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510.76 T527C PHAM TRONG THlT Chuyen Nguyen Quang Dieu - Dong Thap) uyen chon di thvc svcc hoc ky I FHAM TRONG THU (GV THPT Chuyen Nguyen Quang Dieu - Dong lhap) uyen cnon di thic sue hoc ky ^^Wl ^^^^ w MON TOAM f NANG CAO BAC-TRUNG-NAM^ Danh chohocsinh Idp 10 chuffng trinh ndng cao On tap vd nang cao ki nojig lam bai • HiJ V;EN 'um\ I ffiG NHA XUAT BAN fiAI HOr OlinC GIA HA NOI NHA xufifT BAN Dfli HOC oud'c Gin Ndl 16 Hdng Chuoi - Hai Bd TrUng - Hd Npi Dien thoai : Bien tap - Che ban: (04) 39714896; Hdnh chinh: (04) 39714899; Tong bien tap: (04) 39714897 Fox: (04) 39714899 Chiu trdch nhi^m xuat ban Gidm doc - Tong bien tap : TS. PHAM TH! TRAM Biin tdp THANH HOA Che ban : CONG TY KHANG VIET Trinh bay bia CONG TY KHANG VIET Tong phdt hdnh vd doi tdc lien ket xuat ban: { 5 \G TV TNHH MTV 1 D!CH Vg VAN HOA KHANG VIET f Dja Chi: 71 Oinh Tien Hoang - P.Da Kao - Q.1 - TP.HCM ^ Dien thoai: 08. 39115694 - 39105797 - 39111969 - 39111968 Fax: 08 3911 0880 Email: khangvietbookstore@yahoo.com.vn \ Website: www.nhasachkhangviet.vn ^ SACH LIEN KET TUYEN CHQN 39 DE THI THLf SL/C HQC KJ MON TOAN 10 NANG CAP Ma so: 1L-113DH2013 In 2.000 cuon, kho 16x24 cm i' ' Tai: Cty TNHH MTV IN AN MAI THjNH DL/C Dia chi; 71, Kha Van Can, P. Hiep Binh Chanh, Q. Thu Dufc, TP. Ho Chi Minh So xuat b^n: 420 - 201 3/CXB/03 - 58/DHQGHN ngay 03/04/201 3. Quyet dinh xuat b^n so: 337LK-TN/QD-NXBDHQGHN, cap ngay 31/07/2013 In xong va nop JOu chieu quy IV nam 201 3 Md^i iidi itdn B6 sach rfVE/V CHON 39 DE THLf SL/C HOC KI MON TOAN I6p 1 0, 11 va 12 nang cao dirac bien soan va tuycn chon diTa trcn noi dung chiTcIng trinh THPT hicMi hiinh; bo sach toan niiy giup cac cm c6 dieu kicn lam qucn \6'\ cac dang dc thi hoc ki cf muTc do cao. Ricng cuon 12 co them phan phu luc giup cac cm tif kiem tra, danh gia, bd sung kie'n thtfc ve toan THPT cho minh nham tao ncn toan can ban vffng chitc cho cac cm \i\S6c khi chinh thtjTc bU'dc vao ki thi Dai hoc, Cao dang. Hi vong bo sach sc gop phiin giiip cac em dat kct qua cao trong cac ki thi, dong thcJi la mot cong cu hd trd cho cac bac phu huynh giiip cho con em hoc tap tot h(<n. Trong qua trinh bien soan, d\x tac gia dfi cdgiing nhiTng cuon sach van co the con nhiJng khiem khuyct ngoai y muo'n. Chung tdi ni't mong nhan di/dc sif gop y chan thanh ciia cac thiiy, co giao, cac em hoc sinh dc trong hln tai ban sau sach dUcJc hoan chinh hdn. Tac gia rii't cam dn Nh;i xuii't ban Dai hoc Qudc gia Ha Noi, Cong ty TNHH MTV DVVH Khang Vict da dong vicn, khuycn khich vii tao moi dieu kien de cud^n sach nay st'lm den tay ban doc. Website: phamtronglhu.com.vn Tac gia PHAM TRQNG THLf Kf HIEU DIJNG TRONG Bp SACH Vectd phap luyen VTPT Vcctd chi ptiiTdng VTCP Dieu phai chuTng minh dpcm Yeu cau bai loan YCBT Mat phang mp [Jat dang thu-f iJDT fhUifng trinh PT HC' phiftfng Irinh HPT Hal phiMng trinh UPT Ve irai VT Ve pha i VP 7 loi khuySn cho thi sink phuung phdp gidi mQt bcU thi Nhif chung ta da bici mon Toan la mon