Đề thi tuyển sinh lớp 10 môn toán năm 2014 2015 THPT chuyên bến tre

so crAo DUC vA DAo rAo BEN TRE Bn cniNn rntlc CAu 1: (4,0 di6m) 1/ Cho bi6u thric A - UN TTTT TUYEN SINH LOP 10 TRUNG HQC PHO THONG CHUYIN BEN TRE NAtu Hoc 2ou4-2ots M6n: TOAN (chuy6n) Thdi gian: 150 phrit (kh6ng kC ph6t de) - Jtq+J+o +Jso * .,fi40 Ji*Ji*Ji Kh6ng dung m5y tinh cAm tay hfly tinh giStri cira A. 2t chobi6u thric , _zJi(Ji + Ju - Jta)+ Jx(zJi - Jx)-z^Jz uJi +J3rb a/ Tim cti6u kiQn c'ia avd b c16 B x6c clinh vd rut gon B. blHdy titth gii,tr! cira B khi a = 1* lJi;b : 10 * t tt6 ,3 CAu 2: (6,0 cli6m) ChophuongtrinhbQchai x' - 2(^- 1)" + 2m' - 3m + 1 = 0 (1), voi m ldtham sd. Il Chungminh ring (1) c6 nghiQm khai vd chi khi 0 < m < 1 2l Goi Xri Xz Id nghiOm cira phucrng trinh (1) a/ Chimgminh lx, + x, * *,*, | < 2 b/ Tim m sao cho (1) c6 hai nghiQm ph6n biet tr6i d6u thoa mdn lx, - *,1= 1 Cdu 3: (4,0 cli6m) 1/Cho x'-x-1=0. Tinh giS,tricriabiiSuthric Q- xu -3x'+-3xo -x'+2014 \ xu -x'-3xt -3x + 2ol4 2l Cho x,y, Z ld crlc sO ducrng. t" l_ !v*, CAu 4: (6 di6m) Cho dycrng trdn (O), dudng thAng d clt (O) tpi hai di6m C vd D. Tir iliem M tty y tr6n d, kd tii5p tuy6n MA vd MB v6i (O), A vd B Id circ ti6p cli6m, Ggi I ld trung di6m cria CD. l/ Chring minh tu giirc MAIB n6i ti6p. 2/ Cdc duong th6ng MO vd AB c8t nhau t4i H. Chfng minh H thu6c dudng trdn ngoai ti6p tam gi6c COD. 3/ Chring minh ducrng thang AB 1u6n di qua m6t <litim cO Airn khi M thay d6i. 4t Chimsminh ry =E{ MC HC, Chring minh b6t ilang thirc f" f, .{;;*{, " SO CT.IO DUC VA DAO TAO BEN TRE on rnr ruytN srNH Lop 10 TRUNG Hec pHo rHONc cnuytN BEN TRE xAwr Hoc zot4-zots MOn: TOAN (chung) Thli gian: 120 ph:iot (kh6ng kC ph6t dC) , v6i x+0. ON CTTINH THIIC CAu 1: (2,5 cli0m) Rrit gon cdc bi6u thric (T b/cho bi6uthirc n=[-If- Ji ='l(.*Ji), v6i x> 0 vd x +r Ix+2Vx+1 x-] ) i/ Rirt gon bi6u thfc B. iil Tim circ gi6,tri nguy6n ctra x OC e nfrpn gi6tringuy6n. Cdu 2: (2,5 di6m) cho hQ phucrng trinh {: * ." = -'. - v6i m ld tham s6. [3x + (m + l)y: -1 I/ Giei h6 phucmg trinh v6i m : 3 2l Giei vd biQn lupn h6 phucrng trinh theo m. 3/ Tim circ giittrf nguyOn ctra m de hg phucrng trinh c6 nghiCm ld s6 nguy6n. CAu 3: (2 di6m) 1/ cho phucrng trinh bdc hai x' - mx + m - 1= 0 (1) , v6i m ld tham s6 il Giaiphucrng trinh (1) khi m:4. iil Tim cdc giirtri cria m d6 phucrng trinh (l) c6 hai nghiCm ld x1; x2thlamdn hQ thilc I 1 _x,+x, xl x2 2014 x'-2x+2014 2lTim gi|trinho nh6t cua bi6u thric C = CAu 4: (3 di6m) Cho tam gi6c d,5u ABC n6i ti6p ducrng trdn dudng kinh AD. Goi M le m6t ditlm di clQng tr6n cung nho AB. (M kh6ng trung vdi c6c cli6m A vd B). 1/ Chimg minh ring MD ld ph6n gi6c ciag6c BMC. 2l Cho AD : 2R. Tinh di6n tfch cira tu giSc ABDC theo R. 3/ Gqi O ld t6m duong trdn dudng kinh AD. Hdy tinh di6n tich hinh vi6n phAn gi6i h4n boi cung AMB vd ddy AB theo R. 4l Gqi K ld giao di6m cria AB vd MD, H ld giao di6m cira AD vd MC. Chirng minh ring ba ducrng thing AM, DB, HK d6ng quy. 2 x . tr6i d6u thoa mdn lx, - *,1= 1 Cdu 3: (4,0 cli6m) 1/Cho x'-x-1=0. Tinh giS,tricriabiiSuthric Q- xu -3 x' +-3 xo -x'+2014 xu -x&apos ;-3 xt -3 x + 2ol4 2l Cho x,y,. crAo DUC vA DAo rAo BEN TRE Bn cniNn rntlc CAu 1: (4,0 di6m) 1/ Cho bi6u thric A - UN TTTT TUYEN SINH LOP 10 TRUNG HQC PHO THONG CHUYIN BEN TRE NAtu Hoc 2ou 4-2 ots M6n: TOAN (chuy6n) Thdi. HC, Chring minh b6t ilang thirc f" f, .{;;*{, " SO CT.IO DUC VA DAO TAO BEN TRE on rnr ruytN srNH Lop 10 TRUNG Hec pHo rHONc cnuytN BEN TRE xAwr Hoc zot4-zots MOn: TOAN (chung) Thli