G(.r) li mQt nguyOn hi,rn cfia /(x

Ma

da

thi

468

Cflu 1.

MOt

kh6i

Hng

trg

c6 diQn rtch d6ry bHng 3 vir c6 thd tictr bXng 6

thi

c5 chi6u cao

bing

A..6. 8.4. c.3. D.2.

Cfiu 2. Gii

sfi

F(x)

^{ld mQr nguyOn} hhrn ^cfra hhm s6

/(x) vi G(x) li

mQt nguy6n hdm cria hi,rn s6 S(x).

H6i khing dinh nio

dtr6i ddy sai?

A.kF(x)

th mQt nguy6n hl,rn cria

kf (x) (v6i

k ld mQt

hing

s6 thUc).

B. F(x)G(x)

lh mQt nguyOn

him

cria

f(x)s@).

C.

f(x) +

G(.r)

li

mQt nguyOn hi,rn cfia

/(x)

⁺ S(x).

D.

F(x) - G(x) li

mQt nguyOn hi,rn

cta f(x) -

S(x).

sd cu vA or eUANG rRI

TRUoNG THPT CHUYoN r,f, QU'f OoN

i c- .i.

uE rm rn0 r0r

^NGHT0P

rHPT NAM

²⁰²⁰

IUON

TOAN

Thdi gian ldm bdi ⁹⁰

phfi,

kh6ng kd thdi gian giao

di

(EA thi g6m cd 6

tang)

D.

-1.

D.y=3'

2 2

Irn'

0

Cdu

3.

N€u

)dx=3thi [,ro )-x)dx=

0

A. 1. B.5. c.2.

CAu

4.

TiQm cfln ngang cira d6

thi

hhm s6

y = Tli

^thrbng

thing A.y=t.

2

B.y=-2. C.Y=-1

^.

CAu

5.

Cho hhm s6

y - f(x)

^c6

bing

^biOn thi6n nhrt sau.

x -oo

^{_Ja 2}

too

v 0+0

v

+oo ¹J

2

-oo

H6i

hem s6 Ca cho d6ng biOn tr6n khoang nAo

du6i

day?

A.(2;3). B.

^(2;

+oo).

^C.

(-3;2).

D.

(-oo; -3).

Cffu

6.

Trong khOng gian Oxyz,

hinh

chi6u vu6ng g6c cfia tlidm

A(-1;2;l)

^trOn

tryc

^Oy

c6 tga

d6la

A. (0;0; 1). B. (0;2;0).

C.

(-1;2;0).

^D.

(-1;0;

^1).

Cfru

7.

Thp xdc

dinh

cria hhm s6

) = log(x -

^{1) 1I}

A.

^(0;

+m). B.

^(1;

+m).

^C.

(-1; +oo). D.

[1; ^+oo).

phudng clfr'a

dlit

A.iq = (1;3;-1). B.iz = (-1;3;-l).

Cffu

9.

Nghi0m cfra phrlong

trinh 2*-s =

^4Id,

A.x=5. B.x=9.

C.it = Q;2;5). D.ir = (1;3;

¹⁾

C.x='7 D.x=-1.

v

Cfiu 8. Trong kh6ng

gian Oxyz,

cho

dudn

g

th&ng

d

^:

x--I-t

y =

²

+ 3t (r e R). M6t vec-to

^chi

1-J-t

x Cffu 10.

Ydi a

li

s6 thrrc dttong t.iu,y

i,,log.lrc

^bhng

v6i

A.log2a. n'f,,,s" C.',lllogra. D.2logra

CAu11.

NOuZ

-2-3i thiz=

A. -2 - 3i. 8.2 - 3i C.2 + 3i

^D.

*2 + 3i.

Cial}.

C6ng

thtlc nio

drr6i ddy

dtng

dd

tinh thd tich V

cria

kh6i

ch6p

v6i

diQn

tich

dity

B vir

chidu

caoh?

A.V = -Bh -

_J1

1

6

o.v - lnt

₂

B.V=

Bh.

C.V =

Bh.

CAu 13.

D6 thi

hdm s5 nho drr6i ddy c6 dang nhu drrdng cong trong hinh bdn?

A.y = -i +2x2 - l.

C.Y =

^x4

+2x2.

B.y = -x4 +2x2.

D.y =

xa

*2x2. o

CAu

14. Tiong kh6ng

gian Oxyz,

khoing

c6ch

til

di€m

M0;2;D dlnmdt phing (P)

:

x -

^{3y +}

z-l=0blng

^+ ,# ".+ ".+

Ciu 15.

Tkong

kh6ng

gian

Oxyz,mlt ciu (S)

:

./ +yz

+ z2

-8x+

^10y

- 6z+25 =

^{O c6 br4n}

kinh

bbng

A.5. B. "t,ffi. C.25. D.75.

Cffu 16.

Cho hai s6 phrlc Zr

= 2- i

vh Zz

= | +

21.

Khi

d6, phAn

io

ctia s6

phtlc azzbdng

A. -2i. B. 3i.

C.

3.

^D.

-2.

Cffu 17.

