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

NcuvEN . THI ruyrN sINH vAo Lop 10 THpr<br /> oAo r4o<br /> NAu HoC: 2Ot7 - 2018<br /> ur6N THr: roAN Hec<br /> Bn cuixH THrIc<br /> ' (Dnnh cho thi sinh thi viro chuy6n<br /> <br /> :r<br /> ,:<br /> <br /> UBND TINH rHAt<br /> sd crAo DUC vA<br /> <br /> crruytx<br /> <br /> To6n)<br /> <br /> Thdri gian<br /> <br /> lim biri:<br /> <br /> phft<br /> <br /> 180<br /> <br /> cau 1(1,0 ili6m). Kh6ng drrng m6y tinh cam tay h6y rut<br /> <br /> (kh1ng ke thdi gian giao<br /> <br /> A=<br /> <br /> so.n<br /> <br /> di)<br /> <br /> ffl';*)<br /> <br /> Ciu2(2,0 di6m). ciei he phuong trinh sau:<br /> <br /> I*'*y'-xy+4y+l=0<br /> <br /> Ir(r- *'- y'*r*)=z(*' +t)'<br /> Cflu 3(1,0 di6m). Cho s0 tg nhi6n A =W<br /> - l8 + 2n vli n e N,z ) 2.<br /> n chilsdT<br /> <br /> Chtmg minh ring<br /> CAu 4(1,5<br /> <br /> A chia h6t cho 9.<br /> <br /> ili6m). Cho a,b,c ld c6c sti duong th6a m6n<br /> <br /> Tim giritrilonnh6t criabi6uthtc: P<br /> <br /> Ji<br /> <br /> a+b+cs<br /> <br /> -+*L+*.<br /> Jo'+t Jo'+t<br /> <br /> cffu 5(1,0 ili6m). vdi m6i sti nguy€n ducing n taky hiQu a,<br /> <br /> li<br /> <br /> si5<br /> <br /> Jc2<br /> <br /> .<br /> <br /> +t<br /> <br /> nguyEn g6n<br /> <br /> Ji *at.<br /> <br /> Vf dU: o, =l;a, =l;az = 2;aq - 2;as = 2;ao = 2;o, = 3 . Tinh gi6 tri cria t6ng:<br /> <br /> 1*<br /> ^s=l*f*l*...*<br /> at a2 a3<br /> dzon<br /> CAu 6(1,0 ili6m). Cho hai duong trdn t6m<br /> duong trdn<br /> <br /> (Q)<br /> <br /> duong trdn tdm<br /> <br /> ta,<br /> <br /> O<br /> <br /> ei6*<br /> <br /> l.<br /> <br /> Phan k6o ddi<br /> <br /> I<br /> azots<br /> <br /> Q vd O, nimngodi<br /> <br /> nhau. DoAn tha"g<br /> <br /> eO, c*t<br /> <br /> cta cloqn OrQ cdtdudrng trOn (q) @i B. Drmg<br /> <br /> ti€p xric ngodi vdi dudmg trdn (Q<br /> <br /> (Or) tqi C (tli6m O khdng nim tren do4n QOr).<br /> <br /> ) tai O vd titip xric trong v6i duong trdn<br /> <br /> Chrmg minh rdng c6c dii:m<br /> <br /> A,B,C,D cing<br /> <br /> nim tr6n mQt duong trdn.<br /> <br /> Ciu 7Q,5 tliGm). Cho ba