Bài tập cơ bản Casio Toán 9

Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh CC BI TP C BN CASIO TOAN 9 1 Bi 1: a) Tnh: M = x4 + 5x3 - 3x2 +x - 1 khi x = 1,35627 b) Tnh gi tr ca biu thcN= 60.2 09,814 0,87 cos52 17' t Bi 2.Cho a thc P(x) = 6x3 5x2 13x + a 1.Vi iu kin no ca a th a thc P(x) chia ht cho 2x + 3 2.Vi gi tr ca a tm c phn 1, hy tm s d r khi chia a thc P(x) cho 3x 2 Bi 3. Lp quy trnh bm phm tnh gi tr lin phn s sau: M = 292111151713++++ Bi 4:Cho phng trnh x b a x b a + = + 1 1 1a)Tnh x theo a v b b)Tnh gi tr ca x bita = 241209;b = 251209 (Ly kt qu vi tt c cc ch s trn my) Bi 5.Tnh chnh xc gi tr ca biu thc s: P = 3 + 33 + 333 + ... +33.....33 13 ch s 3 Bi 6.BcAnvaymtngnhngvisvnl100triung,lisutl1,25%trn thng, thi hn l 4 nm, tnh theo d n, tr ng ngy quy nh. Hi hng thng, Bc An phi u n tr vongnhngmt khon tin c gclnlil bao nhiu n khi va ht 4 nm th Bc An tr ht c gc ln li cho ngn hng? Bi 7.Cho x1000 + y1000 = 6,912 v x2000 +y2000 = 33,76244 Tnh x3000 + y3000 . Tm tt cch gii Bi 8.Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Tm hai s nguyn dng x b nht sao cho khi lp phngmi s ta c mt s c 2 ch s u (bn phi) v 2 ch s cui (bn tri) u bng 4, ngha l 344......44 x = . Nu qui trnh bm phm. Bi 9.Cho hnh ch nht c chu vi l 17,356; t s 2 cnh l 75. Tnh di ng cho ca hnh ch nht. Bi 10. Cho hai dy s vi cc s hng tng qut c cho bi cng thc : 1 1111; 222 1517 12n n nn n nu vu v uv v u++= = = = vi n = 1, 2, 3, , k, .. a) Tnh 5 10 15 18 19 5 10 15 18 19, , , , ; , , , , u u u u u v v v v vb) Vit quy trnh n phm lin tc tnh1 nu + v 1 nv + theo nuv nv . ____________ Ht __________ HNG DN GII TON TRN MY TNH CASIO LP 9 Bi 1: a) Tnh: M = x4 + 5x3 3x2 +x 1 khi x = 1,35627 b) Tnh gi tr ca biu thcN= 60.2 09,814 0,87 cos52 17' t Hng dn chm: a. M =10,695587 b. N = 40,997439 Bi 2: Cho a thc P(x) = 6x3 5x2 13x + a 1.Vi iu kin no ca a th a thc P(x) chia ht cho 2x + 3 2.Vi gi tr ca a tm c phn a, hy tm s d r khi chia a thc P(x) cho 3x 2 Hng dn chm:1) a =12; 2)r = 298 Bi 3: Lp quy trnh bm phm tnh gi tr lin phn s sau: M = 292111151713++++Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Hng dn chm:M = 3331024687 Bi 4:Cho phng trnh x b a x b a + = + 1 1 1c)Tnh x theo a v b d)Tnh gi tr ca x bita = 241209;b = 251209 (Ly kt qu vi tt c cc ch s trn my) Hng dn chm: ( )( )222 22 241 4 41 2 1 21 1 2 1 11 1 1ba bxa x b ax b a x b a x b ax b a x b a+ = = = + + = + Tnh c x = 0,99996177 Bi 5.Tnh chnh xc gi tr ca biu thc s: P = 3 + 33 + 333 + ... +33.....33 13 ch s 3 Hng dn chm: P = 37037037036992,5 im Qui trnh bm phm2,5 im Bi 6. Bc An vay mt ngn hng vi s vn l 100 triu ng,li sut l 1,25% trn thng, thi hn l 4 nm, tnh theo d n, tr ng ngy quy nh. Hi hng thng, Bc An phi u n tr vongnhngmt khon tin c gclnlil bao nhiu n khi va ht 4 nm th Bc An tr ht c gc ln li cho ngn hng ? Hng dn chm : Gi s tin vay l N ng, li sut m% /thng, s thng vay l n, s tin tr hng thng l A ng. - Sau thng th nht s tin gc cn li trong ngn hng l : N 1100m | |+ |\ . A= N.x Angvi x = 1100m | |+ |\ . - Sau thng th hai s tin gc cn li l: (Nx A)x A = Nx2 A(x+1) ng. - Sau thng th ba s tin gc cn li l: [Nx2 A(x+1)]x A = Nx3 A(x2+x+1)ng - S tin gc cn li sau thng th n l :Nxn A(xn-1+xn-2++x+1)ng. V lc ny s tin c gc ln li tr ht nn ta c : Nxn - A (xn-1 +xn-2 ++x+1) = 0 A = n1 2Nx... 1 + + + +n nx x x= ( 1)1nnNx xx Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Thay bng s vi N = 100 000 000 ng, n = 4nm = 48 thng, x =1+0,0125=1,0125 Ta c : A = 2 783 074, 827 ng. Bi 7 :Cho x1000 + y1000 = 6,912 v x2000 +y2000 = 33,76244 Tnh x3000 + y3000 . Tm tt cch gii Hng dn chm : t a = x1000, b = y1000. Theo bi ra ta c : a + b = 6,912 v a2 + b2 = 33,76244 => x3000 + y3000 = a3 + b3 = ( a+b)3 3ab ( a + b) m:3ab = 32 2 2( ) ( )2a b a b + + =>a3 + b3 = (a +b)3 32 2 2( ) ( )( )2a b a ba b+ ++ => Thay s tnh trn my ta c: x3000 + y3000~184,9360 Bi 8. Tm hai s nguyn dng x b nht sao cho khi lp phngmi s ta c mt s c 2 ch s u (bn phi) v 2 ch s cui (bn tri) u bng 4, ngha l 344......44 x = . Nu qui trnh bm phm. Hng dn chm: Tm c hai s 164 v 7642,5 im Qui trnh bm phm ng.2,5im Bi 9.Cho hnh ch nht c chu vi l 17,356; t s 2 cnh l 75. Tnh di ng cho ca hnh ch nht. Hng dn chm: Gi cnh hnh ch nht l a v b. Khi y ng cho d ca hnh ch nht l2 2b a d + =Theo bi ra ta c : = +=2336 1775,b aba ( ) ( )2 212712571277 51257 55b a d b a b b a abb ab aa+ = + = + = =+=+=+=+,,

