}= C {2, 3, 5}= D {2, 3, 5}= C D= (360 2 2 2 3 3 5= )E {4, 5, 6, 7, ..., 32}= ... Math E-Book Release 2.1 ( ) 11. O-NET/A-NET 12 (FiniteSet) A n(A) n(A) 7= , n(B) 5= , n(C) 3= ,n(E) 29= (Null Set Empty Set) { } n( ) 0 = (Infinite Set) F 2,G 0 1F {1, 0, 1, 2, 3, ...}= , n(F) G { | } G { x | 0 x 1}= < < x () 0 x 1< < () 2 B , 3 C , 0.5 G 2.5 B , 4 C , 0 G (Relative Universe) U U U { 2, 1, 0, 0.5, 7}= U H { x | x 0 }= > H {0, 0.5, 7}= =U H {0, 1, 2, 3, ...}= U (R ) H { x | x 0 }= > H { x | x 0 }= >R1.1 (Subset) B A B A ( B A B A) B A B A B A B A A {m, p, r, w}= B B A 16 {m} {p} {r} {w}{m, p} {m, r} {m, w} {p, r} {p, w} {r, w}{m, p, r} {m, p, w} {m, r, w} {p, r, w}{m, p, r, w}S oae! Sao {a, b} A a A a b AS uio! Seoie{ , 0, 1, {2, 3},(4, 5)}oo 5 a e, e 0,e 1, e {2,3}, aoaa (4,5)aoeae 1 oaaae 1{(1, 2),(2, 1), {1, 2}, {2, 1}}oo 3 a oaa (1,2), oaa (2,1), ae {1,2}(oaa 1-2 a 2-1 oa e1-2 ae 2-1 oeoaaoaaa)eooaeaeeaooa ... ooeaa ia oaa..Math E-Book Release 2.1 ( ) 12. O-NET/A-NET 13 ( 16) n r n n !r (n r)! r ! = x ! 1 2 3 ... x= 7 3 7 7 ! 1 2 3 4 5 6 7353 4 ! 3 ! 1 2 3 4 1 2 3 = = = 1. A 2. A A3. n n2 ... ( 42 16= )4. (Proper Subset) n2 1 ( ) ( A A A A ) ... (Power Set) A P (A) A n P (A) n2 A {m, p, r, w}= P(A) {m} {p} {r} {w} {m, p} {m, r} ... {m, p, r, w}= { , , , , , , , , } . A {a}= 12 2= {a} P (A) { , {a}}= . B {a, b}= 22 4= , {a} , {b} {a, b} P (B) { , {a}, {b}, {a, b}}= . C {2, 3, 5}= 32 8= , {2} , {3} , {5} , {2, 3} ,{2, 5} , {3, 5} {2, 3, 5} P (C) { , {2}, {3}, {5}, {2, 3}, {2, 5}, {3, 5}, {2, 3, 5}}= . D = 02 1= P (D) { }= S uio! So aaaa a { }ao ... (e) eeooe oaoae (iea 0)aeaae { } ooeoo aeoeoooeaeoaa eoe { }eeoo ...ooa o n( ) 0 = n({ }) 1 =S oae! Sao {a, b} P(A) {a, b} Aao a A a b AMath E-Book Release 2.1 ( ) 13. O-NET/A-NET 14 E { , {0}, { }}= P (E) , { }, {{0}}, {{ }}, { , {0}}, { , { }}, {{0}, { }}, { , {0}, { }} { } A, B A {1, 3, 5, 7}= B {1, 2, 3, 4, 5, 6, 7}= . X X P (A) X P (A) X A X 42 16= 4 4 44 41 4 6 4 1 161 40 2 3 + + + + = + + + + = . X X P (A) n(X) 2< X P (A) X A 16 ( .) n(X) 2< ... 4 441 4 6 1110 2 + + = + + = ...( ). Y A Y Y B A Y 1, 3, 5, 7 Y ... Y B 2, 4, 6 Y ( 1, 3, 5, 7 Y B ) ... 2, 4, 6 Y {2, 4, 6} 32 8= 1.1(1) A, B A B A B x A y B (1.1) {x} B (1.3) {A} {B}(1.2) {y} A (1.4) {A} {B}(2) A {{ }, a, b, {a}, {a, b}}= (2.1) { } A (2.3) {{a}, b} A(2.2) { } A (2.4) {a, b} A {a, b} A(3) (3.1) A B B C A C(3.2) A B B C A C(3.3) A B B C A CMath E-Book Release 2.1 ( ) 14. O-NET/A-NET 15(4) A (4.1) { x | x A } {A}= = (4.3) { x | {x} A } {A} =(4.2) { x | x A } A = (4.4) { x | {x} } = (5) (5.1) n(A) 5= A 32 (5.2) n(A) 5= A 32 (5.3) n(A) 5= A 32 (5.4) n(A) 5= A 32 (6) A 511 A 511 5 (7) (7.1) (7.5) P ( ) (7.2) (7.6) P ( ) (7.3) { } (7.7) { } P ( ) (7.4) { } (7.8) { } P ( ) (8) A { , a, {b}, {a, b}}= (8.1) P (A) (8.6) a P (A)(8.2) { } P (A) (8.7) {a} P (A)(8.3) P (A) (8.8) {b} P (A)(8.4) { } P (A) (8.9) {{b}} P (A)(8.5) { , a, {b}} P (A) (8.10) { , a, {b}} P (A) (9) A { , 1, 2, 3, {1}, {1, 2}, {1, 2, 3}}= (9.1) { , {1}, {1, 2}} P (A) (9.3) {{1}, {2}, {3}} P (A)(9.2) { , {1}, {1, 2}} P (A) (9.4) {{1}, {2}, {3}} P (A)(10) [Ent39] S {1, 2, 3, 4, 5, 6, 7}= n(X) n(Y) X { A P (S) | 1 A= 7 A } Y { A X |= A 6 }1.2 - (Venn-Euler Diagram) U ( ) A, B, C S uio! Sae A a B a oiao(eoa) aeoii ooei.. ooiaoa..Math E-Book Release 2.1 ( ) 15. O-NET/A-NET 16UA BUA BUBAACB2 310 45 7911UUA BUA BUBAUA BUA BUBAUAUA BUA BUBAA B A B A B A {0, 1, 2, 3, 4}=B {1, 3, 5, 7, 9}=C {2, 3, 5, 7, 11}= 1. (Union : ) ... A B A B A B B2. (Intersection : ) ... A B A B AB ( ) A B A B A3. (Complement :) A A cA A4. (Difference Relative Complement : )B A B A ... B A B A = B A B A n(B A) n(B) n(A) n(B A) n(B) n(A B) = Math E-Book Release 2.1 ( ) 16. O-NET/A-NET 17 A (B C) (A B) (A C)A (B C) (A B) (A C)A (B C) (A B) (A C)A (B C) (A B) (A C) = = = = (A B) AB (A B) AB P (A) P (B) P (A B)P (A) P (B) P (A B) = = = A B A cup B A B A cap B A, B A {1, 3, 5, 7}= B {1, 2, 3, 4, 5, 6, 7}= ( . . ). Y A Y Y B (A Y B ) ... A Y 1, 3, 5, 7 Y ( A Y = ) {1, 3, 5, 7} 42 1 15 = ... Y B 2, 4, 6 Y ( 1, 3, 5, 7 Y B ) ... 32 8= ... 15 8 120 = . Z {1, 2, 3} Z Z A . ... {1, 2, 3} Z 1, 3 Z( A Z = ) 2 Z (Z A ) ... 22 1 3 = ... Z A 5, 7 Z ( 1, 3 Z A ) ... 22 4= ... 3 4 12 = . Z {1, 2, 3} Z = Z A {1, 2, 3} Z = 1, 2, 3 Z Z A 5, 7 Z ( Z = Z A ) ... 22 4= Math E-Book Release 2.1 ( ) 17. O-NET/A-NET 18C P(C)2 4 60 C { } 0 {{ }, 0} { , {0}} {{ , {0}}}= { , , , , , } . n(P (C)) n(C) 6= 6n(P (C)) 2 64= =. n(P (C) C) n(P (C) C) 64 6 58 = ... C P (C) n(P (C) C) C P (C) ( ) ... { } C ( C ) C ... 0 !... {{ }, 0} C () { } C 0 C ... { , {0}} {0} C ... {{ , {0}}} { , {0}} C C () C P (C) 4 n(P (C) C) 64 4 60 = =. n(C P (C)) n(C P (C)) 6 64 ... P (C) C . 4 n(C P (C)) 4 = ... n(C P (C)) 6 4 2 = = ( .) n(C) 6= n(P (C)) 64= . n(C P (C)) 4 = (.) n(C P (C)) 2 = (.) n(P (C) C) 60 =. n [(P (C) C) (C P (C))] . . () 60 2 62+ =( ) 1.2(11) A B {0, 1, 2, 3, 4, 5} = A B {1, 3, 5} = B C {2, 3, 5} =A C {0, 1, 2, 3, 5} = A C {0, 3, 5} = . A B{0} = . B C{1} = . A C{1} = . B A{2, 4} =(12) CB { x | 1 x 10 }= < R[2] (Transitive Property) a b b c a c> > >[3] a b a c b c> + > +a b a c b c , c 0> > >a b a c b c , c 0> < + >a c b c a b , c 0> > >a c b c a b , c 0> < [6] a b a b ()[7] a b c a b< < ( , a) { x | x a }< ( , a] { x | x a }< ( , ) R* 23 25 2x a x b 2 2(a , b )- a 0 0 ( 0 ) 2a 2b x ( 4, 3) x 1, 0, 1 ... 0 9, 16 ... 2x [0, 16) : x 2x () 2 a x b< < c y d< < xy ac, ad, bc, bd ... xy x ( 1, 3) y ( 5, 4) xy 5, 4, 15, 12 ... xy ( 15, 12) 1/5, 1/4, 3/5, 3/4 ... x / y ( 3/5, 3/4) x y+ (a c, b d)+ + ( ) x y (a d, b c) y d y c < < ... xMath E-Book Release 2.1 ( ) 40. O-NET/A-NET 41-3 0 1 1 2 2 2- + - + - + - +-3 0 1 2-3 0 1 1 2 2 2- + - + - + - +-3 0 1 1 2 2 2 (Equality) (Inequality) ( > < ) S oaoaaa1. oaooo aaooa eo2. oaooo oaaeoeeooaoo oaeo/o3. aee aoao eaaeaeooi (oaeaoaeoo)1. ( > ) 1 2 31 2(x c )(x c )(x c )...0(x d )(x d )... > 23(x 3)(x 1)0x(x 2)+ >2. 1 2 3 1 2c , c , c , d , d , ... () 3. +, -, +, - + 4. + ( 1 2x d , d , ... )5. () x [ 3, 0) {1} (2, ) * 2 ( 2) 2 x ( -1 /) (x+1)(3-x) > 0 (x+1)(x-3) < 0 S uio! Seooaoaaaa.. eeaaee 0 e (x-2)(x-3) = 0 a x = 2, 3o ..eo (x-2)(x-3) < 0ae x < 2, 3 e!ooeeaaa!Math E-Book Release 2.1 ( ) 41. O-NET/A-NET 42-1 3 4- + - +-1 3 4- + - + 2x 2x 194x 4+ = ( x 4 0 x 4 ) 2x 2x 19 4(x 4)+ = ... 2x 2x 3 0 = (x 1)(x 3) 0+ = ... { 1, 3} 2x 2x 194x 4+ < x 4 < 4 ... 2x 2x 194 0x 4+ < 2x 2x 30x 4 < (x 1)(x 3)0x 4+ < ( x 4 ) ... ( , 1] [3, 4) (2B B 4AC2A ) ( ) 2(x 1)(x 3)(x 2x 2)0x 4+ + +< (The Axiom of Completeness) (Least Upper Bound Axiom) S {0, 1, 2, 3, 4, ...}= 0 0.5 1.8 S 0 (a, b) (a, b] [a, b] b ( , b) ( , b] b (a, ) [a, ) ( , ) R R Q S uio! Seaaoeoo oaaa.. aooo ex2+x-3 < 0 1 1 122 +ee aoo ,1 13 1 132 2 + Math E-Book Release 2.1 ( ) 42. O-NET/A-NET 43 2.3(21) (21.1) (a b)(b c)(c d) 0 > a b c d> > >(21.2) a b< n N n na b , b 0> a b a bab2+>(21.4) a 0> , b 0> a b 2 2b a 1 1a ba b+ > +(22) a b c< < (22.1) a ba b2+< < (22.3) 3 3 3a b c< + m n+(30) a b 22x 4x 5 0+ > (30.1) {ab} {a, b} (30.2) {a b} {a, b}+ (31) 3 2x a x a 2+ x 1 5 a Math E-Book Release 2.1 ( ) 43. O-NET/A-NET 44(32) (32.1) x(x 1)(x 2)0(x 1)(x 2) (32.3) 32(x 4)(x 1)(x 2){ x | 0 } x (x 5)+ + >(33) 3 2x x 4x 4 0 + >(34) A 3 2x 2x 5x 6+ +(36) A 2x 50x 2+> B 2x 11x 5+ a S 2a 1+ (38) (38.1) 2{ x | x 7 }< (38.3) ( 2, 6] [3, 8) (38.2) { 1, 5, 7, 9 } [6, ) (38.4) { x 2n | n }= I(39) a nA { x | x , n }n 1+= = +I b 1B { x | x , n }n= = I a b+(40) 22x 5x 2 5 + [2] a a= a b b a = [3] ab a b=nna a=[4] aab b= b 0[5] 2 22a a a= =[6] a b a b+ +< a b a b >* [7] n n nnn n a ,aa ,=== ( )* [1] x b= 2 2x b= () x b= x b= ()* [2] x b x b< x b> x b> x b< x b> 3 x 1 = 3 x 1 = 3 x 1 = 3 x 1 = ... x 2= x 4= ... {2, 2, 4, 4} 3 x 1 < 3 x 1 < ... 1 3 x 1 < < ... 3 4 x 2 < < 2 x 4< < [ 4, 2] [2, 4] 1. 2x 1 x 2 x 3+ = + ... 2 2 S uio! Soia ex 2 x+ = .. x 2 x+ = o x 2 x+ = eoiaoao a (ao) aooeoaa eaoai a..eo ex 2 x+ < ! x x 2 x +< < eao ... ioaoiaoaa..Math E-Book Release 2.1 ( ) 45. O-NET/A-NET 46-1/2 2-1/2 2x < -1/2-1/2 < x < 2x > 2-1/2 2x < -1/2-1/2 < x < 2x > 2 x x 1/2< , 1/2 x 2 ( : )2. ... 3 3 ( ) ( ) x 3x 3 x 3x 3 = + = += -2x - 1 -x + 2 (2x 1) ( ) x 33x 1 x 3x 2+ = + = +=-x + 2 (2x 1) (x 2) x 3x 3 x 30 0+ = ++ = +=3. () () ( : 0 0= 3 0> 1 0= 3 0< )x 3= x 2> x { 3} [2, ) 2.4(41) (41.1) n + I n 1> nn a a=(41.2) a, b 0> a b a b = (42) m (42.1) 4x 0.5 m+ < 3 2x 1 0.5 < (21.2) 2 1 < 2( 2) < 21(21.3) ... (a b) / 2 ab+ >2 2a b 2 ab a 2ab b 4ab + > + + >2 2 2a 2ab b 0 (a b) 0 + > >( a b )Math E-Book Release 2.1 ( ) 51. O-NET/A-NET 52x2 2h x+h+ - +3 2 3 2 ++ - +1/2 2/3+ - +4 5/2+ - +3/2 7/3+ - +1 3.5 1 3.5 +(21.4) ... 3 32 2b a b aaba b+ +>3 3b a ab(b a) + > +(b a) + 2 2(b ab a ) ab(b a) + > +2 2 2b 2ab a 0 (b a) 0 + > >( a b )(22.1) (22.2) ... ( min maxx X x < < )(22.3) ( 3x ) (22.4) b 0= ab bc=(23.1) 27 x 5 0 x 49 < < 3.5 1.8 a 0, b 2= = . {0} {0, 2} . { 2} {0, 2} Math E-Book Release 2.1 ( ) 52. O-NET/A-NET 53+ - +2 3-1 0 1 2 2- + - + - +-2 1 1 3+ - + - +-4 -2 3- + - +-4 -1 0 2 5 5+ - + - + - +-2 1 2- + - +-3 -1 2- + - +-5 -3 -1 2-1 1/3 1- + - +-1 0 2 2 8- + - + - ++ - +-2 5/2+ - +-5 6+ - +5 2+ - +-1/2 3+ - +1/2 2-1/2 1/2 2 3(31) 3 2(1) a (1) a 2 5+ >2a a 6 0 (a 3)(a 2) 0 > + > a ( , 2) (3, ) (32.1) ( , 1) (0, 1) (32.2) AB(AB ) A B [ 4, 1) (1, ) = = [ 4, ) {1} (32.3)| 3 | | 2 | | 0 | | 1 | | 5 | 11 + + + + =(33) (x 1)(x 2)(x 2) 0 + > [ 2, 1] [2, ) (34) 3 2x 2x 5x 6 0+ 224x 4 x 4x 40(x 2) (x 1)+ + +>2 22 2x 8x x 8x0 0(x 2) (x 1) (x 2) (x 1) + + +> > 40x 2> x 2 > (2, 8](36) 2x 5A ; 0x 2+>2x 1 2x 1 x 5B; 1 0 0x 5 x 5 < + +x 5 x 50 0x 2 x 2 + > 1 53 ( )2 2+ =Math E-Book Release 2.1 ( ) 53. O-NET/A-NET 54-1 1. . .3 4. . .-2/3 0. . .-2/3. .