[r]
(1)so co vA or euANc rnr
TRUoNG THPT cnuv0lv r,0 euf pON
lr^^
Dfr THr rn0 r0r NGffiP THPT NAwI zozo VTON TOAN
Thdi gian ldru bdi 90 philt, khdng kd thdi gian gtao di
(Di thi sim c6 trang)
Cffu 1 Gi6 st F(x) ln m6t nguy6n hi.,rn cria hhm s6 /(x) vi G(x) lir m6t nguy€n him cria him s6
g(x) H6i Lt fr"g diuh nio du6i ddy sai?
A f'(;r) + G(x) li mOt nguy6n him cria f (x) + g(x).
B.kF(x) li mQt nguy6n hd,rn cria kf(x) (vdiklir mQt hhng s6 thqc)
C F(x) - G(x) li m6t nguyEn him cfia f(x) - S@).
D.F(x)G(x) li m6t nguy6n hhm crta f@)s@).
Cdu2 Cho him s6 y = f(x) c6 bing bi6n thi0n nhrt sau
x -@ -3 *oo
v 0+0
v
+oo
2 -oo
H6i ham s6 Oa cho d6ng bi6n tr6n khoing nio du6i ddy?
A.(2;3) B (-3;2) C (2; +oo) D (-m; -3).
(x-t-t
I
CAu3 Trongkh6ng gianOxyz, cho dttdng thing d , ly=2+3t 0 e R).MQtvec-td chi lo-\-t
[(-J-',
phrrong c:0ra dlit
A.iq = (1;3;-1) B.iz = Q;2;5) C.it = (1;3; 1) D,iz = (-1;3; -1).
Cffu 4 TiQm cfln ngang cfia d6 thi him s6 y -
=
li tludng thfirg
5-X
2
A.y=- B.y=-l C.y=-z D.y=3.
Ciu 5 C6ng thrlc nio dudi day dtng tld tinh thd tich V cria kh6i ch6p vdi diQn tich driy B vi chidu caoh?
d,.v =
f,nn,
2
CAu 6 NCu
Ir(x)dx = 3 thi n.v =
!nn.
2
Iu
c.v = !nn. D.V = Bh
(x)-x)dx-0
Ma d6 thi 3s7
(2)-l
Ciu 7 Trong khdng gian Oxyz, hinh chi6u vu6ng g5c cira didm A(-1 ;2;1) tr6n truc O1' co toa
d0le
A (0;0; 1) B (0;2;0) C.(-1;2;0) D'(-1;0; 1)' cau 8 o6 ttri him s6 ndo drr6i day c6 dang nhtt drrdng cong
hinh b6n?
A.y= -x4+2x2-7- B.Y= x4+2x2. C.y = -xa +2x2 D.Y = xa -2x2.
v
o x
CAu 9 Nghi6m cria phrlong trinh 2'-s = 4lb,
A.x=] B.x=-1 C.x=9 D'x=5'
Cfiu1.0 NOuZ -2- 3lthiz=
A -Z - 3i 8.2 + 3i C- -2 + 3i- D'2 - 3i'
Cffu 1 1 Ydi a 1)r s6 thgc dttong tioy !',log,,5a bXng v6i
1
I
d,.)bgra B.2log2a C.logra D' l'log2a'
CdaL2 Tip x6c dinh cria hhm s6 y = log(x - 1) lir
A (0; +m) B (-1; +oo) C (1;+m) D [1; +oo)'
Ciu 13 M6t kh6i l[ng rrg c6 di6n tich drly bhng vi co thd tich bhng thi c6 chi6u cao bhng
L.2 B 3 c.6 D.4.
Ciu 14 Trong kh6ng gtan Oxyz,khoing c6ch tr) di€m M(1;2;l) d6n m[t phing (P) : x - 3y +
z-l=0bhng
s Vl I Vls ^ 411 ^ln
o.- ir' B li c.t D 3
C6u 15 Cho c6c s6 thgc a va b th6a mln tog, (s, 16,) = lo816 5 Kh8ng dinh niro dudi tldy
&ing?