Vy d = 2 2) (127) (125|.|

\|+ +|.|

\|+ b a b a =7412) () (14474) (14449) (144252 2 2b ab a b a b a+= + = + + +=7424336 , 17742 . 12336 , 17=Tnh d = 6,213746285 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Bi 10. a) u5 = -767 v v5 = -526; u10 = -192547 v v10 = -135434 u15 = -47517071 v v15 = -34219414; u18 = 1055662493 v v18 = 673575382 u19 = -1016278991 v v19 = -1217168422 b) Qui trnh bm phm: 1 Shift STO A, 2 Shift STO B, 1 Shift STO D, Alpha D Alpha = Alpha D +1, Alpha :,C Alpha = Alpha A, Alpha :, Alpha A Alpha = 22 Alpha B - 15 Alpha A, Alpha :, Alpha B, Alpha =, 17 Alpha B - 12 Alpha C, = = =...___________________________ Cha s dng Bi 1: Tnh v lm trn n 6 ch s thp phn: A = 013 , 0 : 00325 , 0) 045 , 0 2 , 1 ( : ) 965 , 1 1 , 2 (67 , 0 ) 88 , 3 3 , 5 ( 03 , 0 6 32 , 0) 5 , 2 : 15 , 0 ( : 09 , 0 4 , 0 : 3 ++ + Bi 1: Tnh v lm trn n 6 ch s thp phn: A = 013 , 0 : 00325 , 0) 045 , 0 2 , 1 ( : ) 965 , 1 1 , 2 (67 , 0 ) 88 , 3 3 , 5 ( 03 , 0 6 32 , 0) 5 , 2 : 15 , 0 ( : 09 , 0 4 , 0 : 3 ++ + Hng dn chm:A = 15Bi 4:a.Gii h phng trnh (ghi kt qu ng 9 ch s thp phn) = + = 121 , 7 y 224 , 4 x 616 , 8147 , 3 y 216 , 4 x 341 , 1 b.Haisctngbng9,45583vctngccsnghchocachngbng 0,55617. Tm hai s (chnh xc n 5 ch s thp phn) Hng dn chm: 4a) x = 0,3984147;y = 0,873167468 4b)Tnh c hai s 7,04124 v 2,4145 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh 2 Bi 1 (5 im): Tnh gi tr ca biu thc: a)A 4 5. 3 5. 48 10. 7 4 3 = + + +b) 2 32B2 3 2 2 32 6 2 3+=+ + + S lc cch giiim a) Tnh trc tip: ghi ra mn hnh \(4+\(5\3+5\(48 - 10\(7 + 4\3)))) A=3 1,5 1 b) Ghi ra mn hnh: (\(2+\3)2)((\(2+\3)2)-(2\6)+(\(2 + \3)(2\3)))B~1,3660 1,5 1 Bi 2 (5 im):a)Tnh s o ca gc o to bi ng thng 4 2 3y x + 12+=vi trc Ox. b)Cho sino = 0,5 (00 < o < 900). Tnh A = cos2 32sin sin o o o . S lc cch giiim a) Gc o to bi ng thng 4 2 3y x + 12+= vi trc Ox c tnh bi cng thc: 4 2 3 3 1tg2 2+ +o = = Tnh gc o bng cch n phm Shift tan-1 ((\3+1)2 ) =., ,, Kt qu: o~ 53047'38" b) Tnh gc o bng cch n phm Shift sin-10.5 =- Kt qu o = 30, gn 30 cho A bng cch tip tc n phm: shift sto A - Ghi ra mn hnh: (cosA)2-2sinA-(sinA)3ri n phm = Kt qu: A = -0,375 0,75 0,75 1 0,75 0,5 0,5 0,75 Bi 3 (5 im): Cho a thc g(x) = 8x3 18x2 + x + 6.a)Tm cc nghim ca a thc g(x). b)Tm cc h s a, b, c ca a thc bc ba f(x) = x3 + ax2 + bx + c, bit rng khi chia a thc f(x) cho a thc g(x) th c a thc d l r(x) = 8x2 + 4x + 5. c)Tnh chnh xc gi tr f(2011). S lc cch giiim a) 11x2= , 2x 2 = ; 33x4= b) Theo trn ta c:g(x) (2x 1)(x 2)(4x 3) = + Theo gi thit ta c: f(x) = q.g(x) + 8x2 + 4x + 5(q l thng) Do vy ta c: 1 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh 1 11 1 1f r 5a b c 52a 4b 8c 41 2 24 2 8f (2) r(2) 45 4a 2b c 45 8 4a 2b c 379 3 25 27 36a 48b 64c 773 3 3 25a b c f r16 4 2 64 4 4 2 | | | | = = + = +|| + = \ . \ . = = + + = + + = + + =| | | | + + = = = || \ . \ .

Vo EQN chn gii h 3 phng trnh 3 n ta c: 23a4= , 33b8= , 23c4= c) Ghi vo mn hnh biu thc: X3 + (234)X2 + (338)X + (234) Bm phm CALC v nhp s 2011 = ta c s hin ra mn hnh l: 8155989328. Sau ta n tip phm - ri nhp 815989328 = c -0.125. Do vy gi tr chnh xc ca f(2011) = 8155989327.875 1 0,5 1 1 0,5 Bi 4 (5 im): Gii phng trnh: x x41 11 41 12 31 13 24 2+ =+ ++ ++ + S lc cch giiim t 1A1112134=+++, ri tnh A c 3043, gn 3043 cho bin A. 1B1413122=+++, ri tnh B c 1773, gn 1773 cho bin B. Phng trnh c dng: 4 + Ax = Bx 4xB A= Ghi ra mn hnh: 4(B-A) n phm = ri chuyn v dng phn s c kt qu l 12556x=-1459 1 1 1 1 1 Bi 5 (5 im): Dy s (Un) c xc nh nh sau: U0 = 1; U1= 1; Un+1 = 2Un Un-1+ 2; vi n= 1; 2; 3; a)Hy lp mt quy trnh bm phm tnh Un ? b)Tnh gi tr ca Un khi n = 1; 2 ; 3 ;.; 20 ? S lc cch giiim a) Quy trnh bm phm tnh Un l : Lu:1 vo bin nh A ( Bm 1 shift stoA) 1 vo bin nh B( Bm 1 shift stoB) 1 vo bin nh C( Bm 1 shift stoC) Ghi vo mn hnh: A= A + 1: B = 2C B + 2: A = A + 1: C = 2BC + 2 v bm = = ..b) Bng gi tr ca Un; n = 1;; 20 U1=1U2= 3U3= 7U4= 13U5 = 21 1 2 (mi kt qu Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh U6=31 U7= 43U8= 57U9= 73U10= 91 U11= 111U12= 133U13= 157U14= 183U15=211 U16= 241U17= 273U18= 307U19= 343U20= 381 ng c 0,1 ) 2 Bi 6 (5 im):Mt s tin 58000 ng c gi tit kim theo li kp (sau mi thng tin li c cng thnh vn). Sau 25 thng th c c vn ln li l 84155 ng. Tnh li sut mi thng? S lc cch giiim Gi a l s tin tit kim ban u ; r l li sut tit kim . Sau mt thng tng s tin c gc ln li l: a + ar = a(1 + r) Sau hai thng tng s tin s l : a(1 + r) + a(1 + r).r = a(1 + r)2 Sau n thng tng s tin l : A = a(1 + r)n . Suy ra:= 1nAra thay s n= 25; A = 84155; a = 58000 c r~ 0,015 Vy : li sut mi thng l : 0,0 15 x 100% ~1,5 %/thng 2,5 1,5 1 Bi 7 (5 im):a) Tm s d khi 759487564:49367 b) Tm xy s 1234xy345 chia ht cho 12345S lc cch giiim a) C s ca thut ton a r aq r q .bb b b| |= + = |\ . - Lu 49367 vo bin nh B. - Ly 759487564:B my tnh hin kt qu 15384.51929 Ta nh phn nguyn q l 15384. -Lyktqucaphpchiatrn triphnnguyn15384rinhnviBta c s d l 25636 Vy r = 25636 2 0,5 b) C 0 s xy s 99.Gi thng ca 1234xy345 cho 12345 l k ta c: 123400345123 s 12345.k s 123499345 9995.969 sk s 10003.99 Xt 9996 sk s 10003 c k = 10001 cho kt qu 123462345 (tho mn) Vy xy = 62 (123462345) 1 1 0,5 Bi 8 (5 im): Cho dy s 11x2= ; 3113nnxx ++= . a)Hy lp quy trnh bm phm tnh xn + 1 b)Tnh x2 ; x3 ; x4

S lc cch giiim a) 0.5 = (Ans3+1)3 cho kt qu x2=0,375 b) Bm lin tip 2 ln phm = th ln lt cho cc kt qu x3 v x4 l: x2 = 0,375; x3=0,3509; x4=0,3477 3 2 Bi 9 (5 im): Cho AABC vung ti A c BC =3 10v AB = 715AC. Tnh AB, ABC(kt qu v gc lm trn n pht). S lc cch giiim Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh a) t AB = x (x>0) AC=15x7 theo nh l pitago ta c: AB2 + AC2 = BC2 22 215x x (3 10)7| |+ = |\ . 4410x274=x ~ 4,0118 (lu vo bin nh B) Vy AB~4,0118 b) Ta c: ABCosBBC=Tnh gc B bng cch n phm: Shift cos-1 (B(3\10)) .,, c kt qu 0B 64 59' ~ 2 0,5 1 1 0,5 Bi 10 (5 im): Cho hai ng trn (O) v (O) ct nhau ti A v B (O v O nm khc pha i vi AB). Mt ng thng i qua imAct (O) v (O)lnlt tihai im Mv N.Tnh dilnnht ca on thng MN nu cho bit AB = 16 cm, bn knh ca ng trn tm O v O ln lt l15 2 cm v10 2 cm. S lc cch giiim Gi I = OO'AB. Ta c: 16IA 82= = ; ABOO' 2 2OI (15 2) 8 19, 6469 = ~lu vo bin nh A 2 2IO' (10 2) 8 11, 6619 = ~lu vo bin nh B OO' = OI + IO' Ghi vo mn hnh A+B, ri n phm = c kt qu OO'~31,3088 lu vo bin nh C. Gi H, K ln lt l trung im ca MA, AN. Ta c: OHMA; OKAN (qh k v dc) OHKO' l hnh thang vung HK s OO' HK ln nht HK = OO' MN = 2HK Tnh MN bng cch ghi vo mn hnh 2C ri n phm = c kt qu MN=62,6176 cm 0,5 0,5 1 0,5 0,5 1 1 A CB IKHNBAOO'M Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh 3

Bi 1.Cho tng: S=15 4 3 2315....34333231+ + + + +a.Vit qui trnh bm phm lin tc tnh tng S? b.Kt qu :S = Bi 2: a)Tnh 12 201220122011 2011201120.200 . 197.....17 . 14 14 . 11 11 . 83994.....6343541543 3 3 32 2 2 2|||||.|

