De thi vao lop 10 tu nam 2002 phan 1

<span class='text_page_counter'>(1)</span>HBNG PHONG,. DE THI VAO L ~ 10 P TRUDNG THPT CHUYEN LE TP H d C H MINH ~ NAM HOC 2002 - 2003 NGAY THONHLT Man Toan cho cac Idp Khoa hoc Tq nhi6n ( Thai gian ldnz bdi :150 phlir). C$u 1. Rlit gon c6c bieu thirc &a) A =. CAU 4. Giii cdc phuung trinh. JKJJZEE; b) ( 4 x + 1)(12x - 1)(3x + 2 ) ( x + 1 ) = 4.. C$U2. Cho phuung- t r h h x2 - 2 ( m - l ) x + 2 m - 4 =0(c6ins618x). a) C h h g minh rang phuung trinh c6 hai nghiem phdn biet;. b) Goi xl, x2 18 hai nghiem cha phuung 2. trinh. Tim gi6 tri nh6 nhdt cch y. Cfiu3. a) C h h g minh b) C h b g rninh x4 c)aa. >. 9 '. + y4. = XI. 2. 2. x +y -2 2. + x2 .. -. (x+yIL. 2. ( x +Y ) ~. y > O Vh + y =. 1 8 ( x 4 + y 4 ) + - 2 5.. XY. 2. 8. '. Chimg. *. CAU 5. Cho d u h g trbn (0 ;R) vii d u h g thing (d) c6t d u h g trbn ( 0 )t.+i hai diim A, B. Til met didm M trCn d u h g thing (d) vh 6 ngohi d u h g trbn (0),(d) kh6ng di qua 0 , ta v& hai ti6p tuye"n M N , M P vdi d u h g trbn ( 0 )(N, P Ih hai ti6p di6m).. - -. a) C h h g minh rang NMO = NPO. b) Chimg minh ring d u h g trbn ngoai ti6p tam giic M N P di qua hai diim co" dinh khi M di dong M n d u h g thing (4. c) Xbc d 3 h vi tri didm M trCn d u h g thing (4sao cho tir gidc M N O P 12 mot hinh vu6ng. d) C h h g rninh tam I cba duang trbn noi ti6p tam gidc M N P di dong trCn mat d&ng cB dinh khi M di dong tr&n(6).. I.

<span class='text_page_counter'>(2)</span> NGAY THOHAI M6n Toan cho cac lap chuygn Toan, chuygn Tin (Th& g i m :Y 4 0 plrrit) . \ \ .. '. C l u 6. E m cdc gid trj cha m d& p h h g trinh sau c6 nghiem vh tinh c i c nghiem gy theom: x + l x2 - 2 x + m l = 0 . I. C l u 7. Philn tich thhnh nhiln tit. '. '. A = X ' ~ + ~ ~ + ~ . C l u 8. GiAi phuung trinh vh hf: phuung trinh : a). x2 -+3. 48. C l u 10. Cho tam gidc ABC c6 ba g6c nhon ngi tigp trong du&ng trbn (0)v i c6 AB < AC. '. h. -=BC. 3. ~. .. Lgy di6m M thuoc cung BC kh6ng chira dikm A cca' d u h g trbn (0).VE MH vubng g6c BC, MK vudng g6c C A , MI vu8ng g6c AB (H thu6c BC,K thuoc AC, I thuoc AB). Chiing minh rhng. x 4. = lo(---). x2. .. Ac. AB. MH MK+MI. C l u 11. Cho tam giBc ABC. GiA sir cdc d u h g philn gidc trong vh philn gidc ngoki cila g6c A cha tam gidc ABC ldn lvqt cht d u h g thing BC tai D , E vh c6 AD = AE.. '. b) ,/~G~ET+./-=~JZ:. CBu 9. Tim gid tri ldn nhgt vh gii tri nhb nhgt cila : x2. .Ainh. Chiink rhng AB2 AC2 = 4 R ~vdi l i bdn kinh d u h g trbn ngoai tigp tam gidc ABC. +. ToAn (TJtdi gian :120 phut). C l u 1. a) n. m gid tri nhi, nhgt ciia bidti th6c. ,LziF+di2TGz.. ... h) ~ h h ti, grhg. . -C l u 2. Cho hf: phuung trinh =". -. .. 81. x + y +xy-3x-4~+4=0. b) Gidi he phuung trinh trCn. C l u 3. C6 t6n tai hay kh6ng hai s6 nguyCn. x, j sao cho 3x2 + 7y2 = 2002 ? I. C ~ 4.~ri3n U mat phfing cho da gidc 16i c6 12. canh. C6 bao nhiCu tam gidc mii cdc dinh cSla n6 1h dinh cha da gidc Ibi d I cho ? (1). (2). a) GiA sir c6 ( X ; Y) thba miid (21, c h h g minh rang 7 llyl-. 3 . , l ,. Clu5.oloMthoiAsCoc6g6c ~ z = 4 0 0 , 0 1; giao dikm hai d u h g chko. Goi H 1k hinh chi& wdng g6c cha 0 trCn canh AB. TrCn tia d6i cc6a tia BC, tia M i &a tia DC lln luqt lily c i c dikm M , N sao cho HM // AN. Tinh sB do g6c MON..

