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Untitled UBND TiNH THAI NGUYEN K t Tffl TUYEN SINH LClP 10 NAM HOC 2021 2022 SO GIAO DUC VA DAO TAO MON TOAN (Danh cho thl sinh thi chuyen Toan) Thai gian lean bai 180 phut, khong ke then gian giao de.
UBND TiNH THAI NGUYEN SO GIAO DUC VA DAO TAO BfeCHnNHIHCTC K t Tffl TUYEN SINH LClP 10 NAM HOC 2021 - 2022 MON: TOAN (Danh cho thl sinh thi chuyen Toan) Thai gian lean bai: 180 phut, khong ke then gian giao de (Be thi gom c6 01 trang) f x+5 ^ Can (1,5 diem) Cho bilu thuc A = -jT -— : -W * + l + yjx ~ x ) \ 4- Rut gon va tinh gia trj cua A x = yj29 + \2y[3-2y/2 Cau (1,5 diim ) Giai phuong trinh V lx + + V lx+ T s + Ax -1 = Cau (1,0 diim ) Cho / (x) la da thuc bac ba thoa man f ( x +1) - f(x ) = -x z, Vx e R va f (0) = 2021 Xac dinh da thiic / (x), tuc tinh t6ng T = l2 + 22 + 32 + + 2 12 Cau (1,0 diim ) Tim n nguyen duemg d l bilu thurc A = 4«3+ 2n2 - In - co gia tri la s6 chinh phucmg Cau (1,0 diem) Ban Nam du dinh chi dimg cac hinh vuong canh 2cm va 3cm de ghep lai mot hinh vuong canh 2021cm Hoi ban Nam co thuc hien duoc ldiong ? Giai thich ? Cau (2,0 diem) Cho hai duong tron ( O) va (O') cit tai hai diim A, B (O va O' nlm vh hai phia d6i voi duemg thing AB) Tu diim C thuoc tia doi cua tia AB ve cac tiep tuyln CD, CE voi duong tron (O), D, E la cac tilp diim va diim E nim duong tron (O') Duong thing AD, AE cit duong tron (O') lin luot tai cac diim M ,N (M & A, N & A) Goi K la giao diim cua hai duong thing DE va MN Chung minha) Tam giac CDA va tarn giac CBD ding dang, tir suy ADBE = BD.AE; b) K la trung diim cua doan thing MN Cau (2,0 diem) Cho diim A c l dinh nim ngoai duong tron (O ) Ke cac tilp tuyln AE, AF voi duong tron (O) ( E,F la cac tilp (film) Diim D di dong tren cung Ion EF cho tarn giac DEF nhon Tilp tuyln tai D cua duong tron (O) cit cac tia AE, AF lin luot tai B, C Goi M, N lan luot la giao diim cua duemg thing EF voi cac duong thing OB, OC a) Chung minh bln diim B, N, M, C cung thuoc mot duong tron; b) Goi DK, OI lin luot la duong phan giac cua cac goc EDF va BOC (K thuoc EF, I thuoc BC) Chung minh duong thing IK luon di qua mot diim c l dinh HET Ho va ten thf sinh: So bao danh I [ l I I I j I I if i I i i UBND TiNH THAI NGUYEN S d GIAO DUC VA DAO TAO KY THITUYEN SINH LOT 10 NAM HOC 2021- 2022 M 6N THI: TOAN Danh cho chuyen Toan HUONG DAN CHAM ( Ban hu&ng ddn chain gom co 06 trang) L Hiring dan chung - Giam khao can nlm vung yeu cdu cua hudng dan cham dl danh gia dung bM lam cua thi sink Thi sinh lam each khac dap an nlu dung vin cho dilm toi da - Khi van dung dap an va thang diem, giam khao can chu d6ng, linh hoat voi tinh than tran bM lMn cua hoc sink - N lu c6 viec chi tilt hoa dilm cac y cln phM dam bao khong sai lech vdi tong dilm va durge thing nhlt toMi hoi dong cham thi - Diem toMi bM la tong diem cua cac cau hoi dl thi, chMn dilm le den 0,25 va khong lMn tron H Dap an va thang diem (V2x + - l ) + (V |2 x + -4 ) + (4 x + ) = „ ( * + l) , -fX+1) + (* + l ) - -J2x + + V2j:+ 18 + v ' f i ^ < = >2(x+ l) ■■ + i +2 =0 v 'W x + f l v x + + j 0,25 x = -1 (t/m) V 2x+3+l — - + = V2 x+18 + 0,25 Voi x > — thi yjlx- f + > ,V x + + > nen ; 0,25 + > >/2x+3 +1 V 2x+1 + Vay phurcmg trinh co iighiem nhit x = -1 0,25 Vi / ( x ) la da thuc bac ba nen fix') = ax* + bx2 + cx + d {a *0; a, b ,c ,d (x2 + 2x +1) + c (x +1) + d / ( x + l ) ~ / ( x ) = 3ox + (3a + 2&)x + or+ Z>+ c Thee bM ra: 3ax2 + (2 a + 2b)x + a + b + c = - x 2, V x e R a— I ° '3a = - l Nen ■3a + 2b = ■b = Can (ft+l)(4ft-6):(4n2-2 n -6 ):c / Talai co (4n2-2 n -5 ):d , suy (4ft2 - 2n - 5) - (4k2 - 2n - 6): d =^>1: d => d = V&y 0,25 DCLN(ft+l,4ft2-2 ft-5 ) = l C au4 Ma (n+l)(4ft2-2 ft-5 } = £2 ndn ft+l;4n2-2 ft-5 la cacsO chinhphuang =>ft+l = a2 va 4ft2-2 ft-5 = 62;a,6eN * Do n+1 la s6 chinhphtrong, neN* nen n > 0,25 Voi « > , taco (2ft-2)2 (x2 + 2x +1) + c (x +1) + d / ( x + l ) ~ / ( x ) = 3ox + (3a + 2&)x + or+ Z>+ c Thee bM ra: 3ax2 + (2 a + 2b)x + a + b + c = - x 2, V x e R a— I ° '3a = - l Nen ■3a +... minh duong thing IK luon di qua mot diim c l dinh HET Ho va ten thf sinh: So bao danh I [ l I I I j I I if i I i i UBND TiNH THAI NGUYEN S d GIAO DUC VA DAO TAO KY THITUYEN SINH LOT 10 NAM HOC... BfeCHnNHIHCTC K t Tffl TUYEN SINH LClP 10 NAM HOC 2021 - 2022 MON: TOAN (Danh cho thl sinh thi chuyen Toan) Thai gian lean bai: 180 phut, khong ke then gian giao de (Be thi gom c6 01 trang) f x+5