\|+ + + ++ + + += BKQb)C = 1 ) 90 ( sin sin 2) 90 ( cos cos ) 90 ( sin sin0 2 20 3 2 0 3 2+ + +o oo o o o bit tan = 0.2345 KQ: Bi 3:a .Tm ch s thp phn th 2011 sau du phy trong php chia 10: 51 +Trnh by s lc cch gii + Ch s thp phn th 2011 sau du phy trong php chia 10: 51 l: b) Tm s d trong php chia 2009201020112012 : 2020S d l :Bi 4: Cho a thcf(x) = ax3 + bx2 + cx + d.Bit f(0) = -7 ;f(1) = - 4;f(2) = 7; f(-1) = -17 a) Tm cc h s ca a thc v tnh f(1,2345) = ? a = b = c =d = f(1,2345) = b) Tm s d khi chia f(x) cho (x - 35 ) v tm h s bc hai ca thng trong php chia trnS d l: H s bc hai ca thng l: Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Bi 5:Cho hai ng thng (d1):y = 73x + 732v (d2): y = 37 x+ 7 a)Tm to giao imA(xA;yA)ca hai ng thng trn.(kt qu ly di dng phns ) a.Ta im A l xA= yA=b) Tnh gc B, gc C ca AABC, trong B, C th t l giao im ca (d1) v (d2) vi trc honh (lm trn n giy).KQ:B ~ C ~ Bi 6: a)Bit : gfedcba111111201220102011++++++ = Tm cc s t nhin a, b, c, d, e, f, g? KQ: a = b = c = d =e = f =g = b)Phn s no sinh ra s thp phn v hn tun hon sau:M = 4,22345234523452345...... KQ M = Bi 7: Chohnh bnhhnhABCD cgc nhAlgc t.Khai ng caoAHv AK (AH vung gc BC ti H, AK vung gc CD ti K). BitHAK Z = 670 36 v di hai cnh ca hnh bnh hnh lAB = 12,2011cm; AD = 10,2010cm.a). Tnh di AH v AK. b)Tnh t s gia dintch ABCDS ca hnh bnh hnh ABCD v din tch HAKS ca tam gic HAK. c) Tnh din tch phn cn liSca hnh bnh hnh khi khot i tam gic HAK. KQ: AH~ AK~

HAKABCDSS=S= Bi 8:Trong t kho st cht lng u nm, im ca ba Khi lp 7,8,9c cho trong bng sau: im109876543 Khi 71614115411124 Khi 8121416711281 Khi 9141510561352 a)Tnh im trung bnh ca mi khi lp. Kt qu lm trn n ch s thp phn th hai. KQ: 7X~ 8X~9X~b) Nu giXs trung bnh cng ca mt du hiu X gm cc gi tr 1 2, 3, ,...,kx x x xc cc tn s tng ng l 1 2 3, , ,...,kn n n n , th s trung bnh ca cc bnh phng cc lch ca mi gi tr ca du hiu so viX :2o=kk kn n n nX x n X x n X x n X x n+ + + + + + + + ........) ( ..... ) ( ) ( ) (3 2 12 23 322 221 1 2ogi l phng sai ca du hiu X v o =2o gi l lch chun ca du hiu X.Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh p dng: Tnh phng sai v lch chun ca du hiu im ca Khi 7, Khi 8, Khi 9. Kt qu lm trn n ch s thp phn th hai. 2o7~ 2o8~2o9~ o7~ o8~o9~ Bi 9:.Cho dy s vi s hng tng qut c cho bi cng thc.Un= ( ) ( )6 2 7 6 2 724 7n n+ + vin =0, 1, 2, 3.a, Tnh U0 , U1, U2, U3 , U4 . Lp cng thc truy hi tnh Un+1 theo Un v Un-1 KQ : U0 =U1= , U2=

, U3= , U4= Lp cng thc truy hi tnh Un+1 theo Un v Un-1 b. Lp qui trnh bm phm lin tc tnh Un+1 theo Un v Un-1 Qui trnh bm phm : Bi 10a) Tm tt c cc cp s nguyn (x , y) tha mn phng trnh: 3 25 11 22 3+ +=xx x xy . Bit rng -25 x , y 25. Cc cp s nguyn (x;y) l:` b) Tm s t nhin x bit : 1 +xx + + + + + + .... 6 5 4 3 26 5 4 3 = 45,354..... Qui trnh bm phm lin tc tm x l: KQ: x = HNG DN GII Bi 1.Cho tng: S=15 4 3 2315....34333231+ + + + +a.Vit qui trnh bm phm lin tc tnh tng S? 1 shiftSTOD 1ab/c3shiftSTOA D ALPHA= D +1 ALPHA: ALPHAAALPHA =ALPHA A+ALPHADab/c3 ^ALPHAD 1.0 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh n du = lin tip khi no D=15n tip=ta c KQ b. KQS=A~0,749999 0.5 Bi 2: a)Tnh 12 201220122011 2011201120.200 . 197.....17 . 14 14 . 11 11 . 83994.....6343541543 3 3 32 2 2 2|||||.|

\|+ + + ++ + + += BB ~ 4,759538 1.0 b)C = 1 ) 90 ( sin sin 2) 90 ( cos cos ) 90 ( sin sin0 2 20 3 2 0 3 2+ + +o oo o o o bit tan = 0.2345 KQ: C~ 0,445862 1.0 Bi 3 a .Tm ch s thp phn th 2011 sau du phy trong php chia 10: 51 +Trnh by s lc cch gii B1: 10: 51 = 0,19607843... 10 - 51 x 0,19607843 = 7.10-8 B2:7 : 51 = 0,13725490...7 - 51 x 0,13725490 =1.10-7 B3: 10: 51 = .... ......Php tnh c lp li nnKQ php chia 10: 51 l s TPVHTH chu k 16 ch s (1960784313725490) Ta c 2011 11(mod 16). Vy ch s thp phn th 2011 sau du phy trong php chia 10: 51 l: ch s 7 1.0 b) Tm s d trong php chia 2009201020112012 : 2020S d l : 972 1.0 Bi 4: a) Tm cc h s ca a thc v tnh f(1,2345) = ? KQ: a =25;b =27 ; c = 3;d = -7 ,( ) x f= 25x3

27 x2 + 4x -7 f(1,2345)~ - 2,692551 S lc cch gii: f(0) = -7 ;f(1) = - 4;f(2) = 7; f(-1) = -17 nn: = + + = + + + = + + + =177 2 4 847d c b ad c b ad c b ad Ly 3 phng trnh cui ln lt tr cho phng trnh u v gii h gm 3 phng trnh n a, b, c trn MTBT cho ta kt qu:a =25;b =27 ; c = 3;d = -7 ,( ) x f= 25x3

27 x2 + 4x -7 1.0 b) Tm s d khi chia f(x) cho (x - 35 ) v tm h s bc hai ca thng trong php chia trnS d l: r =|.|

\|35f=2741 0.5 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh 6736'DA BC KHb a H s bc hai ca thng l: 32 0,5 Bi 5:Cho hai ng thng (d1):y = 73x + 732 v (d2): y = 37 x+ 7 a)Tm to giao imA(xA;yA)ca hai ng thng trn.(kt qu ly di dng phn s ) a.Ta im A l xA= 2948yA= 2991

1.0 b) KQ:B ~2301154 C ~11301154 1.0 Bi 6:gfedcba111111201220102011++++++ = Ta c: 21411191111619991201220102011++++++ = KQ:a =9991 ; b =16 ;c =1 ; d =9 ;e =1;f = 4 ;g = 2 1.0 b)Phn s no sinh ra s thp phn v hn tun hon sau:M = 4,22345234523452345......KQ M = 99990422303 1.0 Bi 7: a) t AB = a = 1,2011 cm AD = b = 10,2010cm Ta c: AKCD; AHCB nnD B Z = Z=o=670 36 ABH A cAH = a sino = 12,2011.sin670 36AH ~ 11,280479 cm ADK AcAK = b sino = 10,2010. sin670 36 AK~9,431294 cm0,75 b) AHKABCDSS =AK AHCD AK. sin .21.o =. sin sin .21o o CDCD

