luyện thi đại học môn toán

ruyeii chifit & Gi&i thifu dethi Todn hqc - Nguyen Phii Khdnh , Nguyen Tai Thu Cau8.a:Tac6 A B = ( l ; - l ; ) , A C = (-l;-l;3)=:> A B , A C H o n niia: C M =(-l;-5;-2) U nen phuang trinh mat phang ( A B C ) : Va B N 3'3 G(?i true tam ciia tam giac A B C la H(a,b,c), ta c6 hf: a - b + 2c = c=l Ion nhat H = A, VTCP cua A la u^ = U j ; A B Do duang t h i n g ( A ) nam ( A B C ) va vuong goc voi (d) nen: u InABC nABC,nd = ( ; l ; l ) va AB = ( l ; ; l ) Ggi H la hinh chieu ciia B len A Ta co: BH < A B , khoang each tir B den iL ie uO nT hi Da iH oc 01 / a + 5b + 2c = u(2;l)=>AC:6x + 3y + l = CauS.brTacoVTCPciiadla: a=2 C H A B = ci> a + b-3c==0 b = l = > H ( ; l ; l ) HG(ABC) n(l;2) la mpt vec to phap tuyen ciia AB nen phuon trinh A B : x + 2y + = - l ( x - l ) - ( y - ) - ( z + l ) = c i x + 5y + z - = BH.AC = x=l +t =(1;-1;-1)=:>A: y = l - t z = -t Cau 9.b: Xet z = la nghi|m cua phuong trinh = (12,2,-11) Xet z * Dat z = a + bi (a,b e ]R,a2 + b^ > o), t u gia thiet ta co: Vay duang t h i n g (A) di qua diem H(2;1;1) vacoVTCP (12;2;-11) + 1=2 z + 6.Z v3 up + = 2a /g + = 2a - 2b z = b(b + l ) = 12a' bo ok TH2: Lay dugc vien co dung mau: co C j j + C15 + C13 - = 8215 3|z|^ = b a > 0, b > -2b +I=4a2 a>0,b>0 b(b + ])=:12a2(l) { 3a2+3b2 =b(2) a>0,b>0 ww w fa ce _, 8215 + 316 n^c xj" r> n ooc => PT = = * 0,065 Vay, PA « 0,935 ^ 125970 4845 ^ B Theo chUcrng trinh nang cao Cau7.b: B = B C n d , => B ( ; - ) => B M = (2;2) Do B M la mgt vec to phap ^3|z| 6z \ z ^ - b = -b =0 om c Cl =1 each z.i + =2a ro gian mau la n(Q) = C^„ = 125970 Gpi A la bien co lay duoc vien c6 du ca mau A la bien co lay dugc vien khong dii ca mau Khi THl Lay dugc vien co diing mau (chi xay lay dug-c bi vang) v | y co :4 + z z.i o z.z^/3 s/ Cau 9.a: Lay ngau nhien vien tu hop gom 20 vien ta c6 so phan t u ciia khong + 1=2 ^3|z|^ + l = | z | ( a - b i ) + Ta , x-2 y-1 z-1 nen A : = = 12 -11 tuyen ciia B C = > M B B C Ke M N / / B C cSt d j tai N , vi tam giac A B C can tai A nen t u giac B C N M la hinh chCr nhat rMN//BC Do \ , r i > M N : x + y - = 0, N = M N n d lQuaM(2;l) ^ NCIBC Do QuaN 3^ ^ •N fS 1^ l3'3 Lay (1) tru (2) ve theove taco 9a2 = 4b2 a^ = - b ^ ( ) The ( ) vao ( l ) ta dugc : ^ b b^ + b « b = 13 a = — , (do a > 0,b > 0) 13 =i> z = — + 13 13 {1 _ N C : x - y - - = 0,C = N C n d i ^ C 3' 3 183 Tuyen chgn b Giai thi?u /3 Cau 9.a: Cho a, p la hai so phuc lien hgp thoa DETHiTH(jfs628 Tinh a I PHAN CHUNG CHO TAT CA CAC T H I S I N H B T h e o c h U o r n g t r i n h n a n g c a o Cau 1: Cho ham so: y = x-* - 3mx^ + 9x +1 c6 thi {C^) Cau 7.b: Trong mat phSng tpa dp Oxy, cho duong tron (C): x^+y^-2x-4y-4=0 a) Khao sat su bien thien va ve thi (CQ) ciia ham so CO tam I va diem M ( ; ) Viet phuong trinh duong thang A, biet A cat (C) tai b) Gia six duong thing ( d ) : y = x +10 - 3m cat thj [C^) cua ham so tgi hai diem phan biet A , B, C c6 hoanh ian lugt Xi,X2,X3 cho t u giac iL ie uO nT hi Da iH oc 01 / diem phan biet A , B ABIM la hinh binh hanh Cau 8.b: Trong mat phang Oxyz, cho mp ( p ) : x + 2y + z - = 0, duong Tim m de: xf +X2 +x^ /3y^ + y + l =m va diem A ( ; l ; - ) Viet phuong trinh duon^ thSng d nam (P), biet d cat A va khoang each tu A den d bang 42 , Cau 9.b: Tim c biet a, b va c la cac so nguyen duong thoa man c=(a+bi)'^ -107i xe'^+1 Hl/dNG DAN GIAI