(41.1) nn n n a ,aa ,=== (41.2) a 0, b 1= = |a b| 1, |a| |b| 1 = = (42.1) 3 2x 1 0.5 2 2x 1.5 < < < (x 1)(x 1)0x +> ( 1, 0) (1, ) ( 1, 0). x 0> 21 x 1x 0 0x x++ > >() (0, ) (0, ) ( 1, 0) (0, ) 2x x 2 0 (x 2)(x 1) 0 < + < ( 1, 2)x ( 1, 0) (0, ) x ( 1, 2) x ( 1, 0) (0, 2) (49.4) . x 1< 3 3x xx 1 2 x 1 + < +>( 1, 1) . x 1> 3 3x x 0x 1 2 x 3 < () 21 4 3 21 3 21[ , 3) [ , )2 2 + 3 21[1, 3) [ , )2+ 3 21( 1, 3) [ , )2+ (49.5) . x 0< x x2 2 0x 1 x 1 < x x2 2 0x 1 x 1 < x 2x 4 0 x 2 2x 8 02++ + + < x x 7 0 7< < 7B ( , )2= A B ( , 2] = ... (A B) (2, ) = (51) 2x |4x 5|< + |4x 5| 10+ < 2x |4x 5|< + . x 5/4< 2x 4x 5 6x 5 x 5/6< < < ( , 5/4) . x 5/4> 2x 4x 5 5 2x x 5/2< + < > [ 5/4, ) x R |4x 5| 10+ < 10 4x 5 10 15 4x 5 + < < < ( , 4) (0, ) (54.3) |x 7| 5 < |5x 25| 5 >. |x 7| 5 < 5 x 7 5 < < 2 x 12< 5x 25 5 > 5x 25 5 < x 6> x 4< . . (2, 4) (6, 12)(54.4) 4 . x 1< x 1 x 3 x 5 1 x ( 1, 1) + + < + < . 1 x 3 22x 5x 41x x 2 + 2 22x 5x 4 x x 20x x 2 ++ >( 6x 2) (3x 1)0 0(x 2)(x 1) (x 2)(x 1) ++ + > < ( , 2) [ 1/3, 1) . 22x 5x 41x x 2 + < 2 22x 5x 4 x x 20x x 2 + + + |x 3| |x 2| < 2 2 2 2 2(x 3) (x 2) (x 3) (x 2) 0 < < (x 3 x 2)(x 3 x 2) 0 + + < ( 1)(2x 5) 0 (1)(2x 5) 0 < > x 5/2> ( , 1/2) (5/2, ) (56.1) . x 0< 2(1 x)(1 x) 0 (x 1) 0+ + > + > x 1= () ( , 1) ( 1, 0) . x 0> (1 x)(1 x) 0 (x 1)(x 1) 0 + > + < ( 1, 1) [0, 1) ( , 1) ( 1, 1) (56.2) (1, )( x 1= 1 (1 |x|)(1 x) + )(57) 3 29 8 9 4 6 = 1 3 2(4x 1) (58x 2) x 3 2( 1) ( 2) 4 = x 5 3 2(19) (288) 5 4 ... 4 5 1(58) ... 252=34(7)+14 .....() 34=14(2)+6 .....()14=6(2)+2 .....() 6=2(3) (... 2) ,, =....... () 14=252+34(-7) () 6=34+14(-2)() 2=14+6(-2) () () 2 =14+(34+14(-2))(-2) =14(5)+34(-2) () 2 =(252+34(-7))(5)+34(-2) =252(5)+34(-37) 2 = 252(5) + 34(-37)(59) ...-504=-38(14)+28...() 28=-504+(-38)(-14)-38=28(-2)+18....() 18=-38+28(2)28=18(1)+10....() 10=28+18(-1)18=10(1)+8....() 8=18+10(-1)10=8(1)+2.... () 2=10+8(-1) 8=2(4) (... 2) () () 2=10+(18+10(-1))(-1)=10(2)+18(-1) ... () 2 =(28+18(-1))(2)+18(-1) =28(2)+18(-3) ... () 2 =28(2)+(-38+28(2))(-3)=28(-4)+(-38)(-3) ... () 2 =(-504+(-38)(-14))(-4)+(-38)(-3) 2 = (-504)(-4) + (-38)(53)(60) x 128 16 384 x 48 = =(61) ... 9 3 3= ... 28,215 3 3 5 11 57= x y 9 x 3 3 5 11 495= =y 3 3 57 513= =(62) ... 1=x y 1 15,015 3 5 7 11 13 = = x 2 80 x 200< < x 13 7= x 13 11= y 3 5 11 165= = y 3 5 7 105= =Math E-Book Release 2.1 ( ) 57. O-NET/A-NET 585 14 . 00 0022 5 14 . 00 0022 5 14 . 00 004122 5 14 . 00 0044 1 142 2 .2 5 14 . 00 00442 1 1484302 2 .2 5 14 . 00 00442 1 148444 30 002 2 . 62 5 14 . 00 00442 1 1484446 30 0026 763 242 2 . 6 72 5 14 . 00 00442 1 1484446 30 0026 764527 3 24 003 16 89.... ....(1)(2)(3)(4)(5)(6)(7)(8)eo ..(1) 514 514 2 14 5 ( ) 2 ( 00 00 )(2) ( 5) ( 5) 2 2 ... 2 (3) 2 2 4 ... 4 5 1(4) () 2 4 ... ( 14) 114(5) x 4x x 114 ( 114)... 41 1 41, 42 2 84, 43 3 129 () 42 2 ... 2 ( 4) 2 42 2 84 114 ( 30)(6) (4) (5) (22) 44 ( 00) 30 3000(7) x 44x x 3000 ( 3000) ... 446 6 6 ( 44) 6 446 6 2676 3000 ( 324)(8) (226) 452 ( 00) 324 32400 x 452x x 32400 ( 32400) ... 4527 7 ... 7 ( 452) 7 4527 7 31689 32400 ... 514 22.67... 514 2 5,14 2 () 903601 3 90,36,01 3 ... 225, 3000, 214.7 :]Math E-Book Release 2.1 ( ) 58. O-NET/A-NET 59~lgc3 (Logic) () (Truth Value) (Proposition Statement) , , 1 2, , , p, q, r 2 (True;T ) (False; F )S uio! Saoeoea aea ... e1. uo eoaeeiiia ioe ea!2. eai oaea eaea e aaoaioe a(eaoia aoe aao 3.4 a..)Math E-Book Release 2.1 ( ) 59. O-NET/A-NET 603.1 () (Connectives)... (and), (or), - (if-then), (if and only if) (not) ... ~ (Negation) p qp q(p q )p q(p q ) p q(p q )p q(p q ) p(~ p )T T T T T T FT F F T F F FF T F T T F TF F F F T T T T T F F - T F - (Truth Table) 2n n ... 1 2, 2 4 (), 3 8 2 (Equivalent) ( ) () p (q r) (p q) (p r) p (q r) (p q) (p r) p q ~ p q ~ q ~ p p q (p q) (q p) ~(p q) ~ p ~ q ~(p q) ~ p ~ q ~(p q) p ~ q ~(p q) ~ p q p ~ q Math E-Book Release 2.1 ( ) 60. O-NET/A-NET 61 3.1(1) p T p T p T p T p F p F p F p F p p p p p p T p p p ~ p p ~ p p F p ~ p p p p ~ p (2) p , r q (2.1) [(p s) (p r)] (p s) (2.2) [(q s) r] [(q s) r] (2.3) [(r q) (p q)] (p ~ q) (2.4) [(p q) (q r)] ~ s (2.5) [(q p) r] ~(~ r) (2.6) [(p q) ~ r] [(~ p q) r] (2.7) [(p ~ q) ~ r] [(p q) (~ q r)] (2.8) [(p q) ~ r] [(r ~ s) (~ p ~ q)] (2.9) [p (q r)] [(q p) r] (2.10) [q (p r)] [p (q ~ r)] (2.11) [(~ p ~ q) (~ r ~ s)] [(~ p r) (s ~ q)] (3) (3.1) (p ~ q) (p q) q (3.2) (p ~ q) (p q) p (3.3) (~ r p) (~(r s) (r ~ q)) p , q r , s (3.4) (p q) (s p) (s q) p , r , r q (3.5) (~ q (p r)) (~ r) p q , q r (3.6) n [(m q) ~ s] q n (3.7) (p r) q p q , q r (3.8) (q p) (r s) (p q) (r s) , q s (3.9) [Ent25] r s (p r) (q s) , p q (3.10) (p r) ~ q (p ~ r) (p q) (3.11) p , q , r (p q) (p r) (3.12) r p (p ~ r) (q r) (3.13) ((p ~ q) ~ p) (p q) (3.14) [ ]p ~(r s) (~ r ~ s)~ p Math E-Book Release 2.1 ( ) 61. O-NET/A-NET 62(4) [(p q) (p r)] (s r) . [(p q) (q r)] (r s) . [(~ p q) (~ q r)] (~ r s) (5) [(p q) (r ~ s)] [(~ p r) (q ~ s)] . ~(p s) ~ r . r (p ~ q) . (s r) (p q) (6) p q r s . [(p ~ q) (r ~ s)] [(~ p q) (~ r ~ s)] . [(p r) (q s)] [(p ~ q) (r ~ s)] (7) . (p ~ q) (~ r s) . (p ~ q) ~ r (8) . . . . (9) . p q ~(~ p ~ q) . ~(p ~ q) ~ q ~ p. ~ p (q p) ~ q p . ~ p q (~ p q) (q ~ p) (10) (10.1) p q. (p q) (q ~ p) . (~ q ~ p) (~ q p) . (p ~ q) (q p) . (p ~ q) (~ p ~ q) (10.2) [ ]((q ~ t) p) ((q ~ t) ~ p) r~ q . q ~ t p . (t q) p . t q r . (t q) r . (t r) p (10.3) [(q r) (p s) (q ~ r)] [(q ~ r) (p ~ s) (q r)] . p q . p q. p q . p q(11) a 0 . a 0> b 0> ab 0 b 0> ab 0>. ab 0< a 0> b 0>. ab 0> a 0 2x x ] , Q(x) x= 3 x 1 . x [P(x)] U (0, 1). x [Q(x)] { }2, 3, 5, 8= U(30) 3 2x(x 5x 1 4) x( 0 x 2)x 1 + < < >(31) N 2[ x(x 1 2) x(x 1 0)] x 0x + < >(32) { }1, 0, 1= U(32.1) 2 2x(x 1) x(x 1) (32.2) 2x(x 1 0) x(x 1) + > (32.3) 2x(x 1 0 x 1) + > (32.4) 2x(x 0) x(x 0) > =(32.5) 2x(x 0 x 0) > =(33) { }1, 0, 1= U(33.1) 2x y (x y 2) + >(33.2) 2x y (x y 2) + >(33.3) 2x y (x y 2) + >(33.4) 2x y (x y 2) + >S uio! Sao 32.2 a 32.3 iieoaaaea a some e ao 32.2 eii oeoeoa ao 32.3 eoiee x eaaa oeaea...ao 32.4 a 32.5 ieoaeaa all e ouiaoaaaall a a, some a oMath E-Book Release 2.1 ( ) 68. O-NET/A-NET 69(34) [Ent21] { }1, 0, 1= (34.1) 2 2x y(x y y x) = (34.2) 2 2x y(x y y x) = (34.3) 2 2x y(x y y x) = (34.4) 2 2x y (x y y x) = (34.5) 2 2x y (x y y x) (35) (35.1) x y (x y y x) { }2, 0, 2= U(35.2) x y (x y 0) + = { }2, 2= U(36) x y (xy 1) x y (xy y) = = . . . . (37) +R . x y [x y xy] + > . x y [x y 0] + (38) (38.1) x [P(x) ~ Q(x)] (38.2) x [P(x) (Q(x) R(x))] (38.3) [ ]P(x)~ x x [Q(x)] (38.4) x y [(x y 5) (x y 1)] + = =(38.5) x y [x 0 y 0 xy 0] > < xy z). [Ent38] x [x 6] x [x 8] < > x [x 6] x [x 8] 3.5 (Reasoning) 2 ( ) (Inductive Reasoning) Math E-Book Release 2.1 ( ) 69. O-NET/A-NET 70 ... , , 1. A {2, 4, 6, 8, 10, ...}= 2 12, 14, 16, ... ()2. 1 1= , 1 3 4+ = , 1 3 5 9+ + = , 1 3 5 7 16+ + + = , 1 3 5 7 9 25+ + + + = n 2n3. 1, 3, 7, 15, 31, ... 2, 4, 8, 16 63 ( 32)4. 11 11 121 = , 111 111 12321 = , 1111 1111 1234321 = 11111 11111 123454321 =5. 3 12 , 51, 96 , 117 , 258 , 543 , 2930 ,5022 , 7839 3 3 3 1. ... ( ) 4 (n 1)2(n 1) 2 + > n n 1, 2, 3, 4= 4 1, 9 2, 16 4, 25 8> > > > n 7, 8, 9, ...= 2n n 5 + n n 1, 2, 3, 4= 2n n 5 5, 7, 11, 17 + = n 5= 2n n 5 25 + = 2. ... ( ) 100 22 70 3. ... ( )Math E-Book Release 2.1 ( ) 70. O-NET/A-NET 71 ( ) (Deductive Reasoning) ... 2 10 2 10 1. (1) ... (2) 2. (1) ... (2) * 3. (1) ... (2) * (valid) ... 1. (1) ... (2) ( )2. (1) ... (2) ( )3. (1) ... (2) ( ) (-) ( ) ( ) ( ) S uio! Sooa aio..euiaaeo oeu(eoao 3.3) e euaaeiaaa eoeuuoeiei aei ...eeoeueuoeeuea eoioaiaa!Math E-Book Release 2.1 ( ) 71. O-NET/A-NET 72. . A BA BC . . ( )1. (1) (2) ... 2. (1) (2) ... ( 2 )3. (1) (2) ... 4. (1) (2) ... 2 3 * ! 3.5(40) a (40.1) 1, 3, 5, 7, a (40.5) 3, 1, 1, 3, a (40.2) 2, 7, 12, 17, a (40.6) 1 2 3 4, , , , a2 3 4 5(40.3) 1, 2, 3, 4, a (40.7) 1, 4, 9, 16, a(40.4) 3, 6, 12, 24, a (40.8) 3, 3 3, 3 3 3, 3 3 3 3 , a(40.9) [ ..47] 125, 726, a, 40328, 362889Math E-Book Release 2.1 ( ) 72. O-NET/A-NET 73(41) 2 ( )(41.1)37 3 11137 6 22237 9 333 = = =(41.5)11 11 12111 12 13211 13 143 = = =(41.2)9 9 819 99 8919 999 8991 = = =(41.6)1089 1 10891089 2 21781089 3 3267 = = =(41.3)1 9 11 212 9 111 3123 9 1111 4 = = = (41.7)2 (3) 3 (3 1)2 (3) 2 (9) 3 (9 1)2 (3) 2 (9) 2 (27) 3 (27 1)= + = + + = (41.4)9 9 7 889 98 6 8889 987 5 8888 + = + = + =(41.8)3 4 2 (1 2 3)4 5 2 (1 2 3 4)5 6 2 (1 2 3 4 5) = + + = + + + = + + + +(42) -(42.1) (42.2) (42.3) (42.4) (42.5) (42.6) (42.12) (42.7) (42.13) (42.8) (42.14) Math E-Book Release 2.1 ( ) 73. O-NET/A-NET 74(42.9) (42.15) (42.10) (42.16) (42.11) (42.17) ()(1) p | F | p | FT | p | p | Tp | T | T |~ p | T |~ pp |~ p | T | F(2) 2.6 2.10 (3) 3.5, 3.7, 3.9,3.12 (3.11) T, T, F(4) . . (5) (6) . . (7) .(p q) (~ r ~ s) . p ~ q r (8) . (9) .(10.1) . (10.2) .(10.3) . (11) .(12) (13) (14.1) . (14.2) .(15) 3:5(16 19) 16.1, 16.2, 17.2, 17.7, 19.1(20) . . (21) (22) (23) (24.1) s r (24.2) r(25) (26) .(27) . (28) .(29) . . (30) (31) (32) 32.1, 32.4 (33) 33.1 (34) 34.2, 34.4 (35.1) (35.2) (36) . (37) .