<span class='text_page_counter'>(3)</span> NAM W N H NriM HOC 2002 - 2003 .. ,.I. ,". 9'. NGAY THONHAT. (_. Man Torn chi cdc ldp Khoa h@cTI# nhien (Thai gian :150 phut). :.. ,,:.l,. '. '. .. .. , 0.-'. CAu 1. 1 ) Chimg minh rang vc3i moi gid trj duung cha n, lu8n c6 1 =--1 -. 1 (n+l)&+nm J;; 2) Tinh tdng 1 1 s=- 1 2+&+3&+2&+4&+3&. +. ,. <. ,. +...+. CAu 4. Cho d u h g trbn (0;R) vdi hai d u h g kinh AB v8 MN. Ti6p tuy6n vdi d u h g trbn (0) tt$ A c8t &&hg th&ngBit4 vh BN tuung dng t@ M , ' - V ~ IJ,: G; P lh trung didm c i a AMI, Q 18 trung di6m cha AN, .: ' 1 ) Chimg minh tir gisic 'MMININ nei ti6p duuc trong met d u h g trbn.. .I. 100J99 + 9 9 f i ' CPu 2. n m trCn d u h g t h h g y = x + 1 n h h g didm c6 toa do th6a rnin ding thdc. -3&+2x =o. CAu 3. Cho hai phuung trinh y2. x2 - ( 2 m - 3 ) ~ + 6 = 0 ; 2x 2 + x + m - 5 = 0 ( x lh in, m 1h tham s6). n m m dd hai phuung trinh d i cho c6 ddng met nghiem chung.. a2 - b > 0. C h h g minh rhng. +. ,). ,,, .. 2 2 ' 2) KhBng sir dung m6y tinh v8 bing s6, chimg t6 rhng. '. 2) N6u MINI = 4R thi to giic PMNQ lh hinh gi ? C h h g minh. 3) D u h g kinh AB c6 dinh, tim tap hqp tam cbc. dultng trbn ngoai tigp tam giic BPQ khi d u h g kinh MN thay ddi. C ~ 5. U ~ h o ' d u irtiA'w h~ ;R) vh hai didm A, B nbny phia ngohi dultng trbn ( 0 ) vdi OA = 2R. Xsic dinh vi tri c i a didm M 'tkbdutYng trbn (0) sao cho bidu thdc P ='MA + 2MB dat gid tri nhb nhgt. Tim gi6 tri nh6 nhgt gy. '. M6n Toan c6c Idp chuyi3n ToBn, chuyi3n Tin ( ~ hgian k :150 phrit). CAu 6 1 ) Vdi a vh b la hai s6 dlrong th6a min. ... 7. 2tfi. -. 2-fi. 3<'m+&-J2-Jj. Y. 29 <20'. CAu 7. Gii sir x, y 18 csic s6 duung th6a min dhgthdcx+y=fi.~m~isitr~cia~vh dk biku t h k P =-(x4 + l)(y4 + ;) dat gisi tr/ nh6 nhgt. Tim gii tri nh6 nhgt gy ?.