c) Ta c: ABCD AHKS S S = 21=sin 1 sin2ab o o| | |\ . ~65,691162 cm2 2,0 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh o2sin2=AHKABCDSS=2,163224 0,75 0,5 Bi 8a)Tnh im trung bnh ca mi khi lp. Kt qu lm trn n ch s thp phn th hai. KQ: 7X~ 7,128X~ 7,389X~ 7,39 1.0 2o=kk kn n n nX x n X x n X x n X x n+ + + + + + + + ........) ( ..... ) ( ) ( ) (3 2 12 23 322 221 1 2ogi l phng sai ca du hiu X v o =2o gi l lch chun ca du hiu X.p dng: Tnh phng sai v lch chun ca du hiu im ca Khi 7, Khi 8, Khi 9. Kt qu lm trn n ch s thp phn th hai. 2o7~5,582o8~ 4,32 2o9~ 4,58 o7~ 2,36 o8~2,08 o9~2,14 1,0 Bi Bi 9:.Cho dy s vi s hng tng qut c cho bi cng thc.Un= ( ) ( )6 2 7 6 2 724 7n n+ + vin =0, 1, 2, 3.a, Tnh U0 , U1, U2, U3 , U4 . Lp cng thc truy hi tnh Un+1 theo Un v Un-1 KQ : U0 =2 ; U1= 3 ; U2= 14 ; U3=138 ; U4= 1358 Lp cng thc truy hi tnh Un+1 theo Un v Un-1 Gi s c cng thc truy hi tnh Un+1 theo Un v Un-1 l : Un+1 = aUn+ b Un-1 +c Ta c U2 = aU1 + bU0 + c U3 = aU2 + bU1 + c U4 = aU3 + bU2 + c Hay 3a + 2b + c = 14 14a + 3b + c = 138 138a + 14b + c = 1538 Gii ra ta c : a = 12 ;b = - 6 ; c = -8 Un+1 = 12Un -6Un-1 - 8 1.0 b. Lp qui trnh bm phm lin tc tnh Un+1 theo Un v Un-1 Qui trnh bm phm : Trn fx -500MS 2 SHIF STO A3SHIF STO B x 12 ALPHA B -6 ALPHA A 8 SHIF STO A x 12 ALPHA A -6 ALPHA B 8 SHIF STO B nhn phm| =| =| =........ta s c KQ cn tnh 1.0 Bi 10: a) Tm tt c cc cp s nguyn (x , y) tha mn phng trnh: Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh 3 25 11 22 3+ +=xx x xy . Bit rng -25 x , y 25. Cc cp s nguyn (x;y) l:` (x, y) = ( 4;21)(x, y) = (-1;-3) (x, y) = ( 2; 3) (x, y) = ( 1; 3) 1.0 b) Tm s t nhin x bit : 1 +xx + + + + + + .... 6 5 4 3 26 5 4 3 = 45,354..... Qui trnh bm phm lin tc tm x l: X = X + 1 A = A + XX=== .... Cho n khi mn hnh hin th KQ:45,33591372..th nhn c x = 38KQ:x = 38 1,0 4 Bi 1: (5 im) Tnh gi tr ca biu thca)3(12 6 3) 3 2(1 2 3 4) 2 4 2 314 8 3A = + + + b)B =( )( )( )( )( )( )22,1 2 3, 2 2, 9: 30, 04 752, 011 9, 1 26, 3 (+ + ( KT QU a)A =b)B = Bi 2: (5 im) Cho a = 2419580247; b = 3802197531. a.Tm CLN(a,b)b.BCNN(a,b). KT QU a) CLN(a,b) = b) BCNN(a,b) = Bi 3 : (5 im) Cho a thc P(x) = x4 + ax3 + bx2 + cx + d C P(1) = 7, P(2) = 28, P(3) = 63, P(4) = 112 a)Tm cc h s a,b,c,d ca a thc P(x) v vit li a thc P(x) . b) Tnh(100) ( 96)8P PA+ = KT QU a) a =; b = ; c = ; d = a thc : P(x) =b) A = (100) ( 96)8P P + = Bi 4 : (5 im) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh a)Tm hai ch s tn cng ca 39999 . b)Tm ch s thp phn th 2008 ca s 1023 KT QU a) b) Bi 5 : (5 im) 1)Tm s d trong cc php chia sau :a)1234567890987654321 :2010 b) 20092010:20112)Cho dyu1 = 5; u2 = 9; un +1 = 5un + 4un-1 (n>2). Tm s hng thu14 ca dy? KT QU 1) a) r = b) r =2) u14 = Bi 6 : (5 im)a) Gii phng trnh : =| |+ | | |+ |\ .231,8263 12, 0414 52,3 73 518 150, 0598 15 6x b)Tm x bit :254 23 16 45 38 57 57989x x+ =+ ++ ++ ++ KT QU a)x= b)x = Bi 7 : (5 im) Tam gic vung ABC (=900) c AB = 3cm; AC = 4cm. AH, AD ln lc l ng cao, phn gic ca tam gic. Tnh chu vi ca tam gic AHD. S lc cch gii Kt qu Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Bi 8:(5 im) T im M nm ngoi ng trn (O; R) k hai tip tuyn MA, MB vi ng trn . Cho bit MO = 2R v R = 4,23 (cm)(tnh chnh xc n 02 ch s sau du phy) 1)Phn din tch ca t gic MAOB nm pha ngoi ng trn (O; R); 2)Din tch phn chung ca hnh trn ng knh MO v hnh trn (O; R). S lc cch gii Kt qu 1) 2) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Bi 9 :(5 im) Cho tam gic ABC, ly im D thuc cnh AB sao cho 14DB BA = . Trn cnh AC lyimEsaocho 14CE AE = .GiFlgiaoimcaBEvCD.BitAB=7,26cm;AF=4,37cm; BF=5,17cm. a) Tnh din tch tam gic ABF? b) Tnh din tch tam gic ABC.( Trnh by s lc cch gii cu b ) S lccch giicu b: KT QU a) SABF = b) SABC = Bi 10 : (5 im)a) Tnh gi tr ca biu thc M vi = 25030', = 57o30

( )( ) ( )( ) ( )( )2 2 2 2 2 2C= 1+tg 1+cotg + 1-sin 1-cos . 1-sin 1-cos o ( b) Cho x2011 + y2011 = 6,916; x4022 + y4022 = 33,76244. Tnh D =x6033 + y6033 Kt qu a)C =b)D = --------------------------- Ht ---------------------------- Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh HNG DN Bi 1: (5 im) Tnh gi tr ca biu thca)3(12 6 3) 3 2(1 2 3 4) 2 4 2 314 8 3A = + + + b)B =( )( )( )( )( )( )22,1 2 3, 2 2, 9: 30, 04 752, 011 9, 1 26, 3 (+ + ( KT QU a)A = 0 (2,5 im) b)B = 0,132871696(2,5 im) Bi 2: (5 im) Cho a = 2419580247; b = 3802197531. c.Tm CLN(a,b)d.BCNN(a,b). KT QU a) CLN(a,b) =345654321(2,5 im) b) BCNN(a,b) = 26615382717(2,5 im) Bi 3 : (5 im) Cho a thc P(x) = x4 + ax3 + bx2 + cx + d C P(1) = 7, P(2) = 28, P(3) = 63, P(4) = 112 c)Tm cc h s a,b,c,d ca a thc P(x) v vit li a thc P(x) . d) Tnh(100) ( 96)8P PA+ =KT QU a) a = -10 ; b = 42 ; c = -50 ; d = 24 (2,0 im) a thc : P(x) = x4 10x3 +42x2 50x + 24(1,0 im) b) A = (100) ( 96)8P P + =23073617 (2,0 im)Bi 4 : (5 im) a)Tm hai ch s tn cng ca 39999 . b)Tm ch s thp phn th 2008 ca s 1023 KT QU a)67(2,5 im) b)2(2,5 im) Bi 5 : (5 im) 1)Tm s d trong cc php chia sau :a)1234567890987654321 :2010 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh b) 20092010:20112)Cho dyu1 = 5; u2 = 9; un +1 = 5un + 4un-1 (n>2). Tm s hng thu14 ca dy? KT QU 1) a) r =471(2,0 im) b) r = 1 (2,0 im) 2) u14 = 13.143.455.289 (1,0 im) Bi 6 : (5 im)a) Gii phng trnh : =| |+ | | |+ |\ .231,8263 12, 0414 52,3 73 518 150, 0598 15 6x b)Tm x bit :254 23 16 45 38 57 57989x x+ =+ ++ ++ ++ KT QU a)x= 043992762 , 1 (2,5 im) b)x = 45,92416672 (2,5 im) Bi 7 : (5 im) Tam gic vung ABC (=900) c AB = 3cm; AC = 4cm. AH, AD ln lc l ng cao, phn gic ca tam gic. Tnh chu vi ca tam gic AHD. S lc cch gii - p dng pitago tnh c BC = 5 (cm) - BH = BCAB2;AH = BCAC AB. - AB ACAB BCBDABAB ACDBDB DCABACDBDC+= +=+ =. - AD = 2222 2. .||.|