hoc chic'm mot vj tri ra't quan trong va then chot, rat can thiet dc hoc cac mon khae tif ticu hoe cho den cac Idp tren. Mon Toan gitjp cac em nhan biet cac moi quan he ve so lifdng va hiiih khong gian cua the gidi hicn Ihifc. Niic) do ma ciic em c6 phifdng phap nhan IhiJc mot so mat cua the' gidi xung quanh va biet each boat dong c6 hieu qua trong dfli song. Mon Toan gop phan rat quan trpng trong viee rcn luyc'ii phifinig pliiip suy nghl, phifclng phap suy luan, phiTcIng phap giai quyct van dc. No gop piian phat irien tri thong minh, each suy nghl doc lap, linh boat, sang tao va vice iilnh thanh cac pham chat can thict cho ngiTrti lao dong nhiT can cu, can than, eo y chi vifdt kho khan, lam vice c6 kc hoach, eo ne nep vii liic phong khoa hoc. Xua't phat tCf vi tri quan trpng ciia mon Toan, qua tlufe te giang day nhieu nam d cap THPT. Toi nhan lhay rang de hpc sinh hoe lot mon Toan thi ngoai vice cac cm nam vffng kicn ihifc trong sach giiio khoa, ky niing tinh toan that tol ma con phai bie't phiTtJng phap giai mot hai thi nhif liie nao trong lue dang thi dc eo diem cao. Muon lam diWc dieu nay tin' sinh can phiii tufin thii Iheo cac biTdc sau day: 1) That binh tinh trong luc lam bai thi. 2) Can doe that cham rai loan bp de, danh gia sc) bp dc) de, kho cija cua cac eau, xem nhfrng can nao quen thupc, la vdi minh. 3) Giai ngay lap tiJc cac eau ma ban thay de. 4) Mot vai eau can thiel den sir suy nghl sau h(<n, thi sinh can phai doe ky eau hoi, gach du'di eiic gia thiet va yeu eau ciia bai toan. Dinh hiTcfng each giai, hinh dung do phi'rc tap ciia eiieh giai dc c6 sir lira chpn diing dan. 5) Trhih bay bai giai thi sinh khong nen lam tat, moi biTdc ncn vic't mot dong de de kiem tra, vl giam khao chain bai thi theo ba rem nen eo mot birdc nao do sai thi van con diem d nhfrng biftk- bien doi diing trifdc do. Cach hay nha't la lam xong biTdc nao kiem tra bifiKc ay de phat hicn ngay cho sai. 6) Trong qua trinh giai mot bai toan ne'u thi sinh gap kho khan giila ehiTng, c6 the chijfa khoang trong trC-n giay thi de bo sung sau va nhanh chong ehuycn sang lam cau khae. 7) Khi da hoan ta't bai thi, neu con thCii gian thi sinh ncn doc lai bai giai va ra .scat lai cac chi liet da trnih bay (thong thirilng cac loi thi sinh hay bo sot bift'lc lam la tap xac dinh, dieu kicn c6 nghla ciia can bac ciian, ham so logarit, doi can khi dung phiTcfng phap doi bien de tinh tich phan, loai bo ngiiiem ngoai lai trt)ng phi/dng trinh ) nham hoan thicn bai thi tot h()n cho den het gid. Nhieu hpc tro toi day ap dung 7 l(1i khuyen tren da tn'f thanh thii khoa dai hpc cua nhieu trirclng, nhiTng thanh cong nha't la loi ed hoc tro thii khoa "kep" khoi A va B ciia trirdng Dai hpc Khoa hpc Tif nhien TP. HCM va Dai hpc Y DiTdc TP. HCM nam 2011. Chuc cac thi sinh dat kel qua cao trong cac ki thi PHAM TRQNG THI/ Bp BE THfir Sljrc HQC KI MON TOAN LdfP 10 A. BO BE THUf sure HQC KI I MON TOAN LtfP 10 DE SO 1 DE THlIr SllTC HOC KI I MON TOAN L6P 10 Thdi gian lam bai: 90 phut Cau I. (1,0 diem) Cho hai tap hdp P = |x e K I |x - 2| < 3|, Q = |x e II x + 2 >4 1. Viet cac tap hdp P va Q diTdti dang khoang, doan, ntj'a khoang hay hctp cija cac khoang, doan, nihi khoang. Bicu dicn cac tap hdp nay tren trijc so. 2. Chiang minh rang Cj^CPnQ) = C^PuCj^Q. Cau 11.