<span class='text_page_counter'>(4)</span> tir didm I d6n c l c canh BC, AC vh AB cha tam gidc. C h, h.g minh. CAu 8. Gili h&phuang trinh. lL. x-y. +-y -Yz. +-=oZ. z-x. 7. . -. .. i :. Cbu 9. Cho tam gilc nhon ABC n6i ti6p trong d u h g trbn (0; R) vdi BC = a, AC = b, AB = c. Lily didm I bilt if ki phia tronb cira tam gidc ABC v i goi x, y, z ldli lugt 1%kho9ng chch. Cflu 10. Cho @p hqp b g 6 m 10 didm trong 66 c6 m6t s6 c$p didm duuc n6i v8i nhau bhng doan t h h g . Sel c l c doan thhng c6 trong tap 9 n6i tir dikm A den c i c di6m khlc goi 1i b4c c l a di6m A. C h h g minh ring bao gia cfing tlm duuc hai didm trong tgp hqp .'? c6 chng bat.. D$ 4 DE THZ VAO LOP 10 TRUONGTHPT NANG KHIEU. T&. PHU,. H h PHONG N&I HOC 2002 -2003 M6n Toan cho Idp chuyQnToan (Thai gian :150phi?). CAu 1. (2 d i h ) Cho phuung trinh dn x : x2 - 2 ( m + l ) x + m - 4 = 0. (1). a) Chimg minh ring phucmg trinh (1) c6 hai nghigm phdn biet. E m m dd phucmg trinh d6 c6 hai nghiem duang. b) Goi x , , x2 1h nghigm c6a phuung trinh (1). Tim gi6 tri nh6 nhQ c3a bidu thdc. Cbu 2. (3 die"m) a) GiAi phucmg t r h h. D m g hinh vubng APQR sao cho tam gilc APB v i hinh vudng nhy thu$ic chng mot nira mat phing bd AP. a) C h h g minh rang tam I c l a d u h g trbn noi ti6p tam gilc APB vh ba didm A,B,, Q chng thuoc mot d u h g trbn. b) @i H 11 hinh chi& vu6ng g6c c l a P trtn AB vA R,,R2,R3 l i bin kinh d u h g trbn n&i ti6p c k tam gilc APB, APH, BPH tuung b g . Xlc d b h vj tri c l a P tren d u h g trbn (0) dd tdng R1 + R2 + R3 dat gil tri 1811 nhB.. CPu 5. (1 die"m) Vai n 11 $6 nguytn ducmg, dip b) Gili h&phuung trlnh trong d6 k! = 1.2 ... k v1. CAU 3. (2 d i h ) Cho ba s6 duung x, y, z c6 tBng bhng 1. C h h g minh rilng. i a k = a l +a2 +. +...+ a,,,. k-1. ,. J. Cbu 4. (2 die"m) Tren d u h g trbn tam 0 d u h g kinh AB, lily didm P bilt ki khdc A, B.. Tim s6 du khi chia. S400 cho 2005..