\|++ |.|

\|= +BCABAB ACAB BCBCAC ABHD AHCV = BCAC AB.+BCABAB ACAB BC2.+ +222. .||.|

\|++ |.|

\|BCABAB ACAB BCBCAC AB Hnh v: Kt qu: CV = 5,16722325 cm (2,5 im) A BC DH Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh (s lc ng cch gii 2,5 im ) Bi 8:(5 im) T im M nm ngoi ng trn (O; R) k hai tip tuyn MA, MB vi ng trn . Cho bit MO = 2R v R = 4,23 (cm)(tnh chnh xc n 02 ch s sau du phy) 3)Phn din tch ca t gic MAOB nm pha ngoi ng trn (O; R); 4)Din tch phn chung ca hnh trn ng knh MO v hnh trn (O; R). 1)Ta c: MA v MB l 2 tip tuyn ca (O, R), nn cc tam gic MAO v MBO vung ti A v ti B. Theo gi thit: MO = 2R, nn IO = IA = OA = R (I l trung im ca MO), do tam gic OAI u, tng t tam gic OBI u, suy ra 0120 AOB = v 0tan 60 3 MA OA R = =Gi S l din tch phn ca t gic MAOB nm pha ngoi ng trn (O, R), th S l hiu din tch t gic MAOB v din tch hnh qut OAB ca (O, R):

( )22 223 31202 3360 3 3MAOB quatOAB MOARR RS S S S Rtt tA= = = = . Thay R = 4,23, bm my: ( 33 -SHIFTt) 4.23 x2

3 =c kt qu12, 25( ) S cm ~2)GiSldintchphnchungcahaihnhtrn(O,R)v(I,R) (ng trn ng knh MO) th Sbng 2ln din tch cahnh to bi cung ABv dy AB: ( )( )22 224 3 33' 2 2 21, 98( )3 4 6quatOAB OABRR RS S S cmttA| |= = = ~ | |\ .. (s lc ng cch gii 2,5 im ) Kt qu 1) 12, 25( ) S cm ~( 1,0 im ) 2/ 221, 98 S cm = )( 1,5 im ) Bi 9 :(5 im) Cho tam gic ABC, ly im D thuc cnh AB sao cho 14DB BA = . Trn cnh AC lyimEsaocho 14CE AE = .GiFlgiaoimcaBEvCD.BitAB=7,26cm;AF=4,37cm; BF=5,17cm. a) Tnh din tch tam gic ABF? b) Tnh din tch tam gic ABC.( Trnh by s lc cch gii cu b ) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh FCEBDAS lccch giicu b: ( 2 im ) a) SABF = 11,16466902 cm2. b) t SABF = 4SBDF = 4x;SACF = 5SCEF = 5y SABF +SAEF = 4x + 4y =45SABC ;SADF +SACF = 3x + 5y =34SABC

Ta c h:ABCABC20x + 20y = 4S12x + 20y = 3S SABC = 8x SABC = 2SABF = 22,32933805 cm2. KT QU a) SABF = 11,16466902 cm2. (2 ) b) SABC = 22,32933805 cm2. (1 ) Bi 10 : (5 im)a) Tnh gi tr ca biu thc M vi = 25030', = 57o30

( )( ) ( )( ) ( )( )2 2 2 2 2 2C= 1+tg 1+cotg + 1-sin 1-cos . 1-sin 1-cos o ( b) Cho x2011 + y2011 = 6,916; x4022 + y4022 = 33,76244. Tnh D =x6033 + y6033 Kt qu c)C =1,754774243 ( 2,0 im ) d)D = 184,8517609( 3,0 im ) 5 Cu 1: Tnh tng ca cc ch s: (6122009)2p s: 76Li gii: ta c: (6122009)2 = (6122000 + 9)2

= (6122.103 + 9)2 = (6122.103)2 + 2. 6122.103.9 + 92 = 61222.106 + 110196.103 + 81 61222.106 = 37 478 884 000 000 110196.103 = 110 196 000 81=37 478 994 196 081 Tng cc ch s ca s trn l: 3 + 7 + 4 + 7 + 8 + 9 + 9 + 4 + 1 + 9 + 6 + 0 + 8 + 1 = 76 Cu 2: Tnh Kt qu ng (khng sai s ) ca cc tch sau: P = 13 032 008. 13 032 009 Q = 3333355555.3333377777 p s: P = 169833245544072 p s: Q = 11111333329876501235 Li gii: ta c: Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh P = 13 032 008. 13 032 009 = (13032000 + 8).(13032000 + 9) = ( 13032.103 + 8).(13032.103 + 9) = (13032.103)2 + (9 + 8).13032.103 + 72 = (13032.103)2 + 17.13032.103 + 72 (13032.103)2 = 169833024000000 17.13032.103 =221544000 72 = 169833245544072 Q = 3333355555.3333377777 = (3333300000 + 55555).(3333300000 + 77777) = (33333.105 + 55555).(33333.105 + 77777) = (33333.105)2 + (55555 + 77777).33333.105 + 55555.77777 = (33333.105)2 + 133332.33333.105 + 55555.77777 = (33333)2.1010 + 133332.33333.105 + 55555.77777 (33333)2.1010 = 11110888890000000000 133332.33333.105 =444435555600000 55555.77777 =4320901235 =11111333329876501235 Cu 3: Tnh Tng: A = 1 + 2 + 3 + . . . + 100 = (1 + 100) + (2 + 99) + . . . + (50 + 51) = 101 . (100 1) 12 + = 101. 50 = 5050 B = 1 + 2 + 3 + . + n =(n + 1)2ni chng minh cng thc trnC = 1 1 1 1...1.2 2.3 3.4 100.101+ + + + = 1 1 1 1 1 1 1 1( ) ( ) ( ) ... ( )1 2 2 3 3 4 100 101 + + + + =1 1 1 1 1 1 1 1...1 2 2 3 3 4 100 101 + + + + = 1 11 101 = 101 1 100101 101 =D = 1 1 1...1 2 2 3 2009 2010+ + ++ + + = 2 2 2 2 221 2 2 3 2009 2010...12 3 2009 2010 2 + + + = 1 2 2 3 2009 2010...1 2 2 3 2009 2010 + + + = 1 2 2 3 2009 2010...1 1 1 + + + Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh = 1 2 2 3 2009 2010...1 1 1 + + ++ + + = -1 +2010= 2010- 1 = 43.83302354 E = 3 5 7 101...4 36 144 2500.2601+ + + + = 3 5 7 101...1.4 4.9 9.16 2500.2601+ + + + = 1 1 1 1 1 1 1 1...1 4 4 9 9 16 2500 2601 + + + + = 1 26001 0.9996155322601 2601 = = Cu 4: Mt ngi gi vo ngn hng mt s tin l a ng vi li sut l m% mt thng. Bit rng ngi khng rt tin li ra. Hi sau n thng ngi y nhn c bao nhiu tin c gc c gc ln li. a)Xy dng cng thc tnh b)Ap dng bng s: a = 100000000m = 0,8 n = 12 Gii: tm% = x, s tin c gc ln li sau nm th n l An Sau 1 nm s tin c gc ln li l: A1 = a + a.m% = a(1 + m%) = a(1 + x) Sau 2 nm s tin c gc ln li l: A2 = A1 +A1.x A2 = a(1 + x) + a(1 + x).x = a(1 + x)2 Sau 3 nm s tin c gc ln li l: A3 =A2 + A2.x A3 = a(1 + x)2 + a(1 + x)2.x = a(1 + x)3 Nh vy Sau 4 nm ta c s tin c gc ln li l: A4 = a(1 + x)4 Sau 5 nm ta c s tin c gc ln li l: A5 = a(1 + x)5 Sau n nm ta c s tin c gc ln li l: An = a(1 + x)n Tng qut: An = a(1 + x)n = a(1 + m%)n B) p dng: vi a = 100000000 m = 0.8 n = 12Ta c: An= a(1 + m%)n = 1.108(1 + 0.8%)12 = 1100338694 ng Cu 5:Mt ngi gi tit kim 100000000 ng (VND) vo mt ngn hng theo mc k hn 6 thng vi li sut 0,65% mt thng. a)Hi sau 10 nm, ngi nhn c bao nhiu tin (c vn v li) ngn hng. Bit rng ngi khng rt li tt c cc nh k trc . b)Nu vi s tin trn, ngi gi tit kim theo mc k hn 3 thng vi li sut 0,63% mt thng th sau 10 nm s nhn c bao nhiu tin (c vn v li) ngn hng. Bit rng ngi khng rt li tt c cc nh k trc . Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh (kt qu ly theo cc ch s trn my khi tnh ton) Gii: a) Vi cng thc thu c cu 4 ta c: An= a(1 + m%)n