C6 bao nhi0u c6ch chia 5 g6i

qui

gi6ng nhau cho

3

drtatr6, sao cho ai cfrng c6 quh?

A.6. B. 15.

C.

10. D.20.

Ciu18. GoiDlihinhph&nggi6ihanb6ic6ctludng y= li,) =

^0,

x=L vix= 3.Khiquay

D

quanh truc

hoinh,

ta thu drtoc

kh6i

trbn xoay

v6i thd tichV

drrgc

tinh b6i

c6ng thrlc

3 J

fi

³

fi

I

^[

A.V =r dx. B.V -

^dx.

C.V

⁼

",1*a*, D. V = ,l-*a*.

Ciu 19. M6t

c6p s6 c6ng c5 hai s6 hang dAu ti0n lAn lrrot

li I vI4, h6i

s6 hang

thrl5

bXng bao nhi6u?

A.

13.

B.

16.

c.7. D.10.

Ciu 20. Cho

c6c s6 thrrc

a

^vd,

b

th6a m5n

tog,

(S,.

fSr) =

^log

f 5. Khing dinh

^nho

drl6i

^ddy

dfng?

A.2a*b=4 C.2a+4b=4. D.a+4b=4.

cda2l.

Tdng m6-dun cdc nghiOm phrlc cria

phuong

tr\nh z2

-

^6z

+ 25 =

^{0 bXng}

A.8 8.6 c.

10.

D.14.

Ciu22.

Cho hhm s6 bac b6n

trtng

phrrong

y = f (x)

^c6

dd

fti

nhrr trong

hinh

vE b6n. 56 nghi6m cfla phrlong

trinh

f (x) =

^".

lit

4.4.

+

B.

3.

c.2. D.1.

Cffu

23.

Cho

hai

s6 phrlc ph6n

bi6t

71vd Zz.

H6i

trong

mit phing

phrlc, _t4p hqp cric didm bidu di6n cria s6 phrlc _z

li

mQt drrdng

thing

n6u di6u ki6n ndo drr6i ddy drroc th6a m6n?

B.2a+b-l

B. li at.

^C.

v

1

-1 0

¹

B. l. - zi +

^lz

-

^zzl

= ln -

^zzl.

D.l.- zzl=1.

ln

x, tich

phAn dang

x6t trd x

1

ciu24.X6t tich ,n*

';ffi dx. B[ng

^crich

ddi bi6n

^s6

r =

A.lr- zi = l.

C.lr-arl=lz-zzl.

thinh

ft at

e

A. ,li

^at.

D.

0 0 ₁

Ciu 25.

Tdp nghi0m cria b6t phrrong

trinh ln.r <

¹

li

A. (-oo; e). '

B. (-oo; 1).

C. (0;

e).

D.

(1;e).

Chu

26.

Trong

ktr6ng

giar_ Oxyz, cho hai didm A(0; 2;

l)

^vit

B(2; -2;-3).

^phuong

trinh

^{mat cAu}

dudng

kinh AB h

A.(x- t)2 +y2 +(z+!)2 =9. B.(x+

¹⁾²

+y2 +(z-l)2 =6.

C.(x-

2)2

+ (y+2)z +(z+312 =36. D.x2 +(J-Z)2 + k-1)2 =3.

Cda27.

_{Cho hi,rn} s6

/(x)

^c6

bing

^x6t

d6u

^ctn

f,(x)

^{nhu sau.}

[, o,

x -oo -2

^{0 2}

*oo

f'(x) +0

0

0+

S6 aidm cgc

tri

cria

him

s6 oa cho

li

A.3

^.

B.

1

c.2. D.0

^.

I I

1

CAu

28. Tiong kh6ng

gran Oxyz, cho hai didm A(1

;2; -3) vi B(-3; 2;9). Min phing ffung trtlc

cira doan

thing AB

c6 phrrong

trinh

lh

A..-4x+l2z-

¹⁰

= 0. B.x- 3y+

¹⁰

=

^0.

C.x+ 3z+

10

= 0. D.x- 3z+

10

=

^0.

Cdu29.

Ggi

Mli

^giri

tri

¹⁶ⁿ nhAt ctra hhm s6

f

^@)

= + . + -2x -1

^{tr6n doan} [0; 2]

.Tinh

^gi6

32

tri cia

bidu

thfc P = 6M +

^2020.

A.P=2019. B.P=2007. C.P=2018. D.P=2014.

CAu

30. Di6n tich

cua

mlt

cAu

ngoai ti6p hinh h6p chrl

nhAt

c6

c6c

kich thu6c li

^1,

2 vh

³

b}ing

A.49n. 8.6n. C.lLn. D.28n.

CAu

31.

N6u m6t hinh non co chiAu cao

vi

brin

kinh

riliy ctrng

blng2 thi

c6 diQn tich xung quanh bXng

A.4tr. B.8zr. C. fir. D.8"12n.

CAu

32.

TAp nghi0m

cta

b6t phrrong

trinh log] x - Zlogrx - 3 > 0lh A.(-*; -1) u (3;+m; B. -oo: '2 - I

^{U (8;}

+m)

".(o,i) , ,', **,

^D.