(38.1) x [P(x) Q(x)] (38.2) x [P(x) Q(x) ~ R(x))] (38.3) [ ]P(x)x x [Q(x)] (38.4) x y [(x y 5) (x y 1)] + = (38.5) x y [x 0 y 0 xy 0] = (38.6) x y (xy 0 x 0 y 0) > > >(38.7) x y [P(y) ~ R(x) Q(x)] (38.8) x y z (x y z + < xy z)>(39) . . (40.1) 9 (40.2) 22 (40.3) 5(40.4) 48 (40.5) 5 3(40.6) 5/6 (40.7) 25(40.8) 3 3 3 3 3 (40.9) 5047(41.1) 37 12 444 = , 37 15 555 =(41.2) 9 9999 89991 = ,9 99999 899991 =(41.3) 1234 9 11111 5 = ,12345 9 111111 6 = (41.4) 9 9876 4 88888 + = ,9 98765 3 888888 + =(41.5) 11 14 154 = , 11 15 165 =(41.6) 1089 4 4356 = ,1089 5 5445 =(41.7) 2 (3) 2 (9) 2 (27)+ +2 (81) 3 (81 1)+ = ,2 (3) 2 (9) 2 (27) 2 (81)+ + +2 (243) 3 (243 1)+ = (41.8) 6 7 2 (1 2 3 = + + +4 5 6)+ + , 7 8 2 (1 = +2 3 4 5 6 7)+ + + + +(42) (42.3), (42.5), (42.6),(42.9), (42.13)Math E-Book Release 2.1 ( ) 74. O-NET/A-NET 75 ()(1) . T p p ... ( T T T, T F F )F p F ... p p p ... p ~ p F ... (). ( )T p T, F p p, p p p, p ~ p T . -T p p, F p T, p T T, p F ~ p ( T F F, F F T )p p T, p ~ p ~ p . T p p, F p ~ p, p p T, p ~ p F ( 1 )(2.1) [(p s) (p r)] (p s) T T T(2.2) [(q s) r] [.....] T T(2.3) [(r q) (p q)] [.....] T F F(2.4) [(p q) (q r)] ~ s T T(2.5) [(q p) r] r T T T T(2.6) [(p q) ~ r] [(~ p q) r] F F F TT F(2.7) [(p ~ q) ~ r] [(p q) .....] F T F .T F(2.8) (p q) ~ r [... ...] F F(2.9) [p (q r)] [.....] F F(2.10) [q (....)] [p (q ~ r)] F F T F .T F(2.11) [(~ p ....) (~ r ....)] [.....] T T T(3.1) (....) (p q) T TT(3.2) (....) (p q) T F .T(3.3) (~ r p) (....) T T(3.4) r q T r q (p q) (s p) (s q) T T T T T(3.5) p T, q F, r T (~ q (p r)) (~ r) F T T F(3.6) n F n [....] T (3.7) q F (....) q F (3.8) q F, s F, r T, p F (q p) (....) T F(3.9) p r T, q s F ( q F, s F )p q T p F r T r s T F F (3.10) p q F p T, q F (....) ~ q T T(3.11) p q T p T, q T p r F r F(3.12) p T, p ~ r T r F(3.13) (3.14) p, q, r, s ( p, q, r, s ) ... (3.13) ( -)((p ~ q) ~ p) (p q) FT FT F p q ... p q Math E-Book Release 2.1 ( ) 75. O-NET/A-NET 76 ... (3.14) ( -)[ ]p ~(r s) (~ r ~ s)~ p FT FT T r s ... r s [ ]p ~ p ... (4) s r F s T, r F p r T p Tp q T q T. [(....) (q r)] (r s) F F F. [....] (~ r s) T T(5) p q T p qr ~ s F r F, s T [(~ p r) ....] T F . ~ (....) ~ r T T. r (p ~ q) T F F. (s r) (p q) T T(6) p q , r ~ s . [.... (r ~ s)] [.... (~ r ~ s)] T T T . . [....] [(p ~ q) (r ~ s)] T T T(7) . ~ [(~ p ~ q) (r s)] (p q) (~ r ~ s) . ~ [~ (p ~ q) ~ r] (p ~ q) r (8) p , q , r (p q) r p q T, r F . p ~ q F . ~ p q F . ~ r ~ q F . p ~ r T .(9) . ~ (~ p ~ q) p q ... . (~ p q) (q ~ p) ... . p (~ q p) ~ q p q p .... .(10.1) . . (p q) (q p) (10.2) {[(q ~ t) (p ~ p)] ~ q} r T[(q ~ t) ~ q] r [(q ~ q) (~ t ~ q)] r T(~ t ~ q) r (t q) r .(10.3) [(q r) (q ~ r)] [(p s) (p ~ s)] [q (r ~ r) (p (s ~ s)] q p F T .(11) . . ab 0, a 0, b 0> < < ... . . (p q) r . (~ p ~ q) ~ r . ~ r (~ p ~ q) (12) . p (q r) . (~ q ~ r) ~ p . ~ p q r . . . (13) . ~ (p ~ r) ~ q ~ p r ~ q q (r ~ p) . p (q r) ~ p (~ q r) q (p r) ~ q ( ~ p r) . (p q) r ~ p ~ q r (p ~ q) (p r) ~ p ~ q ~ p r (14.1) p q p*p q*q (p*p)*(q*q)TTFFTFTFFFTTFTFTTFFF p q .(14.2) F*F ... ( T,T,T,F) p q ~(p q) ... . ~ (~ p q) ~(p q) Math E-Book Release 2.1 ( ) 76. O-NET/A-NET 77(15) p q r q*r p*(q*r)TTTTFFFFTTFFTTFFTFTFTFTFFFFTFFFTFFFFTTTF : 3:5(16.1) (p q) [(p q) r] FT FT T T T F (16.2) (p q) [(p q) r] FT FT T T T F (16.3) [(p q) (q r)] (p r) FT T FT T F F T F q (16.4) [(p r) (q r)] [(p q) r] FT T FT T T T T T F r (16.5) [(p r) (q r)] [(p q) r] FT T FT FF F F F F F p q p q (16.6) [(p r) (q s) (p q)] (r s) FT T T FF F F F T T F F p , q ... (16.7) [ ](p q) r (p r)(p q) FT T FT F F T T T F q (17.1) ~(p ~ q) ~(~ p ~ q) p q (17.2) (~ p q) p (~ p p) (q p) Tq p (17.3) (p q) ~ p (p ~ p) (q ~ p) Fq ~ p (17.4) (p q) (p q) (q p) (~ p q) (~ q p) (17.5) (p q) (p q) ~ (p q) ~(p q) (~ p ~ q) (~ p ~ q) (17.6) ~ p (q r) (~ p q) (~ p r) (p q) (p r) (17.7) ~ p ~ q r ~ (~ p q) r (p ~ q) r (17.8) p q r TTTTFFFFTTFFTTFFTFTFTFTFTFFTFTTFTFFTFTTF (18.1) [(p r) (q r)] (p q) FF FF F p q r r (18.2) [(~ p q) ~ p] (p q) FF FF T T T F q (19.1) (p ~ p) (q ~ q) F F T () ()(19.2) [p T] [~ p F] p ~ p F Math E-Book Release 2.1 ( ) 77. O-NET/A-NET 78(19.3) p q ~ p ~ q ~ (p q) (~ p ~ q) ~ F ... (20) p, q, r . (p q) (~ p ~ q) FT FF T F T . (p q) (~ p q) . ~((p q) r) (~(p q) ~ r) FT FF F F F F T r . (~ p r) (~ q r) (~ p ~ q) r (p q) r . (~ p q) (~ p r) ~ p (q r) p (q r) . . (21) (22.1)(22.2) p (r s) ~ p r s (23.1) 1. p q2. (p q) r3. ~ (s r)4. p s(23.2)1. p ~ q2. r s3. r q4. ~ s p(24.1)1. p (q r)q (p r)3. qp r2. s p s r(24.2)1. ~ p q2. q ~ r~ p ~ rr p3. p 3. r(25)1. p ~ q2. q ~ p (26)1. p q2. ~ p r3. s ~ r4. ~ q ? ~ s . ~ s p . ( ). s p. ~ r ~ s ~ r ( r ). p ~ q(27) . x 2x > 0 x 0=. x 2= 8 4, 2 4> (0, 1)...=U . x ... x ... 3 x 1 ... 2, 3, 5 , 8 ... 3 1 . .(30) 3x (x 5x 1 4) + < x 1= 7 4 < 2x(|x 1| 0 x 2) < > F T T T T (31) 2x(x 1 ) x 2= 22 1 3 = x(x 1 0) + > ( + 1 0 )2x( 0)x < x 1= 21< 0 (T T) F F (32.1) 2x(x 1) x 0= ,2x(x 1) x 1= , T F F (32.2) x(x 1 0) + > x 0=2x(x 1) T T T (32.3) x(x 1 0 + > 2x 1) x 0= T(32.4) 2x(x 0) > x 0=x(x 0) = x 1= F F F (32.5) 2x(x 0 > x 0)= (x 1, 0, 1= ) T(33.1) x y 2x y 2+ > x 1, y 1= =(33.2) x y x 1 y 0= = x 0 y 0= = x 1 y 0= = (33.3) x y x 0= y (33.4) x y x 0, y 0= = (34.1) x 1, y 1= = 2 0(34.2) x y x 0, y 0 x 0, y 1 x 1, y 1= = = = = = (34.3) x y x 1= y 1= x 0= y 1= x 1= y 1= (34.4) x y (34.5) x y x 0, y 0= = x 1, y 1= = x 1, y 1= = (35.1) x y (y x= )(35.2) x y x 2, y 2= = , x 2, y 2= = (36) . x y(xy 1) = x 2= y I x y(xy y) = x 1= xy y= y F T F . x y(xy 1) = x y(xy y) = ( .) F T F . x y(xy 1) = x 0= y R x y(xy y) = () F T F . x y(xy 1) = x + R y + R x y(xy y) = () T T T ... .Math E-Book Release 2.1 ( ) 79. O-NET/A-NET 80 . (37) . x 10, y 5= = 15 50>. x, y 0< . x y ( x y x> ). x y y x> .(38.1) x [P (x) Q(x)] (38.2) x [P (x) Q (x) ~ R(x))] (38.3) [ ]P (x)x x [Q (x)] (38.4) x y [(x y 5) (x y 1)] + = (38.5) x y [x 0 y 0 xy 0] = (38.6) x y (xy 0 x 0 y 0) > > >(38.7) x y [P (y) ~ R(x) Q (x)] (38.8) x y z(x y z + < xy z)>(39) . . x[x 6] x[x 8] < 0 () m < 0 () m = 0 x y m [2] [2.1] 1 1(x , y ) m 11ymx=yx 1 1y m ( x ) = y x[2.2] 1 1(x , y ), 2 2(x , y ) (2.1) 2 11 12 1y yy ( x )x x = y x[2.3] (Intercept) Intercept Form 1a b+ =x y a, b x y x (a,0) y (0,b) a, b Math E-Book Release 2.1 ( ) 86. O-NET/A-NET 871. (Common Form) A B C 0+ + =x y2. 3 Slope-Intercept Form m c= +y x c ySlope-Point Form 1 1y m ( x ) = y xIntercept-Intercept Form 1a b+ =x y3. A C-B B= y x AmB= CcB= P(1, 3) Q(5, 9). P Q PQ9 3m 3/25 1= =. 1L PQ PQ 1L PQ L12m3= ( 1 ) PQ 1 5 3 9( , )2 2+ +... (3, 6) 1L 2(y 6) (x 3)3 = ... 3y 18 2x 6 = + ... 2x 3y 24 0+ = 5L y (0, 1/3) x 1/2 6L ( 1, 2) 5L. 5L 6L L51/3m 2/31/2= = 6L 5L L6m 3/2= : x 1/2 x ( 1/2, 0). 5L 6L ... 5L x y11/2 1/3+ = 2x 3y 1 = 6L 3(y 2) (x 1)2 = + 3x 2y 1+ = (1/13, 5/13)S uio! Seoaao -A/B a i x y eoia aoao Ax+By+C=0 oeo aa..Math E-Book Release 2.1 ( ) 87. O-NET/A-NET 88Ax+By+C1=0Ax+By+C2=0d2 122C CdA B=+Ax+By+C=0d1 122A x B y CdA B+ +=+P (x1,y1)[3] [4] 1L : 2x 3y 24 0+ =. S( 2, 5) 1L SL1 2 22( 2) 3(5) 24 13d 13132 3 + = = =+. 1L 2 13 1L () 2x 3y C 0+ + = C 2 224 C2 132 3 =+... 26 24 C = C 2, 50= 2x 3y 2 0+ + = 2x 3y 50 0+ =. 2L : 2x y 6 0+ = 1L 2 13 1 1(x , y ) 1 12 22x 3y 242 132 3+ =+ ... 1 1(x , y ) 2x y 6 0+ = ... 1 12x y 6 0+ = 1x 8, 5= 1x 8= 1y 22= 1x 5= 1y 4= ... ( 8, 22) (5, 4) . 2L . . 1L 2 13 3L 3x y 2 3+ = 4L 3x 3y 18+ =. 3L A/B ... 3/1 3 = . 4L x 4L 3/ 3 3 = (y : x ) 3S oaa! Saoaeaoeo Ax+By+C=0 eo... a A,B ooeoa oeoaoaaMath E-Book Release 2.1 ( ) 88. O-NET/A-NET 89m21 21 2m mtan1 m m =+m1Ans1Ans2L: Ax+By+C=0P1 (x1,y1)Q1P2 (x2,y2)Q2L: Ax+By+C=0P (x1,y1)Q x 60( : ). 3L 4L 3L 4L ( . .) 2 122C CdA B=+... A, B 4L 3 3x y 6 3+ = L3L4 2 26 3 2 3 4 3d 2 323 1= = =+... 3L 4L 2 3 3 . 3L , x , y 0 (0, 0) x y ... x y x ( y 0= ) 2 y ( x 0= ) 2 3... (1/2) (2) (2 3) 2 3 = [5] 1 1 1 2 2 22 2 2 21 1 2 2A x B y C A x B y CA B A B+ + + +=+ + () [6] (Projection) P L Q 1 2PP L 1 2Q QMath E-Book Release 2.1 ( ) 89. O-NET/A-NET 90 ( P L ) ( P ) 1 1P (x , y ) y x= ( 45 x ) 1 1 1 1x y x yQ ( , )2 2+ + 4.2(17) A (1, 2), B (2, k), C (3, 4) k(18) (1, y) PR P ( 2, 6) R (4, 2) y(19) AB x y x 4 y 3 AB 3 A B(20) A (4, 5), B (1, 2), C (2, 8), D ( 2, 4) AB CD (21) D ABCD A ( 4, 1) , B ( 5, 4) , C (1, 2)(22) (k, 7) , ( 3, 2) (3, 2), (1, 4) k(23) A (1, 5) B (3, 6) C (m, 4) D ( 1, m) m(24) C (5, 6) L ( 3, 1) L(25) ABC A (1, 7), B (8, 6), C (7, 1)(26) (7) (27) (3, 0) (0, 2)(28) L ( 2, 5) (1, 3) x y (29) (6, 8) x 3x 4y 12+ =(30) ABCD A (1, 2), B ( 2, 1) , C ( 3, 6) , D (2, 5) P P (31) 2x 3y 10 0+ + = x y 1+ = 2x y 5+ =Math E-Book Release 2.1 ( ) 90. O-NET/A-NET 91(32) x 3x 4y 5 0 + = y (33) L 2x 3y 5 0+ + = (1, 5) L x (34) M 3x 3y 5 7 + = N 2x 5y 7 4 + = L M y N(35) 1L (2, 2) ( 2, 0) , 2L 1L ( 2, 0) 3L x 4/3 y 4 (36) 1L 2x 3y 6 0 + = , 2L ( 2, 3) 1L 3L (2/3, 1) 1L 2L 3L (37) A (3, k) 1 4 L A x L(38) L A ( 1, 2) B (2, 1) PQR , x , y . PQR 6 3 2+ . PQR 4.5 (39) ABC A ( 2, 5) , B (4, 8), C (2, 3) x y (40) x y (1, 3) (41) ( 2, 4) X-intercept Y-intercept 9 x (42) [Ent24] L 0.5 C ( 3, 0) y A AB L B y B x C BC (43) ABC B A ( 3, 5) , C (4, 4) , AB 3/2 (44) 2x 3y 6 = 4x 6y 25 = (45) C Ax 2y C 0+ + = 3x 4y 5 0 = Math E-Book Release 2.1 ( ) 91. O-NET/A-NET 92(46) 1L 2L 4 L 12x 5y 15 0 = 1L 1L , 2L x 1L 2L(47) A ( 2, 1) , B (5, 4) , C (2, 3) A BC(48) L 5x 12y 3 k + = L P ( 3, 2) 4 k (49) 2x 4y 15 = 3x 4y 10+ = 3 (50) 5x y 0 = 2x 3y 1 0 + =(51) 1L ( 3, 2), (0, 1) 2L (2, 3), (1, 4) 1L 2L(52) 1L (2, 3), (1, 0) 2L O 1L C 1L 2L 30 CO(53) 3x 4y 1 0+ + = 4x 3y 6 0 =(54) A ( 2, 1) x B ( 5, 6) y AB(55) A (1, 0), B ( 5, 8) , P AB Q B x 1= PQ PQ(56) ( 2, 1) x y 0 =(57) (0, 7) 4x 5y 6 =4.3 : (Conic Section) () 1. ()2. ()3. ()4. 2 ()Math E-Book Release 2.1 ( ) 92. O-NET/A-NET 93 (Circle) (Ellipse) (Parabola) (Hyperbola) x y , , [1] (Translate Shift) f (x, y) 0= f (x h, y-k) 0 = h, k h k ( (h, k) )[2] () (Scale) y f (x)= my f (nx)= m, n 1 ... n m ( m, n 1 ) h, k yxOy = x2yxy = (x-3)2(3,0)yxy+1 = x2(0,-1)yxy+1 = (x-3)2(3,-1)yxOy = x2yx3y = x2yxy = (2x)2yxy/4 = x2 1 3 1 2 4 Math E-Book Release 2.1 ( ) 93. O-NET/A-NET 94 1. * 2. () [3] () (2) (Flip) h, k ( x , y )4.4 : (Center; C ) (Radius; r ) () C (0, 0) r 2 2 2x y r+ = C (h, k) 2 2 2(x h) (y k) r + =yx2y = (x-3)2-2 2(y+1)=(x-3)2 (3,-1) 1 2yxOy = x2yx (3,-1) -(y+1) = (x-3)22 2 2(x h) (y k) r + = C (h, k) r 2 2x y Dx Ey F 0+ + + + =C(h,k)rMath E-Book Release 2.1 ( ) 94. O-NET/A-NET 95 (1, 2) (2, 1) 2 2Ax By Dx Ey F 0+ + + + = (1, 2) (2, 1) 2 21 3 10+ = 2 2 2(x h) (y k) r + = 22 2 2 2 2 2(x 1) (y 2) 10 x 2x 1 y 4y 4 10 x y 2x 4y 5 0 + + = + + + + = + + = 2 2x y 2x 4y 10 0+ + = x y 2 2(x 2x) (y 4y) 10+ + = () 2 2(x 2x ) (y 4y ) 10+ + =+ 1 + 4 + 1+ 4 2 2(x 1) (y 2) 15+ + = ( 1, 2) 15 1. 