Check 0-9, 9,, - 6, 6, 6, =0.04, (-0.) = , =64 8 8, -8 (-6) =6 (-6) 6, -6 7, , -0. 8, -8 6, '7 ' '

Transcription

1

2 Check 0-9, 9,, - 6, 6, 6, =0.04, (-0.) = , =64 8 8, -8 (-6) =6 (-6) 6, -6 7, , -0. 8, -8 6, '7 ' ' 0.5 ;!; ;!; æ;!; '7 ' -' 0.5 Æ;!; 0-6 =(-6) =6 ' 6=6 0.7 =(-0.7) =0.49 'ƒ0.49=0.7 =(-) = ' = {;@;}={-;@;}=;9$; -Æ;9$;=-;@; ;@; a>0 5a>0 " (5a) =5a a<0 a<0 " (a) =-a a>0-4a<0 " (-4a) =-(-4a)=4a a<0 -a>0 " (-a) =-a 5a -a 4a -a 04-7x= _x x= 5 _5 = x x x=_5= x>7 7+x 9, 6, 5, y x 7+x=9 x= 5+x>5 5+x 6, 5, 6, y x 5+x=6 x= 0-x<0 0-x 6, 9, 4, x 0-x=6 x=4 00-x<00 00-x 8, 64, 49, y x 00-x=8 x= =49, (-7) = , -7 7+(-7)=0-4 4, - (-) =4 (-) a=- (-5) =5 5 b=5 a-b=(-)-5= 'ƒ.96=.4 'ƒ44= 004- ('7) =7 (-') = " (-5) =5 ('6) =6 -('6) =-6 ' 6="ç4 =4

3 005- ' 6=" 6 =6, " (-5) =5, ('7) =7 ' 6+" (-5) -('7) =6+5-7=4 ' 64=" 8 =8, (-') =, (') = ' 64 (-') _(') =8 _= a<0 " a =-a -a>0 -" (-a) =-(-a)=a -6a>0 " (-6a) =-6a a a a æ =æ { } < a a æ = " 4a =-" (a) a<0 -" 4a =-(-a)=a 05- ='4 4<5 <'5 ='9 9>6 >'6 ;!;=Æ;4!; ;6!;<;4!; Æ;6!;<;!; ='4 7>4 '7> -'7<- 4=' 6 6<0 4<' 0-4>-' 0 ;!;=Æ;4!; ;!;>;4!; Æ;!;>;!; -Æ;!;<-;!; < > < < > < 007- a<0, b>0 a<0, -b<0 " (a) +6"çb -" (-b) =-a+6b-{-(-b)} =-a+4b 008-0<a<b -a<0<b-a " (-a) =-(-a)=a, " (b-a) =b-a " (-a) -" (b-a) +"ça =a-(b-a)+a =a-b a-b 8n _7_n 009- = n 5 5 n=5_7= n 0 -n=0,, 4, 9 n=,, 9, 4 n ++9+4=8 8 ' A-x (A ) 0 A. Check 05- < < > > < < 0- '5<'7 -'>-' 5 -' 5, -', 0, '5, '7 -' 5, -', 0, '5, '7 0- ='9, 4=' 6 ' 4>, ' 4<4 ' 4->0, ' 4-4<0 " (' 4-) +" (' 4-4) =' 4-+{-(' 4-4)} = 0- ='9, 4=' 6 <'ƒn-<4 '9<'ƒn-<' 6, 9<n-<6 0<n<7 a=6, b= a-b=5 04- '=, '4=, '9=, ' 6=4 N()=0 N()=N()=N(4)= N(5)=N(6)=N(7)=N(8)=N(9)= N(0)=N()=N()= ( )=0+_+_5+_ =

4 0 0, cm , a, a, 'a, Æ;a!;, ;a!; 9 x=0, y= 0 Guide a(aæ0) a x a x =a x= 'a. 0 Guide a>0,a 'a, a 'a ' (-7) =49 7 " (-5) =5, 0 Guide a>0,('a) =(-'a) ="ça =" (-a) =a "ç6 +" (-7) =6+7= " (-) -(-') =-=8 -(-') _'4=-_=-4 -' 49 æ {-;7!;}=-7 ;7!;=-49 "ç8 _{-Æ;#;}=8_;#;= 06 Guide a>0, b>0, a<'x<b a <x<b 6=' 6, 9=' 8 6<' 9x<9 ' 6<' 9x<' 8, 6<9x<8 4<x<9 x 07 Guide a(a>0) 'a. 9 90_ =9(cm ) +9 y` cm y` cm 9 90_ =8(cm ) +9 9 cm. 08 Guide a (aæ0) a " (-4) =4 0.9 ' 0.9 (-9) = a (aæ0) 04 Guide "ça =[ -a (a<0) "ça ="ç(a) a<0 "ça =-a 05 Guide a>0, b>0, a<b 'a<'b 5<6 '5<'6 -'5>-'6 09 Guide a>0, a 'a, a -'a {-;$;} æ {-;$;}=;$; a=;$; 0.H4=;9$; ;9$; -;@; b=-;@; a-b=;$;-{-;@;}= ;4!;<;5@; Æ;4!;<Æ;5@; 5=' 5 4<5 ' 4<5 0.=' >0.04 ' 0.>0. ='9 9>7 >'7 -<-'7 0 Guide a>0, "ça =" (-a) =(-'åa) =a ' 44="ç =, 'ƒ0.09="ç0. =0., " (-6) =6, (-') = ( )= 0.-6_ =40-=8 4

5 Guide "ça =-a a<0 ='9 <' 0 -' 0<0 "ça =-a a<0 " (-' 0) =-(-' 0)=-+' 0 " (4a) =-4a 6"ça =-6a " 5a =" (5a) =-5a, 6 Guide a>0, b>0, 'a<'ßx<'b a<x<b Guide -a (aæ0) "ça =[ -a (a<0) -4<-'ƒx+<-'5 '5<'ƒx+<' 6 a>0-6a<0, -a<0, a>0 y` 5<x+<6 <x<: : " (-6a) =-(-6a)=6a 9" (-a) =9{-(-a)}=9a x,, 4, 5, =0 0 " (a) =a ( )=6a-9a+a =0 y` 0 7 Guide x 'ßx. 'ƒ00=0 N(00)=0 5<<6 5<' <6 N()=5 N(00)-N()=5 -(a-b (aæb) Guide " (a-b) =[ -(a-b) (a<b) -<a< 0<a+<4 " (a+) =a+ -<a< -4<a-<0 " (a-) =-(a-)=-a+ ( )=a+-(-a+) =a+ 8 Guide 0<a< a. a=;4!; a=;4!;, ;a!;=4, 'a=;!;, æ;a!;='4=, a =; 6; a <a<'a<æ;a!;<;a!; a, a, 'a, æ;a!;, ;a!; a, 'a, æ;a!; 4 Guide a = _5 y` ' 80a=" _5_a a=5_() y` a=5_, 5_, 5_, y a a=5_ =0 y` 0 80 a=5_() a a=;4!;, ;9!;, ; 6;, y. 9 Guide m-n m,n. 'ƒ-x -x -x=x=0 y` 'ƒy+6 y y+6=64y= y` x=0, y= 5 Guide " (A-B) A, B. x y 5

6 Check 06- ' 6=6 øπ0.h=æ;9!;=;!; 05- ' 6 '=,.H4=;; 9 ;;, " (-) =, =;$; p, -' 0.9 p, -' '4=-, øπ.h7=æ ;; 9 ;;=;$; -'4, -'4, øπ.h7,, -0.5 p, '- -'4, p, '-, øπ.h7,, 'ƒ 'ƒ 'ƒ 'ƒ , 4, 4, ' -4, 6, 6, '6-06- () (0 ) 07- ' ' 'ƒ x=.4 'ƒ y=0.5 x-y=.4-0.5= , '4<'7<'9 <'7< 5<+'7<6 +'7 5 a=5, b=(+'7)-5='7- a=5, b='7-08- '9<' <' 6<' <4 ' ' - ' 5<' <' 65<' <6 ' 5 ' -5 <'<4<+'<5 +' 4 +'-4='- -<-'<-<5-'<4 5-' 5-'-=-', ' - 5, ' -5 4, '-, -' m, n, m+'n 'n. Check 09- PQRS=_-4_{;!; }= PA =PQ =' A +' PB =PS =PQ =' B -' +' -' 09-. ' 6

7 0- -'5, <, <, < 0- > > < < < > 09- ' A(-' ), B(-+' ), C(-' ), D(-+') 00- ' ' 0, 0- '6+-('6+'7 )=-'7='9-'7>0 '6+>'6+'7 5-'5-"ç =-'5='9-'5>0 5-'5>"ç ' 0+-4=' 0-=' 0-'9>0 ' 0+>4 '-' 5-(-' 5+)='-='-'>0 '-' 5>-' 5+ æ;8!; --{æ;5!; -}=æ;8!; -æ;5!; <0 04- <'< -4<'-5<- -<-'<- <5-'<4 '-5 5-' -, -, -, 0,,, 7 '-5 5-' ' -5 5-' 0, P(--'), Q(+') a<b<c 06 C ' 0 0 P(--'), Q(-+'), 4 5 -' 6 7 +' 0 8 +p 0 Guide '9= øπ.h7=æ ;; 9 :=;%;, æ;8!; -<æ;5!; - 0- a-b=('-)-='-='-'4<0 a<b b-c=-('-)=-'='4-'>0 b>c a-c=('-)-('-)='-'<0 a<c a<c<b a<c<b 0- '9<' <' 6 <' <4 +<' +<4+ 4<' +<5 ' + D 0 Guide. a=.5, b=. a-b= Guide a 'a ABCD=_-4_{;!; }= CP =CB =' PC ' P --' ' FQ =FH =' 7

8 QF ' Q +' P(--' ), Q(+' ) 04 Guide a, b a-b>0 a>b, a-b<0 a<b ('5-)-('-)='5-'>0 '5->'- (6-')-4=-'='4-'>0 6-'>4 ('7+)-6='7-='7-'9<0 '7+<6 (8-'5)-(8-'6)=-'5+'6>0 8-'5>8-'6 (--')-(--'5)=-'+'5>0 --'>--'5 05 Guide a, b, c a<b b<c a<b<c a-b=('6-)-='6-='6-'9<0 a<b y` b-c=-(+' )=-'='-'<0 b<c y` a<b<c y` a<b<c 08 Guide. <'ß0<4 'ß0, 'ß0-09 Guide a 'a ABCD=4_4-4_{;!; }=0 AP =AB =' 0 y PA ' 0 P +' 0 y +' 0 AP P 0 Guide '. ' D C OP =OD =' A O B P- - 0 Q OQ =OC =' P(--'), Q(-+') P(--'), Q(-+') a, b b, c a, b, c Guide. 06 Guide 'a n<'a<n+ n. '4<'7<'9 <'7< -<'7-<- -<'7-<0 '7- C C 07 Guide a -a, a (). (') = " _(') =" = '_'-= -_(') =-4 '+ Guide a, b, c a<b b<c a<b<c a-b=-+'6-('6-')=-+'=-'+'>0 a>b b-c='6-'-(-')='6-='6-'4>0 b>c c<b<a Guide -'<x<' x. -'-<-'<-'<-<-'<'-<', 8

9 4 Guide x '5 '5<x< 6 Guide m<'5<m+, n<' 0<n+ +'5-='5-='5-'4>0 +'5> +'5 '5 m, n. <'5< 4<'ß0<5, 4 '5+ '5, '5 <'55<'5+ 'ß0<5'ß0<'5+ '5+ 5 Guide,. -'6, -'5 -'6-(-'5)=-'6+'5<0 -'6<-'5 -', -' y` -'-(-')=>0 -'>-' y` -'6<-'5<0<-'<-' y` -' y` -' 7 Guide 'a n ( )='a-n 6<'ß40<7[40]=6 <'ß0<4<0>='ß0- [40]+<0>=6+'ß0- =+'ß0 +'ß0 8 Guide a pa p A +0.5p_=+p +p 9