<span class='text_page_counter'>(5)</span> BE THZ VAO LOP 10. TRUONGTHPT CHUYEN HUNG. VUONG,. PHU THO NAM HOC 2002 -2003 M6n Toan cho 16p chuygn Toan. cgU1, tho phuong v h xZ -mx+m-. 1 ) Dudng phphgn giic ngoiii cGa g6c A cat lai d u b g trbn ( 0 ) tai N. Chimg minh M,O,N. 1 =O. c6 hai nghif:m xl , x2.. 1 ) Tinh gid tri bidu that M =. 3 32 + 3x22 -3 ~:*2+x&'. -. -. 2) Tim gid tri cba rn dd x: + x: = 10. CBU 2. Cho hai s6 X , y thoA rnHn'he thee. .. ,. --. 2) G i l sir dudng phdn gidc ngohi g6c A cat. 4.. d h g thhg BC @i E. C h h g minh AM0 = CEA,. 'i)Trkn canh. AC lgy didm D tu3 9 &hic. x, y dd tich. * A viiC). D U h g thing BD cat dudng trbn ( 0 ) tqi di6m thtl har F. Dutmg thing qua A vuang g6c vdi AB vii d u h g thing qua F vuang g6c vdi FC c8t nhau tai P. C h h g t6 rang P, D,O thing hhng .. P X ~ + ~2 =2. X ~ + ~ CAu 4. Cho tam gidc ABC nQi tigp d u h g trbn ( 0 ) .Tia phdn gidc trong cfia g6c A cat d u h g trbn ( 0 )tai digm M .. C l u 5. C h h g minh rang vdi moi s6 tu nhiCn n , ta luan c6. 2x 2 ,+ 1 X. y2 = 4. Hiy xdc dinh +4. xy dat gi6 tfi nh6 nhgt.. C l u 3. Gidi hf: phumg trinh. &+Jzl<Jm.. NGAY THOHAI (Th& gian :150 phlit) C l u 6.1) Chimg minh r h g. &(A. s6 n = + 1 ) d z 1h s 6 hUu ti. 2) Cho x 2 1 . Hiy rrdt gon biiu thdc. Clu7.Choa20, b2O 1 ) a, b thol m k 2a+3b I 6 vh 2a + b I 4. Tim giii ldn d s l t GI nh6 nhrlt cba bidu thirc A = a2 - 2a - b. 2 ) a + b = & 6 . Chitngrhinh. 6. (1 + a4)(1+ b 4 ) 5 101. . ,. -,-. C l u 8. C h h g t6 rang nt?u p lh s6-$$en 16, a 1ii s6 nguyen duung sao cho 1+ 24a q$yiii s6 nguyen 16 tbi phu&g ti& x2 - Z & . ; - ~ = O kh8ng c6 nghif:m hitu ti.. . ' 'i'. ,. .. ,. ... I. C l u 9. Cho ta gidc 16i ABCD nQi tigp d u h g trbn (0). 1) Tren cdc canh AB, BC, CD, DA lily c6c didm M, N, P, Q tuung img sao cho. Chimg minh rgng MP. INQ.. 2) VE tia Ax vu6ng g6c vdi AD cat BC tai E, tia Ay vu6ng g6c vdi AB cat C D tai F. C h h g minh rang EF di qua 0 . C l u 10. Tim cdc s 6 dumg! a, b, c thoA rm miin hf: -1+ $- +4- =9 3a b c r a+b+cll2. ' ,. t.

<span class='text_page_counter'>(6)</span> NAM HOC 2002 2003 I-. ( T h a gian :150 phut). Cho phuung trinh (2m-1)x2 -2mx+1 =O. a) Dinh m db phucmg trinh trCn c6 nghiem thuec khoing (-1 ; 0) ; b) Djnh rn dd phuung trinh c6 hai nghiem XI,x2 thoimiin lx: -x:1. =I.. CAu 2. (5 die"m) GiAi c l c phucmg tr'hh vA he phuung trinh sau day : a) z + a = x 2 -12x+38 ;'. L.,. a) Cho a > c, b > c, c > 0. C h h g minh. ~-c)+&F&&. b)Cho x 2 1 , y 2 1 . Chimgminh. Tir dibm A b ngohi d u h g trbn (0). ki cic tigp tuyi5n AB, AC vdi dutrng trbn (B, C 1A cic tigp dibm). Tren tia d6i cha tia BC lgy didm D. Goi E 11 giao dibm cha DO vh AC. Qua E ki tigp tuygn thtl hai vdi d u h g trbn (0). tigp tuygn nhy cdt d u h g thing AB b K. C h h g minh ring b6n dibm D, B, 0,K cDng thuec met d u h g trbn. CAu 5. (2 diim) Cho tam gilc ABC vudng ~i A c6 M 18 trung digm cGa BC. C6 hai du&g thing di dong vh vudng g6c vr3i nhau tai M cit cic d o g AB vh AC lSin l u g Qi D vh E. Xic dinh clc vj tri cha D vh E db dien tich tam giic DME dat gil trj nh6 nhgt. CAu 6. (3 di&) Cho hai d u h g trbn (0)vh (0')cdt nhau 13 hai diem A vh B. ~ u A avE hai d u h g thing (d) vh (d), d u h g thing (d) cht (0)tai C vh cht (0') D, d u h g thhng (d) cit ( 0 ) tai M vh cdt (0'). -. t+i N sao cho AB lh phan gizic cha g6c MAD. Chimg minh ring CD = MN.. NAM HOC 2003 -2004 Man ToAn cho Idp chuyen Toin. (Thdi gian :150 phut). ., a) Cho M =. /zzz. RlitgonMv8i O I x I 1 .. +x+l.. b) GiAi phumg trinh CAu 2. (2,5 d i h ) a) Cho x, y th6a miin. +. x3 +2y2 - 4 y + 3 * 0 x2 +x2y2 - 2 y = o .. =&..