2 2x y Dx Ey F 0+ + + + = (h, k) ( D/2, E/2)= 2.1 3 D, E, F h, k, r 3 3 2 2x y Dx Ey F 0+ + + + = 2.2 r 2 h, k h, k r 2 2 2(x h) (y k) r + = () () 1 1P (x , y ) Q 4.4(58) (58.1) (x 4)(y 3) 1 1 + = =xy(58.2) y x 1 2= + =y x(58.3) 2 2 2 2x y 2x 4y 5 9 k+ + + = + =x yCQP (x1,y1)2 21 1 1 1d x y Dx Ey F= + + + + 2 2 21 1d (x h) (y k) r= + ddMath E-Book Release 2.1 ( ) 95. O-NET/A-NET 96(59) (59.1) (3, 4) (1, 1)(59.2) (1, 1) (2, 2)(59.3) y 2x= (1, 1)(59.4) ( 6, 3) , (2, 3) ( 2, 7)(59.5) (1, 5) 2 2x y 2x 2y 8 0+ + = 2 2x y 3x 3y 8 0+ + =(60) (0, 1) 2 23x 3y 11x 15y 9+ + + = (61) (61.1) 2 2x y 8+ = (2, 2)(61.2) 2 2x y 17+ = 4[Hint: ](61.3) 2 2x y 16+ = ( 1, 8)[Hint: ](62) [Hint: ](62.1) 2 2 2(x 2) (y 1) 1 + + = 2 2(x 6) (y 2) 4 + = 1(62.2) 1 , y x 2= + , 2 2x y 4x 2y 1 0+ + + =(62.3) 2x 3y 21 0 + = ,3x 2y 6 0 = , 2x 3y 9 0+ + =(63) k 2 2x y 6x 8y k 0+ + + = (64) [Ent32] k 0> y kx= 2 2 2x y 14x 49 k+ + =(65) C 2 2x 4x 2 (y 8y 9)+ + = + + OC OC (66) [Ent38] 4/3 2 2x y 4x 2y 4+ + = A B D ( 1, 2) ABD(67) P (x, y) 2(x 1) (1 y)(1 y) = + A ( 1, 0) 4.5 : (Focus; F ) (Directrix; ) (Axis)Math E-Book Release 2.1 ( ) 96. O-NET/A-NET 97 (Vertex) V (0, 0) c 2x 4 c y= ( y , c , c ) 2y 4 c x= ( x , c , c ) V (h, k) 2(x h) 4 c(y k) = 2(y k) 4 c(x h) = (Latus Rectum) 1. 2. 3 ( D, E, F h, k, c ) (1, 2) (2, 1) 2 2Ax By Dx Ey F 0+ + + + = 2(x h) 4 c(y k) = (h, k) (1, 2)= 2(x 1) 4 c(y 2) = + c (2, 1) x, y ()2(x h) 4 c (y k) = V (h, k) c 4c 2x Dx Ey F 0+ + + =2cV (h,k)F (h,k+c)Directrix : y=k-cccAxis :x=h ()2(y k) 4 c (x h) = V (h, k) c 4c 2y Dx Ey F 0+ + + =V(h,k)F (h+c,k)Directrix :x=h-c2ccAxis : y=kcMath E-Book Release 2.1 ( ) 97. O-NET/A-NET 982(2 1) 4 c(1 2) 4 c 1/3 = + = ... 2(x 1) (1/3)(y 2) = + 2 23(x 2x 1) y 2 3x 6x y 1 0 + = + + = (h, k) (2, 1) r 2x 2x 2y 3 0 = 2y () x y 2(x 2x) 2y 3 = + ... 2(x 2x ) 2y 3 = ++ 1 + 1 2 2 2(x 1) 2y 4 (x 1) 2(y 2) (x 1) 4(0.5)(y 2) = + = + = + (1, 2) (1, 2 0.5) (1, 1.5) + = y 2 0.5 2.5= = ( 2y 5 0+ = )( ) 4.5(68) (68.1) ( 2, 3) (5, 3)(68.2) O ( 3, 6)(68.3) O ( 4, 6) x (68.4) (2, 3) (8, 2.1) x(68.5) (5, 2) (3, 0) y(68.6) (2, 2) x 2 0+ =(68.7) (1, 3) , (9, 1) , (51, 2) x(68.8) ( 2, 3) , (3, 18), (0, 3)(69) P (4, 3) 22x 3y 0+ = (70) (70.1) 2x 12y 0 =(70.2) 2y 10y 12x 61 0 + + =(70.3) (4, 2) x 1 0 =(70.4) x (0, 1/3) (0, 7/6)(71) P (x, y) (71.1) y 4= ( 2, 8)(71.2) x 4= (3, 1) 5 (72) 24y (x 1)= 13 x Math E-Book Release 2.1 ( ) 98. O-NET/A-NET 99(73) 2x y 8 = 2y 8x= (74) (1, 6) 2y 4x 4y 8 = (75) y 5= 2 2x 6x 6 2y y = (76) x y= 2 2x y 6x 0+ + = x (77) 2y 4y 8x 20 + = P, P , (78) 6 8 4.6 : ( 1 2F , F ) (2a) C (0, 0) 2a 2b 2 2x y1a b + = ( x) 2 2y x1a b + = ( y) ()2 22 2(x h) (y k)1a b + = C (h, k) 2a 2b 2 2c a b= 2 2Ax By Dx Ey F 0+ + + + =V2 F2bacF1(h+c,k)V1(h+a,k)C(h,k)B1 (h,k+b)B2Math E-Book Release 2.1 ( ) 99. O-NET/A-NET 100 (Major Axis) ( 1 2VV ) (Minor Axis) ( 1 2B B )1. x, y 1 2. a b> a ()3. 4 4 ( 4 ) (2, 1) (2, 4) (2, 4) 2 2Ax By Dx Ey F 0+ + + + = x y ... 2 22 2(y k) (x h)1a b + = a ( 4) (1) 5= = c (4) (1) 3= = 2 2b 5 3 4= = (h, k) (2, 1)= a, b 2 22 2(y 1) (x 2)15 4 + = 2 2 2 216(y 1) 25(x 2) 400 16(y 2y 1) 25(x 4x 4) 400 + = + + + =2 225x 16y 100x 32y 284 0 + = 2 27x 16y 28x 96y 60 0+ + + = 2x 2y 1 2 2 2 2(7x 28x) (16y 96y) 60 7(x 4x) 16(y 6y) 60+ + = + + = ... 2 27(x 4x ) 16(y 6y ) 60+ + = + 4 +9 + 28 + 144 ... (28 7 4= , 144 16 9= ) ()2 22 2(y k) (x h)1a b + = C (h, k) 2a 2b 2 2c a b= 2 2Ax By Dx Ey F 0+ + + + =V2F2bacF1(h,k+c)V1 (h,k+a)C (h,k) B1 (h+b,k)B2Math E-Book Release 2.1 ( ) 100. O-NET/A-NET 101 2 27(x 2) 16(y 3) 112+ + = 112 2 2(x 2) (y 3)116 7+ + = ( 2, 3) a 4, b 7= = c 16 7 3= = ( 2 4, 3) ( 2 3, 3) ( 2, 3 7) 4.6(79) (79.1) (3, 1) y 8 6 (79.2) (0, 8) (0, 5)(79.3) ( 4, 2) (2, 2) 4 (79.4) ( 2, 1) ( 2, 4) ( 6, 1)(79.5) (2, 1) (2, 4) c : a 2 : 5=(80) (80.1) 2 24x 9y 36+ =(80.2) 2 29x 5y 54x 50y 26 0+ + =(80.3) 2 25x 9y 10x 40+ =(81) P (x, y) (81.1) (4, 0) ( 4, 0) 12 (81.2) (2, 7) (2, 1) 10 (82) 6 10 (82.1) (82.2) x (83) [Ent39] 2 24x 9y 48x 72y 144 0+ + + = 3x 4y 5+ =(84) [Ent37] 45 x 2 2x 3y 4x 2 0+ = (85) [Ent38] 1F 2F 2 2kx 4y 4y 8+ = y B x 1 2FF B 3 7/4 k (86) 4 1 80 . Math E-Book Release 2.1 ( ) 101. O-NET/A-NET 1024.7 : ( 1 2F , F ) (2a) C (0, 0) 2a 2b2 2x y1a b = ( x ) 2 2y x1a b = ( y ) (Transversal Axis) 1 2VV (Conjugate Axis)1 2B B (Asymptote) 1. a b ( )2. a b= () (Rectangular Hyperbola) ()2 22 2(x h) (y k)1a b = C (h, k) 2a 2b 2 2c a b= +2 2Ax By Dx Ey F 0+ + + + =F2 V2bca V1(h+a,k)C(h,k)B1 (h,k+b)B2F1(h+c,k)Asymptotea(y-k)=b(x-h)Asymptote ()2 22 2(y k) (x h)1a b = C (h, k) 2a 2b 2 2c a b= +2 2Ax By Dx Ey F 0+ + + + =F2V2bcaV1 (h,k+a)C (h,k) B1 (h+b,k)B2F1 (h,k+c)Asymptoteb(y-k)=a(x-h)AsymptoteMath E-Book Release 2.1 ( ) 102. O-NET/A-NET 1031. () .2. 2 2Ax By Dx Ey F 0+ + + + + =Cxy C 0 4 ... abc cba (2, 1) (2, 4) (2, 4) 2 2Ax By Dx Ey F 0+ + + + = x y ... 2 22 2(y k) (x h)1a b = a (4) (1) 3= = c ( 4) (1) 5= = 2 2b 5 3 4= = (h, k) (2, 1)= a, b 2 22 2(y 1) (x 2)13 4 = 2 2 2 216(y 1) 9(x 2) 144 16y 9x 32y 36x 164 0 = + = x 1 2 29x 16y 36x 32y 164 0 + + = 2 2x 5y 10y 25 0 + = 2 2x 5(y 2y) 25 = ... x x 2 2x 5(y 2y ) 25 =+ 1 - 5 ... 2 2x 5(y 1) 20 =( ) 20 22(y 1)x120 4 = () (0, 1) a 20, b 2= = c 20 4 4= = ( 20, 1) ( 4, 1) (0, 1 2) (Eccentricity; e ) e c / a= e 0 1 ( e ) e 1 ( e )S ei! S a u eoo c uaa a2=c2+b2aa c2=a2+b2Math E-Book Release 2.1 ( ) 103. O-NET/A-NET 104 xy k= k 4.7(87) (87.1) ( 3, 1) (2, 1) 6 (87.2) ( 1, 6) ( 1, 4) 6 (87.3) (0, 4) (0, 4) (3, 0)(88) (88.1) 2 29x 4y 36 =(88.2) 2 29x 16y 18x 64y 199 0 =(88.3) 2 26x y 36x 2y 59 0 + =(88.4) 2 26x 10y 12x 40y 94 0 =(89) P (x, y) P (x, y) (3, 0) ( 3, 0) 4 xy k= k 0> C (0, 0) 1V ( k, k)2V ( k, k) 1F ( 2k, 2k)2F ( 2k, 2k) F2V2V1C (0,0)F1xy k= k 0> C (0, 0) 1V ( k, k)2V ( k, k) 1F ( 2k, 2k)2F ( 2k, 2k)F2V2V1C (0,0)F1Math E-Book Release 2.1 ( ) 104. O-NET/A-NET 105(90) [Ent32] P (x, y) 4x 3y 11 = 4x 3y 5+ = 144/25(91) (91.1) xy 4= (91.2) xy 2x y 3+ =(92) [Ent32,36] 2 29x 18x 16y 64y 199 = + + 3x 4y 8+ = (93) [Ent34] 1F 2 26x 10y 12x 40y 94 0 = 4 1F (94) [Ent39] 2 29(x 1) 4(y 2) 36 = x 8 (95) [Ent37] E 2 26x 5y 12x 20y 4 0+ + = E , E , E (96) (96.1) 2 2x y 6x 8y 12 0+ + = (96.6) 2 23x 3y 9x 6y 20 0+ + =(96.2) 2 2x 2y 2x 4y 13 0+ + = (96.7) 2 23x 3y 9x 6y 20 0 + =(96.3) 2x 2x y 3 0+ + = (96.8) 2 23x 2 y 4y = +(96.4) 2 2x y 2x 2 0 = (96.9) 2 23x 2 y 4y = +(96.5) 2 2x y 4 = (96.10) 23x 2 4y = ()(1) 61 (2) 2(3) 5 (4) (5) 2 (9 2 34) +(6) 3 10 (7) (8) (29/4 , 0) (9) (4, 3)(10) 41 26 17+ +(11) 3 (12) 10(13) 72 , (5, 4) (14) 15(15) (16) 31(17) 3 (18) 2(19) ( 4, 6),(8, 3) (20) (21) (2, 3)(22) 30 (23) 2(24) 8/5 (25) 10(26) ... (27) 2x 3y 6+ =(28) 1/48 (29) y 4 x 16= (30) 5 (31) 2x 3y 1 0+ + =(32) (0, 20/9) (33) ( 7/3, 0)(34) y x 3/5= + (35) 10(36) ( 2, 3) , 2Q (37) 16/3(38) (39) y (11/2)x 1= + ,a 2/11= , b 1=(40) x 2y 7 0+ =(41) 1/2, (6, 0) 4, ( 3, 0)(42) 7.5 (43) 19.5(44) 13/2 (45) 0 , 5(46) 11/12 41/12 2.5 + =(47) 40/ 58(48) 88 16 72 + = (49) (2, 11/4) , (8, 1/4)(50) 45 (51) 75(52) 3(53) x 7y 7 0 = 7x y 5 0+ =(54) y 3x 6= +(55) 4x 3y 20 0 + = ,3x 4y C 0+ + =(56) ( 1/2, 1/2) (57) (4, 2)Math E-Book Release 2.1 ( ) 105. O-NET/A-NET 106(58.1) (4, 3) (58.2) ( 1, 2) (58.3) ( 1, 2)(59.1) 2 2x y 6x 8y 12 0+ + =(59.2) 2 2x y 3x 3y 4 0+ + =(59.3) 2 2x y 4x 2y 0+ + =(59.4) 2 2x y 4x 6y 3 0+ + =(59.5) 2 2x y 3x 3y 8 0+ + =(60) 3 (61.1) x y 4+ =(61.2) 4x y 17 = (61.3) 4x 3y 20+ = , 12x 5y 52 = (62.1) 2 2(x 2) (y 2) 4 + =(62.2) 2 2(x 2) (y 2) 1 + = , 2 2(x 1) (y 1) 1+ + + =(62.3) 2 2(x 1) (y 2) 13+ + = (63) k 25 4 3(65) 2 2x 4x 2 (y 8y 9)+ + = + + 2 2(x 4x 4) (y 8y 16) 2 9 4 16+ + + + + = + +2 2 2(x 2) (y 4) 3 + + + = C( 2, 4) OC 4y x y 2x2= = OC 2 0 4 0(h, k) ( , ) ( 1, 2)2 2 + + = = 2 2 2 2r 1 2 5 (x 1) (y 2) 5= + = + + + =2 212 (6,2)(2,-1)(h,k)Math E-Book Release 2.1 ( ) 113. O-NET/A-NET 114(66) 2 2x y 4x 2y 4+ + = (2, 1) 4y 1 (x 2)3+ = A(0.2, 1.4) B(3.8, 3.4) 0.2 1.41 23.8 3.40.2 1.41ABD2 = 1(0.68 7.6 1.4 5.32 3.4 0.4)2= + + + + 9= .(67) 2(x 1) (1 y)(1 y) = + 2 2 2 2 2(x 1) (1 y ) (x 1) y 1 = + =() ... (x, y) ( 1, 0) (x, y) ( 1, 0) r = (x, y) (1, 0) r 1= + 2 2 2 2(x 1) y 1 (x 1) y+ + + = + 2 2 2 2 2 2x 2x 1 y 2 (x 1) y 1 x 2x 1 y+ + + + + + + = + +2 22 (x 1) y 4x 1 + + = 2 2 24(x 1) 4y 16x 8x 1 + + = + +2 212x 4y 3 = (68.1) x c 7=2(y 3) 4(7)(x 2) = +2y 28x 6y 47 0 =(68.2) x c 3= ( 1 : 4 y)2 2y 4( 3)(x) y 12x 0 = + =(68.3) x x ... 2y 4cx= ( 4, 6) c36 4c( 4) 4c 9 = = 2 2y 9x y 9x 0= + =(68.4) x y ... 