(2,0 diem) J 1. Vcdothi y = -x~+4x-3. 2. Tim m dc phiTitng trinh x^ - 4 x + m = Oco it nha't ba nghicm. C-duUL(2,0diem) 1. Cho phifcfng irinh (m - l)x~ - 2(m + l)x + m - 2 = 0 (1). Tim cac gia tn nguycn cua m dc phiTcJng Irinh (1) c6 hai nghicm phsln biet x,, X2sao cho tdng X| + Xj la Ciic so' nguycn. 2. Giai va bien hian phiTdng trinh -—— + ^ = 2 • X -2 X tamG ,M la trung diem BC. Di/dng tron ngoai ticp tam giac ABC cat Cau IV. (2,0 diem) 1. Trong mat phang Oxy cho tam giac ABC c6 A(-2; 1), B(l; 3), trong I \ difclng lhang AM lai E. Tim loa do diem E. V 1 Mu- 1 »r,^ ~ cosA cosB cosC a ^ 2. Nhan dang tam giac ABC thoa man + + = — ( )• a b c be Cau\. (2,0 diem) 1. Giai phirong irinh X/4-3N/10-3T = X -2 . * i ^ , j 2. Tim gia tri nho nha't ciia y = x + —^— (voi x > 3 ). i •'.•-> J, X - 3 • Cfiu VI. (1,0 diem) Cho tam giac ABC vuong tai A coAB = 3, AC = 4 va Irung tuycn AD. Tim diem E e AC sao cho BE 1 AD. DAP AN THAM KHAO Cau Dap an I (1,0 diem) 1. (0,5 diem) Vie't cac tap hi/p P va Q Axidi dan^ khoang, doan Taco x-2 <3c:>-3<x-2<3o-l<x<5. Vay P = |-l; 5|. Tifdng tir x + 2 > 4 <=> X + 2 < -4 X + 2 > 4 Vay Q = (-a);-6)u(2;+<z5). X < -6 x>2 -6 J. P Q 2, (0,5diem) Chxin^ minh rilns C^(PnQ) = CjjPuCjjQ. • Taco PnQ = (2;51 =>Cp,(PnQ) = (-oo;2]u(5;+oo). .Cg^P = (-<x.;-l)u(5;+«); C.^Q = !-6; 2] =^C.:jPuC3^Q = (-c»;2|u(5;+«). Viiy C.^(PnQ) = C5^PuCr.Q. II (2,0 diem ) 1. (1,0 diem) Ve do thj y = -x^ + 4x - 3 (doc giii tif giai). 2. (1,0 diem) Tim m de phii'ofng trinh 1 / -2 -l\ y = 111 - 3/ \ / • ' -3 Ta CO x~ -4 + m = 0 o -x~ + 4 -3-m-3 PhiTitng trinh trcn lii PT hoaiih do giao diem ciia do thi hiim so 4 III (2,0 diem) y = -x^ + 4 x -3 va diTdng thiing y = m - 3. + Hiim so y = -x^ + 4 x -3 la hiim so' chSn ncn do thi do'i xifng qua true tung. Khi x>0 thi ham so' trd thanh y = -x^ + 4x -3. Do do do thj ciia ham so y = -x^ + 4 x - 3 bao gom philn do thj ham so y = -x~ + 4x -3 d ben phai true tung vii phan do'i xiJng ciia no qua true tung. -^^M.'- ; V \ Thco do thi, phiTdng trinh dii cho c6 it nhat ba nghiem khi v& chi khi -3 < m - 3 < 1 <=> 0 < iTi< 4. 1. (1,0 diem) Txm cac gia trj nguyen cua m Phu'dng trinh da cho co hai nghiem phan biet khi va chi khi m ^ ! ](*)• m - 1 ;t 0 A' = 5m-1 >0 m > - 5 Ta CO X| + X, = 2(m + l) m-1 = 2 + - m-l De tong X| + X2 la so nguyen thi dieu kien can vii dii la m-1 lii iTc'k- ciia 4. Co cac Iri/cJng hdp: « m-1 =::±1. m-1 = ±2. m-1 ^±4. • Giiii ciic triTdng hdp tren vii ket hdp dieu kien ta difde me {2; 3; s}. 2. (1,0 diem) Giai va hiC'n luan phif(/ng trinh Dieu kiC-n < X ^ 2 X ^0' VcTi dieu kien do PT da cho tiTdng diTdng (m +1 )x = 6 (*) »Vdi m = -1 thi (*) VP nghiem nen PT da cho v6 nghiem. 