or xrnvr rRA cuol Hoc rY I PHONG GIAO DUC VA DAO TAO THANH prrOrrAl DTIOI\G NAvr Hec zoz2 - zozt M6n: Toin Thoi gian ldm bdi: 90 phrit EC bei gdm:05 c6u,01 trang Cflu (2,0 di6m): 1) Thlrc hiQn c6c phdp tinh: a) x.(2x + 3) - 2* b) (r'-t 2x* b) ,'-y'-4x+4 1) : (x + 1) 2) Phdn tich c6c da thirc sau thdnh nhdn tri: a) Zxz - 6x Cffu (2,0 tli6m): Tim x biiSt: a) 3(x + 1) - 2x=0 b) *'- 3x:0 c) x(x - 8) - 2x+ 16:0 Ciu (2,0 ili6m): a) Thlrc hiQn ph6p I I 3x-6 tjnh: 3x1- 3x{z- 4:g7 b) Tim a dC da thric : 3x3 + 2* - 7x* a+ chia h6t cho da thric 3x - Ciu (3,0 tli6m): Cho tam giSc ABC nhqn (AB < AC), dudng cao AH Gqi M ld trung diOm cta AB, N ld di6m dOi xrmg cria H qua M a) Chtmg minh ttr giSc b) TrCn tia d6i ciatiaHB 6y di6m E cho H ld trung di6m cria BE Chrmg minh: AE c) Ggi I K6 li ANBH H hinh binh hdnh : NH giao di6m cria AH vd NE Duhng thing VII cit AC tai K NQrKH t4i Q Chung minh AQ r BQ Ciu (1,0 tli6m): Cho si5 Tinh thpc x > th6a mdn: xz giStyibirSu thric: B - 4x* = : (*' - 4xo +x' + x' l4r)'0" / * uot SBD: Gi6m thi 1: Ho vd t6n thi sinh: Gi6m thi 2: (x,'r+ l6x'l)' + 2020 PHoNG GIAo DUC va oAo r4o TH4IyH PHo nAr PtIoNc HrJcrNG UAN cnAvt oB runiu rRA cuol HQC rV r xAwt Hec zo2z - zo23 M6n: ToSn - 16,'p Hu6ng d6n chAm g6m: 02trmg D6p 6n Di6m - 2x2 :2x2 + 3x_ 2x2 0,25 Y CAU la x.(Zx+ 3) :3x 1b Ciu 0,25 (x2+ 2x+ 1) : (x+ 2a 2b (x * 1)2 : (x + 1) 0,25 :1*1 (2 tli6m) : 1) 0,25 0,5 -6x:2x(x-3) x' - y' -4x + : (x2- 4x * 4) - Y' 2x2 0,25 : (x - 2)' -y2 : (x - -yXx - + y) a 0,25 3(x+1)-2x=0 0,25 + 3x+3-2x:0 +x: -3 0,25 V6yx=-3 b Ciu (2 tli6m) x'-3x=o=x(x-3):0 [x=0 [x=0 >l [x-3=0 =l [x=3 Vay c 0,25 0,25 I 0,25 x e {o;:} *(r-8)-2x+16=0 + x(x- 8) - 2(x-8) : 0+(x [x-8=0 [x=8 t- t | - )t lx-2=0 8)(x - 2) : 0,25 lx=2 0,25 Vpy xe {2;s} a Ciu (2 tli6m) +- 3x-6 3x-6=- 3x-2 3x+2 4-* 3x - 3x + (3x + 2)(3x - 2) 3x - 3x-2 + 3x+2 I (3x - 2)(3x+2) (3x + 2)(3x-2) 3x+2-3x+2+3x-6 (3x + 0,25 (3x + 0,25 0,25 2)(3x-2) 02s 2)(3x-2) 3x-2 = (3x+ 2)(3x-2) 3x+2 0,25 ax, v 1iliff\ *of, I 'i;v / /-4 ffi I b Thlrc hiQn ph6p chia da thric 3x3 * 2x2 da thric 3x * dugc da thirc du ld a +1 E6 3x3 + 2x2 - + a:-1 7x*a+3 chiah6t cho 7x* a * cho 3x- thi a +1 : VSy v6i a: -l thi da thirc 3x3 + 2xz cho da thirc 3x - Tir gi6c ANFIB c6 b 0,25 eOi xtmg v6i H qua M) 0,25 NA: tIE (: BH) 0,25 - Chrmg minh dugo llIJE, 0,25 :> Tir giSc NAEH h hinh binh henh 0,25 : 0,25 - Suy dugc AE NH X6t INQH vu6ng t?i Q, c6 QM ld dutxtg trung en mi NH - AR Suy eM = l*, Suy =+ Cffu (1tli6m) AAQB vu6ng tai Q=+ AQ I BQ (r,'+ 1)' l6x' Do d6 : B f: : 0,25 0,50 0,25 0,25 , (-1)2022 0,50 0,25 eM =;AB Tac6:x5- 4x4+x3+x2-4x : x3(x2-4x + 1) + (x2 - 4x* 1) - I : -1 x2 - 4x* I : :> x2 * : 4x:) (x2 + l)2 : l6x2 -.? l Chri 0,25 -> Tri gi6c ANBH le hinh binh henh viNA c 0,25 : M le trung tli0m cria NH (vi N (3 tli6m) 0,25 0,25 M le trung di6m ctra AB (gt) Cdu 7x* a +3 chia h6t -VC hinh dring dugc: a 0,5 1 + 2020 : (_ 2022 Ial dung Lins vAn cho di6m N6u thi sinh ldm theo c5ch kh5c, c6 lcvi gi6i da ... [x=0 [x=0 >l [x-3=0 =l [x=3 Vay c 0,25 0,25 I 0,25 x e {o;:} *(r -8) -2x+16=0 + x(x- 8) - 2(x -8) : 0+(x [x -8= 0 [x =8 t- t | - )t lx-2=0 8) (x - 2) : 0,25 lx=2 0,25 Vpy xe {2;s} a Ciu (2 tli6m) +- 3x-6... Cffu (1tli6m) AAQB vu6ng tai Q=+ AQ I BQ (r,''+ 1)'' l6x'' Do d6 : B f: : 0,25 0,50 0,25 0,25 , (-1 )2022 0,50 0,25 eM =;AB Tac6:x5- 4x4+x3+x2-4x : x3(x2-4x + 1) + (x2 - 4x* 1) - I : -1 x2 - 4x* I... 0,25 M le trung di6m ctra AB (gt) Cdu 7x* a +3 chia h6t -VC hinh dring dugc: a 0,5 1 + 2020 : (_ 2022 Ial dung Lins vAn cho di6m N6u thi sinh ldm theo c5ch kh5c, c6 lcvi gi6i da