2(x 2) 4c(y 3) = + (8, 2.1) c36 4c(0.9) 4c 40= = 2(x 2) 40(y 3) = +2x 4x 40y 116 0 =(68.5) y 2(x 5) 4c(y 2) = + (3, 0) c4 4c(2) 4c 2= = 2(x 5) 2(y 2) = +2x 10x 2y 21 0 + =(68.6) Directrix : x 2, F(2, 2)= x, (0, 2) [] c 2= 2(y 2) 4(2)(x) =2y 8x 4y 4 0 + =(68.7) 2x y Dx Ey F 0 + + + = D, E, F (1, 3),(9, 1), (51, 2)2(3) D(1) E(3) F 0+ + + = ..... (1)2(1) D(9) E(1) F 0+ + + = ..... (2) 2( 2) D(51) E( 2) F 0 + + + = ..... (3) 1 19D , E 6, F2 2= = = 2 1 19y x 6y 02 2 + =22y x 12y 19 0 + =(68.8) y 2x Dx Ey F 0+ + + = D 2, E 1, F 3= = = 2x 2x y 3 0+ + =(69) 2 2 32x 3y 0 x y2+ = = 2 3x 4( )y8 = V(0, 0) 3(0, )8 2 23 1,4654 (3 )8 8+ = (70.1) 2x 4(3)y= (0, 0) y F(0, 3), 4(3) 12= = , y 3 y 3 0= + =(0,3)(-2,3)(3,18)Math E-Book Release 2.1 ( ) 114. O-NET/A-NET 115(70.2) 2y 10y 25 12x 61 25 + = +2(y 5) 4( 3)(x 3) = + x V( 3, 5), F( 6, 5), 12,= x 3 3 0= + = ( y)(70.3) Directrix: x 1= (4, 2) , c 3= F(7, 2)(70.4) 1 7V(0, ), F(0, )3 6 ,7 1 3c ( )6 3 2= = 2 3 1x 4( )(y )2 3 = + x; y 0 2 3 1x 4( )( ) 2 x 22 3= = = ( 2, 0),( 2, 0)(71.1) y 4= Directrix, F( 2, 8) y ( F Directrix) V( 2, 2)c 6 = 2(x 2) 4(6)(y 2)+ = 2x 4x 24y 44 0 + =(71.2) x 4= F(3, 1) 5 Directrix: x 4 5 1= + = x V(2, 1) c 1 = 2(y 1) 4(1)(x 2) = 2y 4x 2y 9 0 + =(72) 2(x 1) 4(1)(y) = y, V(1, 0) F(1, 1) F(1, 1) 13 (a, b) 2 213 (a 1) (b 1)= + ..... (1) 2(a 1) 4b = ..... (2) b 12, 14= b 12 a 1 4 3= = (a, b) (1 4 3, 12)= + (1 4 3, 12) b 14,= ( a ) x 12 (73) (8, 8) (2, 4) 2 26 12 180 6 5= + = = (74) 2y 4y 4 4x 8 4 + = + +2(y 2) 4(1)(x 3) = + x, V( 3, 2) F( 2, 2) 6 2y 6 ( )(x 1) 4x 3y 14 01 2 = + =+(75) 2 2(x 6x 9) (y 2y 1) 6 9 1 + + + + = + +2 2(x 3) (y 1) 16 + + = C(3, 1) Directrix: y 5,= F(3, 1) y V(3, 2) c 3 = 2(x 3) 4( 3)(y 2) = 2x 6x 12y 15 0 + =(76) (0, 0) ( 3, 3) 2 x (0, 0) 2(y) 4c(x)= ( 3, 3) c9 4c( 3) 4c 3 = = 2 2y 3x y 3x 0= + =(77) 2y 4y 4 8x 20 4 + = + +2(y 2) 4( 2)(x 3) = x, V(3, 2), F(1, 2) x 3 2 5= + = P(5, 2) (0, 0),(1, 2),(5, 2) D, E, F 2 2x y Dx Ey F 0+ + + + = (59.4),(59.5) 1D 6, E , F 02= = = 2 2 1x y 6x y 02+ + = 2 2 1 1 1(x 6x 9) (y y ) 92 16 16 + + + + = + 1 145916 16= + =(78) (0, 0) 2y 4cx= c (6, 4)16 4c(6) =16 2c24 3 = = 23= (4,2)x=1(6,4)(6,-4)Math E-Book Release 2.1 ( ) 115. O-NET/A-NET 116(79.1) C(3, 1), a 4, b 3, = = y2 22 2(y 1) (x 3)14 3+ + =2 29(y 1) 16(x 3) 144 + + =2 216x 9y 96x 18y 9 0 + + + =(79.2) C(0, 0), V(0, 8) a 8= y, F(0, 5) c 5=2 2b 8 5 39 = = 2 22 22y x1 64x 39y 2496398+ = + =(79.3) V( 4, 2),(2, 2) x C( 1, 2) a 3 =2 22 2(x 2) (y 1)13 2 + + =2 24(x 2) 9(y 1) 36 + + =2 24x 9y 16x 18y 11 0 + + =(79.4) C( 2, 1), F( 2, 4) y C 3 ,= ( 6, 1) B( 6, 1) 2 2b 4, a 3 4 5= = + = 2 22 2(y 1) (x 2)15 4 ++ =2 216(y 1) 25(x 2) 400 + + =2 225x 16y 100x 32y 284 0 + + =(79.5) C(2, 1), V(2, 4) y a 5 ,= c : a 2:5= c 2=2 2b 5 2 21 = = 2 22(y 1) (x 2)1215 + =2 221(y 1) 25(x 2) 525 + =2 225x 21y 100x 42y 404 0 + =(80.1) 36 2 2x y19 4 + = x2 2(a 3, b 2 c 3 2 5)= = = = C(0, 0), V(3, 0),( 3, 0),F( 5, 0),( 5, 0), B(0, 2),(0, 2) (80.2) 2 29(x 6x 9) 5(y 10y 25) + + +26 81 125= + +2 29(x 3) 5(y 5) 180 + = 180 2 2(x 3) (y 5)120 36 + = y (a 6, b 20, c 4)= = = C(3, 5), V(3, 5 6)F(3, 5 4), B(3 20, 5) (80.3) 2 25(x 2x 1) 9(y ) 40 5 + + = +2 25(x 1) 9y 45 + = 45 2 2(x 1) y19 5 + = x (a 3, b 5, c 2)= = = C(1, 0), V(1 3, 0), F(1 2, 0), B(1, 5) (81.1) F(4, 0),( 4, 0) xc 4, C(h, k) (0, 0)= = 12 2 2a 6 b 6 4 20= = =2 22x y1206+ =2 25x 9y 180 + =(81.2) F(2, 7),(2, 1) yc 3, C(h, k) (2, 4)= = 10 2 2a 5 b 5 3 4= = = 2 2(y 4) (x 2)125 16 + =2 225x 16y 100x 128y 44 0 + =(82.1) ()(82.2) 6 2c c 3= =10 2a a 5 b 4= = =2 22 2x y15 4+ =2 216x 25y 400 + =(83) 2 24(x 12x 36) 9(y 8y 16) + + + +144 144 144= + +2 24(x 6) 9(y 4) 144 + + = C(h, k) (6, 4)= (6, 4) 33x 4y 5 (m )4+ = = L4 4m y 4 (x 6)3 3= + = 4x 3y 36 0 =Math E-Book Release 2.1 ( ) 116. O-NET/A-NET 117(84) 2 2(x 4x 4) 3(y ) 2 4 + + = +2 22 2 (x 2) y(x 2) 3y 6 16 2 + = + = x C(h, k) (2, 0), c 6 2 2= = =F(2 2, 0) (4, 0) = (0, 0) (4, 0) (0, 0) 45 xd 4 sin 45 = 2 2= (85) 2 2 1kx 4(y y ) 8 14+ + = +2 21kx 4(y ) 92 + =22221(y )x 2 1(3 / 2)(3 / k) + = x 2 2 9 9c a bk 4= = 3 7 1 9 9 3(2 ) ( )4 2 k 4 2 = = 9k4 =(86) C(h, k) (0, 0)= 2 22 2x y12 1+ = P 80 . x 1.2= 2 22 2(1.2) yy 12 1 + =y 0.8 = 80 .(87.1) C( 3, 1), V(2, 1) xa 5,= 6 b 3= 2 22 2(x 3) (y 1)15 3+ =2 29x 25y 54x 50y 169 0 + + =(87.2) F( 1, 6),( 1, 4) yC(h, k) ( 1, 1) c 5= = ... 6 2 2a 3 b 5 3 4= = =2 22 2(y 1) (x 1)13 4+ + =2 216y 9x 32y 18x 137 0 + =( -1 2 29x 16y 18x 32y 137 0 + + = )(87.3) F(0, 4),(0, 4) yC(0, 0), c 4= ... B(3, 0) 2 2b 3 a 4 3 7= = =2 22y x17 3 =2 29y 7x 63 0 =( 2 27x 9y 63 0 + = )(88.1) 2 29x 4y 36 = 36 2 2x y14 9 = x,a 2, b 3 c 4 9 13= = = + = C(0, 0), V( 2, 0), F( 13, 0), B(0, 3) (88.2) 2 29(x 2x 1) 16(y 4y 4) + + +199 9 64= + 2 29(x 1) 16(y 2) 144 + =2 2(x 1) (y 2)116 9 + = xa 4, b 3, c 5= = = C(1, 2), V(1 4, 2), F(1 5, 2) B(1, 2 3) (88.3) 2 26(x 6x 9) (y 2y 1) + + +59 54 1= + 2 26(x 3) (y 1) 6 + = 2 2(y 1) (x 3)16 1+ = ya 6, b 1, c 7= = = C(3, 1), V(3, 1 6), F(3, 1 7) B(3 1, 1) (88.4) 2 26(x 2x 1) 10(y 4y 4) + + +94 6 40= + 2 26(x 1) 10(y 2) 60 + =2 2(x 1) (y 2)110 6 + = xa 10, b 6, c 4= = = C,(1, 2), V(1 10, 2), F(1 4, 2) B(1, 2 6) (89) F(3, 0),( 3, 0) C(h, k) (0, 0), c 3 = = , x , 4 2 22a 4 a 2 b 3 2 5 = = = = 2 22x y152 =2 25x 4y 20 0 =4dcF1 F23/2(0,1/2)BMath E-Book Release 2.1 ( ) 117. O-NET/A-NET 118(90) 2 2 2 2|4x 3y 11| |4x 3y 5| 144254 3 4 3 + + + =+ +|(4x 3y 11)(4x 3y 5)| 144 + + + =2 216x 9y 64x 18y 55 144 + + + = 2 216x 9y 64x 18y 199 0 + + + = 2 216x 9y 64x 18y 89 0 + + =(91.1) xy k= (2, 2),( 2, 2) (2 2, 2 2),( 2 2, 2 2) (91.2) xy 2x y 3+ =x(y 2) (y 2) 3 2 + + = (x 1)(y 2) 1 + = xy k= ... (1, 2)(92) 2 29(x 2x 1) 16(y 4y 4) + + +199 9 64= + 2 29(x 1) 16(y 2) 144 + =2 2(x 1) (y 2)116 9 + = xC(1, 2), c 16 9 5 = + = (1 5, 2) (6, 2) = ( 4, 2) 2 2 2 2|3(6) 4( 2) 8| |3( 4) 4( 2) 8|3 4 3 4+ + ++ +2 2865 5= + = (93) 2 26(x 2x 1) 10(y 4y 4) + + +94 6 40= + 2 2(x 1) (y 2)110 6 + = xC(1, 2), c 10 6 4 F(1 4, 2) = + = 1F (5, 2) 4[Q ] x 1= V(5, 2) Directrix: x 1= x c 4= 2(y 2) 4(4)(x 5)+ = 2y 16x 4y 84 0 + + =(94) x (y 0= ) 29(x 1) 16 36 =52x 13 = ... 52(1 , 0)3 52F(1 , 0)3 8 C(h, k) (1, 0),= x,52 52 92c , a 4 b 163 9 3= = = =2 2(x 1) 9y116 92+ = 2 223(x 1) 36(y ) 368 + =2 223x 36y 46x 345 0 + =(95) 2 26(x 2x 1) 5(y 4y 4) 4 6 20+ + + + = + +2 2(x 1) (y 2)15 6+ + = yC(h, k) ( 1, 2), a 6, b 5,= = =c 6 5 1= = V( 1, 2 6), F( 1, 2 1) C( 1, 2), V( 1, 2 1), (b 5= )2 22(y 2) (x 1)151 + = 2 25(y 2) (x 1) 5 + =2 25y x 20y 2x 14 0 + =( 2 2x 5y 2x 20y 14 0 + + = )(96) 2 2Ax By Dx Ey F 0+ + + + =... A B 0 A B= A B A B (96.1) (96.2) (96.3) (96.4) (96.5) (96.6) (96.7) (96.8) (96.9) (96.10) Math E-Book Release 2.1 ( ) 118. O-NET/A-NET 119f(n)=c+tn5 aa/a (Ordered Pair) (a, b) (a, b) (c, d)= a c= b d= (Cartesian Product) A B () A B A B {(a, b) | a A = b B } A {0, 1, 2}= , B {1, 3}= {(0, 1),(0, 3),(1, 1),(1, 3),(2, 1),(2, 3)}A B ={(0, 0),(0, 1),(0, 2),(1, 0),(1, 1),(1, 2),(2, 0),(2, 1),(2, 2)}A A =1. n(A B) n(A) n(B) = 2. n(A ) n(A) n( ) 0 = = A = 3. A B B A = A B= Math E-Book Release 2.1 ( ) 119. O-NET/A-NET 1205.1 (Relation : r ) (2 x,y) A B (from A to B) A B ... A B A B n (A B)2 A B r {(x, y) A B | .....}= A {2, 3, 4}= B {1, 3, 5, 8}= {(2, 1),(2, 3),(2, 5),(2, 8),(3, 1),(3, 3),(3, 5), ...,(4, 8)}A B = r A B 3 42 4096= ... 1r {(x, y) A B | y x }= < 1r {(2, 1),(3, 1),(3, 3),(4, 1),(4, 3)}=2r {(x, y) A B | y x 1}= = + 2r {(2, 3),(4, 5)}=3r {(x, y) A B | x= y } 3r {(2, 8),(3, 3),(4, 8)}=34r {(x, y) A B | x y }= < 4r = 1. 2 2. r {(x, y) A A | .....}= A (in A)3. R R 5.1(1) (1.1) a b [(a, b) (b, a)] (1.2) a b [(a, b) (c, d) a c b d ](1.3) a b [(a 2b, 1) ( 1, b a/2)] + = +(2) (3x 5, 8 4y) ( 5, 6)+ = (y, 2) ( p, 2)= (xp, x/p)(3) (a, b) (c, d) (a c, b d) = + (3, 4) (0, 0) (x, y) (3, 4) = (x, y)(4) A, B, C (4.1) A B A B (4.2) A B A B (4.3) A B A C = B C=Math E-Book Release 2.1 ( ) 120. O-NET/A-NET 121(4.4) A B = A B= = (4.5) A B B A = A B=(4.6) (A B) C A C (A B) C (4.7) A B A A B B (4.8) A A (A B) (5) (5.1) A {4, 5, 6, {4, 5, 6}}= B {4, 5, {4, 5}}= n [P(A) P(B)] 128 =(5.2) A {3, 4, 5, ..., 32}= , B {7, 8, 9, ..., 40}= C {0, 1, 2, ..., 25}= n [(A B) (A C)] 570 =(5.3) A {0, 1, 2, ..., 28}= B { 3, 2, 1, ..., 4}= n [(A B) (B A)] 439 =(6) 1 2 3 mA {a , a , a , ..., a }= , 1 2 3 kB {a , a , a , ..., a }= m k< (A B) (B A) (A B) (B A) = n [(A B) (B A)] (7) n( ) 10=U , n(AB ) 2 = , n(AB ) 9 = n(B) n(A) 1 = A B(8) [Ent39] n(A) 10= A A A(9) A {1, 2, 3}= B {0, 4}= (9.1) A B 64 (9.2) A B A 27 (10) n(A) 3= n(B) 4= (10.1) A B B A(10.2) A B A 315 (10.3) B A B 2401 (10.4) A A 343 (11) 1 2r r (11.1) 1r {(x, y) | x y 1}= + =I I , 2r {(x, y) | x y 3 }= =I I(11.2) 2 21r {(x, y) | x y 16 }= + = , 22r {(x, y) | y 4 x }= = (12) A {1, 2, 3, ..., 20}= , B {0, 1, 2, ..., 25}= r {(x, y) A B | y x }= > r5.2 (Domain; D) (Range; R) rD { x | (x, y) r }= rR { y | (x, y) r }= Math E-Book Release 2.1 ( ) 121. O-NET/A-NET 122O2-2 2yx 1rD {2, 3, 4}= , 1rR {1, 3}= , 2rD {2, 4}= , 2rR {3, 5}= 4 4r rD R= = r A B rD A rR B R () , , , bac= c 0 na b= n a 0> b 0> na b= n a 0> a b= a 0> y ...(x)...= ( y x) x ...(y)...= ( x y) 2r {(x, y) | y 4 x }= = (1) 24 x 0 > 2 x 2 < 2x 4 y= 24 y 0 > 2 y 2 < < 0 y 2< < rD [ 2, 2]= rR [0, 2]= 2y 4 x= 2 2x y 4+ = ( y 0> ) 1r (Inverse) r 1r {(y, x) | (x, y) r }= 1r r x y r {(2, 1),(3, 3),(4, 5),(0, 1)}= 1r {(1, 2),(3, 3),(5, 4),( 1, 0)}= r {(x, y) | y 2x 3 }= = 1r r {(y, x) | y 2x 3 }= = r {(x, y) | x 2y 3 }= = x 3r {(x, y) | y }2+= = ( y) 1 rrD R = 1 rrR D = Math E-Book Release 2.1 ( ) 122. O-NET/A-NET 123 5.2(13) (13.1) r {(x, y) | xy 2 }= =(13.2) r {(x, y) | (x 2)(y 1) 1}= =(13.3) 1r {(x, y) | y }x 1= =(13.4) 2x 3r {(x, y) | y }x 1= =+(13.5) x 1r {(x, y) | y , x 1}x 1+= = >(14) [ Hint : ](14.1) 2r {(x, y) | y x }= =(14.2) r {(x, y) | y x }= =(14.3) 2r {(x, y) | y x 2x 3 }= = (14.4) r {(x, y) | y 3 x 1 }= = + +(14.5) 2 2r {(x, y) | x y 16 }= + =(14.6) 2r {(x, y) | y 16 x }= = (14.7) 21r {(x, y) | y 4 3x x }2= = (14.8) 2 2r {(x, y) | x y 6x 4y 3 0 }= + + =(15) (15.1) 21r {(x, y) | y }x x= =(15.2) 21r {(x, y) | y }x 4x 3= = +(15.3) x 1r {(x, y) | y }x+= =(15.4) 2 2r {(x, y) | 2x y 2xy x 1 0 }= + + + =(15.5) 2 2 2r {(x, y) | x y y x 2 0 }= =(15.6) 2 2r {(x, y) | xy xy 2y 2y 6x 11 0 }= + + =(16) (16.1) 3r {(x, y) | y }x 3 4= =+ (16.2) r {(x, y) | y x 2 x }= = + (16.3) 2r {(x, y) | y x 4 }= = (17) (17.1) 21r {(x, y) | y }x 4= =Math E-Book Release 2.1 ( ) 123. O-NET/A-NET 124(17.2) 21r {(x, y) | y }x 4= =(17.3) xr {(x, y) | y }x 2= =(17.4) 2r {(x, y) | y 3x 1 2 2x 3x 2 }= = + (18) r {(x, y) | xy 1 y }= = + r rR D (19) r R x 2 , x 11r {(x, y) | y }15 x , x 11 = = >< r rA D R= (20) 2 2r {(x, y) | y 2xy x 1 0 }= + = r rR D (21) 21r {(x, y) | y }x 2x 3= = 1rD (22) rR 2 2 1r {(x, y) | y (9 x ) }= = . x y [x y y] + = . x y [x y 0] + =5.3 r (x, y) r ( ) 1r {(1, 2),( 1, 2),(2, 3),( 2, 0),(0, 2)}= 22r {(x, y) | y x } {(0, 0),( 1, 1),( 2, 4), ...}= = = I I 23r {(x, y) | y x }= =R R ... (, ) O32-2-2 -1 1 2yxr141-2 -1 1 2yxr2yxr3OOMath E-Book Release 2.1 ( ) 124. O-NET/A-NET 1251. y mx c= + m c y2. 2y ax= 2x ay= a 3. () y a x= x a y=4. 