10 'ƒ0.7=æ = 00 0 Check - '5' ='ƒ5_=' 65 '''5='ƒ 5=' 0 -æ : :_æ;7(;=-æ : :_;7(;=-'6 ' 5_4æ;!;=_4_æ 5_;!;=8'5 ' 65 ' 0 -'6 8' = 'ƒ7. 'ƒ0.07=æ = = , '5, '5, 'ƒ7. '5 5 ' 45 - =æ : :=' 5 ' ' ' '7= =æ : 7 :=' '7 4'6 4'6 (-')=- =-4æ;^;=-4' ' ' ' ' ' 0 = _ =æ ;5@;_: º:='6 '5 ' 0 '5 ' - ' 4=" _6='6 -' 45=-" _5=-'5 5 æ;4%;=æ = '5 7 '7 'ƒ0.07=æ ;0&0;=æ = 0 0 ' 5 ' -4' '6 '5 '6 -'5 '7 0 _' ' 4- = = ' ' _' 5 5_'6 5'6 = = '6 '6_'6 6 '5 '5_' ' 5 = = ' '_' _'7 '7 = = = = ' 8 " _7 '7 '7_'7 4 ' 5'6 ' 5 ' '_'7='ƒ_7=' -'_' =-'ƒ_=-' 64=-"ç8 =-8 5'_'=5 'ƒ_=0'6 æ;5^;_æ : º:=æ ;5^;_: º:='4="ç = - '7=" _7=' 8-5'=-" 5 _=-' 50 ' - =-æ =-æ;4#; '5 5 =æ =æ ; 0; 0 0 ' 8 -' 50 -æ;4#; æ ; 0; - 00, 0, 7. 00, 0, 'ƒ7='ƒ7._00=0'ƒ7. 0_.668=6.68 'ƒ70='ƒ7._00=0'ƒ7. 0_8.48=84.8 ' =æ : 6 :='7 '6 ' 0 ' 0 '= =æ : º:=' 0 ' ' ' = _' 5=æ;5#;_' 5 '5 ' 5 '5 =æ ;5#;_5='9="ç = ' 0 = _' 0= =æ : º:=' 5 ' ' 0 ' ' ' ' ' ' = _ =æ : 4 :_æ : : '4 ' '4 ' =æ : 4 :_: :=', 0

11 ' 5 >' >' 0 > >'7 ' 'ß8_'8_'ß='ƒ8_8_ =øπ _ _ =øπfl _ _ =øπ( _) _ =4' a=4 'ß8_'8_'ß='_'_' = (') _' =4' 'a 'a_'6 ' 6a ' 6a 0- = = = 7'6 7'6_'6 4 4 ' 6a ' 0 = 6a=0 4 4 a=5 5 4 ' 4 ' 0- _ ' 48= _ 4' '8 7 ' 7 7 ' = ' 7 4' =7_;7@;_;4!;_æ ;!; ;!; =;!;æ;!; = = ' ' 4 a=;4!; ;4!; '6 08- =æ ; 5; 0.04+k=; 5; 5 6 +k= k=; 5;=;5!; 'ß50=" 5 =5''=5ab 0- ( )='5_'=6' 0 x ( )=;!;_4'_x='x 'x=6' 0 6' 0 x= =;^;_æ ;; º;;='5 ' 00- ' 46='ƒ4.6_00=0' 4.6 0_.49=.49 'ƒ4700='ƒ47_00=0' 47 ' 47 'ƒ49400='ƒ4.94_0000=00'ƒ _.=. 4.8 'ƒ4.8 'ƒ0.048=æ = = 'ƒ4.6 'ƒ =æ = = 'a a a ' 00a, æ, 'ƒ0000a, æ, y a " 0 «a æ (n ) 0 «0- x cm ;!;_p_(') _x=8'5p, x='5 4x=8'5 0 0 a=5, b= 0 04 ' '5<' <5<4' , ' ß0 cm 6 cm 'a 0 Guide a>0, b>0, 'a'b=' ab, =æ;ba; 'b ' 4 _6æ;7!;=_æ 4_;7!;='

12 0 Guide a>0, b>0,a'b=" a b 5'5="ç5fi _5='ƒ5 a=5 y` 'ƒ08=" 6 _=6' b= y` a=5, b= a b 06 Guide. ' ' '6 '5_ ='6 =æ 6_;5!;_;@; ' '5 ' '5 = = '5 5 '5 5 0 Guide ' 7-' 80=" _-" 4 _5='-4'5 =x-4y 07 Guide a>0, b>0, c>0, 'a'b'c=' abc ' 0_æ _' a=æ 0 a=' ƒ6_a æ _' 5=æ _5=' _a=0a=5 04 Guide. 'ƒ0.5=æ ; 0º0;= 7.07 = 'ƒ0.05=æ ;0%0;=.6 =0.6 0 '5 'ƒ0.0005=æ ;00%00;= 00.6 = 'ƒ500='ƒ5_00=0'5 0_.6=.6 'ƒ5000='ƒ50_00=0' 50 ' 50 0 '5 0 0_7.07= Guide a>0, b>0, c>0, 'a 'b 'c=æ a_ '7 ' b _ c 4 '7 æ (-' )= {- } 9 ' ' 4 ' 7 =- æ =-6æ =- =- ' ' =- =-' ' 09 Guide a>0, b>0, a'b="ça b. 5=' 5, 4'=', '5=' 0 '5<' <5<4' '5<' <5<4' a 05 Guide b>0, = 'b ' '8=' 4 4_' 4' = = =' ' '_' a'b b '6 '6_' ' 8 6' = = = =' ' '_' 6 6_'_' 6'6 = = ='6 '' '_'_'_' 6 0 a>0, b>0, "ça b=a'b, æ b Guide = a ' 0.48=æ ; 0 0;=æ =æ _ = 5 5 a=;5@; ' 8=" 8 _=8' b=8 ' 5 ' 5ab=æ 5_;5@;_8=' 6=4 4 'b a

13 Guide. 7 8 ' 0.7=æ =æ =æ 00 5 ' a ' 0.7= = ('5) b _ 5 5 Guide x cm. x cm ' 0x=' 'x=' 0 ' 0 x= =' ß40=' ß0 ' ' ß0 cm Guide a>0, b>0, "ça b=a'b ' 00=" _0 =0' 0_.7=7. y ' 750=" 0_5 =5' 0 5_5.477=7.85 y 7., 7.85 ' 00 ' 750 b Guide a>0, = 'a b'a a 6 Guide a 'a AB =' 4='6(cm) y BC ='6(cm) y ABCD='6_'6=(cm ) y cm AB BC ABCD 5 5 5' 0 ' 0 = = = ' 40 ' a=;4!; b b_'5 b'5 = = '5 '5_'5 5 b =;$; b=0 5 7 Guide m>0,m =a m='a m, n.5 5 m='.5, n=' 5 5 ' 50+' 0.005='ƒ.5_00+æ 0000 ' 5 ' ' 50=0' a-b=4_;4!;-0=-9 n ' ' 50=0m Guide. 8 ' 54 ' -4' 0_æ =-8'5_ 5 '5 =-8'5_ ' '5 _ =-8 æ 5_ '6 '6 _ =-4æ =- =-8' ' 8 Guide x>0, y>0, x'y="çx y b a a b ab aæ +bæ =æ +æ a b a b =' ab+' ab =' 5+' 5 =5+5=0 0

14 Check 5- '5+'5=(+)'5=5'5 ' ' + ={;!;+;#;}'=' '-7'+4'=(-7+4)'=-' 4'6+'-9'6-6'=(4-9)'6+(-6)' =-5'6-4' 5'5 ' -' -5'6-4' 5- ' 54+' 4='6+'6=5'6 ' 75-' 48=5'-4'=' ' 7-6'+'='-6'+'=-' '7+' 8-' 6-'='7+'-'7-' 4 ' 0 '5 =-'7+' -'8='-'=-' ' -'6+ = -'6+ ' 4 ' '6 '6 = -'6+ 4 =- 5'6 ' -' -'7+' -' 5' ('6+')_'=' +'6='+'6 ('5-') =('5) -_'5_'+(') =5-' 5+ =8-' 5 5'6 4 (+'6)(-'6)= -('6) =4-6=- ' 0+'6 '+'6 8-' 5 - '- 6- = '+ ('+)('-) ='- ('5-') = '5+' ('5+')('5-') ('5-') = ='5-' ' '(+') = -' (-')(+') ='+'6 ' ' '6 '+' ('+') = '-' ('-')('+') =+'6+ =5+'6 '- '5-' '+'6 5+'6 04- A=4'-6'+5'=(4-6+5)'=' B='-5'+7'='+(-5+7)'='+' A+B='+('+')=4'+' 4'+' a'-' 8=5'+a'-' ' =(+a)' +a=6 a= 'a+'5b='('+'5)+'5('-'5) =+' 0+' 0-5 =-+5' 0 -+5' 0 '8-4 ' 0+' ' '5 ('-4)_' ('5+' 0 )_'5 = + '_' '5_'5 4-4' 0+0' = + 5 =-'++'=4 '-' 08- +('-')_' ' '6- = +4-'6 ='6-+4-'6 =-'6 -'6 09- A=('-) =(') -_'_+ =-' B=('-4)('+)=_(') +(6-4)'-8 =-+' B-A=-+'-(-') =-+'-+' =-5+4' -5+4' 4

15 040- '5 { - }+'('-a) ' 0 '5 ='-+4-a' =+(-a)' -a=0 a=;!; ;!; 04-4(' 7+' 48+' 75 )=4('+4'+5') =4_' =48' (cm) 48' cm 045- <'< -<-'<- <4-'< x=(4-')-=-' x -4x-=(-') -4(-')- =4-4'+-8+4'- =-4-4 x=-' x-=-' (x-) =, x -4x+4=, x -4x=- x -4x-=--=-4 ' ' '- '+ '('+) '('-) = + ('-)('+) ('+)('-) '6+' '6-' = + ='6 '+' 04- x= = ='+', '-' ('-')('+') '-' y= = ='-' '+' ('+')('-') x+y=('+' )+('-' )=' xy=('+' )('-' )= x +xy+y =(x+y) +xy =(') + = a +b =(a+b) -ab a +b =(a-b) +ab (a+b) =(a-b) +4ab (a-b) =(a+b) -4ab ('+) 044- x= = ='+ '- ('-)('+) x -x+5=('+) -('+)+5 =+'+-'-+5 =7 7 x='+ x-=' (x-) =, x -x+= x -x= x -x+5=+5=7 0' ' 4 ' ' ' 0 8'6 cm Guide "ça b a'b. '-' 75+' ='-5'+6'=' a= 0 Guide a>0, b>0, c>0, 'a('b+'c)=' ab +' ac '7A-'B='7('7-')-'('-'7) =7-' -6+' =-' 0 Guide. 4 4 ' 4 4 ( )= _' - _' 8- + ' ' '6 '6 '6 ( )=8-4'6-+ 0'6 ( )=6-6- 0'6 5