6 m + 1 iWvri'-V'J' ' Vdi m ^ -1 thi CO nghiem x = PhUdng irinh da cho c6 nghiem treno ^2 • " ^ 6 m +1 ^0 Ket luiin: m = -1 hay m = 2 : PhU'Ong trinh dii cho v6 nghiem. m ^ -1 va m 2: PhMng Irinh da cho c6 nghicm x = m +1 IV (2,0 diem) 1. (1,0 diem) 'Vim to a do diem E. G lii Irong lam cua lam giac ABC ncn Xj =3X(, -(x^ +X3) = 3.^-(-2 + l)==2 yc=3yG-(yA+yB)=3J-(i+3)=-3 •C(2; -3). (3 ' ( 7 ^ f 3 1 -; 0 U ; , MA = —; 1 . ME = XE-:^; yE V / -; 0 U ; XE-:^; yE V / • Ta CO M 7 21 • • 1-2 37 MA.ME = —x +y,. +— va MB.MC = —BC = 2 4 4 4 , . , fMA.ME = MB.MC Mai khac \ [MA cung phi/dng ME 7 2 7 21 37 Xc + Vc + = E -' E 4 A ''E 3 2 _ 7 2 209 — h 53 37 yE 53 <=> \ 1 Vay E 7 58 ^ -2^E + yE+y=o 2xp + 7yp=3 209 37' ^53' 53 J 2. (7,0 diem) Nhan dan^ tarn giac Ta CO (*)« bccosA + accosB + abcosC = (**) Tir a- - b- + c^ - 2bccosA ^ bccosA = ^(b^ + c^ - ) (1) TiTdng liT: accosB - ^(a- + c^ - b") (2); abcosC = ^(a^ + b" - c") (3) The (1), (2) va (3) vao (**) va nil gon la diTdc: b" + c" = a" c::> AABC vuong lai A. 6 V 1. (1,0 diem) Giai phtfc/nj? trinh (2,0 diem) PhiTclng irinh da cho liTOng diTdng 74 10 — <x< — 27 3 0,5 4-3V 10-3x =(x- 74 10 — <x< — 27 3 74 10 — <x< — 27 3 • » «f 3Vl()-3x =4x -) - X' <=> 74 10 — <x < — 27 3 <=>' 9(10~3x) = (4x 74 10 — <x < — 27 3 -x^r 0,25 x-^-SxVlfix 2 + 27x-90 = 0 o < 74 10 — <x < — 27 3 (x-3)(x + 2)(x^ -7x + i5)-0 ("=) Vc'Ji 74 10 . — <x <— va 27 3 X- -7x + 15- ( 7^ X — + —>0,VxeR. 4 0,25 Nc-n (*)<=> X = 3 . Vay phirong trinh c6 mol nghicm x = 3. 2. (1,0 diem) Tim jjia tr j nho nha't ciia Ta CO y = X - 3 + - X 1 -+3. 3 0,25 Ap dung BDT Co-si ta c6: y > 2 j(x - 3) • —+ 3 = 5. V x-3 0,5 Vay miny = y(4) = 5 0,25 VI 'llni diem K (1,0 diem) • Ta CO AD.BE = - '• •( AB +AC)(AE -AB) i*J <i • (1,0 diem) 2 1 2 f • . -2 AB.AE-AB + AC.AE-AC.AB 0,5 Ma ABl AE ABIAC AB.AE-O AB.AC = 0 0,25 Ncn AD.BE = ^(AE.AC-AB^). . Ma AD 1 BE AD.BE = 0 o AE.AC = AB^ => AE = - • 4 0,25 DE SO 2 DE THCT SOC HOC Ki I MON TOAN LdP 10 Thdi gian lam bai: 90 phut Caul. f7,tf^/t'//ijCho lap help S - {l; 2; 3; 4; 5; 6}. j 1. Tim lap hop con A, B ciia S sao cho A u B |l; 2; 3; 4|, A n B = |l; 2 • 2. Tim cac lap C sao cho Cu(AnB) = AuB. CSu II. (2,0 diem) 1. Ve do ihj y = 3x + 4. 2. Xac djnh a, c dc do ihi ham so y = ax- -4x + c di qua hai diem A(l;-3), B(2;5). 3. Xac dinh giao diem cua hai do ihi Ircn. Cau III. (2,0 diem) 1. Giiii phifiJng Irinh yjl-x' +x\J\ 5 = ^3 - 2x - x 2. Giiii va bicn luan phifdng Irinh m^x - m~ - 4 = 4m(x - 1). Cau IV. (2,0 diem). Trong mill phdng Oxy, Um diem M biel: 1. MNPQ la hinh binh hanh vdi N(2; 3), P(-6; -3), Q(l; 8). 1 2. M ihuoc inic hoanh va gck giiJa hai vecld MA, MB la 135" vdi cac Ipa do ciia diem A(4; - 3), B(3; 1). Cau V. (2,0 diem) 1. Giai he phiTdng Irinh x^y(l + y) + x-y-(2 + y) + xy^ -30 = 0 x"y+ x(l + y+ y") + y-l 1 = 0. 