Ôn tập môn Toán 12 - Đề 3

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oAruH cHo rRUNG noc pxd rxOruc vA rnuruc Hoc co s6
Tru s6: Tdng 12, tda nhd Diamond Flower, s6 
.1 Hoang Dao Thriy, Thanh Xudn, Ha NOi
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Trong kh6ng gian v6i hg trUc tgadd Oxyz,cho
f x =2-t
tluong thingd,ly=1, , telR. Vecto ndo du6i tl6y
lz=2+5r
ld vecto chi phuong cua d?
THrr SIIC TR{,OC Xi rmr
OE Sd 3 gnm gran hm bdi:90 pht*t)
chohdm ro y=4. H6y chgn ciutling: Trongcdchdmsauhiychirahdms6 gi6mtr€n IR
A. Hdm sd c6 hai chidu bi6n thi6n. t. y =(T l' s., = l,*)-'. ..r:,n)r.. o. y = []-'l'' \r/ " \3e) \2,12.)
B. Hdm sO aOng biiin tr6nlR.
C.Hdmsi5tl6ngbitintr6nc6ckhoingr-.",;l"a[;*) 
Nghi.mcriab^tphuongtrinh 1og3(4'r-3)>2lit
\ L) / A..r>3. ,..rri. C..r>3. D. i<x<3.
D. D6 thihdm sr5 c6 hinh d4ng
Trong kh6ng gian v6i hQ trUc tgadQ Oxyz,cho
hai tliiim A(1;-2;3) vdB(5;4;7). Phuong trinh mflt ciu
nh4n l,B ldm duong kinh ld
A.(r-D2 +(y+2)2 +(z-3)2 =t7.
B. (x 
-3)z + (y -l)2 + (z - S)2 =17 .
C. (x 
- 
5)2 + (y 
- 
4)2 + (z 
-7)2 =17 .
D. (x-6)2 +(y-2)2 +(z-10)2 =t7.
Khing dinh ndo sau d6y ln sai?
IA.2017', ZOn ex>-1.
B. Hdm st: y =lsgr2* x6c dinh khi x > 0.
C. D6 thi hdm s5 y = 2* vd y= [1)' aai ximg nhau quaJ I tt
tryc fung.
D. Ntiu ln(x 
-1)(x- 2) = ln(x *l) + ln(x - 2) thi x phii
nghidm dung b6t phuong trinh (x-1)(;r 
-2)>0.
Cho s6 phirczl:7+2i, zz=3+i. M6dun cria
si5 phtc z1+2z2bdng
A. 65. B. 65. c.21. D. J2t.
SO phfc 1i6n hqp v6i sii phuc
z=(1+02 4!+2il2 tit
A. 
-9*10, B.9+101. C.9-10,. D. -9+10t
Trong kh6ng gian vdi hQ trqc tgadQ Oxyz,cho
L =l +ai
"lduongthdng d :1v=t vamit phlng
l: = _2 _3t
(P):2x+y+z-2=0.
Giao di6m M cria d vd (P) c6 tqa d0 ld
A. M(3;1; 
-5).
C. M(a; 3; s).
B. M(2; r; 
-7).
D. M(1; 0; 0).
S. a=(2; 0; 2).
C.a=G\ 
-3; 5).
B.a=Q; _3; 5).
p. 6 = (-1; 3; 5).
Ndu Y: 9'+2017 thi Y'1ln Z1 bang
A. 2017 . g. ,201e . C. 2e2017 . D. 2oll + e.
Trong kh6ng gian v6i h€ trUc tgadQ Oryz,cho
vectoffi=(0; 1; 
-1) vd M(l;O; 2) thi toa d6 ttitim
ryld
A. N(l; 1; 1). B.N(-l; 1; 
-3).
C.N(-l; 
-1; -l). D.N(l; -l; 3).
Gii su hdm sii / 1i6n tpc tr€n khodng K vri
a, b, c lit Ua sO b6t ki thuQc K. Khing dinh ndo sau
dAy ld sai?
aba
A. If{x)ax=0. B. !f (x)&=-!ffia*.ouurob
c. lf{iax+ [f(.)dr= lf @)dx, c e(a; b).
bb
o. lf{iax= I"fqat
, 
^ 
TOAN HQCll'ctrdi[@
A.2x-y-4=0.
C,2x+1t+4=0.
t. |+\+i:o
B.2x-1'+1-0.
D.2x+y-4=0.
.,,; . Bd A gui 100 triQu vdo ngin hdng theo the
thuc ldi kdp (d6n ki han md ngurri gui kh6ng rut lii ra
thi ti6n lii dugc tinh vdo v6n cua ki k5 ti6p) v6i lai
sultlyo m6t ndm. H6i sau 2 ndm bir A thu duoc lii ld
bao nliSu tgia su ldi su6t kJrong thay doit?
