Vitit phuong trinh duong thing iti qua hai.
Trang 1Di, KIEM TRA CI{AT LIIQNG DAUNAM
NAM Hgc 201G2017
M0n thi: Toin 12
Thiri gian lim biri: 180 phit, khdng k6 thiri gian ph{t dii
Ciu I (t,0 -li6m).
l Cho n ld sli tu nhi6n th6 a menC| = 45 Tinh gi6 t{ bi6u thric 1 - 24
2 Cho /(x) = sin2x+cosx fi* f'(r)
Ciu II (1,0 ili6m) Cho mm st5 71x; = mxt - 3x' + nu + l Tim m d6 /' (r) > 0, Vx e R.
Ciu III (r,0 ili6m) Cho him ,6 y =:l+ Vi€t phuong trinh ti6p ruy6n voi AO tH Ui.it ti6p tuyiin c6
r ^ i ,:,
ne so goc Dang - i
Ciiu IV (1,0 ili6m) Tinh gioi tt* ' x+2 hry*#
yt +5x_14 Ciu V (1,0 iti6m) Trong m4t ph'ing voi hQ tqa d0 Oxy, cho hai di6m A(1;2), Bt3;l) Vitit phuong trinh duong thing iti qua hai <ti6m A, B Tim tqa d0 diilm M thuQc ttuong thdng AB sao cho OM = rE ysi O
li g6c tEa itQ.
Ciu YI (1,0 ili6rn);
luy€n vi6n cua m6i dQi cAn trintr tro ng tii m6t danh s,ich slip thu t.u 5 cAu thu rong sa t t cAu thri
dC d6 luAn luu 1l mdt Trong sd cic ciu thri tl6 c6 hai ciu thu Tin vi C6ng Tinh xric suit dA cAu
i- t .,
thiTin vi C6ng c6 m{t trong s6 5 ciu thri di ludn luu
Ctu VII (1,0 di6m) Trong lfi6ng gian cho hinh ldng tru ABCA'B'C' c6 d6y ld tam gi6c vu6ng d C, AC
: 4 AB = 2a Hinh chii5u cua A' tdn m4t phing (ABC) H trung <litim cua A3, goc gita ducrng theng A'C
vi mdt phing (ABC) bin€ 600 Tinh di€.n tich tam gi6c ABC, chiAu cao cua kh6i t4r vA cosin g6c gita
hai ttudng thingA'B vn AC
Cau 14II (1,0 ifi6d Trong m{t phing voi hQ tga tlQ Ory, cho tri gi6c ABCD nQi ti6p trong rtudng trdn, hai ttudng chdo vu6ng g6c voi nhau vd cit nhau tai E(l;-l) Hinh chiiiu cua E l6n duong thing CD h
Ciu IV (1,0 iti6n) Giai bdtphuong tdnh Jir-r-x' -Jzx+5+t <r-J3-r -.6+4
Cliu V (1,0 tliSm) Cho x,y,z lAba st5 duong thda miin x2 +y2 +22 +2xy =3(x + y+ z).
l Tim gind kin nhat cua t=x+y+z
2 nm giefrinh6 nhit cua biAuthric I =
" + y +, +
#.#
H&
Ha vdten thi sinh .56 b6o danh
SO GT} $ DT BAC NINH
TRI'ONG THPT HAN TIilTY$N
Trang 250GD) i)l:, ;- ' ,
TRTTO\'G TIPT F!\.\ TiJL'i.T
.- :.- .1
| ttlU\trU.\\(i,l
Ei hJE.U TRA CIi.\T LL'I'J\L; D \L'.\ i.\I
NAII rIQC 2016-?0r:
ilIo|i: ToiN 1:
I l.+) DK: n> 2;n eff khi d6 C"z
+) P,, -24 =361872O
2.+) f (x)=2cos2r-sinx
+)f {r):z
02s
03s 02s
tr +) f (r) = 3mxz - 6x + m> o,vx e R
+)m=0 tac6 f (x)=-6x; "f'(t)>-0 <=x<0(loai)
-r)m+u.;
r1r) > o, vr e .n - {l : : *
{^ ={:r:,=, *
{_si.'