16 04 Guide. 0 Guide a+b a-b. =('6+') +(' 5-'5) =(6+4'+)+(5-0'+5) =8-6' 05 Guide ( ) =_{( )+( )} {(' 4-' )+(' 8-'6 )} ={('6-' )+('-'6 )} =('+'6) =4'+'6 (cm) 06 Guide (x+y)(x-y)=x -y. ' 0+ ' 0- = + ' 0- ' 0+ (' 0+) (' 0-) = + (' 0-)(' 0+) (' 0+)(' 0-) =(0+6' 0+9)+(0-6' 0+9) =8 07 Guide x+y, xy. x+y=(+')+(-')=4 xy=(+')(-')= (x+y) + = = x y xy 08 Guide 'a n ( )='a-n <'7< 5<+'7<6 a=(+'7)-5='7- a +4a=('7-) +4('7-) =7-4'7+4+4'7-8 = a='7- a+='7 (a+) =7, a +4a+4=7 a +4a= 09 Guide. ' +'=4'+'= 5 ' ' 0+' 45='5+'5=5øπ 5 ' 7-'ƒ08+ ='-6'+'= - ' ' 5+5+(-)=8 8 '-'6 '+'6 ' a+b= + = =' y '-'6 '+'6 -'6 a-b= - = =-'6 y (a+b)(a-b)='_(-'6)=-' y -' a+b a-b (a+b)(a-b) Guide a, b a-b. +'5-'5=-'5<0 +'5<'5 -' 8-(-4' )=-'-+4'='->0 -' 8 >-4' '5+'6-(' 0+'6 )='5+'6-'5-'6 ='6-'5 >0 '5+'6>' 0+'6 '-'8-(4'-' )='-'-4'+' =5'-6' =' 75-' 7>0 '-'8 >4'-' '-'-('8-' )='-'-'+' =-'+' >0 '-'>'8-' Guide. ' ' ' ( )= _5- _' 0+4'_'5- _'5 '5 '5 ' 0 ( )=' 0-+4' 0-4 =5' 0-6 a=-6, b=5 a+b=- Guide (a+b)(a-b)=a -b. ( )=(4'+' )('-4') =('+4' )('-4') =(') -(4') =7-=-5 6

17 4 Guide. A=('-) =-'+ =4-' y` B=('+)('-) =_(') +(-4+)'- =4-' y` A-B=(4-' )-(4-') =' y` ' A B A-B 8 Guide a>0, b>0, 'a-'b = = 'a+'b ('a+'b)('a-'b) 'a-'b a-b = ' '+'5 '5+'7 '7+'9 (-') ('-'5) = + (+' )(-') ('+'5 )('-'5) ('5-'7) ('7-'9) =+ + ('5+'7 )('5-'7) ('7+'9 )('7-'9) =-(-' )-('-'5 )-('5-'7 )-('7-'9) =-+'-'+'5-'5+'7-'7+'9 =-+'9 =-+ = 5 Guide p, q ' m, p+q' m q=0 b='(a-')+'8('6-' 8 ) ='(a-')+'('6-') =a'-+8'- =(a+8)'-5 b a+8=0 a=-4, b=-5 a-b= 6 Guide ( ) =_{( )+( )} 80 ( )=80 4'= 4' 0 ( )= =0'(m) ' ( )=(4'+0') =8'(m) 7 Guide ( )= _( )_() = _(' 50-' )_(' -') = _(5'-' )_('-') = _(0'6-0-+'6) = _('6-)=6'6-6'6-9 Guide a 'a BC, AD _-4_{;!; }=4-= BP =BC =' a=-' AQ =AD =' b=' b ' = a -' '(+') = (-')(+') =--' 0 Guide x. x -4x+7=('6+) -4('6+)+7 =6+4'6+4-4'6-8+7 =9 " x -4x+7='9= x='6+ x-='6 (x-) =6 x -4x+4=6 x -4x= " x -4x+7='ƒ+7='9= --' 7

18 Guide n+'. Guide. <'< n+<n+'<n+ n+' n+ a=(n+' )-(n+)='- + = + a a+ '- '+ '+ '- = + ('-)('+) ('+)('-) ='++'- =' ( )= + +y+ '+' '+' '5+'6 '-' '-' ( )= + ('+')('-') ('+')('-') '5-'6 ( )=+y+ ('5+'6)('5-'6) ( )=-{('-')+('-')+y+('5-'6)} ( )=-('-'+'-'+y+'5-'6) ( )=-('-'6)=-+'6 Guide a 'a 6 cm, 4 cm, 54 cm '6 cm, ' 4 cm, ' 54 cm, '6 cm, '6 cm, '6 cm a`cm b`cm 54`cm@ Â6`cm 4`cm@ c`cm 6`cm@ Â6`cm Â6`cm Â6`cm a+b+c='6 (cm) =(a+b+c)+_'6+_'6+_'6 ='6+'6+4'6+9'6 =8'6 (cm) 8'6 cm 4 Guide ( )=()-( ) 8<' 80<9 f(80)=' 80-8=4'5-8 6<' 45<7 f(45)=' 45-6='5-6 4<' 0<5 f(0)=' 0-4='5-4 f(80)-f(45)+f(0) =(4'5-8)-('5-6)+('5-4) =4'5-8-6'5++'5-4=0 f(80) f(45) f(0) f(80)-f(45)+f(0) y` y` y` y` 0 8

19 Check 7- x +x a +a+ x -x- a x, x(a+b) a, a(-b) x, x(x+) xy, xy(x+y) x+, (x+)(x-) x-y, (x-y)(a+b) 8- a -4a+4=a -_a_+ =(a-) x +6xy+9y =x +_x_y+(y) =(x+y) 4x +4x+=(x) +_x_+ =(x+) 9a -4ab+6b =(a) -_a_4b+(4b) =(a-4b) (a-) (x+y) (x+) (a-4b) 8- a -=a - =(a+)(a-) -x +6=6-x =4 -x =(4+x)(4-x) 4a -b =(a) -b =(a+b)(a-b) 6x -5y =(4x) -(5y) =(4x+5y)(4x-5y) (a+)(a-) (4+x)(4-x) (a+b)(a-b) (4x+5y)(4x-5y) 9-, 4-4, - -, 7-0, 9- x +5x+6-6, -6 -, -6, - -, - x +5x+6=( x+ )( x+ ) x -x-4-4, -4 -, -4, x -x-4=( x+ )( x-4 ) 0-4x +8x+ 4x +8x+=( x+ )( x+ ) x +7x < x +7x-5=( x- )( x+5 ) 6x +x < 6x +x-=( x- )( x+ ) x -x < +< x -x-0=( x+5 )( x- ) 046-,, 047- x +6x=x(x+) a +a =a (a+) ax y+bxy=xy(ax+b) x(x+y)+xy=x(x+y+y) =x(x+y) =x(x+y) (a-b) -(a-b)=(a-b)(a-b-) 048- a -6a+9=a -_a_+ =(a-) x +;@;x+;9!;=x +_x_;!;+{;!;}={x+;!;} x -0x+5=x -_x_5+5 =(x-5) 9x +5x+5=(x) +x_5+5 4x -xy+9y =(x) -_x_y+(y) =(x-y) 9

20 048- x +8x+8=x +_x_4+8 x -x+6=x -_x_6+6 =(x-6) x -0x+00=x -_x_5+0 x +x+=x +_x_+ x +; 0;x+; 5;=x +_x_; 0;+{;5!;} 9a -;9!;b =(a) -{;!;b} ={a+;!;b}{a-;!;b} 05- a -8=(a ) -9 =(a +9)(a -9) =(a +9)(a - ) =(a +9)(a+)(a-) a + a -8 ;9!;x +;@;x+={;!;x}+_;!;x_+ ;9!;x +;@;x+={;!;x+} 049-4x +ax+9=(x) +ax+ (x ) a a= = (x-)(x-6)+b=x -8x++b =x -_x_4++b (x-4) +b=6 b=4 a-b=-4= <x<;!; x+;!;>0, x-<0, x-;!;<0 ( )=æ {x+;!;}+" (x-) -æ {x-;!;} ( )={x+;!;}+{-(x-)}-[-{x-;!;}] ( )=x+;!;-x++x-;!; ( )=x+ x x = -(x) =(+x)(-x) x -; 6;=x -{;4!;}={x+;4!;} {x-;4!;} 4a -6b =4(a -9b ) =4 {a -(b) } =4(a+b)(a-b) x +x-6=(x-)(x+) x -x-6=(x-)(x+) x -7x+=(x-4)(x-) 6 5 x +5x+6=(x+)(x+) x -4x-=(x-7)(x+) x -8x+6=(x -4x+) x -8x+6=(x-)(x-) x x -x-8=(x-6)(x+) x x-6, x+ (x-6)+(x+)=x- 05-6x -x-=(x-)(6x+) a=-, b=6, c= a+b+c=(-)+6+=5 05- x +5x-=(x-)(x+4) x +x-4=(x-)(x+4) x+4 x x -4xy-5y =(4x+y)(x-5y) 054-,,, 4 0

21 055- x+ x +8x+k x +8x+k=(x+)(x+m) (m ) x +8x+k=x +(m+)x+m 8=m+, k=m m=7k=7 0 Guide x y-x =x (y-) x y-x, x, x, y-, x(y-), x (y-) x y-x 056- ax +bx+c x x (x-)(4x+5)=4x -7x-5 b=-7, c=-5 x x (x-)(x-)=x -7x+6 a=, b=-7 x -7x-5 x -7x-5=(x-5)(x+) (x-5)(x+) 057- (x+) -4 =x +x-5 x +x-5=(x+5)(x-) x- x ;!;_{(x-)+(x+4)}_()=x -x- (x+)_()=(x+)(x-) ()=x- x- 0 0 {;4!;x+;@;y} x 09, x Guide a +ab+b =(a+b), a -ab+b =(a-b) ; 6;x +;!;xy+;9$;y ={;4!;x}+_;4!;x_;@;y+{;@;y} ; 6;x _;!;xy+;9$;y ={;4!;x+;@;y} {;4!;x+;@;y} 0 Guide a -b =(a+b)(a-b) 5x -6y =(5x) -(6y) =(5x+6y)(5x-6y) y A=5, B=6 B-A= y 5x -6y B-A 04 Guide x +(a+b)x+ab=(x+a)(x+b) (x-)(x+b)=x +(-+b)x-b a=-+b, -5=-b a=, b=5 a+b=7 -b=-5 b=5 x +ax-5=(x-)(x+5) =x +x-5 a= 05 Guide. x +x-6=(x-)(x+6) 6x +7x-5=(x-)(x+5) x (x+)(x-6) Guide. 6x -x-0=(x-5)(x+)

22 07 Guide x +ax-8 x+. x +ax-8=(x+)(x+). x+ x +ax-8 x +ax-8=(x+)(x+b) (b ) x +ax-8=x +(6+b)x+b a=6+b, -8=b b=-4 a= 08 Guide ( )=( )_( ) 64x -49=(8x+7)(8x-7) y 8x-7 {(8x+7)+(8x-7)}=x y x 64x -49 9x +x+=9x +_x_;6!;+ ={;6!;}=; 6; a (aæ0) Guide " a =[ -a (a<0) -<x< x+>0, x-<0 ( )=" (x+) -" (x-) =(x+)-{-(x-)} =x++x- =x- Guide a -b =(a+b)(a-b) -x +50y =-(6x -5y ) =-(4x+5y)(4x-5y) a=-, b=4, c=5 a+b+c= Guide ma+mb ^jjjjjj& m(a+b) a b -4ab ab, 0 Guide (x+8) (x-) (x-5y) {a+;5!;} Guide x +ax+b a= b, x +ax+b b={;a;} x + x+5 = 5=0 4x + x+ = =4 9x + x+4 = = x +;!;x+=x +_x_;4!;+ ={;4!;}=; 6; 4 Guide. (x+)(x+)-=x +5x+6- =x +5x+4 =(x+)(x+4) 5 Guide x +(a+b)x+ab=(x+a)(x+b) x -5x+6=(x-)(x-) x -x+6=(x-6) x +x+6=(x+4)(x+9) x +0x+6=(x+)(x+8) x +kx+6 a, b. 6=_6=_8=_=4_9=6_6 k -7, -0, -5, -, -, 7, 0, 5,, 6 Guide acx +(ad+bc)x+bd=(ax+b)(cx+d) 9x +x-4=(9x-7)(x+) (9x-7)+(x+)=0x-5 0x-5 7 Guide. x +x=x(x+) x +x+=(x+)