A. 15 (triQu d6ng) 8.14,49 (triQu d6ng)
C. 20 (triQu d6ng) D. 14,50 (triQu d6ng)
Cho hinh ch6p S.ABCD, d6y ld hinh chir nhAt
ABCD c6 BC =2A8, SA L(ABCD)vit M lit didm tr6n
c1nh AD sao cho AM =AB. Gsi ,'r, l'2 lAn lu-ot lA the
tich cua hai kh6i chop S.ABM va S.-4BC thi $ bingl/.
A.i B.* c.i
o
Ciu 16. Gi6 tri nio ci:r. a d€, !{l*' +Z\a* = a3 +2 ?
0
A. 0. B. 1. C.2. D.3.
Cau 1 7. Nguyen hdm cua hdm si5 f @) = d (l-2017 e*) lit
A. lf @)dx = d + 2or7 e-' + C.
B. lf 61at = "' .2017 e-' +C.
c. [f@)ar="* *20]1 "-'*c.
t. [f {iax=e'-20-}7 u-'*c.
Ciu 18. Trong kh6ng gran voi hQ trUc tpa dQ Oxyz, ggi
(ct) ld m[t pheng cit ba t4rc taa d9 tai ba di6m A@; 0; 0),
B(0;-2; 0), C(0 0; 6). Phucrng trinh cira (cr) ld
i r,,, , Cho hdm sO y=(x-l)(x+2)2.Trung di€m crla
do4n thing nOi hai di6m cuc tq cua d6 thi him s6 nim
tr6n duong thbng ndo du6i dny?
CAu 21. Cho hai st5 phric 4=a+bi vir z2=a-6;
(a,b e R vir z2*0 ) Hay chqn c6u sai?
A. z1+ z2ld s6 thUc. B. z1- z2U s6 thuan ao.
C. zlz2lit sO thyc. o. 4 ta s6 thuAn 6o.
Z2
Ciu 22. C6 bao nhi6u duong tiQm cqn cua ttii thi hdm
. 
-tl
s6 v=-4?
' 
'lq*' +2x +l
A. 1. 8.2. C. 3. D.4.
Ciu 23. Di€m bi6u di6n s5 phhc z th6a mdn
(3 + 2i)z :5 
-l4i c6 tqa d0 ld
A. (-l 
-a). B. (L -a). c. (-L a). D. (-a; -l).
Ciu 24. Trong c6c phuong tinh du6i ddy, phuong
trinh ndo c6 hai nghiQm li 1ti.6.
A.xz +i.,Ex+l:0.
C. x2 
-2x+ 4=0.
CAu 25. Trong kh6ng gian v6i hC trUc t1a dQ Oxyz, cho
duong thnrrg O, --r=+=+ vd mflt phing
(a):2x+4y+62+2011=0. Trong c6c mQnh d6 sau,
mQnh dC niro dring?
A. d song song v6i (cr).
B. d citnhrmg kh6ng vu6ng g6c v6i (o).
C. d vu6ng g6c v6i (o).
D. d ndrmtr6n (o).
Ciu26. Chohinh ch6p S.ABC, diry ABCldtamgi6c
d6u canh bing a, SA I(ABC) vd SB hqp vcri d6y mQt
g6c 45o.Xdt2 cdu:
(l) Th6 rich cua hinh chop S.ABC ld V :':f .
' t2
(II) Tam gi6c SAB ld tam gi6c cdn.
HEy chgn cdu dring.
A. Chi (I) dnng. B. Chi (II) dfng.
C. Ca 2 d[ng. D. Ca 2 sai,
CAa 27. Phuong trinh 5'+1 +6.5'-3.5'-1 =52c6 m}t
nghiQm duy nh6t xs thuQc khoing ndo ducri ddy?
A. Q; 0. B. (-1; 1). C. (1;2). D. (0;2).
Ciu 28. Hdm s6 y=Ex-f ddng bi6n tr6n kho6ng
nio ducri ddy?
A. (-;o; l). B. (0; 1).
n. i+\+i=t
B.:r2+2x+4=0.
D.12-2-r-4=0.
C. (l; 2). D. (1; +"o).
D.+
C.3x-6y+22-1,2:0. D.3x-6y+22-l:0.
Cffu 19. DiQn tich ba m[t cria hinh hQp cht nhpt bdng
2Ocm2,28cm2,35cm2.rn6 ticn cria hinh hQp d6
bing
A. l60cm3. B. 190cm3. C. 140cm3. D. l65cm3.
Ciu 20. ci6 fi lon nh6t cua hdm s6 .11*S=t !^20 +{*1
tr6ndopnfl; 4] ld
4.9. 8.32. C.33. D.42.