1 1 2. Cho a, b la hai so dUdng. Chiang minh a" + b~ + - + - > 2(\/a + >Jb). a b C'Au\l. (1,0 diem) Cho lam giiic ABC c6 A = 120", AB.AC =-6 va AM.BC =-16 (vdi M la irung diem ciia BC). Tinh do dai cac canh AB va AC. 8 DAP AN THAM KHAO Cau Dap an Diem I (1,0 diem) 1. (0,5 diem) Tini tap hop con A, B ciia S sao cho Tir AuB = |i; 2; 3; 4| suy ra hai ph;1n liV 3 vii 4 phai Ihuoc mpl vii chi mol irong hai lap A va B. Do do c6 bon kel qua sau: A = {1; 2; 3| A = {1; 2; 4} A = {l; 2; 3; 4} A = jU 2) B = {l; 2; 4)' B = {l; 2; 3) ' B = {,;2| • B = {l; 2; 3; 4 2. (0,5diem) Tm cac tap C sao cho Cu{AnB) = AuB. ViCu(AnB) = AuB ma AuB = jl; 2; 3; 4},AnB = {l; 2} ncn 3, 4 € C. Do do cac lap C Ihoa man yeu cau bai loan la: {3; 4}, {l; 3; 4}, {2; 3; 4}, {l; 2; 3; 4}. 0,5 II (2,0 diem) 1. (0,5 diem) Ve do thj y = 3x + 4 (doc gia liT giiii). 2. (0,5 diem) Xac dinh a, c de do thj ham so' Vi do Ihi da cho di qua hai diem A(l: -3), B(2; 5) ncn -3 = a-4 + c a + c = l [a = 4 5 = 4a-8 + c 4a + c = i3 [c = -3 3. (1,0 diem) Xac djnh jjiao diem ciia hai do thj tren Toa do giao diem ciia hai do ihj IrC-n la nghiem ciia he jy = 4x 4x-3^l3x + 4 = 4x~-4x-3 y = 3x + 4 [y = 3x + 4 X =• 4x -7x-7 = {) y = 3x + 4 X = • 7 + N/I6T 8 y = 3x + 4 7 + >/l6i X = X = OS y = - 53 + 3V16T hoac y = • 7-V16I 8 53-37161 9 Vay giao diem ciia hai do Ihj ircn lii [7 + 7I6I 53 + 3V16I ] [7-Vl61_ 53-3VI6I 8 ' 8 ' 8 ' 8 0,25 Ill (2,0 diem) 1. (1,0 diem) Giai phiidnn trinh Ill (2,0 diem) Die 11 kiC-n < 3 - 2x - x^ > 0 7-X2+XN/X + 5>0 (1) x + 5>0 0,25 Ill (2,0 diem) Khi do PT da cho tn^ lhanh 7-x- + x\/x + 5=3-2x-x- <=> xVx + 5 =-4-2x 0,25 Ill (2,0 diem) <=> < x(-4-2x)>0 [-2<x<0 x-(x + 5) = (-4-2x)- [x-^ + x- -16x-16 = 0 0,25 Ill (2,0 diem) <=> 1 Vaj -2<x <0 ^ <=> X -I (ihoa man (1)). (x + i)(x 16) = 0 / phifdng trinh da cho c6 nghiem x -1. 0,25 Ill (2,0 diem) 2. (1,0 diem) Giai va bien luan phUc/ng trinh Ill (2,0 diem) Ta CO nr^x - - 4 = 4ni(x - 1) <=> m(m - 2)(m + 2)x = (m - 2)"^ 0,25 Ill (2,0 diem) • m ±2 va m ^0 ihi PT da cho c6 nghic m x = —• m(m + 2) 0,25 Ill (2,0 diem) • Vc'ii m = -2 hoac m = 0 ihi PT da cho v6 nghicm. 0,25 Ill (2,0 diem) • Vdi m = 2 Ihi PT da cho c6 nghicMii liiy y. 0,25 IV (2,0 diem) 1. (1,0 diem) T\m toa do diem M IV (2,0 diem) Goi M(x;y)e{Oxy).Tac6 PN = (8; 6), PQ = (7; 11) la hai vccld khong ciing phifdng iiC-n ba diem N, P, Q khong lhang hang. 0,25 IV (2,0 diem) MNPQ la hinh binh hanh <=> NM = PQ 0,5 IV (2,0 diem) fx -9 «(x-2; y-3)-(7; 1 Do^ • Vay M(9; 14). [y = 14 0,25 IV (2,0 diem) 2. (1,0 diem) Tim toa do diem M IV (2,0 diem) Taco MA-(4-x; -3), MB = (3-x; 1) 0,5 Theogia lhietcosl35" =cos(MA, MB) = MA.MB MA MB (4-x)(3-x)-3 - V(4-x)-+(-3)-V(3-x)2+l2 • n ''if o 2(-x-' + 7x - 9) = yj2(\- - 8x + 25)(x-^ - 6x + 10) (*) DieiikiC-n - x" + 7x-9 > 0 (I) (='^)c:>x"^ -14x-^+ 51x-~22x-88 = 0 •o (X - 4)(x + l)(x- - 11X + 22) - 0 <=> X = 4, X = -1 1 1± V33- X = So dic3u kien (1) chon x = 4, x = -N/33 Vay M,(4; 0), M, V (2,0 diem) 1. (1,0 diem) Giai he phiTc/ns trinh He phifting liinh da cho tiftJng dufcJng xy(x + y)"' +x"y"(x + y) = 3() xy(x + y) + xy + X + y 1 1 <=> i xy(x + y)(x + y + xy) = 30 xy(x + y) + xy + x + y = ll X + y = 11 . T Dal <! , dieu kien u" > 4v, HPT Iren lai thanh xy = v iivdi + V) = 30 <=> i uv(ll-iiv) = 30 (1) uv + 11 + v = 11 uv + 11 + V = 11 (2) .Tir(l): uv = 5 uv = 6 • Vdi uv = 5 u + V = 6. Giai trifttng hrtp nay HPT dii cho c6 , , f5-V2l 5 + N/2TV5 + N/2T nghicni (x; y) = • Vdi uv = 6 => u + V = 5.Giai Irifctng hdp nay HPT da cho c6 nghiem (x;y) = (l; 2),(2; 1). Vay HPT da cho c6 nghiem (x; y) la (1; 2),(2; 1), 5-y[2\ + V2T 5 + V2T 5-x/2T' 11 2. (1,0 diem) Chrfn}; minh Ap dung BDT Co-si ta c6: a-+l>2l 1=27:^(1), h'-^'->2.