23 x -=(x+)(x-) x +x+=(x+)(x+) x -x-=(x+)(x-) 8 Guide. x -xy-y =(x+y)(x-y) x -xy-y =-6, x+y= -6=(x-y) x-y=- - Guide ( )=( )_( ) (x-)(x+7)-6(x-) =x +x--6x+8 =x +5x- x +5x-=(x-)(x+) x+ x-. 9 Guide mx+n ax +bx+c ax +bx+c=(mx+n)(px+q) (p, q ) x +7x-5=(x-)(x+5) x +ax- x- x+5 x- x +ax-=(x-)(x+m) (m ) x +ax-=x +(m-)x-m a=m-, -=-m m=4a=5 x+5 x +ax-=(x+5)(x+n) (n ) x +ax-=x +(n+0)x+5n a=n+0, -=5n n=-;; 5 ;;a=;; 5 ;; a a=5 5 Guide. 0<x< 0<x<;[!; x-;[!;<0, x+;[!;>0 ( )=æ {x-;[!;} -æ {x+;[!;} ( )=-{x-;[!;}-{x+;[!;} ( )=-x Guide f(x). f(x)=- x f(x)={-;[!;}{+;[!;} f(x)= x- x _ ( ) x+ x 0 Guide. x (x-5)(x+)=x -4x-5 x -4 y (x+)(x-4)=x -x- - y x -4x- x -4x-=(x+)(x-6) y (x+)(x-6) =;!;_;#;_;@;_;$;_y_;!9*;_;@9);_;!0(;_;@0!; =;!;_;@0!;=;4@0!; 4 Guide. n +8n-48=(n+)(n-4) y n+>n-4 n-4= n=5 y n +8n-48=(n+)(n-4) =7 y 7 x n +8n-48 n n +8n-48

24 Check - a -ab =a(a -b )=a(a+b)(a-b) x+=a (x+) -4(x+)+4=A -4A+4 =(A-) ={(x+)-} =(x+) a(a+b)(a-b) (x+) - x+ x a -a b+ab =a(a -ab+b )=a(a-b) a b-b =b(a -b )=b(a+b)(a-b) a-b 059- x-y=a (x-y) -0(x-y-)+5=A -0(A-)+5 =A -0A+5 =(A-5) =(x-y-5) a=, b=-5 a-b=7 7 - x +xy+5x+y+6 =(x+)y+(x +5x+6) =(x+)y+(x+)(x+) =(x+)(x+y+) (x+)(x+)(x+5)(x+6)- ={(x+)(x+6)}{(x+)(x+5)}- =(x +7x+6)(x +7x+0)- x +7x=A ( )=(A+6)(A+0)- =A +6A+48=(A+4)(A+) =(x +7x+4)(x +7x+) =(x+)(x+4)(x +7x+4) (x+)(x+y+) (x+)(x+4)(x +7x+4) 060- x+=a, y-=b (x+) +(x+)(y-)-0(y-) =A +AB-0B =(A+5B)(A-4B) ={(x+)+5(y-)} {(x+)-4(y-)} =(x+5y-)(x-4y+6) a=5, b=-4, c=6 a+b+c= x -x y+6y-6x=(x -x y)+(6y-6x) =x (x-y)-6(x-y) =(x-y)(x -6) =(x-y)(x+4)(x-4) x -6-7_8+7_=7_(8+) =7_0=70 8 +_8_+ =(8+) =0 = =(-) =0 = =(07+7)(07-7) =4_00= x +4x+4=(x+) ={('5-)+} =('5) =5 x -xy+y =(x-y) ={(+'5 )-(-'5)} =('5) = x -9-y +6y=6x -(9+y -6y) =6x -(y -6y+9) =(4x) -(y-) =(4x+y-)(4x-y+) A=4x+y- 4x+y- 06- y x -xy-x+y-6=-y(x-)+(x -x-6) =-y(x-)+(x+)(x-) =(x-)(x-y+) (x-)+(x-y+)=x-y- x-y- 4

25 064- (x+)(x+)(x-)(x-5)+6 ={(x+)(x-)}{(x+)(x-5)}+6 =(x -x-)(x -x-5)+6 x -x=a ( )=(A-)(A-5)+6 =A -8A+8 =(A-9) =(x -x-9) (x +ax+b) =(x -x-9) a=-, b=-9 a+b=(-)+(-9)= =(5 - )+( -9 )+(7-5 ) =(5+)(5-)+(+9)(-9) +(7+5)(7-5) =8_+0_+_ =(8+0+)_ =60_ =0 -' 066- a= = =-', +' (+' )(-') +' b= = =+' -' (-' )(+') a +b -ab-=(a -ab+b )- =(a-b) - ={(-' )-(+' )} - =(-') - =- = a +a b-4a-4b=a (a+b)-4(a+b) =(a+b)(a -4) =(a+b)(a+)(a-) a- ={(a+b)(a+)+(a+b)(a-)+(a+)(a-)} =(a +ab-4) =6a +4ab-8 6a +4ab x-, a(a+b)p 7 (0, 6), (-, -8), (6, 0), (-8, -) 8 5, 7 0 Guide. =4x (x+)-(x+) =(x+)(4x -) =(x+)(x+)(x-) 0 Guide. x-=a (x-) -4(x-)-5 =A -4A-5 =(A+)(A-5) ={(x-)+}{(x-)-5} =(x-)(x-7) y a+b=(-)+(-7)=-8 y -8 a+b 0 Guide. x -8x y+8xy =x(x -4xy+4y )=x(x-y) x y+xy+y=y(x +x+)=y(x+)(x+) xy-x-y+6=x(y-)-(y-) =(x-)(y-) x (y+)-4y-8=x (y+)-4(y+) =(y+)(x -4) =(y+)(x+)(x-) x -y +4x+4=(x +4x+4)-y =(x+) -y =(x++y)(x+-y) =(x+y+)(x-y+) 5

26 04 Guide 09 Guide x +(a+b)x+ab=(x+a)(x+b). y x +xy-x-y-=y(x-)+x -x- =y(x-)+(x-)(x+) =(x-)(x+y+) A +AB-6B =(A+)(A-) (x+) +(x+)(x+)-6(x+) =A +AB-6B =(A+B)(A-B), ={(x+)+(x+)}{(x+)-(x+)} =x(6x+5) 05 Guide. 04 -_04_4+4 =(04-4) =00 = =(0+99)(0-99) =00_= _04_ = = Guide. x='+' '-' y= = ='-' '+' ('+' )('-') x +y -xy=(x-y) ={('+' )-('-')} =(') =8 07 Guide. ( )=0a (a-b)+ab(a-b)-b (a-b) =(a-b)(0a +ab-b ) =(a-b)(a+b)(5a-b) 08 Guide. (x +x) -5x -5x+=(x +x) -5(x +x)+ x +x=a ( )=A -5A+ =(A-)(A-) ={(x +x)-}{(x +x)-} =(x +x-)(x +x-) =(x +x-)(x+)(x-) x- 0 Guide. xfi -x -x+=x (x-)-(x-) =(x -)(x-) =(x +)(x -)(x-) =(x +)(x+)(x-)(x-) y x x+, x-, x- y (x+)+(x-)+(x-)=x- y x- xfi -x -x+ Guide. ( )=64-(x +xy+y ) =8 -(x+y) =(8+x+y)(8-x-y), Guide. z ( )=z(x-y)-(x +xy-y ) =z(x-y)-(x-y)(x+y) =(x-y)(-x-y+z) Guide ( )( )( )( )+k. (x-4)(x-)(x+)(x+)+4 ={(x-4)(x+)}{(x-)(x+)}+4 =(x -x-)(x -x-)+4 6

27 x -x=a ( )=(A-)(A-)+4 =A -4A+48 =(A-6)(A-8) =(x -x-6)(x -x-8) =(x+)(x-)(x -x-8) 6 Guide r pr ( )=;!;p(a+b) +;!;pa -;!;pb ( )=;!;p{(a+b) +a -b } ( )=;!;p{(a+b) +(a+b)(a-b)} ( )=;!;p(a+b)(a+b+a-b) ( )=;!;p_a(a+b) 4 Guide. ( )=a(a+b)p a(a+b)p ="._ _49.5 ="._( ) ="._( )( ) ="._00_ =" = 5 Guide. a -b +4b-4=a -(b -4b+4) =a -(b-) =(a+b-)(a-b+) y =('+-)('-+) y =('-)('+) =- = y a -b +4b-4 7 Guide 7. xy+x+y+=x(y+)+(y+)=(x+)(y+) (x+)(y+)=7 x+=, y+=7 x=0, y=6 (0, 6) x+=-, y+=-7 x=-, y=-8 (-, -8) x+=7, y+= x=6, y=0 (6, 0) x+=-7, y+=- x=-8, y=- (-8, -) (0, 6), (-, -8), (6, 0), (-8, -) (0, 6), (-, -8), (6, 0), (-8, -) 8 Guide. fl -=( +)( -) =( +)( +)( -) =57_7_ , 7 7

28 Check 4- x =(x+) x =x+ x -x-=0 x +x=4-x x +x-4=0 (x-)(x+6)=0 x +4x-=0 x(x+)=x -x+9 x +x=x -x+9 4x-9=0 4- (-) -=0 _(-) +_(-)=-+0 5_(-) +6_(-)+=0 (-) -4_(-)-=+0 x=-, 068- x =0 x +=x- x -x+=0 x(x +4)=x -x + x +4x=x -x + x +4x-=0 5(x-) =5x -x+ 5x -0x+5=5x -x+ -7x+=0 (x-)(x+)=-x x -9=-x x -0= x +=a(x-) x +=ax -4ax+4a (-a)x +4ax+-4a=0 x -a+0 a x - x=0,,, x -4x+=0 x 0,,, x=0 x= x= x= 0-4_0+=+0-4_+=0-4_+=-+0-4_+=0 x= x= x= x= 07- x= x +x-a=0 +_-a=0 a=0 x= x +bx-9=0 _ +b-9=0 b=;!; a=0, b=;!; 07- x=a x -x-=0 a -a-=0 a -a= x=b x -x+=0 b -b+=0 b -b=- a -b -a+b=a -a-(b -b) =-(-)=4 4 Check 5- x(x-)=0 x=0 x-=0 x=0 x= (x+5)(x-)=0 x+5=0 x-=0 x=-5 x= (x+4)(x-)=0 x+4=0 x-=0 x=-4 x=;!; 070- x= +_-=+0 =9+ -5_+6=0 +4_=+5 (-)(+)=+0 x= (x+)(5x-)=0 x+=0 5x-=0 x=-;!; x=;5@; x=0 x= x=-5 x= x=-4 x=;!; x=-;!; x=;5@; 8

29 5- x +4x=0 x(x+4)=0 x=0 x+4=0 x=0 x=-4 x -6x+5=0 (x-)(x-5)=0 x-=0 x-5=0 x= x=5 x +x-=0 (x+)(x-)=0 x+=0 x-=0 x=- x=;!; x +=-7x x +7x+=0 (x+4)(x+)=0 x+4=0 x+=0 x=-4 x=- x +x= x +x-=0 (x-)(x+)=0 x-=0 x+=0 x=;!; x=- x -x+7=x+ x -5x+6=0 (x-)(x-)=0 x-=0 x-=0 x= x= x=0 x=-4 x= x=5 x=- x=;!; x=-4 x=- x=;!; x=- x= x= 6- x -x+=0 (x-) =0 x=() x +4x+4=0 (x+) =0 x=-() x -0x+5=0 (x-5) =0 x=5() x -8x+6=0 (x-4) =0 x=4() 4x -4x=- 4x -4x+=0 (x-) =0 x=;!;() 9x =x-4 9x -x+4=0 (x-) =0 x=;@;() x=() x=-() x=5() x=4() x=;!;() x=;@;() 6- a={;^;}=9 x +6x+9=0 (x+) =0 x=-() -4 a={ }=49 x -4x+49=0 x=7() (x-7) =0-4 -+a={ }=4 a=5 x -4x+4=0 (x-) =0 x=() 5+a={;*;}=6 a= x +8x+6=0 x=-4() (x+4) =0 9, x=-() 49, x=7() 5, x=(), x=-4() 7- x =7 x= '7 x = x= ' = ' x -5=0 x =5 x =5 x= '5 4x -9=0 4x =9 x =;4(; x= Æ;4(;= ;#; x -5=0 x =5 x =;%; x= Æ;%;= x += x = x =6 x= '6 ' 0 x= '7 x= ' x= '5 ' 0 x= ;#; x= x= '6 7- (x-) = x-= ' x= ' (x-4) =6 x-4= '6 x=4 '6 (x+) -7=0 (x+) =7 x+= ' x=- ' (x+) -0=0 (x+) =0 x+= ' 0 x=- ' 0 (x+) =5 x+= '5 x=- '5 x= - '5 9