2 2 2x y r+ = r ()5. [Ent22] () x y k+ = k 6. x y c=c OcyxyxOm > 0Ocyxm < 0cm = 0OyxyxOa > 0Oyxa < 0a > 0y = ax2y = ax2x = ay2OyxyxOa > 0Oyxa < 0a > 0y = a|x|y = a|x|x = a|y|Oyxrr-r-r Oyxkk-k-kxOc > 0yxOc < 0yS eiei! S aaaaaa eeoaeao eoeo aeeea..Math E-Book Release 2.1 ( ) 125. O-NET/A-NET 126 () ( r , r ) ( 1r) r y x= x y 5.3(23) (23.1) r {(x, y) | x y 4 }= + =(23.2) r {(x, y) | x 2 y 2 }= + =(23.3) 2r {(x, y) | y x 2x 2 }= = + (23.4) 2r {(x, y) | y x 2x 2 , 3 x 2 }= = + 2r {(x, y) | 2x y 4 0 }= + < 3r {(x, y) | y 1 0 }= + >(26) () 1 2r r (26.1) 1r {(x, y) | 2 x y }= +< 2r {(x, y) | x y 4 }= + 4Oyxyxrr-1(-3,-1)(-1,-3)y = xMath E-Book Release 2.1 ( ) 126. O-NET/A-NET 127(26.2) 1r {(x, y) | x 2 y 4 }= + < 2r {(x, y) | 2 x y 2 }= + >(26.3) [Ent21] 2 21r {(x, y) | y 4 x }= < 2r {(x, y) | y x }= >(26.4) 21r {(x, y) | y 16 x }= < 12 1r r=(27) () 1r r r {(x, y) | 2 x y 8 }= + 2r {(x, y) | x 2 y 4 }= + < A B (29) 1r {(x, y) | x y 5 }= = 2 22r {(x, y) | x y 53 }= + < 1 2r r(30) 2A {x | x 2x 3 }= < 2r {(x, y) A | x y 1 0 }= =R r(31) (31.1) 2r {(x, y) | y x }= =R R 1r r=(31.2) 2r {(x, y) | y x }+= =R R 1r r=(31.3) 2 2r {(x, y) | x y 25 }= + =R R 1r r=(31.4) 2 2r {(x, y) | x y 25 }+= + =R R 1r r=(32) r 1r r 5.4 () (Function : f ) x y 1r {(0, 1),(1, 2),(1, 3),(2, 4)}= 1 2 32r {(0, 1),(1, 2),(3, 1),(2, 4)}= ( )Oyx(-2,-2) (0,-1)(0,1) (2,2)S eiei! Sa eeoeoae x eaaaa y oo..aa aea e x eiea y eeiooaeo..Math E-Book Release 2.1 ( ) 127. O-NET/A-NET 12801212341r12401232r012ab5r0123A B A Babc01237rA Babcd6r 23r {(x, y) | y x }= = x 4= y 2= 224r {(x, y) | y x }= = x y x y ( x ) 1. y ...(x)...= * 2. f y f (x) ( ) 2f (x) x= A B (from A into B f : A B> ) fD A= fR B A B (from A onto B ontof : A B> ) fD A= fR B= A B A B A B (one-to-one 1 1f : A B> ) fD A= fR B y x A B (one-to-one correspondence 1 1ontof : A B> ) fD A= fR B= y x yxO3rOyx4rS uio! Sa A B aooe (oe A) uaaa iaaaA B o A Math E-Book Release 2.1 ( ) 128. O-NET/A-NET 1298rA B01239rA Babcd124abcd012ab5rA B ( 15) 1-1 1-1 A B 1-1 A B y x y 1-1 1-1 (Constant Function) f (x) a= () (Linear Function) f (x) ax b= + () (Quadratic Function) 2f (x) ax bx c= + + () (Polynomial Function) n n 1 n 2n n 1 n 2 0f (x) a x a x a x ... a = + + + + (Rational Function) p(x)f (x)q(x)= .. p(x), q(x) (Absolute Value Function) f (x) ax b c= + + () (Increasing Function) (Decreasing Function) ... 1 2x , x [a, b] f [a, b] 2 1x x> 2 1f (x ) f (x )> f [a, b] 2 1x x> 2 1f (x ) f (x )< (1) f (x) 2x 3= f (3x 1) f ( ) 2( ) 3 = f (3x 1) 2(3x 1) 3 6x 5 = = ... f (3x 1) 6x 5 = f (x)yxO3rOyx4ryxO10rMath E-Book Release 2.1 ( ) 129. O-NET/A-NET 130 A 3x 1= A 1x3+= f (3x 1) 6x 5 = A 1f (A) 6( ) 5 2A 33+= = f (x) 2x 3= ... f (3x 1) 6x 5 = f (2) 2 3x 1= x 1= f (3x 1) 6x 5 = f (2) 6(1) 5 1= = ... f (x) 2x 3= f (3x 1) f (x) f (3x 1) 2(3x 1) 3 6x 5 = = x f (x) f (x) 3f (x) 2x 3 x2+= = f (x) 3f (3x 1) 6( ) 5 3 f (x) 42+ = = + ... 5.4(33) f (33.1) 2f (x) x= (33.6) f (x) 1/x=(33.2) 2[f (x)] x= (33.7) 2f (x) x x 1= + +(33.3) f (x) x= (33.8) 3f (x) x=(33.4) f (x) x= (33.9) 2f (x) 1/x=(33.5) f (x) x= (33.10) 2/ 3f (x) x=(34) (34.1) r {(x, y) | x y 1}= + R (37.1) 2f {(x, y) | y 9 x }= = (37.2) 2f {(x, y) | y 9 x }= = +(37.3) f {(x, y) | y x 1}= =(37.4) f {(x, y) | x y 5 0 }= + =(38) ontof : R A> A [0, )= (38.1) 4f {(x, y) | y x }= =(38.2) 2f {(x, y) | y x 2x 3 }= = +(38.3) 2f {(x, y) | y x 4 }= = (38.4) 3 2f {(x, y) | y x 3x 3x 1 }= = + + +(39) R (39.1) f (x) 5x 2= (39.4) 2f (x) x 2x 1= + +(39.2) f (x) 2x 5= + (39.5) 3f (x) (x 2) 2= +(39.3) 2f (x) x 3= + (39.6) 3 2f (x) x 3x 3x 1= + + +(40) (40.1) 2f (x) x 2x 4= +(40.2)2x 25f (x)x 5=(40.3)21 xf (x)x+=(41) 2f (x) x= 2 x 8 < < f (t 3)+ t (42) (42.1) f (x) 2f (x 1) x 3x 9+ = + +(42.2) f (2) 2 2f ( x 1) x 2 = +(42.3) f (4x) f (x) xf (x)x 2=+5.5 (Composite Function) f g f (0) 3= g(3) 7= g(f (0)) 7= g(f (1)) 8= g(f (2)) 7=Math E-Book Release 2.1 ( ) 131. O-NET/A-NET 132fgA B CfgA B C g(f (x)) A C g(f (x)) (g f)(x)= f g (g f)(x) fR gD (g f)(x) f gR D gof gof * f gR D gof fD D= ( f ) f gR D () gof fD D ( f g ) ... g f f (x) x 1= 2g(x) x= gofD... (g f)(x) g(f (x)) g( x 1) x 1= = = x ( gofD = R ) f (x) x 1= x 1> f (x) g gofD [1, )= (2) f (x) 2x 3= g(x) 3x 4= + (g f)(x) (g f)(x) g(f (x)) g(2x 3) 3(2x 3) 4 6x 5= = = + = ... (g f)(x) 6x 5= g(x) 3x 4= + f (x) (g f)(x) g(f (x)) 3(f (x)) 4= = + (g f)(x) 6x 5= 3(f (x)) 4 6x 5+ = f (x) 2x 3= ... (g f)(x) 6x 5= g(x) 3x 4= + f (2) (g f)(2) g(f (2)) 3(f (2)) 4= = + (g f)(2) 6(2) 5 7= = 3(f (2)) 4 7+ = f (2) 1= ... (g f)(x) 6x 5= f (x) 2x 3= g(x) (g f)(x) g(f (x)) g(2x 3)= = (g f)(x) 6x 5= g(2x 3) 6x 5 = g(x) 3x 4= + ... Math E-Book Release 2.1 ( ) 132. O-NET/A-NET 133 (g f)(x) 6x 5= f (x) 2x 3= g(1) g(1) f (x) 1= 2x 3 1 x 2 = = x 2 (g f)(2) g(1) 6(2) 5 7= = = ... (Inverse Function) r ( 1r ) f 1f 1f 1f 1f (x) 1f f 1f ( )= f ( ) = 1 1 1(f g) g f = 1 1(f ) f = (3) f (x) 2x 3= 1f (x) 1f (x) 2x 3 f (2x 3) x= = 1f (x) 0.5 x 1.5= + ... ( x y ) f (x) 2x 3= 1f (5) 1f (x) 2x 3 f (2x 3) x= = 2x 3 5 = x 4= x 4 1f (5) 4= ... f (x 1) 4x 3 = 1f (x) 1f (x 1) 4x 3 f (4x 3) x 1 = = 1f (x) 0.25 x 0.25= ... f (x 1) 4x 3 = 1f (5) 1f (x 1) 4x 3 f (4x 3) x 1 = = 4x 3 5 = x 2= x 2 1f (5) 1= ... [Ent35] 1 xf (x)x 2= (f g)(x 2) 3x 6+ = + g(2) g(2) x 2 2+ = x 0= (f g)(x 2) 3x 6+ = + (f g)(2) 6= f (g(2)) 6= 1f (6) g(2)= 1 6f (6) 1.56 2= = g(2) 1.5= ... Math E-Book Release 2.1 ( ) 133. O-NET/A-NET 134 (Algebra of Function)(f g)(x) f (x) g(x) = f g f gD D D = , , ,+ ( g(x) 0 ) 5.5(43) g f f g (43.1) f (x) 2x= g(x) x 3= +(43.2) f (x) x 1= + g(x) x=(43.3) f (x) 4x 1= + 2g(x) x=* (43.4) 4 x , x 0f (x)6 x , x 4 = >< 2g(x) x 1= + x 2>(44) [Ent33] 2(g f)(x) 3 [f (x)] 2 f (x) 1= + 2g(x) x x 2= + (g f)(1)(45) x 1f (x)x+= x 0 (f g)(x) x= g(x)(46) 2g(x) x x 2= + + 2(g f)(x) x x 2= + f (x)(47) f (x) Ax B= + A 0> (f f)(x) 4x 9= B(48) (48.1) f {(x, y) | y x x }= =(48.2) 2f {(x, y) | y (x 1) }= = +(48.3) 2f {(x, y) | y 9 x }= = (48.4) f {(x, y) | y 1 / x }= =(49) 1f (x)(49.1) f (x) 5 x= (49.5) x 2f (x)x 3=(49.2) f (x) 5x 4= + (49.6) xf (x)2x 1=(49.3) x 1f (x)3= (49.7) 2x 3f (x)3x 2=(49.4) 1f (x)x 1=(50) 1f (x) 22x 2 , x 0f (x)x 1 , x 0+= (51) 1f (x)(51.1) f (3x 4) 4x 3 = +Math E-Book Release 2.1 ( ) 134. O-NET/A-NET 135(51.2) [Ent21] x xf ( 1) 12 2+ = (51.3) 5x 7f (x 1)x 3+ =(51.4) 1f [ 3 f (2x 1) 3x 2 ] 2x 1+ + = +(52) 3 2f (x 1) x 3x 3x 5 = + + 1f (5)(53) f (x 3) 4x 5+ = g(x 3) 2 3x = (53.1) 1(f g )(5)(53.3) 1 1(f g )( 4) (53.2) 1(g f )( 1) (53.4) 1 1(g f )(3) (54) f (x 1) 2x 3+ = + 2x 1 , x 0g(x)3x 1 , x 0+= + (54.1) 1 1(f g )(0) (54.2) 1 1(g f )(0) (55) 2x , x 0f (x)3 , x 0= 2x , x 3g(x)x , x 3 >= (43.3) 2(g f)(x) (4x 1)= + ,2(f g)(x) 4x 1= +(43.4) 25 x , x 0(g f)(x)(6 x) 1 , x 8 2(f g)(x) 5 x= x 2> (44) 11/4 2(45) 1x 1 x 1(46) x 1 x (47) 3(48) (48.1) (49.1) 25 x x 0>(49.2)2x 45 x 0>(49.3) 3x 1+(49.4) 1 1 / x+ x 0(49.5) 3x 2x 1 x 1(49.6) x2x 1 1x2(49.7) 2x 33x 2 2x3(50) 10.5x 1 , x 2f (x)x 1 , x 1+= < >(51.1) 3x 254(51.2) x 2+(51.3) 4x 12x 5 x 5(51.4) 4x 73+(52) 1(53.1) 33 (53.2) 19(53.3) 4 (53.4) 4(54.1) 2/3 (54.2) 1/2(55.1) 3 x, x 0+ < x, 0 x 3 < < 22x x , x 3 >(55.2) {0}R(56.1) 21 x 1 1 x + + 1 x 0 < rD (1, )= . xy y x 1 xy x y 1 = + = + y 1xy 1+=... x 1> y 11y 1+>y 1 y 1 y 11 0 0y 1 y 1+ + + > > 20 y 1y 1 > > rR (1, )= (14.1) 2r ry x D , R [0, )= = = R (14.2) r ry x D [0, ), R [0, )= = = x (14.3) 2 2y x 2x 3 y 3 1 x 2x 1= + + = +2y 4 (x 1) + = r rD , R [ 4, )= = R (1,-4)( x y )(14.4) y 3 x 1 = +( 2(y 3) x 1 = + )rx 1 0 D [ 1, )+ = >ry 3 0 R [3, ) = >(14.5) r rD [ 4, 4], R [ 4, 4]= = . 2 2y 16 x 16 x 0= >(x 4)(x 4) 0 4 x 4 + < < (14.8) 2 2(x 6x 9) (y 4y 4) 3 9 4 + + + + = + +2 2 2(x 3) (y 2) 4 + + = (3, 2) 4 r rD [ 1, 7], R [ 6, 2]= = 14.1 14.22.51.25(1.5,0)Math E-Book Release 2.1 ( ) 138. O-NET/A-NET 139(15.1) . 2x x 0 x(x 1) 0 rD {0, 1} = R. 2 21 1 1 1x x x xy 4 y 4 = + = +21 y 4 y 4(x ) 02 4y 4y+ + = > rR ( 4, 0]= R(15.2) . 2x 4x 3 0 (x 3)(x 1) 0 + rD {1, 3} = R. 2 21 1x 4x 3 x 4x 4 1y y + = + = +2 y 1 y 1(x 2) 0y y+ + = > rR ( 1, 0]= R(15.3) . x 1 0 x 1,+ > > rx 0 D ( 1, ) {0} = . 22x 1 x 1y yx x+ += = 22 221 1 4yx y x 1 0 x2y + = = 2 2 11 4y 0 y4+ > > ()rR = R(15.4) . 2 2y 2xy 2x x 1 0 + + + =2 22x 4x 8x 4x 4y2 =2y x x x 1 = 2 2x x 1 0 x x 1 0 + +> < 21 3(x ) 02 4 + + < rD = . rD = rR = (15.5) . 22 2x 2 x 2y 0x 1 x 1+ += >x 20(x 1)(x 1)+ +> rD [ 2, 1) (1, )= 2x 1 0 . 2 2 2x y x y 2 0 =4 221 1 4y 8yx2y + + =4 21 4y 8y 0 + + > rR = R(15.6) .221 212(y )2 2x1 1(y )2 4 = (y-1/2) (13.4) 21 25x 46 25x 46(y ) 02 4x 8 4x 8 = > r46D ( , 2]25= R.222y 2y 11x (y 3)(y 2) 0y y 6 = + rR {3, 2} = R(16.1) . | x 3 | 4 0 x 3 4+ + rD { 7, 1} = R. 3 3| x 3 | 4 | x 3 | 4y y+ = + = +3 3 4y4 0 0y y+ + > > r3R ( , 0]4= R(16.2) . rx D =R R x. y |x 2| |x|= + .. x 0 y | x 2 x | 2 = + => 2 x 0 y |x 2 x| |2x 2| < = + + = +< x 2 y | x 2 x | 2< = + = rR [0, 2]=(16.3) 2y x 4= y 0> y r rD , R [0, ) = = R(17.1) 1 rrR D = 2x 4 0 (x 2)(x 2) 0 + 1rR {2, 2} = R(17.2) 2 2x 4 0, x 4 0 > 12rx 4 0 R [ 2, 2] > = R(17.3) 1rR {2} = R-12Math E-Book Release 2.1 ( ) 139. O-NET/A-NET 140(17.4) 22x 3x 2 0 >(2x 1)(x 2) 0 x ( , 1/2] [2, )+ > 23x 1 2 2x 3x 2 0 + >22 2x 3x 2 1 3x > 2 21x 4(2x 3x 2) 1 6x 9x3 +> > 21x ... (x 3) 03< + < 1rR [2, ) = (18) r1 yx R {0}y+= = Rr1xy y 1 y D {1}x 1 = = = R r rR D {1} =(19) . x 11; x 2 0 x 2 >x 11; 15 x 0 x 15> > < rD [2, 15]=. 2 x 11< < 2y x 2= y 0 3 11 x 15< < 2y 15 x= y 2 0() r r rR [0, 3] A D R [2, 3]= = = 3 2 5+ =(20)2r2y 1x R2y 1+= =+R2rx 1 x 1 1y 0 D ( , 1]1 2x 2x 1 2 = = < r r1R D( , 1]2 = R 2(21) 12rr1D R x 2x 3y = = 2 1x 2x 1 3 1y + = + + 2 1 4y 1 4y 1(x 1) 4 0y y y+ + = + = > ( , 1 / 4] (0, ) ( 1 / 4, 0](22) 2 22 21 1y 9 x9 x y= = 2 222 2 21 9y 1 9y 1x 9 0y y y = = > 2(3y 1)(3y 1)0y +> r1 1R ( , )3 3= = UR. x y[x y y] + = x y y+ = x 0= U 0. x y[x y 0] + = x y (23.1) rD [ 4, 4]= rR [ 4, 4]= (23.2) rD [0, 4]=rR [ 2, 2]= (23.3) 2 2y 2 x 2x y 3 (x 1)+ = + + = +rD = RrR [ 3, )= (23.4) rD [ 3, 2)= rR [ 3, 6)= (24)(24.1) 1 . (24.2) 1/2 .