k hn 6 thng vi li sut 0,65% mt thng. m% = 6x0,65%= 3,9% 10 nm m k hn 6 thng: n = 10x2 =20A20= 108(1 + 3,9%)20 = 214936885,3 (VND) b) k hn 3 thng vi li sut 0,63% mt thng. m% = 3x0.63% = 1,89% 10 nm m k hn 3 thng: n = 10x4 =40 A40= 108(1 + 1,89%)40 = 211476682,9 (VND) Cu 6: Mt ngi hng thng gi vo ngn hng mt s tin l 1.000.000 (VND) vi li sut 0,8% mt thng. Bit rng ngi khng rt tin li ra. Hi cui thng th 12 ngi y nhn c bao nhiu ch vng (c vn ln li) bit mt ch vng l 1.760.000 (VND) Gii:Xy dng cng thc: t 1.000.000 = a 0,8% = x S tin ngi c cui thng 1 l: C1 =a + a.x = a(1 + x) S tin ngi c u thng 2 l: 2 = C1 + a == a(1 + x) + a = a[(1 + x) + 1)] = ( )221[(1 ) 1][(1 ) 1][ 1][(1 ) 1] (1 ) 11(1 )aa x x ax x xxx ( (+ + + = = + + ++ S tin ngi c cui thng 2 l: C2 = 2 + 2.x == 2[ 1](1 )axx+ + 2[ 1](1 )axx+.x = 2 3[ 1](1 ) [ (1 )]2(1 ) (1 )a ax xxx x + = ++ + S tin ngi c u thng 3 l: 3 = C2 + a == 3[ (1 )]2(1 )axx ++ + a = 3 3[ (1 ) ] [ 1](1 ) (1 )a ax xx xx x + + = + + S tin ngi c cui thng 3 l: C3 = 3 + 3.x = = 3[ 1](1 )axx+ + 3[ 1](1 )axx+.x = 3 4[ 1](1 ) [ (1 )](1 ) (1 )a ax xx xx x + = ++ + .. .. C nh vy s tin ngi c cui thng th nl: Cn = 1[ (1 )](1 )naxxx+ ++Ap dng: C12 = 12 11.000.000[ (1 0, 8%)]0, 8%(1 0,8%)+ ++ 613[ (1 0, 008)]0, 00810(1 0,008)= ++ Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh = 12642675,41 (VND) S ch vng l: 12642675,41 : 1760000 = 7,1833383(ch vng) Cu 7: Tnh gi tr ca biu thc M vi 030'25o = ; 030'57| = M = ( ) ( ) ( )( ) ( ) ( )2 22 2 2 21 1 1 1 . 1 1cotsin cos sin costg go | o | o | (+ + + ( = ( )( )2 22 2 2 21 1 . .cotcos sin cos sintg go | o | o | (+ + + ( = ( )( )2 22 22 21 1 .sin coscos .sin cos .sincos sino |o |o | o | ( | || | ( + + +| | | | (\ .\ . = ( )( )2 22 21 1.cos .sin cos .sincos sino |o | o | ( | || | ( +| | | | (\ .\ . = ( )( )( )2 221.cos .sin cos .sincos .sino | o |o | ( (+ ( ( =( )41cos .sin o |+ Tnh 0cos cos 30'25o =gn cho X 0sin sin 30'57| =gn cho Y Tnh M~ 1,3358 Cu 8:Gii phng trnh (ly kt qu vi cc ch s tnh c trn my) 130307 140307 1 x + += 1 +130307 140307 1 x +Gii:t: 130307 = m 130407 = n 1 m n x + += 1 +1 m n x +1 m n x + +-1 m n x += 1 ( 1 m n x + +-1 m n x + )2 = 12 1 m n x + ++1 m n x +- ( )2221 n xm + = 1 2m -1= 2 22 (1 ) xm n + 2m -1= 2 2 22 xm n n (2m -1)2= (2 2 22 xm n n )2 (2m -1)2 = 4(m2 n2 n2x) 4m2 4m + 1 = 4m2 4n2 4n2x 4n2x= 4m - 4n2 1 x = (4m 4n2 -1) : 4n2 Thay vo ta c x = - 0,99999338 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Cu 9: Gii phng trnh (ly kt qu vi cc ch s tnh c trn my) 178408256 26614 1332007 x x + + +178381643 26612 1332007 x x + += 1 Gii: 178408256 26614 1332007 x x + + +178381643 26612 1332007 x x + += 1