30 (x-) -8=0 (x-) =8 x-= ', x= ' x= ' x= ' x=- ' x=4 '6 - '5 x= x= '5 8- ;4(;, ;4(;, ;4(;, ;#;, ;4%;, ;#;,, '5 x=- ' 0 ' 076- x -x-4=0 (x+)(x-4)=0 x=-;!; x=4 x +(a-)x+8=0x=4 4 +4(a-)+8=0 a= x=- x -6x+a=0 (-) -6_(-)+a=0 a=-7 x -6x-7=0(x+)(x-7)=0 x=- x=7 x=- 5x +bx-=0 5_(-) +b_(-)-=0 b=4 5x +4x-=0(x+)(5x-)=0 07- (x-4)(x+)=0 x-4=0 x+=0 x=- x=;5!; p>qp=7, q=;5!; p=7, q=;5!; x=4 x=-;!; (x-4)(x-)=0 x-4=0 x-=0 x=4 x=;!; (x+4)(x+)=0 x+4=0 x+=0 x=-4 x=-;!; (x+4)(x-)=0 x+4=0 x-=0 x=-4 x=;!; -(x-4)(x-)=0 x-4=0 x-=0 x=4 x=;!; 074- x -0x+8=0 (x-4)(x-)=0 x=;$; x= a>b a=, b=;$; a-b=-;$;=;@; ;@; 075- x=-4 x +5x+a=0 _(-4) +5_(-4)+a=0 a=- x +5x-=0 (x+4)(x-)=0 x=-4 x=;#; b=;#; ab=-_;#;= x =0 x=0() x -=0 (x+)(x-)=0 x=- x= x =x-8 x -x+8=0 (x-) =0 x=() x +4x+=0 (x+)(x+)=0 x=- x=- (x+4)(x-)=-9 x +x+=0 (x+) =0 x=-() x(x-)=-;4!; x -x+;4!;=0 {x-;!;}=0 x=;!;(),,, a={ }=4 -a=- a= x -4x+4=0 (x-) =0 x=() b= a+b= x =-4 x =4 x= '6 x =00 x =50 x= 5' x -=0 x =, x =;!; x= ' 0

31 x -8=0 x =8, x =9 x= '5 5x =9 x =;5(; x= (x+a) +4=0 -(x+a) =-4, (x+a) =7 x+a= '7 x=-a '7 -a=5, b=7a=-5 b-a=7-(-5)= 0, 0 x= x=;5!;() a=40, x=-5 () [ a=-40, x=5 () p=;4%;, q=;%6&; bæ0 08- x -x+=0 x { x -4x+;!;=0, -4 } 4 x -4x=-;!; x -4x+4=-;!;+4 (x-) =: : p=, q=: : p+q=: : : : 084- x -6x+k=0 x -6x=-k -6 { } 9 x -6x+9=9-k, (x-) =9-k x-= 'ƒ9-k x= 'ƒ9-k 9-k= k=7 7 0 Guide x (x )=0 x =x + 0= 4x(x-)=x +4x 4x -4x=x +4x x -8x=0 (x-) =x +4 x -6x+9=x +4-6x+5=0 x -x+=x -x+=0 x(x +)=x -x +6 x +x=x -x +6 x +x-6=0, 0 Guide x x=-, -, 0,, x +7x-8=0 x -, -, 0,, x=- (-) +7_(-)-8=-8+0 x=- (-) +7_(-)-8=-4+0 x=0 0 +7_0-8=-8+0 x= +7_-8=0 x= +7_-8=0+0 x +7x-8=0 x= x= 0 Guide. x=- x +(a+5)x-a=0 (-) +(a+5)_(-)-a=0 -a-4=0 a= Guide AB=0. x +x-0=0 (x+5)(x-)=0 x+5=0 x-=0 x=-5 x= 05 Guide. x +x-0=0 (x+5)(x-4)=0 x=-5 x=4 y x +9x-5=0 (x+5)(x-)=0 x=-5 x=;!; y

32 x=-5 m=-5 y -5 x +x-0=0 x +9x-5=0 m 06 Guide ()=0. (5x+)(5x-)=-4 5x -0x-=-4 5x -0x+=0, (5x-) =0 x=;5!;() x=;5!;() 07 Guide (x-p) =q (qæ0) x=p 'q 4(x+) =0 (x+) =5 x+= '5 x=- '5 a=-, b=5 a+b= 0 Guide x=a ax +bx+c=0 aa +ba+c=0. x=a a +a+=5a+, a -a+=0 a+0 a a-+ =0 a+ = a a a + ={a+ }-= -=7 a a Guide ()=0. (x+4)(x-)= x +5x-5=0 (x+5)(x-5)=0 x=-5 x=;%; y a=;%;, b=-5 4a-b=4_;%;-(-5)=5 y 08 Guide ()=(). x -x+=0 x { x -4x+=0, -4 } 4 x -4x+4=-+4 x -4x=- (x-) = x= ' A=4, B=, C= A-B+C=5 5 ax +bx+c=0. 4a-b Guide x=a x a. x=-4 x +ax+9a-=0 (-4) +a_(-4)+9a-=0 5a=-5 a=- x -x-8=0 (x+4)(x-7)=0 x=-4 x=7 x= Guide ax +bx+c=0 x a+0 (ax-)(4x+)=x -x 4ax +ax-8x-6=x -x (4a-)x +(a-7)x-6=0 x Guide x(x-5)=- x -(k+5)x+k=0. x(x-5)=- x -5x+=0 (x-)(x-)=0 x=;!; x= 4a-+0 a+;4!; x=;!;

33 x=;!; x -(k+5)x+k=0 x =x-;4(; x -x+;4(;=0 _{;!;}-(k+5)_;!;+k=0, k= k= 4 Guide,. x +5=7(x-) x -7x+=0 (x-)(x-4)=0 x= x=4 x -4x=- x -4x+=0 (x-)(x-)=0 x= x= y x= y x= x -mx+(m+)=0 _ -m_+(m+)=0, -m=-0 m=0 y 0 m {x-;#;} =0 x=;#; () x +0x+5=0 x=-5 () 4x +4x-=0 (x+5) =0 x +x=;4!; x +x+;4!;=;4!;+;4!;, {x+;!;} =;!; x= 4x -x+;4!;=0 x=;4!; () {x-;!;}=0 7 Guide x +ax+b=0. b={;a;} - ' 4x +ax+00=0 4 x +;4A;x+5=0 5 Guide x=- x +ax=5. (x+)(x-b)=0 x=- x=b x=- x +ax=5 9-a=5 a=- x -x-5=0 (x+)(x-5)=0 x=- x=5 b=5 ab=-0-0 x +ax=5 x +ax-5=0 (x+)(x-b)=0 x +(-b)x-b=0 a=-b, b=5 b=5, a=- ab=-0 6 Guide. ()=0 x -x-=0 (x+)(x-)=0 x=- x= 5={;8A;} a =600 a= 40 a=40 4x +40x+00=0 4(x+5) =0 x=-5 () a=-40 4x -40x+00=0 4(x-5) =0 x=5 () a=40, x=-5 () [ a=-40, x=5 () 8 Guide (x-p) =q (qæ0) x=p 'q (x+) -6=0 (x+) =6 x+= '6 x=- '6 (--'6)_(-+'6)=(-) -('6) =- 9 Guide (x-p) =q qæ0 9(x-) æ0 9(x-) =k+5 k+5æ0 kæ-5 k

34 (x-p) =q q>0, x=p 'q q=0, x=p () q<0,. :qæ0 (x-p) =q : q<0 x=- '7 x+= '7 (x+) =( '7) x +6x+9=7, x +6x+=0 x +x+4=0 x -4ax+b=0-4a=, b=4 a=-, b=4 a+b= 0 Guide x +bx+c=0 (x-p) =q. (x-4)(x-)=x x -5x+4=x x +5x-4=0 x +;%;x-=0 y x +;%;x=, x +;%;x+{;4%;}=+{;4%;} {x+;4%;}=;%6&; y p=;4%;, q=;%6&; y Guide x (x-m)(x-n)=0 (, m, n ) x -ax-=0 x -ax-=(x-m)(x-n) (, m, n, mn=-) - _(-), -_, _(-6), -_6, _(-4), -_4 a=m+n -,, -4, 4, -, a p=;4%;, q=;%6&; x +bx+c=0 (x-p) =q p, q Guide (x-p) =q (qæ0) x=p 'q x -4ax+b=0 Guide x=- a. x=- (a+)_(-) +(a+)_(-)+a -4a+=0 a -a-=0, (a-)(a+)=0 a= a=- a++0 a+- a= a=- a+-. x -ax+;b;=0, x -ax=-;b; { -a }=a x -ax+a =-;B;+a (x-a) =a -;B; x-a= æ a -;B; x=a æ a -;B; 4 Guide [ x ]=A. [ x ]=A A -9A+4=0, (A-)(A-7)=0 A= A=7 [ x ]= [ x ]=7 x< 7 x<8 x a=-a -;B;=7 b=4 a+b= [ x ]=n (n ) n x<n+ (, [ x ] x ) 4

35 Check ' 9-, -, -,,, 0- x -x+, 6' 0, x -0x+4, 6 0, 5x +x-, ;5@; 0- x -4x+= x -4x=0,x(x-4)=0 x=0 x=4 8 x +8x-5=0-4 " 4 -_(-5) x= = 00 x -0x+5=0,(x-5) =0 x=5 () x=0 x=4 x= x=5 () - x+;!;, A-, ;#;, ;#;, ;6&; - (x-) +4(x-)-=0 x-=a A +4A-=0, (A+6)(A-)=0 A=-6 A= x-=-6 x-= x=-4 x=4 {x-;!;}+{x-;!;}=4 x-;!;=a A +A=4, A +A-4=0 (A+4)(A-)=0 A=-;$; A= x-;!;=-;$; x-;!;= x=-;6%; x=;#; -4 ' 6 (x-) x- - -=0 x-=a 6 A A - -=0, A -A-6=0 6 ' -4 ' 6 (A+)(A-)=0 A=-;#; A= x-=-;#; x-= x=-;4!; x=;#; x=-4 x=4 x=-;4!; x=;#; x=-;6%; x=;#; 085- a= b=-7 c= -(-7) " (-7) -4 7 ' 7 x= = _ a= b=5 c= -5 " ' 7 x= = _ 4 a= b'=- c=- -(-) " (-) -_(-) ' 0 x= = a=5 b'= c=- - " -5_(-) - ' 9 x= = ' 7-5 ' 7 x= 4 ' 0 - ' 9 x= x -9x+5=0 -(-9) " (-9) ' x= = _ 6 9+' 9-' p=, q= ' 9-' ' p-q= - = x -Ax+=0 -(-A) " (-A) -4 x= _ A " A - 5 ' B x= = 6 6 A=5, B=A -= A+B= x -+4x=8x -8, x -4x-5=0 -(-) " (-) -_(-5) x= = ' 4 ' 5

36 +' 4 a= +' 4 a-=_ -=' x -9=0x+6 0x -0x-5=0, x -4x-=0 -(-) " (-) -_(-) x= ' 0 x= 089- ;!;x+=a A -8A-=0,(A+)(A-)=0 A=-;!; A= ' 4 x -6x-=0-6 ()=- =6 - ()= =- 4x -x-=0 - ()=- =;4!; 4 - ()= =-;4#; 4 x +5x+=0 ()=-;%; ()=;!; ;!;x+=-;!; ;!;x+= x=-7 x= -(-7)=0 Check - x -x-6=0 (-) -4 (-6)=8>0 x -5x+9=0 (-5) -4 9=-47<0 0 8x +x-7=0-4_8_(-7)=5>0 -x +8x-6=0 8-4_(-)_(-6)=0 0 - x +x=0 ()=-;@;=- ()=;);= (-4) -4 =8>0-4 (-4)=49>0 4x +5x-=0 5-4_4_(-)=57>0 (-7) -4 =77>0 9x -x+4=0 (-) -4_9_4=0 () 09- (-0) -4_4_5p= p=0 p=5 {-(p+)} -4 q=0 p=5 64-8q=0 q=8 p+q= 09- x -8x+k-7=0 (-8) -4 (k-7)æ0-8k+0æ0 k 5 k 5 5 6