(24.3) 1 . (24.4) 44-4-4(2,0)22(-1,-3)(-1,-3)(-3,2)(2,6)11-1 1111-1-11Math E-Book Release 2.1 ( ) 140. O-NET/A-NET 141(25) (1, 2),( 2, 1),(2.5, 1) 13 4.52= 6.75= .(26.1) 18 82= 14 42 32 8 24= = .(26.2) 14 ( 2 3)2= 12= .(26.3) 21( 2 )4= = .(26.4) 21( 4 )4= 4= .(27) = 4 ( + )1 1 84( 8 4 4)2 2 3= + 25685.333= .(28)r1 r2A D [ 4, 4]= = B [ 2, 2]= A B [ 4, 2) (2, 4] = 4 3 3 4 0= + + =(29) ( 7, 2) r1 r2D [ 7, 5] [5, 7] = (30) A [ 1, 3]= 2r {(x, y) |x y 1, x [ 1, 3]}= = + rR [ 1, 8]= (31)(31.1) (31.2) (31.3) (31.4) (32) 14( 1 2)2= 4= .(33) x y ( y |y| , x |x| 1-1) ( 1 , 1 1-1)(33.1) 1 1(33.2) (33.3) 1 1(33.4) 1 1(33.5) (33.6) 1 1-11-142442242212441r12 1r r=1 2r r4482844 (8/3,8/3)42225-5 53- 53(0,-1)(-1,0)(3,8)1r r=r 1r1r r= 1rr1233.133.233.333.433.5 33.6Math E-Book Release 2.1 ( ) 141. O-NET/A-NET 142(33.7) 21 3f(x) (x )2 4= + + 1 1(33.8) 1 1(33.9) 1 1(33.10) 1 1(34.1) (34.2) (35) (35.4) (36) 1 1 (36.4) (37) R R fD = R(37.1) 29 x 0 > 3 x 3 < < (37.2) 29 x 0+ > x R(37.3) x 0(37.4) x 5 |y| x 5= (38.2) 2y 2 (x 1) y 2 = >(38.3) 2x 4 4 y 0 > >(38.4) 3y |x 1| y 0= + >(39.1) 5(39.2) ( 2 )(39.3) (39.4) ()(39.5) 3f(x) 2 (x 2) = (39.6) 3f(x) (x 1)= + (40.1) 2 2y x 2x 4 y 3 (x 1)= + = f fD , R [3, ) = = R ()(40.2) (x 5)y=(x 5)x 5+fD {5} = R fR {10}= R ... x 5(40.3) .2f1 xy D {0}x+= = R.22 y y 4x xy 1 0 x2 + = =2fy 4 0 R ( 2, 2) = > R(41) 2 t 3 8 5 t 5 + < < < < 2f(t 3) (t 3)+ = + 5 t 5 < x 0< 2(gof)(x) g(6 x) (6 x) 1= = + x 4> |6 x| 2 > x 8 >. 2 2(fog)(x) 4 (x 1) 3 x= + = |x| 2> 2x 1 0+ < ... 2 2(fog)(x) 6 (x 1) 5 x= + = |x| 2> 2x 1 4+ > |x| 2 >(44) 2 23f(x) 2f(x) 1 f(x) f(x) 2 + = + 2 12f(x) f(x) 1 0 f(x)2 = = 1 1(gof)(1) g(f(1)) g( )2= = g(1)11 / 4= 2(45) g(x) 1x xg(x) g(x) 1g(x)+= = +1g(x) ; x 1x 1 = (46) 2 2f(x) f(x) 2 x x 2+ + = +2 21 1[f(x) ] [x ]2 2 + = f(x) x 1 = f(x) x= (47) (fof)(x) 4x 9= A(Ax B) B 4x 9 + + = 2A 4= AB B 9+ = A 0> A 2 B 3= = (48) f 1-1 1-1 (48.1) 2y x= x 0> 2y x= x 0< (48.2) y=1 x=0 -2(48.3) y=0 x=3 -3(48.4) y=1 x=1 -1(49.1) y 5 x ; y 0= > 2x 5 y y 5 x ; x 0= = >(49.2) y 5x 4 ; y 0= + > 2x 4x 5y 4 y ; x 05= + = >(49.3) x 1y3= y 1x y 3x 13= = +(49.4) 1yx 1=1 1x y 1; x 0y 1 x= = + (49.5) x 2yx 3=y 2x xy 3x y 2y 3= = 3x 2y ; x 1x 1 = (49.6) xy2x 1=yx 2xy x y2y 1= =x 1y ; x2x 1 2 = (49.7) 2x 3y3x 2=2y 3x 3xy 2x 2y 33y 2= = 2x 3 2y ; x3x 2 3 = 48.448.148.248.3Math E-Book Release 2.1 ( ) 143. O-NET/A-NET 144(50) x 2y 2 ; y 0= + >xy 1 ; x 22 = + >( y 0 2y 2 2 +> > ) 2x y 1 ; y 0= (51.1) 1f (4x 3) 3x 4+ = A 3A 4x 3 x4= + = 1 A 3 3A 25f (A) 3( ) 44 4 = =1 3x 25f (x)4 =(51.2) 1 x xf ( 1) 12 2 = + xA 1 x 2(A 1)2= = + 1 2(A 1)f (A) 1 A 22 += + = + 1f (x) x 2 = +(51.3) 1 5x 7f ( ) x 1x 3 = + 5x 7 3A 7A xx 3 A 5 = = 1 3A 7 4A 12f (A) 1A 5 A 5 = + = 1 4x 12f (x) ; x 5x 5 = (51.4) f(2x 1) 3f(2x 1) 3x 2+ = + +13 3f(2x 1) x 1 f ( x 1) 2x 12 2 + = = + 3 2A x 1 x (A 1)2 3= = + 1 2 4A 7f (A) 2( )(A 1) 13 3 += + + =1 4x 7f (x)3 + =(52) 1 3 2f (x 3x 3x 5) x 1 + + = 3 2x 3x 3x 5 5 + + = x 0= 1f (5) 0 1 1 = = (53.1) 1g (5) 1g (2 3x) x 3 = 12 3x 5 x 1 g (5) 4 = = = 1(fog )(5) f( 4)= x 3 4+ = x 7 f( 4) 33 = = (53.2) 1f ( 1) 4x 5 1 x 1 = =1f ( 1) 1 3 4 = + =1(gof )( 1) g(4) = x 3 4 x 7 = =g(4) 2 3(7) 19 = = (53.3) 1g ( 4) 2 3x 4 x 2 = =1g ( 4) 2 3 1 = = 1 1 1(f og )( 4) f ( 1) 4 = = ()(53.4) 1f (3) 4x 5 3 x 2 = =1f (3) 2 3 5 = + =1 1 1(g of )(3) g (5) 4 = = ()(54.1) 1 1g (0)2= 12 >0 1 1g (0)3= 103 < 1 1f ( )3 12x 33+ = 5x3 = 1 1 5 2f ( ) 13 3 3 = + = (54.2) 1f (0) 32x 3 0 x2+ = = 1 3 1f (0) 12 2 = + = 1 1 3g ( )2 4 = 34 > 0 1 1 1g ( )2 2 = 102 < 12(55.1) 2(f g)(x) 2x x = x 0> x 3 x 3> > (f g)(x) 2x x x = + = x 0> x 3 0 x 3< < < (f g)(x) 3 x = + x 0< x 3 x 0 1 x 1 0 x 0 + > < x 1 x 0 < 21 x 0 x 1, x 1 x x ( , 1) { 1} Math E-Book Release 2.1 ( ) 144. O-NET/A-NET 145(57.1) f(2x 3) 3x 2 = A 3 3x 5f(A) 3( ) 2 f(x)2 2+ + = =1 2x 5f (x) ...3 = 2(f g)(x) x x 3+ = + 2 3x 5g(x) x x 32+= + 1 2 3x 5 2x 5(g f )(x) x x 32 3 + + = + +2 x 43x6= +(57.2)2 3x 523x 52x x 3g( )(x)f+++ =22x x 11 5; x3x 5 3 = +(58) 2g(x 5) x 25+ = 2 2g(A) (A 5) 25 g(x) x 10x = = 2f x 5( )(x) ; x 0, 10g x 10x+ = (59.1) 1 1f ( 2) 4x 2 x2 = = 1 1f ( 2)2 = 2g( 2) ( 2) 1 5 = + = 1h ( 2) 3 = 3 >0 1h ( 2) 1 = 1 0 < 1 75 12 2 + =(59.2) 1(gof )(2) h(2)1 1f (2) 4x 2 x2 = =1 1 1 1 5f (2) ; g( ) 12 2 4 4 = = + =h(2) 2 1 3= + = 5 1534 4 =(60.1) f(x) g(x) 2x 1+ = + f(x) g(x) 3 4x = f(x) 2 x= g(x) 3x 1= (fog)(x) 2 (3x 1) 3 3x = = 1(fog) ( 2) 53 3x 2 x3 = =1 5(fog) ( 2)3 =(60.2) f(1) 2 1 1= = 1 1 2 5g (1) f (1) 13 3 + = + =(61.1) f(2) xf( ) xx 2= x2 x 4 f(2) 4x 2= = = g(2) (fog)(x) x 2 f(g(2)) 4= + =1 4g(2) f (4) 24 2 = = = (f g)(2) 4 2 6+ = + =(61.2) 1f (4) 2= ()(gof)(4) g(f(4))= f(4) x 84 xx 2 3= =8f(4)3 = 8g( )3 8 8 14f(g( )) 23 3 3= + =18 14 14 / 3 7g( ) f ( )3 3 14 / 3 2 4 = = = 7 724 2 =(62.1) 1f(3)f (3)g(3)+ f(3) f(2x 3) x 1 2x 3 3+ = + + =x 0 = f(3) 1 =1f (3) 1f (x 1) 2x 3 x 1 3+ = + + =1x 2 f (3) 2(2) 3 7 = = + =g(3) f(g(3)) x 1 3 x 4 = =f(g(3)) 20 1 21 = + = 1g(3) f (21) 2(20) 3 43= = + = 1 17 743 43+ =(62.2) 1f (1) x 1 1 x 0+ = =1f (1) 2(0) 3 3 = + = (fg)(3) f(3) g(3)= 1 43 43 =Math E-Book Release 2.1 ( ) 145. O-NET/A-NET 146eo fog.. 2f (x) x 6= + 2g(x) 3 x= fogD fog fog ( )22 2 2(f g)(x) 3 x 6 3 x 6 9 x= + = + = 29 x 0 > x [ 3, 3] !! (f g)(2) g(2) .. fog 2 fog () .. ( fog) (1) f(g(x)) g(x) f ( g(x) x )(2) fogD f(g(x)) g(x) x fogR g(x) f(g(x)) 21f (x)1 x= 2g(x) 4 x= fogD fogR 21(f g)(x)1 g(x)=. ; 21 g(x) 0 > 1 g(x) 1 < < x 2 2 21 4 x 1 0 4 x 1 3 x 4 < < < < < y 0> x y 3. (Feasible Region) x y 4. ( x y ) (0, 0),(0, 4),(2, 3),(5, 0) x y P 5. x y P P (x,y) = (2,3) P 30(2) 50(3) 210= + = 1 2 3 210 1. P (Profit), C (Cost)2. x 0> , y 0> ( x y )Math E-Book Release 2.1 ( ) 148. O-NET/A-NET 149Oyx1,50020015 20(8.67,850)(15,375)3. x y () 4. ( ,, ) 15 1,500 . 200 . ( 75 .) 6,000 100 x y Z Z 6000 x 100 y= + (1) 15 0 x 15< (1.4)5 x 3 y 0x 2 y 02 x 4+>>< > >(2.7)Z x 2 y 4x y 4x 2 y 2x y 2x 3= +++ >>>> >(3) (3.1) (3.2)(3.3)(4) 4 7 2 - ( 30 )- ( 20 ) 1 3 1 1 4 3 Math E-Book Release 2.1 ( ) 151. O-NET/A-NET 152(5) 1 1 1 A 2 1 3 .. B 1 3 5 .. 1.00 1.20 (6) 250 . 10. 25 . 260 20 100 10 4 30 25 1 (7) x y 3 x 5,000 y 3,500 1 x 1 y 1 1 3 .. 2 .. 24 .. 2 1 .. 2 .. 16 .. 3 1 .. 1 .. 9 .. (8) 2 A B A 250 B 300 A 80 B 100 200 (9) 1 15 12 1 5 4 60 40 500 400 (10) A 400 6 8 B 800 8 12 5,600 72 (11) 5 12 18 1 3 3 1 2 6 25 22 Math E-Book Release 2.1 ( ) 152. O-NET/A-NET 153Oyx42 4(14/5,6/5)3x-2y=6x+y=4 Oyx42 4(8/3,4/3)2x-y=4x+y=4(12) 9 8 7 1 3 1 1 50 2 1 2 1 40 (13) 2 A 1 B 3 C 5 2 A 80 B 150 C 200 ( 6,000 )* (14) 6 1 : 2 : 2 4 1 : 1 : 5 3 : 4 : 10 ()(1.1) (0,0), (0,4), (2,0), (14/5,6/5)(1.2) (0,0), (0,4), (2,0), (8/3,4/3)(1.3) (0,2), (0,3), (4,0), (6,0)(1.4) (2,1), (4,2), (2,-10/3), (4,-20/3)(1.5) (0,0), (0,4), (1,0), (1,3), (7/4,3/4)(2.1) 410 (2.2) 8 (2.3) 30(2.4) 13, 0 (2.5) 2400, 1100(2.6) , 434 (2.7) 12, -1(2.8) , 23(3.1) x y 2 < , x y 3+ < , x 0> , y 0>(3.2) 5x 8y 40+ < , 15x 4y 60+ < ,x 0> , y 0>(3.3) 3x 4y 1800+ < , x 3y 1200+ < ,x 0> , y 0> ()(1.1) (1.2)(4) 120 , 360 (5) 48 , 84 (6) 8 , 5 (7) x 6 , y 3 (8) A 80 , B 120 , 56,000 (9) 10 (10) A 8 , B 3 , 100 .(11) 2 .., 3 ..(12) 220 ( 1 2 )(13) 36 22 34 24 (14) 5 : 14Math E-Book Release 2.1 ( ) 153. O-NET/A-NET 154Oyx34 62x+4y=12x+2y=42Oyx(2,-10/3)(4,2)x-2y=05x+3y=0(2,1)(4,-20/3)x=2 x=4Oyx61 2 4(7/4,3/4)x-y=1x+y=43x+y=64 (1,3)Oyx9070 90 150(70,20)60 (50,40)Oyx54 54(2.5,5)Oyx105 10 155 (10,10/3)Oyx44 (3,2)Oyx4(5,40) (60,40)(60,5)(10,30)Oyx(0,62/5)(30,0)(4,10)Oyx4(1,3)(3,1)(3,-2.5)(-2,0)Oyx(0,6)(8,0)(1,3)(3,1)(1.3)(1.4)(1.5)(2.1)maxP (70, 20)maxP 5(70) 3(20)410= +=(2.2)minC (4, 0)minC 2(4) 3(0)8= +=(2.3)maxP 10(10, )3max10P 2(10) 3( )330= +=(2.4)maxZ 13= (3, 2)minZ 0= (0, 0)(2.5) maxZ 2,400= (60, 40)minZ 1,100= (10, 30)(2.6) maxZ minZ 434= 62(0, )5(2.7)maxZ 12= (3, 2.5)minZ 1= (1, 3)(2.8)maxZ minZ 23= (1, 3)(3.1) x y 3 , x y 2 ,+ < >(3.2) intercept form( x y1a b+ = ) .. x y1 15x 4y 60 ,4 15+ = + >Math E-Book Release 2.1 ( ) 154. O-NET/A-NET 155Oyx600400 (120,360)Oyx90100 (48,84)Oyx10(8,5)10(5,8)Oyx8(6,3)8(2,7)Oyx(100,100)(80,100)(80,120)Oyx1040/12Oyx127 (8,3)(3.3) 3.2x y1 3x 4y 1,800 ,600 450+ = + >(4) P 4x 7y= +3x 4y 1, 800+ < ()x 3y 1, 200+ < ()x 0 , y 0> >maxP 3,000= (120, 360) 120 360 (5) P x 1.2y= +2x y 180+ < ()x 3y 300+ < ()x 0 , y 0> >maxP 148.80= (48, 84) 48 84 (6) P 30x 25y= +10x 25y 250+ maxP 40,500= (6, 3) x 6 y 3 (8) P 250x 300y= +x 80 , y 100> >x y 200+ >maxP 4,000= (0, 10) 10 (10) P 8x 12y= +400x 800y 5, 600+ maxP 100= (8, 3) A 8 B 3 100 .Math E-Book Release 2.1 ( ) 155. O-NET/A-NET 156Oyx(0,6)(6,0)(2,3)(4,1)Oyx(6,1)(2,3)(1,6)Oyx(0,100)(80,0)(25,37.5)(35,22.5)Oyx(0,28/17)(25/17,0)(5/17,14/17)(25/51,28/51)(11) C 25x 22y= +x y 5+ >3x 2y 12+ >3x 6y 18+ >x 0 , y 0> >minC 116= (2, 3) 2 .. 3 ..(12) C 50x 40y= +3x y 9+ >x 2y 8+ >x y 7+ >minC 220= (2, 3) 220 (14) C 6x 4y= +x y 35 7 17+ >2x y 45 7 17+ >2x 5y 105 7 17+ >x 0 , y 0> >minC 86= 5 14( , )17 17 5 : 14(13) C 6, 000x 6, 000y= +x 2y 80+ >3x 2y 150+ >5x 2y 200+ >x 0 , y 0> > x, y IminC 345,000= (35, 22.5) y . y y 22= x 36=( x x 2y 80+ = ) C 348,000 =. y y 23= x 34.67=! y 24= x 34=( x 3x 2y 150+ = ) C 348,000 = C (36 , 22 ) (34 , 24 )[ C C ]Math E-Book Release 2.1 ( ) 156. O-NET/A-NET 157= rig+n 7 aoii (Trigonometry) , , 6 (Trigonometric Function) (Sine; sin) (Cosine; cos) (Tangent; tan) (Cotangent; cot) (Secant; sec) (Cosecant; cosec csc) 0 90 < < 2 asincbcoscsin atancos b = = = =1 ccosecsin a1 cseccos bcos1 bcottan sin a = = = = = = = c abMath E-Book Release 2.1 ( ) 157. O-NET/A-NET 158 0 30 45 60 90sin 0 1/2 1/ 2 3/2 1cos 1 3/2 1/ 2 1/2 0tan 0 1/ 3 1 3 1. 2 2sin cos 1 + = sin cos ( 2 2 2a b c+ = .. 