21332007 2.13307. 133200713307x x + + + + 21332007 2.13306 133200713306x x + + += 1 ( )21332007 13307 x+ + ( )21332007 13306 x+ = 1 1332007 13307 x + +1332007 13306 x + = 1 Trng hp 1:1332007 13307 x + +1332007 13306 x + = 1(cn phi tm iu kin) 21332007 x += 26614 1332007 x += 13307 x = 133072 1332007 = 175744242 (l mt nghim ca pt) Trng hp 2:1332007 13307 x + + 1332007 13306 x + += 1(cn phi tm iu kin) -2 1332007 x += -26612 1332007 x += 13306 x = 133062 1332007 = 175717629 (l mt nghim ca pt) Cu 10: Tm nghim ca phng trnh sau (ly chnh xc 0,001) f(x) = x4 5x3 10x2 + 30x + 4 = 0 Gii: nhn thy: vi x = 2 th f(x) = f(2) = 0nn f(x) chia ht cho (x 2) v x4 5x3 10x2 + 30x + 4 = (x 2)(x3 3x2 16x -2) = 0 (chia a thc hoc dng s hoocne) Phng trnh cho c x1 = 2V gii phng trnh (x3 3x2 16x -2) = 0 trn my ta tm c x2 ~ 5,8121;x2~ - 2,6839;x4~ -0,1282 Cu 11:Xc nh cc h s a, b, c ca a thc P(x) = ax3 + bx2 + cx 2007 sao cho P(x) chia cho (x 13) c s d l 2 v chia cho (x 14) c s d l 3. ( Kt qu ly vi 2 ch s phn thp phn) Gii: P(x) chia cho (x 13) d 2ax3 + bx2 + cx 2007 = (x 13).Q(x) + 2ax3 + bx2 + cx 2007 - 2 = (x 13).Q(x) ax3 + bx2 + cx 2009 = (x 13).Q(x) = f(x) f(13) = 0 133a + 132b + 13c 2009 = 0 (*) phn tch tng t : P(x) chia cho (x 14) d 3ax3 + bx2 + cx 2007 = (x 14).H(x) + 3 ax3 + bx2 + cx 2007 - 3 = (x 14).H(x) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh ax3 + bx2 + cx 2010 = (x 14).H(x) = f(x) f(14) = 0 143a + 142b + 14c 2010 = 0 (**) Cu 12: Cho 1 22008x x+ =v1 2. 2009x x =Tnh: a) 2 21 2?x x+ =b) 3 31 2?x x+ =c) 4 41 2?x x+ =Gii: a) Ta c: 2 21 2 x x+ =2 21 2 1 2 1 22 2x x x x x x+ + == ( )21 221 2x x x x+== 20082 2x2009 = 4.028.046 b) 3 31 2 x x+ = 33 2 2 21 1 2 1 2 1 2223 3 31 23 x x x x x x x xx x+ + + =( )( )31 2 1 231 2x x x x x x ++ = 20083 3.2009x2008 = 8.084.282.296 c) 4 41 2 x x+ =( ) ( )2 22 2 2 21 2 1 22 22 21 2x x x x x x+ + =( ) ( )222 221 2 1 2x x x x+ = 4.028.0462 - 2x20092 = 16.225.146.505.954 Cu 13: Tnh tng sau: A = 2 2 2 2...3 100 1 2+ + + +B =3 3 3 3...3 100 1 2+ + + +Gii: A = 2 2 2 2...3 100 1 2+ + + +Ta c: 1= 12 1 + 3 = 4 = 22 1 + 3 + 5 = 9 = 32 1 + 3 + 5 + 7 = 16 = 42 1 + 3 + 5 + 195 + 197 + 199= 10000 = 1002 (ta tha nhn c mt cng thc: 1 + 3 + 5 + . . . +(2n 1) = n2 ) T ta c: A = 100.1 + 99.3 + 98.5 + . . . + 195.3 + 197.2 + 199.1= Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh 6 Bi 1(5 im):a) Tm y bit: 13 2 5 1 1: 2 115, 2.0, 25 48, 51:14, 7 44 11 66 2 51 y3, 2 0,8 5 3, 252| | |\ .=| |+ |\ . b) Gii phng trnh 2x4 21x3 + 74x2 - 105x + 50 = 0 Cch giiKt qu a) Tnh thu gn tng phn li ta c 15,2 x 0,25 48,51 : 14,7 = 0,5 A | | |\ .13 2 5 1 1: 2 144 11 66 2 5 = 0,1 B | |+ |\ .13, 2 0,8 5 3, 252 = 5 C (A x C) : B = 25 y = 25 Chm2,5 im b) Ch ra cc bc nhm nghim bng my dng phm slove ( x = 1) Dng Horne phn tch c PT bc 3 (x-1)(2x3 19x2 + 55x 50) Dng my gii PT bc 3:2x3 19x2 + 55x 50 = 0 x1 = 1 x2 = 5 x3 = 2 x4 = 2,5 Chm2,5 im Bi 2 (5 im): 1) Cho a thc P(x) = x3 + bx2 + cx + d. Bit P(1) = -15; P(2) = -15; P(3) = -9. a. Tm cc h s b, c, d ca a thc P(x). b. Tm s d r khi chia P(x) cho x 4. Cch gii Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Cch gii a) thay P(1), P(2), P(3)vo ta c h PT 164 2 239 3 36b c db c db c d++ = + + = + + = dng my tnh gii h c KQ3215bcd= == Thay vo c P(x) = x3 + 3x2 - 2x + 15 Tnh P(4):x3 + 3x2 - 2x + 15 Bm CALC nhp A = 4 kt qu P(4) = 9 Bi 3 (5 im): a) Tm s d trong php chia sau y: 30419753041975 : 151975 b) Tm UCLN v BCNN ca hai s A = 1234566 v B = 9876546 Cch giiKt qu Tm s d ln 1: 304197530: 151975 = 2001,628751 Sa thnh: 304197530 151975 x 2001=95555 ( s d ln 01 ) Tm s d ln 2: Vit9555541975 : 151975 = 62875,74913 Sathnh:Vit9555541975151975x62875=133850 (s d ln 2) Kt lun: S d ca php chia 30419753041975 cho 151975 l r = 113850 r = 113850 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Cch giiKt qu b) Tm UCLN ca A v B 9876546 1 54869781234566 68587 68587= =UCLN (A; B) = 9876546 : 548697BCNN = 9876546 x 68587kt hp tnh trn giy = (9876.103 + 546 ) 68587 Bm my:9876 x 68587 = 677365212 9876.103 x 68587 =677365212000 456 x 68587 =37448502 9876546 x 68587 677402660502 UCLN = 18 BCNN= 677402660502 Bi 4 (5 im): Cho ng trn tmO , bn knh3,15R cm = . T mt imA ngoi ng trn v hai tip tuynABvAC( B ,Cl hai tip im thuc (O )).Tnh din tch phn mt phng gii hn bi hai tip tuyn v cung trn nh BCbit rng7, 85AO a cm = =(chnh xc n 0,01 cm). Cch giiKt qu Tnh o: 3,15cos7,85OB ROA ao = = = 13,15cos7,85o=SOBAC = 2SOBA = aRsino Squt = 2 2.2 .360 180R R t o t o=Sgch = SOBAC - Squt = aRsino - 2.180R t o~ 11,16 (cm2) KQ= 11,16 cm2 Bi 5 (5 im):a) Tm x chnh x ti 5 ch s thp phn. O BaACGenerated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh b) Gii h phng trnh sau: 3x y 2z 302x 3y z 30x 2y 3z 30+ + = + + = + + = Cch giiKt qu a)Tnh: + + + 172 20 5 400 = 13,3041347 AA-4=9,304134696 A = =+++x xA1 4311 302134=> x = A : 3043 = 13,33593 x=13,33593 b) Gii trc tip trn myBm MODE 3 ln bm 1 (chn EQN)bm 3 Nhp cc h s:a1 = 3 ;b1=1 ;c1 = 2 ;d1= 30a2 = 2 ;b2=3 ;c2 = 1 ;d2= 30 a3 = 1 ;b3=2 ;c3 = 3 ;d3= 30 Bm = x1= 5;=y2 = 5;=z3 = 5 x =5 y =5 z =5 Bi 6 (5 im): Cho tam gic ABC vung ti A vi AB = 15, BC = 26(cm). K ng phn gic trong BI ( I nm trn AC) . Tnh IC. Cch giiKt qu + = + + ++++x4 172 20 5 4001112134Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Cch giiKt qu Dng tnh cht ng phn gic v t l thc 2 226 15 4113, 4672126 15BC BACI AI CI AI= => = = = cm Bm my 2 226 15 => A = 13,46721 26A:41 =CI~ 13,46721 cm Bi 7 (5 im): Mt ngi hng thng gi vo ngn hng s tin l 10 000 000 vi li sut 0,9% mt thng. Hi sau 2 nm ngi y nhn c bao nhiu tin c gc ln li? Cch giiKt qu Phntch:gistingihangthnglang,lixuthng thng l x (%) ta c uthng 1 c: a ng Cui thng 1 c: a + ax =a(1 + x)( ng ) u thng 2 c: Cui thng th 2 c: = 268958811 2 2(1 ) ( ) [( 1) -1]a aa x a x x x xx x+ + = + + = +2 2[( 1) -1] (1 ) [( 1) -1] (1 )22[( 1) -1] (1 ) (1 ) [( 1) - 1] (1 )a ax x x x xx xa ax x x x xx x ((= + + + + + (( (= + + + = + + ( A B C I Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Cch giiKt qu u thng 3 c: Cui thng th 3 c: a a 3 3 =[(x+1) -1] +[(x+1) -1].xx xa 3=[(x+1) -1] (1 + x)x u thng n c ng Cui thng n c ngThay s bm my tnh: (10000000 0,009)(((0,009 + 1).24-1)(1 + 0,009) = 268958811 Bi 8:(5 im )Cho dy s ( vi n nguyn dng )Un = ( ) ( )3 23 10 3 10n n + a/Tnh cc gi tr U1; U2 ; U3 ; U4 . b/Xclp cng thc truy hi tnh Un+2 theo Un+1 v Un . c/Lp qui trnh n phm lin tc tnh Un+2 theo Un+1 v Un, ri tnh U7 n U10

Cch gii a) 0 SHIFT STO A ((10 + \3).A (10 - \3) .A) : 2\3 : A = A + 1 Tnh c U1 = 1, U2 = 20, U3 = 303, U4 = 4120. b) ( 1) -1anT xx(= + (

[( 1) -1] (1 )a nT x xx= + + a a 22=[(x+1) -1] (1 + x) +a =[(x+1) -1] (1 + x) + xx x( (

a a3 3=(x+1) -1 - x + x=(x+1) -1x x (( (( Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Cch gii Gi s n 2 n 1 nu au bu c+ += + +Vi n = 1, 2, 3 4, ta tnh cU1 = 1, U2 = 20, U3 = 303, U4 = 4120. Thay vo c h + =+ + =+ + =a c 2020a b c 303303a 20b c 4120 => = = =a 20b 97c 0 H thc truy hi: Un+2 = 20Un+1 97Un c) A = 20B - 97A : B = 20A 97B = Bm phm: 0 SHIFT STO A; 1 SHIFT STO B;1 SHIFT STO X A=20B 97A : B = 20A 97B C th gn thm bin m m. Bi 9 (5 im) Cho tam gic ABC c gc C = 200 v AB = AC. Gi I l trung im ca AC. Tnh gn ng s o (, pht, giy) ca gc IBC. Cch giiKt qu I l trung im => ID l ng TB ca tam gic => BM = MH = HL Tnh tagB (tag 200) C tanB = 0,3639700234DMBM

