SO GIAO DUC VA DAO TAO TAY NII\H Ky rrrr cHoN Hec srNH Gror Lop 12 THpr voNG riNn NAvl Hec 2ot3 - zot4 Ngay thi: 25 thing nlnr Z0l3 thi: ToAx - Btroi ttri thri,ntrdt Tho'i gian: 180 phut (khong kA thdi gian giao Mdn DE CHfI\H THTIC thi gont co t trang, thi ,sinh khong phai chep @A dA) di vao giay thi) Bii (4 dient) Cho ba s6 ducvnga,b, c tho6 mdn cli6u kiqn Chirngminhr6ng: a+b+c * b * t ,3 -L l+bc l+ca l+ab = Ri i (4 client) Cho harn s6 f(x) xac clinh vcyi rnQi gia tri x > rra thoi m6n + y) = f(x).f(y), Vx > vy> o Irfx Lrf28) - Q Chu'ng mi nh r6ng: f(x) = 0, Vx > Ilii 3, (4 diem) cho lrinh ch0'nh$t ABCD Tr0n c6c cluong thang BC va cD, l6y lAn lugt c6c di6m di = e00 Gqi H rd hinh chi6u vu6ng g6c cria A tr6n MN rirn qu! fl:il*"x,,il;i?r:n" ffir Bni g aiam) cho cludng thing d cri clua trtrc tam H cria ta,r gi6o ABC Gei ;, dz, d3 lan lucyt la oac dudng ttring dtii xung vdi d qua BC, CA, AB Chring rninh rang ba dtrong th[ng dr, d2, d-, d6ng quy Bei s G aiiim) tno't minh rf,ng I I s5 thuc khirc thu6c croan 10001 o6 the chon cluoc hai [l; , so x vdy cho: < x _y 28 thi f(*o)=f(xo -28+28):f(xo-28).f(28)=0 t(28) = f(l +14): f(l4).f(14) = =+ f(l4) = Lim tuong tU nhu trOn thi f(x) LAp lupn tucrng thi co: Vay f(x) f(x) - 0, Vx > 14 0, vx >7; f(x) = 0, vx a! - 0, Vx > trang I rlei g diem) Cho hinh chfr nhQt ABCD TrAn cdc itudng thhng BC vd CD, ldy tdn lw,qt cdc ifiAm di itQng M, N c/ro = 900 Ggi H ld hinh chi6u vuAng gdc ctia A tr€n MN Tiim qu! tich ctic iti6m H ffi M(a; ma) B(a; 0) DUng hQ trpc toa d0 Oxy nhu hinh ve Gi6 sri B(a;0), D(0; b), y = mx thi M(a; ma) l)Ni5u & ) v6i A = O(0;0) 0, b > vd phuong trinh duong th[ng AM ld m*0: Phuong trinh cludrng thdng AN Phucmg trinh dudrng thing h y= -l* m Suy N(-mb; b) MN lA (b - ma)x + (a + mb)y - ab(l + m2) : g (1) Phuong trinh dulne th6ng OH le (a + mb)x GillhA;il""s;'i"h TU d6 thu dugc * * aoI (1, = ;irfiil d;;;; l - (b - ma)y = (2) Phusng trinh ndy phuong trinh cfia dudng thing BD 2) NOu rD = : Khi d6 M = B, N Vfly quy tich cdc - D Suy H eBD di6m H la dudrng thang BD Gtti chfi: Ndu thl sinh s* dung ki6n ththc itudng thiing Simson gidc CMN vd di€m A dd gidi thi: - Phdn thudn: 2il - PhAn ddo: 2d diSi vdi tam trang Bni G dieln) Cho itudng *dng d iti,qua trgc tdm H cfia tam gidc ABC Ggi d1 , dz, dj lhn lwgt ld gdc itudng thdng ddi x*ng: vt6,i d qua BC, CA; AB Ch*ng minh rdng ba dwd'ng thdng & , dz, dj cl6ng quy Ggi A', B', I' lAn luqt ld c6c