2c ) 2sin 2 21 cot cosec+ = 2cos 2 2tan 1 sec + = 2. sin cos (90 ) = - (Co-function) 90 sin cos tan cot (90 ) = sec cosec (90 ) = 7.1 2 2sin cos 1 + = ( ) sin , cos x, y 1 x cos y sin x 0 +x ( 90 +y, 180 x, ...) sin 45 1/ 2cos 60 1/2sin 90 1cos 90 0sin 120 3/2cos 120 1/2sin 180 0cos 180 1sin 225 1/ 2cos 225 1/ 2sin 300 3/2cos 300 1/2 = = = = = = = = = = = = 1 (; degree) 60(; minute)0 (1,0)90 (0,1)180(-1,0)270 (0,-1)45 ( 12, 12)1/260 ( 12, 32)yx30 ( 32, 12)322/23/22212120( 12 , 32)225( 12 , 12 ) 300 ( 12, 32 )OMath E-Book Release 2.1 ( ) 158. O-NET/A-NET 159 (Unit Circle) , 90 (), 1. sin , cos 1 1 2. sin ( ) sin = ... , cos ( ) cos = ... , tan ( ) tan = ... sin ( ) cos ( ) 7.1(1) (1.1) sin x sin 2x sin 4x+ + x 60= (1.2) cos 4x cos 3x cos x + x 120= (2) sin cos + (2.1) (0, 0) (3, 4)(2.2) y 2x 1= (3) (3.1) 2 2 2 2 2 2cos 35 sec 70 cosec 47 sin 35 tan 70 cot 47 + + + (3.2)22 2 2 2 22sec xcot x cot x sin x sin x cosec x2 2 ta n x+ + + +(4) (4.1) 2 2 2 21 1 1 11 sin 1 cos 1 sec 1 cosec+ + ++ + + + (4.2) 6 6 4 42(sin x cos x) 3(sin x cos x) 1+ + +[Hint: 2 2 3(sin x cos x)+ 2 2 2(sin x cos x)+ ](5) sin cos a = sin cos (6) 2 2(sin cos ) a = cosec sec (7) ABC A tan B 3/4= sec C cot B cosec A(8) ABC B BD AC D AB 10= , BD 8= sin, cos A BC , CD(9) BC 10= ABC 10 3 ACD C D B EA120Math E-Book Release 2.1 ( ) 159. O-NET/A-NET 160(10) sin 0.7310 = 0 90< < ( cos 43 0.7314 = cos 43 10 0.7294 = )7.2 (Degree; ) () (Radian; rad) 360 2 () 180 90 /2 60 /3 45 /4 30 /6 () a r a / r = rad sin 30 1/2 n n /2 sin(2 ) , cos( )+ , sin( /2 ) , sin( 2 ) sin = cos( 2 ) cos = sin( ) sin = cos( ) cos = sin( /2) cos = cos( /2) sin = aryx+--/2+/20/2y3/2/3x/4/62/33/45/67/65/44/3 5/37/411/6S uio! Su ee aeea 180 180 aa ...eeoi ( a 3.14.. eei)Math E-Book Release 2.1 ( ) 160. O-NET/A-NET 161 n n /2 ( ) 7.2(11) 24 . (11.1) 2/3 (11.2) 130(12) 4 . 8 . (13) 5 20(14) 22.5 4 . (15) 2 4 53 3 33 73 4 6sin cos tancos tan sin + + (16) f ( ) cos3 = f (2 ) f (0) (17) (17.1) 0 /2< < sin (17.2) /2 cosec (18) (18.1) sin 1 sin 1 > (18.4) sin( /6) 0 tan cos (26) tan 15/8 = 3 /2< < sin cos + (27) sin x 5/13= cos x 0< sin(x ) cos(x ) + (28) sec 5/3 = 0 < < sin costan csc sin + ALL +tan + cos +Math E-Book Release 2.1 ( ) 163. O-NET/A-NET 164(29) [Ent..43, ] sin x 3/5= tan x 3/4= det 2cosec x sec x1 cos x (30) 0 2< < (30.1) cos 3/2 =(30.2) cos 2 3/2 =(31) tan x sec x 2+ = cos x(32) cosec cot 5/3 + = sin (33) 2 sin x sec x= 4 4sin x cos x+(34) 2 sin x sec x= 2 2sin x cos x11 cot x 1 tan x + +(35) sin cos 1/5 + = 0 < < tan (36) 22 tan sec 1 = 0 /2 < < sec (37) 24 sin x 11cos x 1 0+ = x 2 < < sin ( x) cos ( x) tan ( x) + + (38) [Ent36] 24 sin 11cos 1 0 + = 2cot ( /2) sec( 3 )+ + (39) x 2cos 2x 3 sin 2x 3 0+ =(40) [Ent38] 4 22 sin x 3 sin x 2 0+ > 0 x 2< U A [0, 2 ]= (44) [Ent39] 2f (x) cos x cos x= + . 0 x < < f (x) 2 cos x=. x 2 < < f (x) 2 cos x=. /2 x 3 /2 < < f (x) 0=. 3 /2 x 2 < < f (x) 0=Math E-Book Release 2.1 ( ) 164. O-NET/A-NET 1657.4 sin cos , , (), sinsinDR [ 1, 1]period 2amplitude 1== ==RcoscosDR [ 1, 1]period 2amplitude 1== ==RtantanD { /2 n }Rperiod= == RRcoseccosecD { n }R ( 1, 1)period 2= = =RRsecsecD { /2 n }R ( 1, 1)period 2= = = RRy = sin xx1-1O 2y = cos xx1-1O 2y = tan xx1-1O 2y = cosec xx1-1O 2y = sec xx1-1O 2Math E-Book Release 2.1 ( ) 165. O-NET/A-NET 166cotcotD { n }Rperiod= ==RR 7.4(45) A ( /2, 0) (0, /2)= A. sin x . cos x . cosec x . sec x(46) y sin x= y cos x= 0 x 2< < 7.5 .. cos ( ) cos cos sin sin = + () cos ( )+ sin ( )+ sin ( ) sin ( ) cos (90 ( ))+ = +(1) cos ( ) cos cos sin sin+ = (2) cos ( ) cos cos sin sin = + (3) sin ( ) sin cos cos sin+ = + (4) sin ( ) sin cos cos sin = .. (1) (2) (3) (4)(5) 2 cos cos cos ( ) cos ( ) = + + ... (1)+(2)(6) 2 sin sin cos ( ) cos ( ) = + ... (1)-(2)(7) 2 sin cos sin ( ) sin ( ) = + + ... (3)+(4)(8) 2 cos sin sin ( ) sin ( ) = + ... (3)-(4) .. ... A = + B = (9) A B A Bcos A cos B 2 cos ( ) cos ( )2 2+ + = ... (5)(10) A B A Bcos A cos B 2 sin ( ) sin ( )2 2+ = ... (6)y = cot x1-1xO 2tan tantan ( )1 tan tantan tantan ( )1 tan tan + + = = + Math E-Book Release 2.1 ( ) 166. O-NET/A-NET 167(11) A B A Bsin A sin B 2 sin ( ) cos ( )2 2+ + = ... (7)(12) A B A Bsin A sin B 2 cos ( ) sin ( )2 2+ = ... (8) .. 2 + = sin (2 ) 2 sin cos = 2 2cos (2 ) cos sin = 2 2cos (2 ) 1 2 sin 2 cos 1 = = 22 tantan (2 )1 tan = 2 2cos (2 ) 1 2 sin 2 cos 1 = = /2 2 sin ( /2) (1 cos )/2 = cos ( /2) (1 cos )/2 = + tan ( /2) (1 cos )/(1 cos ) = + sin(3 ), cos(3 ), tan(3 ) n , n /2 7.5(47) sin (75 ) , cos (5 /12) , tan ( /12)(48) cot A 2.4= A ( , 3 /2) sin B 0.6= B ( /2, ) (48.1) cos (A B)+ sin (A B)+ (48.2) A B+ (49) cos A sin (A B) 1/5+ = , cos (A B) 2/5 = sin B 3/5=(50) cos B A B 5 /4+ = tan A 1= 0 B < 3 5 7[ , ] [ , ]4 4 4 4 (41) sin cos 0 + < y x 0+ < 3 7[ , ]4 4 (42) xA xdet(A ) 0=2 22 sin x cos x 2 2 sin x cos x 0 =2 sin x cos x (1 2 sin x cos x) 0 =sin x 0 = cos x 0= 1sin x cos x2= 1sin x cos x2= ... x [ 2 , 2 ] 9 (43) 3 2x 9x 23x 15 0 + =(x 1)(x 3)(x 5) 0 =x 1= 3 5 {x | cos( x) cos x}= U > cos x cos x 2 cos x 0 > >1 4cos x 0 (Q , Q ) > cos 1 0 ,>cos 3 0 , cos 5 0< > 1 5 6+ =y+x=0sin x 1 / 2=sin x 1 / 2=sin x = 0cos x = 0Math E-Book Release 2.1 ( ) 178. O-NET/A-NET 179(44) f(x) |cos x| cos x= + 1 4cos x 0 (Q , Q )> f(x) 2 cos x= 2 3cos x 0 (Q , Q )< f(x) 0= . (45) . cosec x( cot x )(46) y sin x= y cos x= sin x cos x= tan x 1= x4 = 54 2 1( , )4 2 5 1( , )4 2()(47) sin 75 sin(45 30 ) = + sin 45 cos 30 cos 45 sin 30= + 1 3 1 1 3 12 22 2 2 2+= + =5cos cos( )12 4 6= + cos cos sin sin4 6 4 6= 1 3 1 1 3 12 22 2 2 2= =tan tan4 6tan tan( )12 4 6 1 tan tan4 6= =+ 113 131 3 113= =++(48) 12cot A 2.45= = 3A Q 5 12sin A , cos A13 13= = 3sin B 0.65= = 2B Q 4cos B5= (48.1) cos(A B) cos A cos B sin A sin B+ = 12 4 5 3 63( )( ) ( )( )13 5 13 5 65= =sin(A B) sin A cos B cos A sin B+ = +5 4 12 3 16( )( ) ( )( )13 5 13 5 65= + = (48.2) cos(A B)+ sin(A B)+ A B+ 4Q(49) 1sin A cos B cos A sin B5+ = ..... (1)2cos A cos B sin A sin B5+ = ..... (2) 3sin B5= 4cos B5= 4cos B5= 4cos B5= (1) 4 3 1sin A cos A5 5 5 + = (2) 3 4 2sin A cos A5 5 5 = 11cos A7= ... 4cos B5= (1) 4 3 1sin A cos A5 5 5+ = (2) 3 4 2sin A cos A5 5 5+ = 5cos A7= ... (50) 5tan A 1 tan( B) 14= =5tan tan B1 tan B4 1 15 1 tan B1 tan tan B4 = =++tan B 0 = 0 B < < B 0= ... cos B 1= 1(51.1) 2 cos 75 cos 75 cos(75 15 ) cos(75 15 )= + + 1cos 90 cos 602= + =(51.2) 2 sin 25 cos 5 sin 20 1(sin 30 sin 20 ) sin 202= + =(51.3) 2[sin 90 sin 60 ] 2[cos 180 cos 150 ] + + + 3 32[1 ] 2[ 1 ] 02 2= + + =(51.4) 1 1[sin 150 sin 66 ] [sin 150 sin( 66 )]2 2+ + + sin 150 1 / 2= = sin A cos B cos A sin B+sin(A B) sin 150 1 / 2= + = =O 2sin x cos xMath E-Book Release 2.1 ( ) 179. O-NET/A-NET 180(51.5)1 1[cos 146 cos 10 ] [cos 34 cos 10 ] cos 102 2+ + + 1[cos 146 cos 34 ]2= + 1 146 34 146 34[2 cos( ) cos( )]2 2 2 + =cos 90 cos 56 0= = - [sin 22 sin 12 cos 22 cos 12 ] cos 10 + cos(22 12 ) cos 10 0= =(51.6) (cos 105 cos 35 ) cos 35 cos 15 + + cos 105 cos 15 2 cos 60 cos 45= + = 1 1 122 2 2= =(52.1) [sin 5 sin ] [sin 5 sin 3 ] [sin 3 sin ] 0 =(52.2) 1[cos 9 cos 3 ]2 1 1[cos 3 cos ] [cos 9 cos ] 02 2 + =(53.1) 2 1 cos 2Asin A2= 1[1 cos 2A 1 cos(120 2A) 1 cos(120 2A)]2 + + + 1[3 cos 2A 2 cos 120 cos 2A]2= 1 3[3 cos 2A cos 2A]2 2= + =(53.2) 2 1 cos 2Acos A2+= 1[1 cos 2A 1 cos(120 2A) 1 cos(120 2A)]2+ + + + + + 1[3 cos 2A 2 cos 120 cos 2A]2= + + 1 3[3 cos 2A cos 2A]2 2= + =(54.1) cos 10 sin 80 (-) ( sin 40 cos 50 ) sin 80 sin 40sin 70 + 2 sin 60 cos 203sin 70 = =( cos 20 sin 70 = )(54.2) 2 cos 45 sin 30 1tan 302 cos 45 cos 30 3 = = (54.3) tan( ) tan 70 tan 10 B = tan 70 tan(60 10 ) = + tan 60 B 3 B1 (tan 60 )(B) 1 3B + += = (54.4) A B 225+ = 1 tan Atan B tan(225 A)1 tan A= =+ cot A cot B( )( )1 cot A 1 cot B+ +( tan A , tan B )1 1( )( )tan A 1 tan B 1=+ + tan B 1 tan A1 tan A1 1( )( )tan A 1 ( ) 1+=+ +1 1 tan A 1( )( )tan A 1 1 tan A 1 tan A 2+= =+ + +(54.5) sin 3 cos cos 3 sinsin cos sin 2 2 sin cos2sin cos sin cos = = = (55.1) [sin 50 sin 10 ] cos 20 + 2 sin 30 cos 20 cos 20= cos 20 cos 20 0= =(55.2) sin 10 [cos 40 cos 20 ] + sin 10 2 sin 30 sin 10= sin 10 sin 10 0= =(55.3) cos 20 [cos 100 cos 140 ] + + cos 20 2 cos 120 cos 20= + cos 20 cos 20 0= =(55.4) (cos 10 cos 50 ) (cos 20 cos 40 )(sin 10 sin 50 ) (sin 20 sin 40 ) + + + + + + 2 cos 30 cos 20 2 cos 30 cos 102 sin 30 cos 20 2 sin 30 cos 10 + = + 2 cos 30 (cos 20 cos 10 )2 sin 30 (cos 20 cos 10 ) + = + cot 30 3= =(56) sin 40 sin 20 2 sin 30 cos 10 + = 2cos 10 1 2 sin 5= = (57.1)32 sin cos cos3 5 5 5cos cos5 5 2 sin5= 2 3sin cos25 522 sin5= sin sin 0 sin15 544 sin 4 sin5 5 = = = Math E-Book Release 2.1 ( ) 180. O-NET/A-NET 181(57.2) 3cos cos5 5+ 32 sin cos 2 sin cos5 5 5 52 sin5+= 2 4 2sin sin sin5 5 52 sin5+ = 4sin1522 sin5= = ( 4sin sin5 5= )(57.3) 2 4cos cos cos7 7 7 2 42 sin cos cos cos7 7 7 72 sin7= 2 2 4sin cos cos7 7 72 sin7= 4 4 8sin cos sin17 7 784 sin 8 sin7 7= = = ( 8sin sin7 7= )(57.4)5sin sin2 sin cos4 624 242 2+= 1 2 1 2 1( )2 2 2 4+= + =(57.5) cos 108 sin 70 sin 50 sin 10cos 10 4sin=70 sin 50 sin 20 cos 20cos 10 cos 20 (sin 70 cos 20 = )2 sin 50 sin 40 (cos 90 cos 10 )1cos 10 cos 10 = = = (58) (tan 9 tan 81 ) (tan 27 tan 63 ) + + (tan 9 cot 9 ) (tan 27 cot 27 )= + + sin 9 cos 9 sin 27 cos 27( ) ( )cos 9 sin 9 cos 27 sin 27 = + + 2 2 2 2sin 9 cos 9 sin 27 cos 27sin 9 cos 9 sin 27 cos 27 + + = 1 1sin 9 cos 9 sin 27 cos 27= 2 2 sin 54 sin 182( )sin 18 sin 54 sin 54 sin 18 = = 2 cos 36 sin 182( ) 4sin 54 sin 18 = = ( cos 36 sin 54 = )(59) 24 sin A 3 cos 2B 2+ = 2 24 sin A 3(1 2 sin B) 2 + = 2 24 sin A 6 sin B 5 = ..... (1) sin 2A sec A sin B=2 sin A cos A sec A sin B =2 sin A sin B = ..... (2) sin B 1, 1= B [0, ]2 B2= 1sin A A2 6= = 22 cos(A B) 2 cos 13+ = = (60) 3 cos 2A 2 cos 2B 3 = 2 23(1 2 sin A) 2(1 2 sin B) 3 = ....(1)sin A 2 sin B= ..... (2) (2) (1) 2 23 24 sin B 2 4 sin B 3 + = 2 1sin B5 = B 1Q1sin B5 = 2cos B5=2 1sin A 2 sin B , cos A5 5 = = = sin(A B)+sin A cos B cos A sin B= +2 2 1 1 4 115 55 5 5 5

math e book release2-1.1

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