\^-=24^(2) a V a b V b Cong (1) va (2) thco vc siiy ra Jpcm. Diing lliifc xay ra khi va chi' khi a = b = 1. 0,5 0,25 0,25 VI (1,0 diem) Tinh do dai cac canh Ali va AC. •AB.AC = -6 => AB.AC.cos 120" - -6 AB.AC. 1 = -6=i> AB.AC = 12 (I) •AM.BC = -16 -(AB+AC).(AB - AC) = -16 =^ AB" - AC" = -32 => AB- - AC" - -32 (2) TCrd). (2) siiy ra AB'^ + 32AB- - 144 = 0 => AB" =4 i=> AB = 2 va AC = 6. 0,25 0,25 0,5 DE SO 3 DE THLT SCrC HOC KI I MON TOAN L6P 10 Thdi gian lam bai: 90 phut CSu I. (1,0 diem). Cho lap hc.tp A = {x e /J |x| < s}, B = jx e Z19 < < 26}. Xac dinh cac lap help A n B, A w B, A \, B \. CSu II. (2,0 diem) 1. Xac dinh cac he so' ciia parabol y = ax- + bx -3bicl rang parabol di qua diem A(5; - S) va c6 Iruc do'i xiJng x = 2. Vc parabol tim dU'dc. 2. Cho parabol (P): y = x"^-4x + 3. Xac dinh m dc (P) va diTdng th^ng d: y = mx - m^ + 12 cal nhaii tai 2 diem c6 hoiinh do trai dau. Cau III. (2,0 diem) 1. Giiii phu'dng Irinh V3x^ +X-1=2 ^7 ^ — X 1 4 + (m + 2)x 2. Giiii va bien luan phiTdng trinh = ni - 1. 3-2x Cau IV. (2,0 diem). Trong mal phring Oxy cho tam giac ABC c6 A(2; 1), B(l; 3), C (- 1. Tim loa do Irong lam G ciia lam giac ABC. 2. Tim loa do Irirc lam H ciia lam giac ABC. CSu V. (2,0 diem) 0). 1. Giiii he phifctng Irinh x" + y- + xy = 7 x-+y-+x + y= 8 2. Cho cac so' difdng x, y, /. Ihoa man x + y + / = 1. Chifng minh: ^2x" + xy + 2y- + ^2y- + y/ + 2/.~ + ^2/~ + /x + 2x- > 75. , ,,. Cau VI. (1,0 diem) Cho hinh binh hanh ABCD. Goi M la diem liiy y. Chu-ngminh MA.MC - MB.MD = BA.BC. Ml DAP AN THAM KHAO •V ; Cau Dap an Diem I (1,0 diem) Xac djnh cac tap h(/p I (1,0 diem) Ta CO x < 5 -5 < x < 5. Vi X nguycn nen A-|-4; -3; -2; -1; 0; 1; 2; 3; 4}. 0,25 I (1,0 diem) Ta CO 9 < x" < 26 o 3 < X < N/26. Vi x nguycn nen B-j-5; -4; -3; 3; 4; s}. 0,25 I (1,0 diem) AnB = {-4; -3; 3; 4}. AuB = |-5; -4; -3; -2; -1; 0; 1; 2; 3; 4; 5J. 0,25 I (1,0 diem) A\ = j-2; -1; 0; 1; 2J. B\ = {-5; 5}. 0,25 II (2,0 diem ) 1. (1,0 diem) Xac djnh cac he .so'ciia parabol II (2,0 diem ) Vi do ihi da cho di qua diem A(5; -8) nen -8 = 25a + 5b-3 o 25a + 5b = -5 (I) Mat khac (P) c6 true doi xifng x = 2 nC-n -— = 2(2) ' ' 2a 0,25 II (2,0 diem ) Tir (1) va (2) suy ra a = -1; b = 4. 0,25 II (2,0 diem ) Ve y = -x- +4x-3(docgia tif giiii). 0,5 2. (1,0 diem) Xac dinh m de (P) va di/tfns thang Phifdng innh hoiinh do giao diem cua (P) va 6\i(1ng thilng d la X- -4x + 3 = mx-m^ +12<=>x^ -(4 + m)x + m^ -9 = 0. 0,5 Parabol (P) vii during thang d cat nhau tai 2 diem c6 hoanh do mi i da'u ichi vii chi khi - 9 < 0 <=> -3 < m< 3. 