37 09- (a-) - =, ;B;=;#; , 05 a=-5, b= ' 7 09 ' 0 ab=-5-5 x=4, y= x=, y= 094-4, , 8, 9 9 ' 9 a+b=- =, ab= = (a+b)=_=4 0 Guide ax +b'x+c=0 (a+0) ;4!;ab=;4!;_(-8)=- -b' " b' -ac x=. a -ab+b =(a+b) -ab a = -_(-8)=8 a+b ;å!;+;!;= = =-;4!; ab -8 x=-(-5) " (-5) -_7 =5 ' a b a +b (a+b) -ab + = = b a ab ab 0 Guide + -_(-8) = =-;%; -8. x -6x+k-=0 -(-) " (-) -_(k-) x= 095- x +ax+b=0 'ƒ5-k x= -a=-5+=-4 a=4 ' ' x= = b=-5_=-5 bx +ax+=0-5x +4x+=0 5-k= k= 5x -4x-=0,(5x+)(x-)=0 ' x= x-= ' x=-;5!; x= x=-;5!; x= (x-) =, 9x -8x-=0 x -6x-= a, a+ k-=- k= - a+(a+)=- =4yy` k- 0 Guide a(a+)= yy`. a+=4 a= 0 k- a= _(+)= x -5(x-)(x+)=x+8 k-=9 k=0 x -x-=0 y -(-) " (-) -_(-) x= 097- a, a '7 x= a+a=4kyy y a_a=yy a =,a =4 a= A=, B=7 A+B=8 y 4a=4k,a=k k= ( k>0) 8 7

38 A+B 04 Guide ax +bx+c=0 b -4ac>0. b -4ac=0 (). b -4ac<0. 08 Guide ax +bx+c=0 (a+0) -b " b -4ac x=. a -(-5) " (-5) -4 5 ' 7 x= = _ 4 5+' 7 k= 4 5+' 7 4k-5=4_ -5=' 7 ' (-)=9>0 (-) -4 7=-55<0 6-4_(-)_5=56>0 8-4_8_=0 (), 05 Guide ax +bx+c=0 b -4ac=0 x -6x-m=0 (-6) -4 (-m)=0 6+8m=0 m=-;(; 06 Guide ax +bx+c=0 ( )=- b a, ( )= -4 4 m=- = 4 m-5=_ -5= Guide : a, a. a, a -5 a+a=- =5 yy k a_a=- yy 5a=5 a= a= k _=- k=-9 c a 09 Guide. 6 (x+)(x-)=x, x +x-6=0 - " -4 (-6) - ' x= = -+' --' a=, b= -+' --' a-b= - a-b=' ' 0 Guide. 4 x +4x+4a=0 - 'ƒ4-a b ' 0 x= = 4-a=0, -=b a=-;!;, b=- ab={-;!;}_(-)= Guide. x+y=a A(A-)=0 A -A-0=0 (A+)(A-5)=0 A=- A=5 x, y x+y=5 x>y x=4, y= x=, y= x=4, y= x=, y= 8

39 Guide ax +bx+c=0 b -4acæ0-4 (5-k)æ0 -+4kæ0, 4kæ kæ: 4 : y k y k Guide ax +bx+c=0 b -4ac>0 4-4_(a-)_(-)>0 6+4a-8>0, 4a>-8 a>- a+ -<a< a> a= 4x-=0. a+ 4 Guide. ()=-(a+4) ()=a(a-6) -(a+4)=a(a-6), a -5a+4=0 (a-)(a-4)=0 a= a=4, 5 Guide ax +bx+c=0 a, b a+b=-;ab;, ab=;ac; x=- x -px-=0 +p-=0 p= x +ax+b=0 x=p x=, x= x= -a=+, b=_ a=-5, b=6 a+b+p= 6 Guide. a+b=, ab=8 a +b (a+b) -ab + = = a b a b (ab) -_8 + = = 8 7 Guide 5 a, a+5. a, a+5 a+(a+5)=-(-k)=k-yy a(a+5)=4k yy a+5=k- a=k- a=k- (k-)(k+)=4k,k -5k-6=0 (k+)(k-6)=0 k=- ( k<0) 8 Guide ax +bx+c=0(a+0) b -4ac=() x +6x+k=0 x=- 'ƒ9-k x 9-k () k 9-k k=0 9-k= 9-k=4 k=9 k=8 k=5 5, 8, 9 9 Guide. (x-) =-(x+)(x-5) x -x+=-x +4x+5 x -6x-5=0 y a, b a+b=, ab=-;%; (a-b) =(a+b) -4ab= -4_{-;%;}=9 y a-b= ' 9 a-b =' 9 y ' 9 a-b 9

40 099- a+b=, ab=;!; Check (a+)+(b+)=a+b+=+=5 - -(x+)(x-4)=0, -(x -x-4)=0 -x +x+4=0 (x-) =0, x -x+8=0 (x -6x+9)=0 (-' )+(+' )=4 (-' )_(+' )= x -4x+=0 -x +x+4=0 x -x+8=0 x -4x+=0 ax +bx+c=0 a, b b a+b=-, ab= c a a - +' k=(-' )_(+' )= --' -k=(-+' )_(--' )=- k= --'5 k=(-+'5 )+(--'5 )=-4 4+' -k=(4-' )+(4+' )=8 k= (a+)(b+)=ab+a+b+=;!;++=;(; a+, b+ x {x -5x+;(;}=0 x -0x+9=0 x -0x+9=0 00- x +ax+b=0-' -;A;=(+' )+(-' )=6 a=- ;B;=(+' )_(-' )=7 b=4 a=-, b=4 0- n 90 n(n+) =90 n(n+)=80 n +n-80=0 (n+0)(n-9)=0 n=9 ( n ) x -48, x, 48, 6, 8, -6, 8, 8, ;%; x 9 9{x+;%;}=0 9{x +: º:x+: 9 :}=0 9x +0x+5=0 a=0, b=5 a+b=55 0- (x, -)(x, x)= x_x-(-)_x= x +x-=0 x -;#;=- x +x-=0-4 (-)=9+=>0. 40

41 0- x, x+ x +(x+) =40 x +4x-6=0 x +x-68=0 (x+4)(x-)=0 x=( x ), 4, x m (0+x)(8+x) m 80 m (0+x)(8+x)-80=88 4x +6x-88=0 x +9x-=0 (x+)(x-)=0 x= ( x>0) m m 04- x x+ 056 x(x+)=056 x +x-056=0 (x+)(x-)=0 x= ( x ),, 05-5 m h=5 h=50t-5t 5=50t-5t 5t -50t+5=0 t -0t+5=0 (t-5) =0 t=5 () 5 m x cm px cm cm p(x-) cm p(x-) =;4!;px x -6x+9=;4!;x 4x -4x+6=x x -4x+6=0 x -8x+=0 (x-)(x-6)=0 x=6 ( x>) 6 cm 6 cm 0 x= () cm 07 x -x-= x=- x= 0 a=5, b=- ' 9 4 +'5 5 4 cm 6 cm 7, Guide a, b x a a(x-a)(x-b)=0 -;@;, ;!; x 6 6{x+;@;}{x-;!;}=0 6{x +;6!;x-;!;}=0 6x +x-=0 a=, b=- x +bx+a=0 x -x+=0 (x-) =0 x= () x= () 6x +ax+b=0 -;@;, ;!; -;6A;=-;@;+;!;=-;6!; a= ;6B;=-;@;_;!;=-;!; b=- x +bx+a=0 x -x+=0 (x-) =0 x= () 4

42 0 Guide ax +bx+c=0(a, b, c ) 06 Guide x cm p+q' m p-q' m(, p, q,. ' m ) x -(k-)x-=0 -' k-=(+' )+(-' )= k=4 x cm (-x)cm x +(-x) =89 x -6x+80=0 x -x+40=0 (x-5)(x-8)=0 0 Guide n. n n(n-) =0 n -n-40=0 (n-)(n+0)=0 n= ( n>) 04 Guide x-, x, x+.(, xæ) x-, x, x+ (xæ) (x+) =x(x-)- y x +x+=x -x- x -4x-=0 (x-6)(x+)=0 x=6 ( xæ) y 7 y 7 x=6 5, 6, 7. x=5 { 0<x<: :} 5 cm 5 cm 07 Guide ax +bx+c=0 b -4ac=0 x -4x+m=0 (-4) -4 m=0 m=, - x (x-)(x+)=0 x -x-=0 x -x-=0 08 Guide m, n x a a(x -mx+n)=0 a+b=-6, ab=- a+b -6 ;å!;+;!;= = =, ab - ;å!;_;!;=;å ;= =-;!; - {x -x-;!;}=0 x -6x-=0 05 Guide 0 m. ()=0-5t +0t+80=0 t -6t-6=0 (t-8)(t+)=0 t=8 ( t>0) 8 09 Guide x. (x+)(x-6)=0 x -5x-6=0-6 4

43 (x+4)(x-)=0 x +x-=0 x x x +x-6=0 (x+)(x-)=0 x=- x= x=- x= 0 Guide ax +bx+c=0(a, b, c ) p+q' m p-q' m(, p, q, ' m ) ax +bx-=0 +'6 y 5 - -'6 +'6 = _ =-;5!; a 5 5 a=5 y b -'6 +'6 - = + =;5@; b=- y a=5, b=- a b Guide ( )=( ). (x -x)+(x+)+6=8++6 x -x-8=0 (x-4)(x+)=0 x=4 ( x ) 9 +++y+9=45,, ;; ;;= x +x+=- x -x-5=0 ' 9 x= Guide x x-, x+ x x(x+)=54 x +x-54=0 (x+4)(x-)=0 x= ( x>0), 8 _8=88 4 Guide 7 x 7 (x+7) 7 x 7 (x+7) x(x+7)=8 x +7x-8=0 (x+9)(x-)=0 x= ( x ) 7 5 Guide. x cm 5 cm (5-x)cm 6p cm 5p px p(5-x) - - =6p y x -0x+=0 x -5x+6=0 (x-)(x-)=0 x= { 0<x<;%;} ' 9 y cm 4 cm y 4 cm Guide. <, x>=- _x+-x =- 4

44 6 Guide AB =x cm. AB =x cmabcdªbcfe AB : BC =AD : BE x : = : (x-) x(x-)= x -x-=0 +'5 x= ( x>0) +'5 AB cm +'5 a:b=c:d ad=bc cm -x +7x=54 x -7x+54=0 x -9x+8=0 (x-)(x-6)=0 x= x=6 PBQ 54 cm 6, 8 Guide a% ()=()_{+;0A0;} a ()=a{+;0{0;} () ()=()_{-;0{0;} 7 Guide PBQ. xpb =(8-x)cm, BQ =x cm PBQ=;!;_PB _BQ PBQ=;!;_(8-x)_x PBQ=-x +7x ()=a{+;0{0;} {-;0{0;} () % a{+;0{0;} {-;0{0;}=a{-;0!0;} (00+x)(00-x)= x =9900 x =00 x=0 ( x>0) 0 44