"e 
nrr,rr-rora, 
T?H#ff 13
B i€t\og2 = a, log3 = b thi log ffi tinh
theoavdbbdng
A.2blo_2. kb-2n-2. r.3h+g-2. r. b+3:t-2.l*3-'3"'3
Vdi gi6 tri ndo cua x thi hdm s6
y=-log3x+log3x c6 gi6tri lcrn nh6t?
B. Jr. c. 6. D. ?
Gi6i phuong trinh: 2 1og3 (;r 
- 
2) + 1og3 (x 
-4)2 = g.
M6t hqc sinh ldm nhu sau:
. ("> f
Battc l. Dieu kign: { ' '^ (*).lx+4
Budc 2. Phu<rng trinh dd cho tucrng tluong vdi
2 log3(x 
- 
2) + 2logj(.r 
- 
4) = Q
Budc 3. Hay ld 1og3(x 
-2)(x-$=0
e(x-2)(x-4)=le x2 
-6x+J =0
ex=3!Ji. OOi ctri6u voi DK (*), suy ra phuong
trinh dd cho c6 nghi€m ld x=3+J1.
Bdi gi6i tr6n dtng hay sai? NEu sai thi sai o buoc ndo?
T4p hqp c6c di6m trong m6t phing phfc bidu
di6n c6c s6 phuc zth6a min )z+2i)--11d dudng tron
c6 phuong trinh ndo sau ddy?
A. (x + 2)2 + y2 =7. B. x2 + (y +2)2 =1 .
C.x2 +y2 +41t-3=0. D.x2 +y2 +4x-3=0.
Cho kh6i 15ng try tam gi6c d6u
ABC. A'B'C' c6 canh d6y bing all vit m6i met b€n c6
di6n tich bing 4a2.ThC tich ttrOi tang tru d6 ld
A.+
J
A. Sai6bu6c l.
C. Sai & bu6c 3.
A.2a3,[6.
".u* C.o316. ". +
t-
Giai bdt phuong,rirr-r f .1l'.[+']'\Js; l.Js;
MQt hgc sinh ldm nhu sau:
Buoc 7. Di6u ki6n x + 0 (*).
r /r\1 /r\5 rBroc2. Yi 'e < I ndn I i_ | <l+ I .='15v) \v:7 \J:7 x
Buoc 3. Tir d6 suy ra 1> 5x e r < -1. Viy tap nghi€m5 '," -
cua bdt phuong rrinh da cho ld S =[--, l'l tot\ Jl
Bdi giai tr€n dfng hay sai? N6u sai thi sai d bu6c ndo?
B. Saidbuoc2.
D. Efng.
A. Dtng.
C. Sai & bu6c 2.
B. Sai 6 bu6c 1.
D. Sai O bu6c 3.
MQt c6i th6p hinh n6n c6 chu vi d6y bang
207,5 m. MOt hoc sinh nam mu6n do chidu cao cria c5i
thrip di lam niu sau. Tai thryi diem nao do. c{u do bong cua
minh dai 3,32 m vd d6ng thcri do dugc b6ng cua c6i thrip
G6 nr chan *r6p) dai 207,5 m. Biet c4u hoc sinh tl6 cao
1,66 m, h6i chi6u cao cua c6i th6p blng bao nhi6u mdt?
A. h =103,75 + 51'875 B. /u = 103 + 51,87n7t
c. tt-tos,ls+25P4 D. h=103,75.
Cho hdm sO 71r.t=ln(x2-3r).T4p nghiQm
cua phuong trinh /'(x) = Q l|
A. (-co;o)u(3:+co). , {;} c.{3} D.o.
MQt qud b6ng bdn duoc dflt ti6p xric voi t6t cd
ciic mit cta mQt crii hQp hinh l6p phuong. ti sO tn6 tich
cua phin khdng gian ndm trong h6p d6 nhrmg nim
ngodi qua bong ban va thd tich hinh hop la
A. L:n. B. I C. 6:4. D. 
=2I 4 6 --3
Di6n tich hinh phing gioi han boi d6 thi hdm
s6 y = 2vz 
- 
ra vir truc hodnh ld
A. q4 B. ryQ c.4.,8. D.2.,0."' t5 rs
MQt c6i m[ bing v6i ctla nhd do thu4t v<yi ciic kich
thuoc nhu hlnh vE. H6y tfnh t6ng di6n tich vii cAn c6 dd ldm
n6n c6i mt d6 (kh6ng ke viAn, mep, ph6n thria).
A. 700n (cm2).
B. 754,25n (cm2).
C. 750,25n (cm2).
D. 756,25n (cm2).
35cm
So s6nh c6c tich phdn
fr
l2l
l= !'lxdr.7= Jsin2x.cosxdx. K = [xe'dx.100
Ta c6 kOt qud ndo sau dAy?
A.I>K>J. B.I>J>K. C.J>I >K. D. K>I>J.