"
o o <.6
0,2s
02s
0'5
+) f (r) =
-i-(x + 2)'
+; M (ro ; yo
) xo * -2 ) h titip di€m cria tiiSp tuy6n
+Yo=4
= f'(x^\=-7 <>l ro =-1'
+)ro = -f ; plg66g trinh tiiip nry6n : ! = - 7x - 3
+) ro =-f ;pttty= -7x-31
0,25it
0ts
0,25
a2s
IV !\I-l;- (J, \ *z -zl(J-*z *z\,f\' /
'
'+2 (x2 + 5.r - l4)lJ.r + 2 + 2)
0,25
0'5
0,25
*1 = 1;* - t:?
= linr
I
JO
v +) phuong trinh tludng thing qua 2 ditim A, B lex -4y+ 7:0
-+)c1i M (4n -7;n) e AB = gld'z = (am -7\t + *, = 5 e 17mz - 56m + 44 = 0
0,5 0'5
Trang 3icosx=-1 | x=tr+k2tr
I )+)i fcos-r=- 1ei r
Lx=!-:+k2n
2)+) Sd phan tu kh6ng gian m5u lOl : ,e,1
+)Ggi A ld bi6n cii " Trong s5 5 ciu thri
TAn vi C6ng" = lQ, | = Cr'.5 1
lol .)
Yiv P(A\=1'-!='
lol 1r
chon ra dd al6 ludn luu c6 m{t hai ciu thri
0rs
0,25
+lBC=aJ3=S".-.=* '*-2
"-+)@,(.4BO) =@c.ca)=Ecu =ao" .Chidu cao A'H = HC.tan60o = ali
le's.ACl
+) - \ I cos(e'.B.;c) AB.AC' A'B =2a
-?
+\ '\t2 A'B.AC =T E A + AAI.AC = IIB.AC = AH.AC =L
.l
YQy
coslAB;ACI=:-C2: hs {mg g6c gita hai tluong th5ng
0as.
025
0,25
0,25
vrn
+) Phuong trinh Ei:4x+3y-l=0 - U(1t-l\ \2 )
+) Chung minh M li tnrng diAm AB
+) cei r(a;-3) e lB; MA: ME * f"-:'l' =2 * + olo = 0
0,25
02s
0,25
0'2s
+ l(s;-3),.8(0;-3)
+) phuong tinh CD: -3x+4y-3:0
Pt BD: 2x-Y-3=0
D CD n BD > D{3;3)
ptAC: x+2y+1:0; C = AC r-tCD = C(-l;0)
vay A(5;3), B(0;-3)- C(-l r0) D(3:3) vn ti l,-, I
\z /
w +) DK -5
-<x<3.
Trang 4+) (*) c+ / s a = rr';6-'3 I.,"1 -1 1 ,12r+5 e.,i-xr -x+12 <x-1
[ '>l
€.(
l2x'-r-11>0
- 1+'u64
€r
f>-+; K6t hqrp ttiiiu kiQn L 6oo
" lJ it2
=, = 3
l.) +)3(x+y+21=e+y)] *r' u('*y-*'\' =x+y+z<6 D6u bdng xay ra
z khi x : 1 ;y = 2;z = 3 Vdy x + y + z lon nhAt bing 6 k*i x :l' y = 2' z = 3
+\T ) y
>x+ ' y+z+; -fr 4+x+z > x+ y+z+L
+++y+t - x+y+z+10
22
+)Ddtt=x +y+2,0<t<6.
r > t * ::| = {r + 1 0) + + +
fi6 - r o > z11r + r o)ffi +
;ft _10 = 26
., ' , ' i
.Vay gie fi nhd nhat ctia T b6ng 26 khi x: \t y : 2' z : 3
0,25
05