45 Check y=-x x y 0, 5-5- y=x,. y=4px,. y=00x, : 4 : y, 0, 0 x 7-0, 0 x=0 8-,, - y=ax (-, ) =a_(-) a=;!; y=;!;x y=;!;x (, b) b=;!;_ =;(; a+b=;!;+;(;=5 5 - x x - y=-;!;x x 08- y=;!;_x_=x y=;!;x (-, a) y=p_x_;!6*0);=px y=x_x=x y=60_x=60x y=px, 09- f(-)=_(-) -_(-)+a=5+a 5+a=7 a= a=;!;_(-) = 4- y=ax (, -6) -6=a_ a=-;#; 0- y=x x=0 x>0 x y x<0 x y 0- y=-x y=x x, 4 y O x, y y=x@ O x y=-x@ y=-;#;x (k, -4) -4=-;#;k, k =6 k=4 ( k>0) 4 5- y=-x (0, 0) y O y=x@ y=x@ x x=0 y=x y=-x@ 45

46 5- a Check 8- y=-x + y=-x y y - O x 9- y=5x - y=-;!;x + 9- (0, ) x=0 40- y=(x-) y=-;4!;(x+) 40- (5, 0) x=5 4- y=- {x+;!;}+6 4- (, -4) x= 9- y=-(x-) y=-x x (, 0) x= y=-(x+) y=-x x - (-, 0) x=- y O -4-4 x - y=-x@ -4-6 y=-{x-}@ y - O -4-4 x - - y=-x@ -4-6 y=-{x+}@ 6- y=-x -4 y O y=-x y -4-4 x -4 - y=-x@ (0, -4), -6-4 x=0 y=-x@-4 y=-x + y y=-x@+ O y=-x y -4-4 x - (0, ), x= y=x y - y=x - (0, -) x=0 y=-x y 4 y=-x +4 (0, 4) x=0 0- y=;@;x x - y=;@;(x+) (-, 0) x=- y=-4x x 4 y=-4(x-4) (4, 0) x=4 - y=-(x+4) x>-4 x y -4 y O x - y=-(x-) + y y=-{x-}@+ y=-x -4 - O 4 x x y y=-x@ 46

47 (, ) x= y=-(x+) - y -O y=-x x -4-4 x - - -y - y=-x@ -4-6 y=-{x+}@- (-, -) x=- - y=;5@;x x -y ;!; y=;5@;(x+) +;!; {-, ;!;} x=- y=-;!;x x y -7 y=-;!;(x-) -7 (, -7) x= 4- y=-(x+) + x x-my y-n y-n=-{(x-m)+} + y=-(x-m+) ++n y=-(x-) + -m+=-, +n= m=5, n= m+n=7 7 y=-(x+) + (-, ) x my n (-+m, +n) y=-(x-) + (, ) -+m=, +n= m=5, n= m+n=7 5- y=4(x-p) +p (p, p ) (p, p ) y=-x+ p =-p+, p +p-=0 (p-)(p+)=0 p=;!; ( p>0) 6- y=a(x-p) +q (, -) p=, q=- y=a(x-) - y=a(x-) - (, ) =4a- a= a+p+q=++(-)= 7- y=x x - y - y=(x+) - y x=- x>- x - O x y - x>- 8- y=(x-) - x= y=- 8- y=-;@;(x+) -4 4 x=0 y=-;@;(0+) -4=-: : O - y - O -4 y {0, -: :} (-, -4) x>- x y 9- a>0 (p, q)4 p>0, q<0 y x x 47

48 a>0, p>0 a+p>0 y=(x-) -x +5 p>0, q<0 pq<0 =x -x+8-x +5 p>0, q<0 p-q>0 =-x+ a>0, q<0 aq<0 y=(x-) +6x (p, q) p>0, q>0 p<0, q>0 p<0, q<0 4 p>0, q<0 y {-, +}, {+, +} O x 4 {-, -} {+, -} =4x -4x++6x =4x +x+ y=(x+) -x =x +x+-x =-x +x+ y=(x-) +x- =x -x++x- =x 0- y=(x-) y x -x y=(-x-) y=(x+) y m y=(x+) +m (-, 5) 5=+m m= x y -y y x -x x -x, y -y 0 Guide f()= a, f(-)=b b. f()=-a+5=6-a 6-a= a=4 f(-)=+a+5=6+a 6+a=6+4=b b=0 a+b=4+0=4 0 Guide y=ax a y. x y (0, ) a>0, p<0, q>0 0,,,, , a=, p=- 0 ;&;, Guide y=ax +bx+c a+0 y=x(x-) =x -x 04 Guide y=ax x y=-ax y=;!;x x y=-;!;x (, a) a=-;!;_ =- 05 Guide y=ax y q y=ax +q y=x y q y=x +q y 48

49 (-, ) =_(-) +q q= y y=x + (0, ) y (0, ) q 0 Guide y x y=ax +bx+c(a+0) y=(ax-)(x+)+4x-5x =ax +ax-x-+4x-5x =(a-5)x +(a+)x- a-5+0a+;%; Guide y=ax, a >>;!; 06 Guide y=a(x-p) x=p,. y=-(x+) x=- x<-x y x>-,x y. 07 Guide y=ax x p, y q y=a(x-p) +q y=-x x y -4 y=-(x-) Guide y=a(x-p) +q (p, q) (0, 4) y (, 0) x (-, -) (-, 4) (, ) - > - > -;!; y=ax Πa>0 : a a<0 : a.,,, Guide y=ax a :,a: y=;@;x, y=4x x y=4x y=-x, y=-;4!;x x, Guide. y=ax +q (, 4), (-4, -) 4=4a+q, -=6a+q y a=-;!;, q=6 y 09 Guide a, p, q. a>0 (p, q) p<0, q>0 a>0, p<0, q>0 aq={-;!;}_6=- a, q aq y - 49

50 4 Guide y=ax x p 8 Guide y=a(x-b) +c x y=a(x-p) f(x)=;#;(x-4) p, y q x x-p, y y-q. y=4(x+) +5 x x-y y+ f()=;#;(-4) =6 f(6)=;#;(6-4) =6 f()-f(6)=0 0 y+=4{(x-)+} +5 y=4(x+) + (m, 9) 9=4(m+) + 5 Guide, (m+) =4, m+=. y=-x x m= m=- m>0 y=-(x-) m= y=-(x-) y O x 9 Guide y=a(x-p) +q - x=p (, 0) x=0 y=- y y=a(x-p) -4 x=p (0, -) p=- y, y=a(x+) -4 (, 5) 5=9a-4 a= y 6 Guide y=ax a=, p=- y=a(x-p) +q, y=ax x y=-ax. p a y=-;!;x, y=-;!;x +;!;, y=-;!; {x-;!;} y=-;!;x -;!; x y=;!;x +;!; y=-;!;x -;!; x x y=ax x a. 7 Guide, y. 0 Guide y=a(x-p) +q (p, q) y=a(x-p) +q (, ) p=, q= y=a(x-) + y=a(x-) + (-, 4) 4=a(--) + a=;!; y=;!;(x-) + y=;!;(x-) + (4, k) y=-;!;(x+) + y k=;!;(4-) +=;&; ;&; - O - x Guide y=-(x-) -. 50

51 y=-(x-) - y O x y=-x x - y - -7 (, -) x= x=0 y=-7 y (0, -7) Guide y=a(x-p) +q (p, q), a>0, a<0. (0, 0) (0, -) (, 0) (-, -5) {;!;, } x x, Guide a, p, q. a>0 (p, q) 4 p>0, q<0 y=p(x+q) -a p>0 (-q, -a) -q>0, -a<0 4 4 Guide. AB =BC CD =DE D x ke x k ( D y)=( E y) a_k =;#;_(k), ak =6k k+0 k a=6 6 5 Guide. y=(x-) - y y=x y=x@ y=x y=(x-) - O x y x= y={x-}@- - x= _= y=ax. 5

52 Check 4-6, 6, 4, 6, 4, 9,,,,,,, 5- y=-x +ax-5 a a 5- y=-[{x -;A;x+ }- ] a 5- y=-{x-;4a;} x=;4a; 4- a<0 y b>0 y c>0 x= y>0 a+b+c>0 a<0 b>0 c>0 a+b+c>0 - y=-x -6x-4=-{(x +x+)-}-4 =-(x+) - p=, q=- p+q=0 0 - y=x -x+a={(x -4x+4)-4}+a =(x-) -+a (, -+a) =b, -+a=-7 a=5, b= a+b=7 y=x -x+a (b, -7) y=x -x+a=(x-b) -7=x -6bx+b -7 -=-6b, a=b -7 b=, a=5 a+b=7 - y=-x +x-8=-(x-) x a,y 4 y=-(x-a-) +4 (, b) a+=, 4=b a=-, b=4 a+b= 4- x x<;4a;x y, x>;4a; x y ;4A;= a= y=x -x+ y=0 x -x+=0, (x-)(x-)=0 x= x= B(, 0), D(, 0) y=x -x+ x=0 y= A(0, ) y=x -x+ y= x -x+= x -x=0, x(x-)=0 x=0 x= E(, ) y=x -x+=[{x -x+;4(;}-;4(;]+ y={x-;#;}-;4!; C{;#;, -;4!;} 7- y=-x -x+ =-{(x +x+)-}+ =-(x+) +4 (-, 4)y (0, ) y 4 y=-x -x+ - O x. y=x +, y=x +4x+=(x+) -,, y=5x +0x+=5(x+) -,, y=-x +8x-9=-(x-) -, 4 5

53 8- y=-x +4x-8=-{(x -4x+4)-4}-8 =-(x-) -4. y (, -4)., 4. x x>,x y. O -4-8 x 9- A, B y=-x +x+ x y=-x +x+ y=0 -x +x+=0, x -x-=0 (x+)(x-)=0 x=- x= A(-, 0), B(, 0) y=-x +x+=-{(x -x+)-}+ =-(x-) +4 C(, 4) ABC=;!;_4_4= a<0 y b<0 y c>0 x=, y<0 a+b+c<0 x=-, y>0 4a-b+c>0 40- y=ax+b a>0 y b>0 y=ax +bx a>0 a, b y x=0 y=0 y=ax +bx 9- A, B y=(x+)(x-4) x y=(x+)(x-4) y=0 (x+)(x-4)=0 x=- x=4 A(-, 0), B(4, 0) y=(x+)(x-4)=x -x-8 ={(x -x+)-}-8=(x-) -9 C(, -9) ACB=;!;_6_9=7 b 9- y=-x +bx+c=-{x-;b;}+ +c 4 x=- ;B;=- b=-4 y=-x +bx+c O c=0 y=-x -4x=-(x+) +4 A(-, 4) y=-x -4x y=0 -x -4x=0, x +4x=0, x(x+4)=0 x=0 x=-4 B(-4, 0) ABO=;!;_4_4= (, ) ;(; 06 a<0, b>0, c> {;#;, : 8 :} (-, 0), (6, 0) ; 5; a ;9$; 8 0 Guide y=ax +bx+c y=()+() y=4x -6x+9 =4{(x -4x+4)-4}+9 =4(x-) -7 a=4, p=, q=-7 a-p-q=4--(-7)=9 0 Guide y=x +ax+ x=-, y=- a, y=(x-p) +q. y=x +ax+ (-, -) -=4-4a+ a= 5

54 y=x +4x+={(x +4x+4)-4}+ =(x+) - x=- AB 4-{-;!;}=;(; ;(; 06 Guide a,b,c y. 0 Guide y=a(x-p) +q. y=;!;x -x-=;!;{(x -6x+9)-9}- y=;!;(x-) -4 y y=ax -bx+c a<0 y -b<0 b>0 y c>0 a<0, b>0, c>0 x -y 7 y-7=;!;(x+-) Guide (p, q) y=a(x-p) +q y=;!;(x-) + (-, b) (, ) y=a(x-p) +q y (, ) y=-x +ax-5=-(x+) +b y=-x +ax-5=-x -4x-4+b a=-4, -5=-4+b a=-4, b=- a-b=-. y=;!;x -x- (, -4) (-, -4+7), (, ) 04 Guide x. y=-(x+) -4x=-x -8x- =-(x+) +6 y=-x x -y 6 05 Guide x y=0 y=x -7x-4 y=0 x -7x-4=0, (x+)(x-4)=0 x=-;!; x=4 A{-;!;, 0}, B(4, 0) A(4, 0), B{-;!;, 0} 08 Guide y=a(x-p) +q x m,y n x x-m, y y-n. y=x -6x+=(x-) -8 x m,y 8 y-8=(x-m-) -8 y=(x-m-) y=x +x+k=(x+) +k- -m-=, k-=0 m=-4, k= m+k=- - y=x -6x+=(x-) -8 (, -8) y=x +x+k=(x+) +k- (-, k-) (, -8) x m,y 8 (+m, -8+8) (+m, 0) (-, k-) +m=-, 0=k- m=-4, k= m+k=- 54