A.a+4b=4. B.Za*b-1. C.2a+4b-4 D.2a*b=4
Ciu 16 MOt c6p s6 c6ng c5 hai s6 hang dAu ti6n lAn luot li 1 vi 4, h6i s6 hang thrl 5 bXng bao nhiOu?
A.13 B 16 c 10 D.].
Cffu 17 Goi D quanh trgc
3
Dldhinhphfrng gi6ih4nb6icric drtdng y = lx,y = 0, x = I vix = 3 Khi quay hodnh, ta thu drroc mr6i trbn xoay v6i thd tichV drrgc tinh b6i c6ng thrlc
333
c.v = n
[*a*
A.V=r D.V=
^lia*.
Ciu 18 Trongkh6ng gianOxyz,m{tcAu (S) : x2 +y2 +22 -8x+ 10y'62+25 = 0 c6brin kfnh
bing
A.ts B \frs c.zs D
fia* B.v=
(3)
Ciu 19 Cho hai s6 phrlc Zt = 2- i vI Zz = l + 2i I{hid6, phAn io cira s6 phrlc ztzzbing
A.3 8.3'. c -2. D.-2i.
CAu 20 C6 bao nhi6u c6ch chia g6i qui gi6ng nhau cho drla tr6, cho cring c6 qui?
A 10 8.6. c.20 D 15.
Ciu 21 Cho him s6 U6c b6n trtng phuong y = f ("r) c6 dd thi nhu hinh v6 b0n 56 nghiOm cria phrrong trinh
{ f(x) = ;lir4
v
1
4.4. c.2.
8.3.
D l.
B (-1;3).
-1 0
-1
D. tfiat
x
Cin22 Cho hdm s6 71x; c6 bing x6t d6u clita f,(x) nhu sau
x -@ -2 0 2 *oo
f'(x) +0 0+
S6 Aldm cuc tri cira hhm s6 Aa cho li
A.3 8.0 c.2. D 1.
ciu23 Tdng m6-dun cdc nghiOm phrlc cria phuong trinh z2 - 6z + 25 = 0 bing
4.14 B 10 c.6. D.8.
Ciu24, Tdp nghiOm cta b6t phrrong trinhloglx-2log2x-3>0li o.(o'
i) u ,t,**,.
C (-*; -1) u (3;+oo).
Cda26 X6t tich phdn
thhnh"
A. tfiat
D oo I U (8; +oo)
2
Cffu 25 Di6n tfch cria m{t cAu ngo4i ti6p hinh h6p chfr nh6t co c6c kfch thrrdc li 1, 2 vi 3 bXng
4.49r ' 8.6n C.2Bn D.l4n.
e_
ruEf ;- pi-^ c6ch ddi bi6n s6 r = hx,
tich ph6n dang x6t tr6 J x u4' uq,6
I
I
e
B.
[, a, C.{, dt
I
Ciu27 Tpp nghiQm cria b6t phrrong rrinh lnx < 1 li
A (-oo; 1) B (1; e) C (0; e) D (-oo; e).
Ciu 28 Cho hai s6 phrlc phdn bi6t 71vd Zz H6i trong mdt phfng phrfc, tap hgp cric tlidm bidu di6n cta s6 phric z li mQt drrdng th8ng n6u didu ki6n nio du6i day drrgc th6a m6n?
A.lz-zl=1 B.lr-zi+lz-zzl=la-zzl.
C.l,-zzl=L D.lz- zi=lz-zzl.
(4)Cit 29 Trong khong gian Oxyz,cho hai didm A(0; 2; 1) vh B(2; -2;-3)' Phrrong trinh mdt cAu drrdng kinh AB li
A.(x+ l)2 +y2 + (z- l)2 = 6 B (x- 2)2 + (y +2)2 + (z+3)2 =36' C.xz +(y-D2 +k-l)2 =3 D.(x- l)z +y2 +(z+ l)2 =9.