<span class='text_page_counter'>(7)</span> Tinh Q = x2 b). + y2.. gil trj nh6 nhgt cch bidu thec. Cllu 4. (2 dilrn) Cho tam gidc ABC vu6ng ir A, c6 g6c. 2 = 20'. ; vE phan giic trong 81, vE g6c. CI. ACH = 30' gk Cho tam gi6c c6 s6 do cdc d h g cao: 1216 c s6 nguytn, bin kinh dudng trbn nQi tigp tam giic b h g 1. Chimg minh tam giic d6 11tarn gSc dlk.. vC phia trong tam gidc. Tinh so" do. CTI .. Bhi 5. (1 diein) C6 hay kh6ng 2003 didm trtn mat phhng mh bgt ki 3 didm nho trong ch6ng d&u tao thiinh mgrt tarn gilc c6 g6c th ?. M l n T O Acho ~ c l c ldp chuyhn Khoa hqc Ty nhign ( T h a gian ldrn bdi :150 phlit). Clu 1. Cho phuung trinh. rmr2 + 2 m x + r n 2 + 3 r n - 3 = 0 (1) a) Dinh rn dd phuung trinh (1) v6 nghigm. b) Djnh rn dd phuung trinh (1) c6 hai nghiem phsn biet x, , x2 th6a min lxl. - x2 1 = 1.. Cllu 2. a) Giii phuung trinh. J-~)+Jx(x-~)=J~;. r. Cllu 4. Cho hinh ch6p S.ABCD c6 diy ABCD lh hinh vu6ng canli a ; mat Mn SAB 1h tam giic deu ; mat bgn SCD lh tam gidc vu6ng can tai $. Goi I, .I l$n luqt 18 trung didm clia AB vh CD. a) Tinh dign tich tam giic SI.1 the0 a ; b) Goi H lh chan d u h g cao k6 tir S cba tam gilc SI.1. C h h g minh r h g SH IAC.. Cllu 5. Ldp 9A c6 28 hoc sinh dang ki du thi v8o cic ldp chuytn Toln, Li, H6a ciia trudng . , (x2 + y2 )(x 2 - y 2 ) = I 4 4 Pti8 th6ng NBng khi6u. Trong d6 : Kh6ng c6 . / ~ - J ~ = y . 'Roc sinh nho chi chon thi vho ldp Li hoac chi chon thi vlo ldp H6a. C6 it nhgt 3 hoc sinh chon Clu 3. Cho tam g i L ABC c6 2 = 45'. Goi t@ v2Io c i ba 1dp Todn, Li vh H6a. S6' hoc sinh ' ,' M vh N ldn Iuqt 121chan duang cab: kg td B v i C chon th: v8o ldp Toin vii Li bang sB hoc sinh c3a tam gidc ABC. chi2chon thi vho ldp Todn. C6 6 hoc sinh chon thi vho ldp Toin vh H6a. S$ hoc sinh chon thi MN a) Tinh ti s6 vho ldp Li vh ldp H6a ggp 5 1Idn s6 hoc sinh, BC ' b) Goi 0 1h tam d u h g tr6n ngoai ti6p tam chon thi vho c i 3 ldp Todn, Li vh H6a. H6i sB hoc sinh chon thi viio timg ldp Ibao nhitu ? gidc ABC. C h h g minh r h g OA I MN. b) Giii he phuung trinh. -.

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