55 09 Guide,. y=-4x -8x+=-4(x+) +7 x k y=-4(x-k+) +7 x=k- k-= k= y=-;4!;x +x+ y=-;4!;{(x -4x+4)-4}+ y=-;4!;(x-) + y O x 0 Guide. y=-;!;x +ax+b (0, ) b= y y=-;!;x +ax+ (4, 0) 0=-8+4a+ a=;#; y y=-;!;x +;#;x+=-;!;{x-;#;}+: 8 : {;#;, : 8 :} y b a {;#;, : 8 :} Guide y=-;4!;(x-p) +q. y=-;4!;x +;!;ax+a+=-;4!;(x-a) +;4!;a +a+ x=a a= y=-;4!;x +x+ y=0 y=-;4!;x +x+ -;4!;x +x+=0, x -4x-=0 (x+)(x-6)=0 x=- x=6 x (-, 0), (6, 0). (-, 0), (6, 0) Guide y=a(x-p) +q. Guide x ( y)<0 y=x +4x-k+7=(x+) -k+ x -k+<0 k> 4 Guide y=a(x-p) +q. y=;@;x +4x+=;@;{(x +6x+9)-9}+ y=;@;(x+) -4 y=;@;x +4x+ y. - O x (-, -4).,,. -4 x=-. y=;@;x x -y -4 5 Guide. y=-x +x+c=-(x-) +c+ C(, c+) AB =6 A(-, 0), B(+, 0) A(-, 0), B(4, 0) y=-x +x+c B(4, 0) 0=-6+8+c c=8 C(, 9) ABC=;!;_6_9=7 7 55

56 6 Guide y=ax +bx+c q a : a b : z c :y y=ax +bx+c a>0 y b>0 y c<0 y=cx +bx+a c<0 y bc y a>0 y O x y=cx +bx+a y=a(x+) -B(4, ) =5a- a=; 5; y a ; 5; a ;9$; y ; 5; a ;9$; A a B a a 7 Guide y=ax +bx+c y=a(x-p) +q. y=ax +ax+a-=a(x +x)+a- =a{(x +x+)-}+a-=a(x+) - (-, -) y AB y A ( ) B - O 4 x y=a(x+) - - A(, ) =9a- a=;9$; y 8 Guide. y=-x +x+=-(x-) +4 y=-x +8x-=-(x-4) +4 y=-x y y=-x@+8x- A B 4 O 4 x A(, 4), B(4, 4) ( )=_4 y=-x@+x+ = 56

57 Check 44- (, ) y=a(x-) + (4, ) =a+ a= y=(x-) +=x -x+9 (-, ) y=a(x+) + (-, 5) 5=a+ a= y=(x+) +=x +6x+5 y=x -x+9 y=x +6x x=- y=a(x+) +q (-, ) =4a+q yy (, -4) -4=9a+q yy a=-, q=5 y=-(x+) +5=-x -x+4 x=5 y=a(x-5) +q (4, ) =a+q yy (7, 6) 6=4a+q yy a=, q= y=(x-5) +=x -0x+7 y=-x -x+4 y=x -0x y=ax +bx+c (0, -) c=- y=ax +bx- yy (-, -) -=a-b- a-b= yy (4, 9) 9=6a+4b- 4a+b= yy a=, b=- y=x -x- y=ax +bx+c (0, 6) c=6 y=ax +bx+6 yy (-, 0) 0=a-b+6 a-b=4 yy (, 4) 4=4a+b+6 a+b=- yy a=, b=- y=x -x+6 y=x -x- y=x -x x (-, 0), (4, 0) y=a(x+)(x-4) (5, -7) -7=7a a=- y=-(x+)(x-4)=-x +x+8 x(, 0), (-, 0) y=a(x-)(x+) (, -4) -4=4a a=- y=-(x-)(x+)=-x +x+ y=-x +x+8 y=-x +x+ 4- (, ) y=a(x-) + (, ) =a+ a= 57

58 y=(x-) +=x -8x+9 a=, b=-8, c=9 a-b+c=9 9 Check 46-,,,,,, -, -4, -,, x=- y=a(x+) +q (-, 0) 0=a(-+) +q a+q=0 yy (0, 6) 6=a(0+) +q 4a+q=6 yy, a=, q=- y=(x+) -=x +8x+6 a=, b=8, c=6 a+b+c=6 4- y=ax +bx+c (0, ) c= y=ax +bx+ yy (, 0) 0=a+b+ a+b=- yy (, -) -=4a+b+ a+b=- yy a=, b=-4 y=x -4x+=(x-) - (, -). (, -) 44- x(-, 0), (, 0) y=a(x+)(x-) (, 4) 4=4a a= y=(x+)(x-)=x -x- y y x(x-4), x(x-4), 4x,, 4,, -4,, -, y=-5x +0x+5=-5(x-) +0 (, 0) x= 0 M=0 y= x -4x+= (x-4) -5 (4, -5) x=4-5 m=-5 M+m=5 46- y=-(x-) +5-4=-(x-) + x= a 47- y=-x +ax=-{x-;a;}+ a a x=. a =8 a =6 a=4 ( a>0) 48- y=;!;x +mx+n x=- y=;!;(x+) +=;!;x +x+ m=, n= m+n= x=- x y=a(x+) 58

59 (, -8) -8=6a a=-;!; x=0 0 cm, 0 cm. 0 cm, 0 cm y=-;!;(x+) y=-;!;x -x- y=-;!;x -x- 54- tp, Q AP =t cm, QB =t cm AQ =(0-t)cm 50- y=-x +kx+k=-(x-k) +k +k M=k +k={k+;!;}-;4!; M k=-;!; -;4!;. :-;4!;, k=-;!; 5- x, y x-6 y=x(x-6) =x -6x =(x-8) -64 x=8-64 8, x y x+6 y=x(x+6) =x +6x =(x+8) -64 x= , 8, y=-5t +0t+5=-5(t-) +5 t= cm {( )+( )}=40(cm) ( )+( )=0(cm) x cm y cm (0-x)cm y=x(0-x) =-x +0x =-(x-0) +00 AQP=;!;_AP _AQ AQP=;!;_t_(0-t) AQP=-t +5t AQP=-{t-;%;}+;; 4 ;; t=;%; ;; 4 ;; ;%;AQP. ;%; 55- P (x, -x+6)prq y y=;!;_pr _PQ y=;!;x(-x+6) y=-;!;x +x y=-;!;(x-) +;(; x= ;(;. PRQ ;(;. 55- ABC BEDFCG DE =FG =x cm BE =FC =x cm EF =(6-x)cm DEFG y cm y=x(6-x) =-x +6x =-(x-4) + x=4. DEFG cm. 59

60 y=x +4x (, -9) 9a+b+6=-9 a+b=-5 yy a=, b=-8 a-b+c=5 0 a=, b=-, c= ;9$;<a< :cm :9cm 0 98 cm Guide y=m(x-p) +q. y=x +6x+5=(x+) + x=- a=-, b= ab=- 0 Guide y=a(x-p) +q (, ) y=a(x-) + (0, -) -=4a+ a=- y=-(x-) +=-x +4x- 0 Guide x=m y=a(x-m) +q x= y=a(x-) +q (-, ) =a(--) +q 6a+q= yy (4, -7) -7=a(4-) +q a+q=-7 yy a=, q=-9 y=(x-) -9=x -x+9 y y Guide c. (0, 6) c=6 y=ax +bx+6 yy (, -) a+b+6=- a+b=-7 yy 05 Guide y=a(x-p) +q. - y=-;!;x -x-=-;!;(x+) 0 y=-;4!;x -4x=-;4!;(x+8) +6 6 y=-x +4x-7=-(x-) -5-5 y=-x +6x-=-(x-) + 06 Guide x=p q y=a(x-p) +q (a>0) x=- - y=a(x+) - (, 6) 6=9a- a= y=(x+) -=x +4x+ y=x +4x+ 07 Guide y=-x+ xy x. x+y= y=-x+ xy=x(-x+) =-x +x =-(x-) +8 x=xy

61 08 Guide =;!; x cm y cm (40-x) cm y=;!;x(40-x) y=(x+4)(x-4)=x -6 a=0, b=-6 a-b=6 y=-;!;x +0x y=-;!;(x-0) cm Guide y=m(x-p) +q. y=ax +4ax-9=a(x+) -4a-9 a<0 x=- -4a-9-4a-9= a=- 09 Guide y cm x, y. (8+x) cm, (8-x) cm y cm y=(8+x)(8-x) =-x +8x+64 =-(x-) +7 x= 7. Guide y=x-6. y=-x -x+4p-=-(x+) +4p+5 (-, 4p+5) 4p+5 (-, 4p+5) y=x-6 4p+5=-5 x= Guide., (, -4) y y=a(x-) -4 (, -) -=a-4 a= y y=(x-) -4=x -x+4 b=-, c=4 y a=, b=-, c=4 a b, c 4 Guide x=p q (p, q). y=a{x-;!;}+4 x -y m y=a{x+-;!;}+4+m y=a{x+;#;}+4+m y=ax +ax+;4(;a+4+m a=, a=n, ;4(;a+4+m=;&; m=-5, n=6 m+n= 5 Guide y=a(x-p) +q. Guide x (x )_;!; y=x +ax+b x 8 x (-4, 0), (4, 0) y=;!;x -mx+5m=;!;(x-m) -;!;m +5m f(m)=-;!;m +5m f(m)=-;!;(m-5) +: : m=5 f(m) : : 6

62 6 Guide y=ax +bx+c x=p q a<0 (p, q). y=ax +bx+c a<0 yy y x= 4 y=a(x-) +4 =ax -6ax+9a+4 y y y 0 y 4 9a+4 9a+4>0 O x a>-;9$; yy -;9$;<a<0 y -;9$;<a<0 a a 4-=(). y 9 Guide r, l, S S=;!;rl. x cm (-x) cm y cm y=;!;x(-x) y=-x +6x y=-(x-) +9 cm 9 cm cm, 9 cm 7 Guide ( )=( )_( ) y x (00+x) (800-x) y=(00+x)(800-x) =-x +400x =-(x-00) x= =00() 00 0 Guide AP =x cm BP =(4-x) cm AP =x cm BP =(4-x) cm y cm y=x +(4-x) =x -8x+96 =(x-7) +98 AP =7 cm 98 cm 98 cm 8 Guide y=-5t +0t+40 y=a(x-p) +q. y=-5t +0t+40 =-5(t-) +45 t= 45.. y t y=0-5t +0t+40=0 t -t-8=0 (t+)(t-4)=0 t=4 ( t>0) y Guide P {x, -;#;x+6} POA. P {x, -;#;x+6}poa y y=;!;x{-;#;x+6} y=-;4#;x +x y=-;4#;(x-) + x= POA 6

63 Guide y=;!;x +ax+b (, 5) 5=;(;+a+b a+b=;!; yy f(x)=ax +bx+c=a(x-7) +q f(6)= a+q= q=-a f(x) -a y=;!;x +ax+b y=- ;!;x +ax+b=- ;!;x +ax+b+=0 - -a=- a= a= b=-;%; y=;!;x +x-;%;=;!;(x+) - - Guide y=f(x) f(a)=f(b) a+b ( x)= f(6)=f(8) 6+8 x= =7-4 Guide. y=x -6x+ x -y=x -6x+ y=-x +6x- =-(x-) +6 (, 6) D x +kax -k A(-k, -k +6), D(+k, -k +6) ABCD AD =k DC =AD =k k=( D y) k=-k +6, k +k-6=0 (k+)(k-)=0 k=- k= k>0 k= ABCD

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