0,5 Ill 1. (1,0 diem) Giai phU"(/njj trinh (2,0 diem ) Bicn doi phi/dng Irinh vc dang 73x^ + x - 1 = 7 - 3x^ - x (1) 0,25 (2,0 diem ) Diit u = VJX" + X -1. Khi do u > 0 vii 3x^ + x = u~ + 1 Phu-dng trinh (1) tnl ihiinh u~ + ii - 6 = 0. 0,25 Phirdng trinh Iron c6 nghicm u = 2 (thoa man) vii u = -3 (loai). 0,25 Vc1i u = 2tac6 \/3x^+x-l = 2<=>3x^+x-5 = 0 -l±76i <=> x = 6 -l±76i <=> x = 6 0,25 ^ f-l-^/6T -\ ^l6\ Vay phifcJng trmh co tap ngnicm S-< ; [6 6 J 2. (1,0 diem) Giai va bien luan phifc/ng trinh Vc'Ji X ^ phifdng trinh da cho Ird lhanh 3mx = 3m - 7. 0,25 • Vc'Ji m ^ 0 ihi x = —^ • Nghicm thoa man dieu kicn khi 3m 3 3m-7 3 ^ „ 14 X 9^-<=> ^-o6m-14?t9mc:>m^ 2 3m 2 3 0,25 • Vdi m = 0 thi Ox = -7: Phi/dng trinh v6 nghicm. 0,25 Kc't luan: 14 • Vdi ni —— vii m 5^0 thi phifdng trinh da cho c6 nghicm , , 3m - 7 duy nhat x = 3m 0,25 14 • V(1fi m = hoiic ill - 0 thi phifdng trinh da cho v6 nghicm. 1/1 IV (2,0 diem) 1. (0,5 diem) Tini toa do tnin;; tam G ciia tam giac ABC. Toa do Irong tam G ciia tam giac ABC lii Xr: = XA, + X|j + Xp _ 2 + 1 -1 _ 2 3 ~ 3 ~ 3 YA+yti+yc _' + 3 + 0 4 •Viiy G 2 4 3' 3 0,5 3 3 2. (1,5 diem) Tim toa do diem trifc tam H cua tam giac ABC Goi H(x; y)e(Oxy) AH = (x-2;y-l), BC = {-2; -3) BH=(x-I;y-3), AC = (-3; -1). H la triTc tam ciia tam giac ABC ncn la c6: AH J_BC BHIAC AH.BC = () BH.AC = 0 <=> i -2(x-2)-3(y-l) = () [2x + 3y = 7 <=> i -3(x-l)-l(y-3) = 0 [3x + y = 6 1 1 7 9 y = - 7 (2,0 diem) Vay; H n 9 I 7 ' 7; 1. (1,25 diem) Giai hy phififng trinh ^ S = X + y T Dat <^ vdiS' >4P(*) P = xy He phiTcfng trinh da cho tret thiinh - P = 7 (1) S 2P + S = 8 (2) Tir (1) va (2) suy ra S" - S - 6 = 0 S = 3 hoac S = -2. • Vdi S = 3 P = 2 (thoa man (*)). Liic do ta cd X +y =3 X = [ a cd <! o <^ hoiic <^ lxy = 2 y = 2 x = 2 y = l • Vdi S = -2 P = -3 (thoa man (*)). X + y = -2 J X = 1 Liic do ta cd a CO < [xy = -3 <=> y = -3 hoac • x = -3 y = l .q !("(> Vily he da cho cd bo'n nghicm (x; y) lii (1; 2), (2; 1), (1; -3), (-3; 1). 0,5 0,25 0,5 0,25 0,25 0,25 0,25 0,25 0,25 15 [...]... n h nay la di/dc X3 = 2; x^ = ^ Vay 18 7l25 f T a c o 21D = 2 2 - x , ; V X = - 2 + N/3 • Vdil = -,lac6 2 lA 1(2; 1) -IA = -(2-x,; Jx|=2 [y|=l 6-y,) 0,25 0,25 0,25 Tuyg'n chgn 39 de thif sifc hqc ki mfln ToanTflp 10 Nflng cao - Phjm Trgng Thu~ 1 (1,0 diem) G i a i (2,0 diem) 1 Chtfng minh rang vdti m o i m, d, vii d ^ l u o n ciCl nhau l a i mot d i e m co djnh phifi/na trinh tren true lung L a y... r i n h he + j 2 y ^ 1 y = - 3 x - + 2 x 1).(-1; 0) 2 (1,0 diem) 10 phut C S u I I (2,0 diem) y = () L 6 P T i m t a p x a c d j n h c i i a c a c h i i m so: =0 —> y = 0 T H L T SVSC D E SO 6 \-\>0 H;im so y - • — ^ — du'dc x a c d i n h k h i < x2-3x + 2 X- -3x 0,25 + 2^0 lUyBII L'lHIII j y ge inu sue not kl mn loAn I6p 10 N5ng cao - Phjm Trgng-Thu X i ^ 1 x^2 X>1 D a l u = N/3 + X + V... 0,25 2(m + l) 0,25 = ———— • X|X2 N la trung diem canh A C , la c6: m-2 Do do — + — = 5 o ^''^ X| Xj m-2 XQ = 2x[si - X A = 6 - 5 = 1 = 5 o 2m + 2 = 5m - 10 m = 4 C(l; - 3 ) yc =2yN - y A = 0 - 3 = - 3 0,25 (thoa man dicu kien (*)) Vay gia in m can lim la m = 4 Vay loa do ba dinh cua tam giac A B C la: 2 (1,0 diem) Giai phifc/ng trinh 2 (0,5 diem) Tinh do dai trung tuyen A P cua tam giac A B C ... 