Trong tam gi6c ABC ke c6c duong cao AE, BF; trong tam giric SBC ke duong cao BK... Duong thAng d ld ttuong vu6ng g6c chung cria hai ducrng thdng ch6o nhau a, b khi vd chi khi d Qt duong
Trang 1so crAo DUC vA DAo rAo
ruAr niNH
DE KIEM Tnn cHAr LUqNG Hgc t(i, n NAM Hec2o162o17
M6n: TOAN 11 Thcri gian ldm bai: 90 phrit; OA gOm 04 trang
Me d6 213
D 2017.220t7
ciu2zcho hdm s6: f (x) \ / | 2m khtx=l =l'*^-,' Ti,)(-:-'" (m ld tham soy uam s6 da cho li6n t.uc tar x: 3 kai m bdng:
r PHAN rnAc NGHTEM 1O,O arcm1
ciu 1: Bitiu thric S = clo,, + 3c]0,, + Scsro,, + .,.+z0l7c33l', c6 giatri bdng:
Ciu 3: Cho hinh ch6p S.ABC c6 canh b6n SA vu6ng g6c vdi
m4t driy Trong tam gi6c ABC ke c6c duong cao AE, BF; trong
tam giric SBC ke duong cao BK Menh <1€ ndo sau ddy sai?
A (sAE) r (SBC) B (BKF) r (SAC)
c (BKF) l_ (SBC) D (SBC) l_ (sAB)
Ciu 4: Cho hdm s6: f (x) \/ 5 ={* 1*'-5x+3.Menh 3 dA nio sau ct6y sai?
A Phuong trinh f(x)=0 c6 nghiQm tren khoang (-Ul)
B Phucrng trinh f(x)=0 v6 nghipm trdn khoang (A+.")
C Phuong trinh f(x)=0 c6 nghiQm tr6n khoang (sO)
D Ham sO f1x; li6n tgc tr6n R
Ciu 5: Cho hinh ch6p S.ABCD c6 ddy ldhinh thang vudng t4i
A vi B, AD : 2AB :2BC; canh b6n SA vudng g6c voi m{t
d6y;l6y di6m M tr6n SB Menh d€ ndo sau ddy sai?
A C6c m{t bOn cria hinh ch6p ld c6c tam gi6c vu6ng
B Ntiu AM l- SB thi AM l- SC
c Mp(MAD)t-mp(sen)
D.AC I SD
Ciu 6: Menh i16 ndo sau ddy sai:
A lim F4 =4
x-+a ,ly:)
(*'-+*)'
x-+4 X-4
32
c lim .'o x-4 -=6 D limx'-4x=4
(G -')' x-+4 x-4
cauT:chohdms6: f(x)={:'-l \ / ,T:*=^t t htharnsoy.Hams,idacholienerctarx=2k}rimbrng:
l3x-1 khi x<2
CAu 8: Cho hdm s6: f (x) = +-+- r2x+1 tao nghipm cria b6tcria b6t phuong trinh f '(x) S 0 li:
D.3
-.7
A (<;-3lv[+;+.o) B o c [-l;+] D (-o;+o)
Trang 2CAu 9: Gicri han limfn \/ -J* 4") c6 gi6 tri bang:
4.4
_" t
Ciu 10: Gioi han W++ co gitttri bdng:
Ciu 1l: Menh dA ndo sau d6y sai:
O
J!g(-*a +2x2 -l)=-.o
c lim 2x-3
- -, x-+< 4-x
A m>-l
A lim -l =1
x-+2;-l
c.2
C m>l
C lim I
=r*
x+3 ; -J
" _11g(-* +3x2 -21)=-<
D lim 2*-3
=-z x-++- { -;
D.3
c I
e 1
2
a 1
cau 12: cho ham s5 y = **-!c6 X_J d6 thi (c) Tim di6m M trdn (c) sao cho tirip tuyiin v6i (c) t4i M
song song v6i tludrng theng d: y = -3x+2.
A M(4;8), M(0;2) B M(0;2), M(s;7) C.M(272), M(4;8) D.M(272), M(5;7)
Ciu 13: Cho hinh ch6p tri giric <16u S.ABCD c5 t6t cit citc canh bang nhau Xet c1cmenh dd sau:
l' Cdc mpt phang(SA.C) vd (SBD) w6ng g6c vcri nhau vd cirng vu6ng g6c vdi mii day
II Hai m{t b6n HAn kC vu6ng g6c voi nhau
III C6c tam gi6c SAC vd SBD lA c6ctamgirlc vu6ng
Sd m€nh <16 sai ld:
CAu 14: Cho hdm s6 y = x sin x 'Hd thric ndo sau rldy itrfing?