Ciu 30 Goi Mli gi6 tri t6n nh6t cira hhm s6 f (x) =
+ + -2x-1 tr6n doan [0; 2] 'Tinh gi6
tri cria bidu thfc P = 6M + 2020
A.P=2007 B.P=2019 C.P = 2014 D.P = 2018
Cflu 31 N6u m6thinh n6n c6 chi6u cao vibrin kinh tt6y ctng bXng thi c6 di6n tich xung quanh
bing
A.4{2r 8.4r C.8zr n.8fin'
Ciu 32 Trong kh6ng gian Oxyz,cho hai tlidm A(1; 2;-3) vi B(-3; 2;9).Mlfiphing trung tnfc
cfia doan thing AB c6phtrong trinh lir
A.x- 3z+ 10 = 0 B.-4x+ l2z- 10 = 0' C.x- 3y+ 10 = 0 D.x+ 3e + 10 = 0'
Cffu 33 56 giao didm ctia d6 thi hirrn s6 y - *l* - 3l vI dudng thing y = 2lb,
A.3 8.4 c.2 D'6'
Cffu 34 dh* hirih rxl*p s*$ sJg#ffi cs nsnh her bfol$ *anh s*f It*i S&s Sffis hei m&r #dx* {#ds} vh (SAD) gAn nhAt v6i k6t qui nho dtt6i dAy?
A.89"31', 8.61"28',
Cffu 35 M6t hinh n6n vi m6t hinh trg c6 ctng chi6u cao hvi b6n kinh ddy r, hdn nfra diQn tich
xung quanh cria chring cflng bing nhau Khi do, ti s6 1 UXng r
.+
c.70'32',.
C \6.
D.109"29',
D.2. z+2 vi
m4t phfing (P) :
4.,
x-7 y
Ciu 36 Trong kh6ng gian Oxyz, cho dttdng thhng d :
2x + y + z - | = 0 Ggi A ld dudng thing nhm (P),
2
catvi vu6ng g6c v6i d.Yec-td nho drr6i
v t-3
dAy lh m6t vec-td chi phttong cria A?
A.iz = (r, -rt -f,) B.i r = (-1 ; -2;o) C,iz = (1; -2; 0) D.it =(r'-I,-l) cffu 37 Cho hirm s6 bac 4 trtng phrtong y = f (x) c5 d6 thi nhu trong
hinh v6 b6n H6i tl6 thi hhm s5 y = lf (x)l c6 t6t cirbao nhi6u didm crrc
tri?
A.2 8.3.
c.4 D.5.
Cfiu 3g Cho kh6i lip phrrong r vi goi B la kh6i b6t diOn d6u c6 c6c dinh 1)r tdm cdc mdt crfra L
Ti s6 thd tich cria B vi l, li
o x
1 1
(5)Ciu 39 Tfnh tdng tdt cac6c nghi0m cria phuong trinh
x * I = 2log2(2" + 3)- logz (zozo - 2'-.)
A.2020 B.logr 2020 C.log, 13
Ciu 40 Tr1 diQn ABCD c6 cdc cpnh AB, AC vit AD d6i m6t
vu6ng g6c vi c6 tlQ dai hn lugt ld 2,2vd 3 Gqi M li trung
didm cria Dc.Trnhkhoing c6ch girla hai dudng thtng AM
D
D 13
M
vd BC
122
A _.