4-Xij=-l Tn((fnii G i a i v a h i y n l u a n phiTdn^ trinh ni(x - j ) - + 5 C(4; hoiic < [y = 0 Taco AB= D C o ( - l ; X + X+3 I- l(3-3y)- +{y-l)- =10 x =4 i X e t t i n h c h a n , It; c i i a h a m so -x-3 4 - 3y =BC^ fx = 4 - 3 y [(x-l)- +(y-l)- -10 T i l p Xiic d j n h D = K \ { 0 } diem) BA.BC = 0 BA- V i l y y - ~3x'^ + 2 x la h i i m so I c (2,0 B A = ( i ; 3); B C = (x - 1 ; y - 1 ) A... 0 = 0 DAP AN THAM KHAO Cdu I (1,0 diem) Dap an 1 (0,5 diem) Tim tap h(/p A n B Viet ket qua dxiiii danj; liC't ke Taco A = {0; 1; 2; 10} Malkhcic x - l < 2 o - 2 < x - l < 2 o - l < x < 3 DE S O S OE T H C T SOC Diem 0,25 Siiy ra B = ( - I ; 3) HOC KI I MON TOAN L 6 P 10 Thdi gian lam bai: 90 phut Dodo A n B = {0; 1; 2} 0,25 2 (0,5 diem) Tim ta't cii cac tap h(/p C sao cho Cau I (1,0 diem) Cho hai... (l-x)(l-y) =6 (2) 0,25 (3) 1 2 C h o a h > 1 C h i a n g m i n h l + a^ cau V I + 1 1 + b- > 2 l + i'^^ (l,OdiSm) Cho l a m giac A B C G o i M lii trung d i e m cua A B vii N lii d i e m Iren canh A C 0,25 thoa miin A N = Chu-ngminh A C G o i K lii trung d i e m ciia M N AK = - A B + -AC 4 6 DAP AN THAM 0,5 0,25 KHAO Dap an I 1 (0,5 diem) 0,25 diem) f>iem Tm\p x a c d i n h c i i a h i i m s6'... Ihoa man 4 0,25 = ^ B = (colx - lanx)" - ( c o l x + lanx)- fi + c = 2a.Chi'fng minh ning: 2 Tmh do dai difi/ng trung tuyen B M ciia tarn giac A B C ^ , ^ a-+c1 a CO i n : = '' 2 ' 2 Riit goii A B - + A C - = 24- + 32- = 1600 (cm") BC- = A C - + A B - => AABC vuong lai A : • Si! >,Aii.; B(2; -10) nC-n -1 2a 0,5 6 = 4a-2b + c - 1 0 = 4a + 2b + c 4S lu iiiJiiU LJU - r iijiiii iigiig iini- luyeii Liiyii... phiTdng trinh 'x = 2 x+y = 5 2 O X = 5 + 4N/7 0,25 _x- - - l ( ) x - 8 7 = 0 IV AM- ^ , N ' -; 2 CP = (2; - 4 ) , AB = (2;()) x =3 7 =2 x = -3 x + y = -10 , CA = (1; - 4 ) 0,5 y = -7 xy =21 va lap cac toa dp , BC = ( - 3 ; 4 ) , BN = xy = 6 Vdi S = -10 => P = 21 Liic do ta c6 he phiTdng Irinh Vay phi/ctng trinh da cho c6 nghicm x = 5 + 4\/l L (1,0 diem) Tinh gia trj bieu thtfc (2,0 ^3 diem) Taco P(2;()),... bien thien va ve do thi (doc gia tii giai) III ^ 9 Tim tap hA = (-oo;l)uf4;+oo) II 2 3 (1,0 diem) Giai phtf(yng trinh Dap an Cdu AB.AD _ -4-6 _ 1 -10 AB.AD " Vro720 " 10V2 " V 2 " CB.Cb -6 + 36 _ 30 _ _1_ C B C D " 720V9O " 30N/2 ~ V2 1 (0,5 diem) Tim m de phif . thoai: 08. 391 15694 - 391 05797 - 391 11969 - 391 11968 Fax: 08 391 1 0880 Email: khangvietbookstore@yahoo.com.vn Website: www.nhasachkhangviet.vn ^ SACH LIEN KET TUYEN CHQN 39 DE THI . thic sue hoc ky ^^Wl ^^^^ w MON TOAM f NANG CAO BAC -TRUNG- NAM^ Danh chohocsinh Idp 10 chuffng trinh ndng cao On tap vd nang cao ki nojig lam bai • HiJ V;EN 'um I ffiG . 16 Hdng Chuoi - Hai Bd TrUng - Hd Npi Dien thoai : Bien tap - Che ban: (04) 397 14896; Hdnh chinh: (04) 397 14899; Tong bien tap: (04) 397 14897 Fox: (04) 397 14899 Chiu trdch nhi^m