{ / TOff FpCl+ ' cltdifie sd a?4tll-mlot
x2 +mx+l 
. Tim rz dc hdm s6Chohdmso y- 
.y+m
d4t cgc dqi tqt x =2? MQt hqc sinh ldm nhu sau:
Bu6c L D =R\{-ru},r' - x2 +?mx +42 -7 .$+mr
Babc 2. Hdm sO d4t cqc d4i tai x =2 <) I'(2) = 0 (x)
Bxctc 3. 1*'1 <+ m2 + 4m + 3 :, *l; 
= -:
Bdi gi6i tr6n dirng hay sai? NC* ,ar thi sai 0 budc ndo?
(P) sao cho \tttl + ut + tttcl nho nhAt 1d
L. (4;-2;-4). B. (-1; 2; 0). C' (3;-2;-8). D. (1;2;-2).
Cho hinh 16p phuonglBCD.A'B'C'D'c6 canh
bing a.X6t 2 c6u:
(I) Khodng c6ch tu
, a',1)0 =- . -
(II) Hinh 1Ap phuong
dOi xrmg.
Hdy chon cAu dting.
A. Chi (I) dfne.
C. Ca2 ding.
A d6n m[t ph6ng (A'BD) lit
ABCD. A'B'C'D' co 9 mflt Phing
A. Saitubu6c 1.
C. Sai tu bu6c 3.
B. Sai tu bu6c 2
D. Ditng.
C.m+O. D. MOt ktit qu6
Gi6 t4 cua nd6 ducrng thing y=2x+mcbt
dudng cong / = #+ tai hai di6m phan biQt la
A. m+1. B.m>0.
kh6c.
Voi gi6 tri nguydn ndo cua ft thi hdm s6
) =kxa +(4k_5)x2 +2011 c6 ba cgc tr!?
A..k=1. B.k=2. C. k=3. D. k-4.
V6i gi6 tri niro cua tham sO m thi hdm s6
), = sinx-cos x+2011Jlmx d6ng bi6n trOn lR ?
A.m>2011. B.m>0. c.*> 
^uL 
D.*>-#
vd D cira cgc (nhu hinh vE). H6i ta ph6i d6t chOt o vi tri
niro tr€n mdt d6t d6 t6ng d6 ddi cua hai sqi ddy d6 ld ngin
nh6t.
L. AM =6 m,,BM=18m. B. AM =7m, BM =llm.
C. AM =4m,BM:20m. D. AM =12m, BM =12m.
Trong kh6ng gian v6i hq tryc tga dQ O-t12, cho
mpt phang (P):x-y+z+3=0 va ba diem l(0; 1; 2),
B(1; 1; 1), C(2; 
-2; 3).Toa dQ cua di6m M thuQc
B. Chi (II) dung.
D. Cd 2 sai.
Tinh the tich I cua vdt th6 nim giira hai mit
phing x = 0, x = 1, bi6t ring thitit diQn cua vat th€ bl c6t
boi mat phing vu6ng goc voi trr,rc Ox tai diem c6
hodnh dO x (0 < x < 1) ld mQt tam gi6c d6u c6 c4nh ld
41C(Ht
A. r 
-4\EQtn2-l). B. v =4$QtL2 1).
c. v 
-BJlQln2-r). D. v =16r(21n2-1).
Trong khOng gian v6i hQ truc tqa dQ Oxyz,
Ir=2+r
,l
cho ducrng thang d :l) =l + nrt va mdt cau
lz - -2r
(S): 
.r2 +y2 +12 
-2x+6y-42+13=0.
C6 bao nhiOu gi6 tri nguy6n cira m d6 d cat 1S) t4i trai
diiim ph6n biet ?
A.5. 8.3. c.2. D.1.
Cho crlc hdm s6 y = I (x),l, =.s(x), 
"- 
= 
f \.*) .r ''\"") g(r)
N6u c6c h$ s6 g6c cua cdc titip tuy€n cua c6rc d6 thi c6c
hdm s0 dd cho t4i di6m c6 hodnh d0 x = 0 bing nhau vir
kh6c 0 thi
I 
- 
| 
' ,-l .A. /(0); D. /(0)+ 4 + -4
PHAM TRQNG THU
(GV THPT chuv€n Nguvin Quang DiAu, D6ng Thap)
TOflN HO( . 
-siSaza(u-zore) i ctrudi6f )
C6 hai chitic coc cao 10m vd
30m lan hqt dit tai hai vi tn A, B.
ei6t khoang c6ch gita hai cqc bang
24m. Nguni ta cho.n mQt c6i ctrOt O vi c
tt M rl)nm{t t#tnim gita hai ch6n 10
cOt d0 grang day nOi d6n hai dinh C A' fu
thLi'c thi trirc nghient n(ry'. Tt'an trotrg tim cm.