Đề thi vào lớp 10 THPT Chuyên năm 2017-2018 môn Toán - Sở GD&ĐT Thái Nguyên

,,<br /> <br /> THI TUYTN<br /> <br /> UBND TINH THAI NGUYEN<br /> <br /> VAO LOP 10 THPT<br /> NIT hsc20l7 - 2018<br /> MON: TOAN HQC<br /> <br /> sd cra.o uuc va oAo rAo<br /> on cniNn rHUc<br /> <br /> ,<br /> <br /> SWTT<br /> <br /> Thdi gian ldm bdi: I20 philt, kh6ng kA thdi gian giao<br /> (Dd tui gdm c6 01 trang)<br /> <br /> CAu 1(1,0 di6m). Kh6ng dung m6y tinh cdm tay hey giiriphuong trinh: xi<br /> <br /> Ciu<br /> <br /> 2(1,0 tli6m). Cho him<br /> <br /> siS<br /> <br /> Uac rirrdt y<br /> <br /> =(2m4)*+5m-l (m<br /> <br /> lirtham<br /> <br /> +2x-8<br /> <br /> di<br /> <br /> = 0.<br /> <br /> ,0,**)1.<br /> ,2,<br /> <br /> Tim m d6hdm siS nghich bi6n tr€n IR. .<br /> b. Tim m d6OO ttri hnm s5 c6t trgc tung t4i.tliiSm c6 tung tIQ h -6.<br /> Cfiu 3(1,0 tli6m)' Kh6ng dtng m6y tinh cAm tay, rut ggn bi6u thrlc:<br /> a.<br /> <br /> , = (S - zJ-z + 2{s)(Jr+ 1o@)<br /> <br /> .<br /> <br /> +-<br /> <br /> L+t *6x+J-xl,f{_:.-r) nai I'=0.<br /> [Jx+3 Jx-3 x-e J(Jx+: ) [x+e<br /> <br /> cho B =(<br /> <br /> vitinh ei|tricria B khi x --12+6Ji.<br /> (mx-v=n<br /> cau 5(r,0 tli6nr). cho h€ phuong<br /> li tham si5).<br /> HEyrutggnbi6uthric.B<br /> <br /> "r* IT;;:r(m;n<br /> <br /> a. Khdng<br /> <br /> dtng m6y tfnh cim tay hay gi6i hg phuong trinh khi<br /> <br /> b. X6c itinh c6c tham sd m<br /> <br /> * --!;n<br /> 2'3-1.<br /> <br /> vi n biltring hQ phuong trinh c6 nghiQm li (-Lr6).<br /> <br /> CAu 6(1,0 tli6m). Cho phuong trinh 2x2+3x-l=0. Ggi xr;xz li hai nghiQm phAn biQt cria<br /> phuong trinh. Kh6ng gi6i phuong trinh h6y tinh gi6 tri cria bi6u thric:<br /> <br /> !r*L-\.<br /> [r, \)<br /> <br /> p =z(<br /> <br /> Cflu 7(1,0 ili6m). MQt tam gi6c vu6ng c6 c4nh huyAn bing 5cm, di$n tich<br /> <br /> li<br /> <br /> 6cm'. Tinh<br /> <br /> dO ddi<br /> <br /> c6c c4nh g6c vu6ng cria tam gi6c vuOng d6.<br /> <br /> Cfiu 8(1,0 tli6m). Hai dulng trOn (O) va (O') cit nhau t1i<br /> OO' . Qua ,,4 k6 tluong thang vu6ng g6c<br /> vir<br /> <br /> D.<br /> <br /> D<br /> <br /> vir B. Gqi<br /> <br /> M<br /> <br /> ldtrung di'5m cta<br /> <br /> vdi AM cit c6c dudrng trOn (O) va (O')<br /> <br /> tan tugt O C<br /> <br /> ring AC = AD<br /> tli6m). Cho dudmgtrdn (O), Auongkinh AB,ctxrg D ni*cirngphfa A6ivA ,lA<br /> <br /> Chung minh<br /> <br /> Cffu 9(1,0<br /> (<br /> <br /> A<br /> <br /> thuQc cung nh6<br /> a.<br /> <br /> fu ).Gqi E ld giao eliiim ciua AC vir BD , F ldgiao diiSm ctn AD vd BC .<br /> <br /> Tinh g6c frE khi<br /> <br /> siS<br /> <br /> r*g D<br /> <br /> do cria<br /> <br /> "*g<br /> <br /> ffi<br /> <br /> D<br /> <br /> bing 800.<br /> <br /> .<br /> <br /> khi g6c<br /> ailne ss' ,<br /> CAu 10(1,0 tli6m). Cho tam gi6c nhgn ABC (AB