6
C
B. 3
.'122
11
n ''[5 ,, 2f
.-.2, u
3
Cfiu 41, Sdn vrldn nhi 6ng An c6 dang hinh chfr
nhat, v6i chi6u dDri vh chi€u r6ng Dn lugt th m6t
vh m6t Tr6n d6, 6ng dho mQt c6i ao nudi cri hinh
b6n nguyQt c6 brin kinh bing mdt (trlc li lbng ao
c6 d4ng mdt ntla cria kh6i trq c6t bdi mIt ph8ng qua ' truc, tham kh6o thdm hinh vE b6n)
Phin dat dho 16n, 6ng san bing tr6n phAn vrJdn cbn lai, vd lam cho m{t ndn cria vrldn duoc ndng l6n 0,1 met H6i sau khi hoin thanh, ao cd c5 dQ sdu bing bao nhi6u? (KOt qui tfnh theo don vi m6t, lim trbn d6n hhng phAn trim.)
A.0,71 m6t 8.0,81 m6t C.0,76 m6t D.0,66 m6t
Cdu 42 C6 hQp dung bi, h6p thrl nhAt drlng 10 bi xanh, h6p thrl hai drrng bi xanh vI5 bi tt6,
hdp rhrl ba dgng 10 bi d6 Ngudi ta chon ngdu nhi6n m6t h6p, sau d6 b6c ng6u nhi6n vi0n bi
ttr hQp d6 thi drrgc cf, bi mhu xanh H6i nOu tiOp tuc b6c thOm vi6n bi nria hQp d6 (hai bi da
b6c trd6c d6 kh6ng dugc tri lai vho hQp) thi x6c su6t b6c tlugc bi xanh bing bao nhi6u?
^.# B.; *I ".#
Ciu43 TrOnm[tphing toad6, cho drrong cong (C) 1y = x4 -4x2 +2vb,hai didma(-f;O), A (",12;O) CO tdt chbao nhi6u didm tr0n (C) md tdng khoing c6ch ttt tlidm tl6 dOn cric didm A vh
B bXng 216?
A 3 8.7 c 6 D 1
Cda44,Timt6tchc6cgi6trithr1ccriathams6md€hims6y_#ddngbi6ntr€n
khoing (r'i)
A.m e (2; +m) B.m e (-*;01 C,m e U;2) D.m e (0; +oo)
CAu 45 Cho hlm s6 /(x) th6a mdn.f(0) = O, f(2) - 2vdlf'@)l < 2,Yx e R Bi6t rhng tflp t6t
2
ch cdc gi6trl cria tich phin Ir(x) dr lir khoing (a;b),tinhb - a B
0
8.2.
(6)CAu 46 Cho him s6 71x; c6 b6ng bi6n thi6n nhu sau
x -oo -2 J *oo
f'(x) +0
f(x)
5
J
-oo 2
56 nghiQm thuQc nrla khoing (-*; 2o2}l cr3ra phrlong trinh 2f (f (2x - 1)) + = 0lir
A.5 8.4 c.3 D.2.
Cil47 Cho hl,rn s6 .f(x) - * - *' : * Gqi S li tdp t6t cir cdc gtdtri thgc cfia tham s6 m d€
x+ I
gi6 tri t6n nhAt cria him s6 g(x) =" tif*>ttrOn doan U;21 datgiri trf nh6 nhAt Tinh tdng c6c phAn
tt cria tap hop S
A.o B 1 c.i
".-;
CAu 48 Cho a ld m6t s6 nguyOn kh6c kh6n g vit b li m6t s6 thgc drrong th6a mdn ab2 = log2b. H6i s6 nio 1)r s6 trung vi trong ddy 0, t,a,U,ll
A.a B.; c.1 D.b.
Ciu49 C6tdtcibaonhi6u capcitcs6nguyon(x;y)th6a ^un'o1,!:'r,.2:-\").!l .n
log2\z + y'- 1)
A 5 8.4 c.2 D.6.
Cffu 50 Cho hinh ch6p ddu S ABC c6 tAS B = 30o M6t mlt phing thay ddi qua A c6t c6c canh
SBviSClAnltrqttfl Mvi.N.Tinhtis6thdtichcriacr4ckh6i chopS.AMNvdS.ABC khichu vi tam gi6c AMN dat giittri nh6 nhAt
A.2(16-,) ".'+ C a(16- t)
D.2(2- 16).