Tag gc IBC = ILBL m13 3IL DM DMBL BM BM= = = 60553 A CB I L D MH Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Cch giiKt qu Bm my: tan 20o = : 3 = tan-1 = . = 6o553 Bi 10 (5 im): Chong thng y = ax + b i qua hai im A(0;-4) v B(2;0) a) Tnh gc o to bi ng thng y = ax + b vi trc Ox. b) Tnh khong cch t ng thng y = ax + b ti gc ta . Cch giiKt qu a) Bit OA = 2;OB = I-4I = 4 o ~ 63o265 c) SAAOB= 4 (v) OI = 8 : AB OI = 8 : 2 24 2 +~ 1,78885(v) o ~ 26o33 Khong cch l 1,78885 (v) 7 Cu 1: (5im) Cho dy s: Un = ( ) ( )2 5 2 52 5n n+ : n = 0,1, 2, 3 a/ Tnh nm s hng u tin ca dy U0; U1; U2; U3; U4. b/ Lp mt cng thc truy hi tnhUn+1 v Un. c/ Vit quy trnh bm phm lin tc tnh Un. Tnh U10; U11; U12: U13; U14; U15; U16 Cu 2: (5im) Vit quy trnh bm phm tnh a thc thng v d trong php chia. f(x) = x7 2x5 3x4 + x 1 cho x - 5. Cu 3: (5im) Dn s ca x A hin nay khong 5000 ngi d on sau 5 nm na dn s x A khong 5282 ngi. a/ Hi trung bnh dn s x A tng bao nhiu phn trm? b/ Hi sau 10 nm dn s x A khong bao nhiu ngi vi mc tng nh trn. c/ Sau bao nhiu nm th dn s x A bt u trn vt 6000 ngi? Cu 4: (5im) Tm gi tr ca x, y vit di dng phn s t cc phng trnh sau: 0 2 -4 I A B Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh a/41 14 11 13 21 12 32 4x x+ =+ ++ ++ + b/11 11 21 13 45 6y y =+ ++ + Cu 5: (5im)a/ Tnh:A = 3 3 30, 29972997... 0, 029972997... 0, 0029972997...+ +b/ Tm tt c cc c nguyn t ca A. Cu 6: (5im)a/ Vit quy trnh bm phm tm d khi chia s 2008200820 cho 2007. b/ Tm d khi chia s 2008200820 cho 2007. c/ Nu mt phng php tm d khi chia s 2008200820 cho 2007. d/ Tm d khi chia s 200820082008 cho 2007. Cu 7: (5im) Cho hnh bnh hnh ABCD. AB = 2AD;AD = 5cm; D=700. Gi H l hnh chiu ca B trn AD, M l trung im ca CD. a. Tnh HMC. b. Tnh chu vi v din tchHMB A .(Lm trn 5 ch s thp phn)Cu 8: (5im) ChoABC Avung A c AB = 3cm, AC = 4cm. Phn gic gc A ct BC ti E.a/ Tnh BE, CE. b/ T E k EMAB, ENAC. Tnh chu vi v din tch^ AMEN. (Lm trn 5 ch s thp phn). Cu 9: (5im)Cho hnh ch nht c chu vi l 29,616 cm; t s hai kch thc l 57. Tnh ng cho v din tch hnh ch nht (lm trn n ch s thp phn th 4). Cu 10: (5im) Cho Cotg =1,2349 Tnh: A = 222sin coscos tgo oo o+B = 2 225 cos sin3sin costgtgo o oo o o+ ++ + (Ly 9 ch s thp phn ) HD Cu 1: (5im) a/ U0 = 0U1= 1U2 = 4 U3=17U4 = 72 (1) b/ Gi s cng thc truy hi c dng: Un+2= aUn+1+ bUn + c Khi 2 1 03 2 14 3 2U aU bU cU aU bU cU aU bU c= + + = + += + + (0,5) 4 417 4 172 17 4 0a c aa b c ba b c c= + = = + + = = + + = (0,5) Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Ta c cng thc truy hi Un+2= 4Un+1 + Un (1) c/ Quy trnh bm phm lin tc tnh Un: V lp li dy phm

Sau dng ly kt qu (1) U10 = 416020 U11 = 1762289 U12 = 7465176 U13 = 31622993 U14 = 133957148 U15 = 567451585 U16 = 2403763488 Cu 2: (5im) Quy trnh bm phm tm thng v d khi chia f(x) = x7 2x5 - 3x4 + x - 1 cho x - 5 l: (2,5)

Vy x7 - 2x5 - 3x4 + x 1 = (x - 5) (x6 + 5x5 + 23x4 + 112x3 + 560x2 + 2800x + 14001) + 70004 a thc thng l: x6 + 5x5 + 23x4 + 112x3 + 560x2 + 2800x + 14001 D l: 70004. (2,5) Cu 3: (5im) a/ a l dn s hin c: A1 l dn s nm th 1, m% l t l tng dn s sau nm th nht dn s c: A1 = a + a.m = a(1 + m) Sau nm th 2: A2 = a(1 + m) + a (1 + n)m = a(1 + m)2 Sau nm th n: An = a(1 + m)n (1 + m)n = Ana 1 + m = nAna 1nAnma= Vi An = 5282 = SHIFTSTOAXSHIFTSTOB1 4 X+ALPHAASHIFTSTO A4 X+ALPHABSHIFTSTO B4 SHIFTSTOA5 Ghi kt qu X=15 XALPHAA-2=23 XALPHAA-3=112 XALPHAA=560 XALPHAA= 2800 XALPHAA+1=14001 XALPHAA-170004= Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh a = 5000 n = 5 552821 0, 01105000m = ~

Vy t l tng dn s l 1,1%/ nm. b/Sau 10 nm dn s x A l: 10 ln n du bng c kt qu l: 5578 ngi. c/Theo trn n tip du 16 ln c 5956 cha vt 6000 n thm mt ln na c 6021. Vy sau 17 nm na dn s bt u vt 6000 ngi. Cu 4: (5im) a/ t A = 11413122+++ B = 11112134+++ Phng trnh cho tr thnh Ax +Bx = 4 x(A+B) = 4x = 4A B + Quy trnh bm phm tnh A. Tnh B:

Bm tnh x: 872 1255642921 2921|

\ hoc 4,298527901) b/ t A = 111135++ ; B = 112146++ SHIFT()- = = SHIFTSTOA x-1 SHIFTSTOB 5000 x5282 = 5=1 =ANS+ANSX=50000,011 abc +=x-1 +=x-1 + 1 2234 abc +=x-1 +=x-1 +=14321 (ALPHA A+ALPHA B)4 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Phng trnh cho tr thnh. Ay 1 = By Ay By = 1 y = 1A B Quy trnh bm phm tnh A: Quy trnh bm phm tnh B: Quy trnh bm phm tnh y: y = 9353 16853|

\ hoc 3,16984321) Cu 5: (5im) a/A = 3 3 30, (2997) 0, 0(2997) 0, 00(2997)+ += 3 3 32997 2997 29979999 99990 999900+ += 3 9999 3 99990 3 9999002997 2997 2997 + += 9999 99990 999900999 999 999+ += 9999(1 10 100) 11098891111999 999+ += =Vy A = 1111 b/ A = 1111 = 11.101 Vy cc c nguyn t ca A l 11 v 101. Cu 6: (5im) a/ Quy trnh bm phm tm d khi chia 2008200820 cho 2007 l: b/ Vy d khi chia 2008200820 cho 2007 l 634. c/ C th s dng quy trnh sau: 200820082008 = 200700000000 + 120082008 = 2007 . 108 + 120082008 = 2007 . 108 + 2007 . 59831 + 1191 d/ D khui chia 200820082008 cho 2007 l 1191. Cu 7: (5im) Gi N l trung im AB, MN ct BH ti E. MN // AD v NA = NB SHIFTSTO = A B N H E 2008200820A abc+=x-1 +=x-1 SHIFTSTOA 1 531 A=1621 abc +=x-1 +=x-1 SHIFTSTOB1642 B=2556 (ALPHA A-ALPHA B)=1 2007 ALPHA A-X2007 1000598=Kt qu l 634 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh NE HB ti E v EH = EB ME va l ng cao va l trung tuyn caMHB MH = MB v HME EMB =(1) Mt khcMCBN ^l hnh thoi nn BMC BME == 0 0170 352= (2) T (1) v (2) suy ra HMC = 3.350 = 1050 b/ HB = AB.sin700~ 5 . 0,93969~ 4,69846 MB = MH = HE : sin350 = 2, 349230, 57358~ 4,09576 ME = HE . tg550 = 2,34923 . 1,42815~ 3,35505 Vy chu viMHB l: HB + 2MB = 4,69846 + 2 . 4,09576~ 12,88998 (cm) Din tchMHB l: 12HB . ME = 2,34923 . 3,35505~ 7,88178 (cm2) Cu 8: (5im)a/ Ta c 34EB ABEC AC= =hay 3 4EB EC== 53 4 7EB EC +=+ EB = 537 EB = 157 EC = 547 EC = 207

ABC vung AE tia phn gic nn: ^ ANEM l hnh vung. Chu vi l 4EN = 4EC . SinC = 4 . 207 . Sin35~ 6, 85714 cm Din tch l EN2 = EC = 1,714292 = 2,93878 cm2 TL EB = 2,14286 (cm) EC = 2,85714 (cm) Chu vi: 6,85714 (cm) Din tch: 2,93878 (cm2) Cu 9: (5im) Gi 2 cnh hnh ch nht l x, y (cm). Chu vi l: 2 (x+y) = 29,616 x + y = 14,808 AN C M E B Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Do t s 2 cnh l 57 nn 5 14, 8081, 2347 5 7 5 7 12x x y x yy+= = = = =+ x = 5 . 1,234 x = 6,1700 (cm) y = 7 . 1,234 y = 8,6380 (cm) ng cho l: x .y = 6,17 . 8,638 = 53,2965 (cm2) Vy ng cho hnh ch nht l: 10,6153 Din tch: 53,2965 (cm2) Cu 10: (5im)A = 0,497467403 B = 7,107032613 Quy trnh bam tnh A:

Quy trnh bm phm tnh B: TANX SHIFTSTOA 1,2349 ( SIN ALPHAA X2 + COS 2 ALPHAA ) ( TANALPHAA X2 - COS ALPHAA = 0,497467403 ( 5 TANALPHAA X2 + SIN ALPHAA ) ( 3 SIN ALPHAA X2 + TANALPHAA + COS ALPHAA ) = 7,107032613 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh minh Khai: GV: THCS Th Trn cu k, Tr Vinh Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.

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