A y"-Y=2sinx B y"+y=2sinx C y"-y=2cosx D y"+y=2cosx
Ciu 15: Ti6p tuy6n cria d6 thihdm s6 y = xa -4x2 +4 tqiili€m M(l;l) c6 phuong trinh ld:
ciu 17: cho hdm so r(x) \/x+m = '1*,1,- t (m ld tham sti; Ni5u f ,(*) , 0 vx + -m rhi ta c6:
CA'u 20: Gioi han
A -+oo
B 1&
J
D avo
2
B m<l
CAu 18: Menh dd ndo sau ddy dfng:
B limx'-1=6 x-+l_ y - |
x _ I (m ld tham sO; cO gi6 tri bang:
CAu 19: Cho hinh ch6p S.ABCD c6 tiliy
PI1r}.r F6ng cqnh a; canh bdn SA vu6ng g6c voi mf;t diry,SA: a;
ggi M ld trung <1i6m SB G6c gifta AM vd BD bdng:
D m <-l
x+2;-l
x-+l
Trang 3Ciu 2l: Cho hinh ch6p S.ABCD c6 d6y ld hinh thoi canh a,
^
g6c ABC - 60"; c4nh b6n SA: SB : SC; m4t b€n (SCD) tao
voi m4t dity g6c 60o Tinh khoang c6ch gita AB vd SD
B D6p an kh6c
D 3u 4
Ciu22z Menh d€ ndo sau cldy thfing?
A Duong thAng d ld ttuong vu6ng g6c chung cria hai ducrng thdng ch6o nhau a, b khi vd chi khi d
Qt duong th6ng nim ttottg mat phdng ndy vd vu6ng
vcri mdt phdng kia
cri ducrng thdng d thi dudng thdng a song song vdi
tP$'*e,
hai dudrne thane phan biOt cirng vu6n g gocvcyi vdi mQt ducrng thdng thri ba thi chring song song voi nhau
CAu 23: Cho hinh ch6p S.ABCD c6 d6y ln hinh chfi nhft, c4nh bOn SA vu6ng g6c v6i m4t d6y MQnh dC niro sau ddy sai?
A d(B,(SCD)) = d(A,(SCD)) B.d(C, (SBD)): d(A,(SBD))
(o\
Ciu24:ChohdmsO f (x)=sin2x-x'+l.Tac6 f"l *l "tt gi6tribdng:
\2)
Cfru 25: Cho parabol(P): y = x2 -3x Ti6p tuytin voi (P) di qua di6m A(5;10) c6 phucng trinh ld:
Cf,u 26: Menh il€ ndo sau ddy tlfing?
A (sin2 2x)'=sin4x
C (cost 2x)'=-2sin4x
Ciu21:Cho hinh ch6p tam gi6c.d6u S.ABC c6 c4nh d6y b6ng 2a, g6c giira m{t b6n vd mft d6y bing 60"
D0 dei canh b6n cira hinh ch6P blng:
A.a
2
c.aa
B (cos 2x)'=2sin2x
D (sin2x)'=-2c'os2x
sau ddy ilfng?
A AM i- (SBC)
B AC r (SBD)
C G6c gita mp(SCD) vd m4t t16y blng 45"
D G6c gifia SD vd m4t d6y bdng g6c ffi
Ciu2gzTrong c6c giOi h4n sau ctdy, gioi h4n ndo b1ng2?
t=
B uv' a
f, )
n+10 Ciu 30: Hdm si5 y = (x + l)rf,C + I c6 tt4o hdm ld:
2x2 +x+l
Trang 4rr PHAN TL/ LUAN (4,0 diam)
CAu 1 (2,0 diAm)
l Vi€t phuong trinh c6c titip tuy6n ctra <16 th! hdm s6 y = + bitit ti6p.tuyiSn vudng g6c voi <ludmg
x-l thEttg d:Y= -x+2017
i x=2
Ciu 2 (2,0 diAm)
cho hinh ch6p S.ABCD c6 t16y ldtrinh chfr nhat voi AD : 2u AB: a; c4nhban sA vu6ng g6c
v6i mpt rt6y (ABCD) cqi E 1i hinh.ftig"
"tG g6c cria A l€n SB vi M ld trung tli6m cria BC'
l Chtmg minh: AE l- SC
2 Chtmg minh: MD I (SAM)'
3 Tinh SR, biOt khoing c6ch tir C tttin mp(SDM) bang
uEr
-a a
L
Trano 4/4 - Me d Ztg