(-1;3).

CAu

33.

56 giao didm cria dd

thi

hhm s6

y =

^x2lx2

-

^{3l vd tludng}

thing ! = 2lb,

4.4

^.

8.3

^.

c.6

^.

D.2

CAu

34. Tinh tdng

tdt

cic6c

nghiOm cira phrtong

trinh

x *

¹

= 2log2(2' +

3)

-

^logz(zOzo

- 2'-.)

A.1og2

2020. 8.2020. C.log, 13. D.13.

Ciu 35.

Cho

kh6i

^16p phuong

L

vh

goi

B

h kh6i

brlt diQn d6u c6 c6c

dinh

lir

tdm cic m\t

^clfra

L.

Ti

s6 thd

tich

cria B

vi L li

I

x

1

D.

6

A.

C. ¹

4 J 2

Ciu

36. Cho hhm s6 bac

4

trtrng phuong

y = f (x)

^{c6 d6}

thi nhtt

^trong

hinh

v6 bOn.

H6i

d6

tfri

hhm s6

y = lf (x)l c6 t6t citbao

nhi6u

didm

crrc

tri?

4.2. B.

^3.

c.4.

^{D. s.}

Cfiu 37.elc hinh *h*p *fu A:xrm ** ewh ll&: bfu€

^,nsrlh

dry. H*i g** *i*s

^{tlei rx6: plrtuW} {,S,{$}

vh

(SAD)

gAn nh6t

v6i

k6t

qui nlo dudi

tl6y?

A.109"29'. 8.7032'. C.89"31'. D.6t"28'.

chobirt*tr$pd&x,x,rar.r

1

v

o

B.

ddy lir mdt vec-td chi phrrong cira A?

A.it =(r,-,-f,) s.i,= (-1; -z;0). c.i+ =(r,-i,-l)

CAu

38.

Trong

kh6ng

gtan Oxyz, cho drrdng thhng

d

^:

2x + y + z

- I =

^0.

Ggi

^A

li

^drrdng

thing nim

trong (P),

A.3. B. i. c.4.

Cia

^{44.T1 diQn ABC}

D

c6 cdc canh AB,

AC

vir

AD

ddi mQt vu6ng g6c

vi

c6 t16 dhi ldn lrrot

li 2,2

^{vd 3.}

Gqi M lduung

didm cfia

DC.Tinhkhoing

cdch gifra hai drrdng

thlngAM vi

BC.

\m p

^{3 1122}

A' 6 ' o' tr

^'

n {1 ^2{1

L' 2' D' 3

^'

4 = 1 = '*=2

^udmdt

phing (P)

^:

cit 2t-3 vi

vu6ng g6c

v6i

d. Vec-to

nio

dtt6i

D,iz = Q;-2;0).

B.me(2;+m). C.me(-*;01. D.me(0;+m).

D.6.

Cffu

39.

MOt

hinh

n6n

vi

^m6t

hinh tru

c6

ctng chi6u

^cao h

vi

b6n

kinh

tl6y

r,

hdn nfra di6n

tich

xung quanh cria chring cfrng bhng nhau.

Khi

d6,

ti

s6

3

_UHng

r

A. 16. B.z. c.r. , +

Cffu

40. Tim t6t ch cdcgi6 trf

thrrc cria

tham

s6

m d€ hims6 y " - i?::-: cosx-m

^d6ng

bi6n

^tr0n

khoing (t,;)

A.m e U;2).

Cau

41.

TrOn m4t ph8ng toa d6, cho tludng cong

(C)

l

! =

^x4

-

^4x2

+ Zvi,hai

^didm

a (- f;

^O),

n

(,,11;O). CO tdt chbao nhi6u didm tron

(O

mn tdng khoang cdch tr)

tlidm

^t16 d6n c6c didm A

vi

B bXng

zlot

A.3. 8.7. c.

^1.

Cia 42.Sdn vrrdn nhi 6ng An c6

d4ng

hinh

chfr nhaL

vdi

chidu dhi

vi

chidu

r6ng Dn hldt li

^{8 m6t}

vh 6 m6t. TrOn d6, 6ng

tlio

mQt c6i ao

nu6i cf hinh

brin nguyQt c6 brin

kinh

bhng

2

mdt (trlc

li lbng

^ao

c6

d4ng mQt

nfta cfla kh6i try

c1t

bdi mdt

phfing qua truc, tham

khio

th6m 6

hinh

v6 b0n).

' Phin

_{dAt dho}

l6n,

_{6ng san}

bing

_tr6n phAn vrJdn cbn

lai, vi

^{thm cho}

m{t

^{ndn cria vrrdn drrgc}

ndng l6n 0,1 m6t.

H6i

sau

khi

hoan thhnh,

ao

c6,c6 dQ sdu

bing

bao nhi6u? ^(KOt

qui tinh

theo don

vi

m6t, ll,rn

trdn

tl6n hdng phAn

tr[m.)

A.0,71 m6t. B.

^0,76

m6t. C.0,66 m6t. D.0,81

^mdt.

Cfru

43.

Cho

hirn

s6

/(x)

^th6a

mdn,f(0) =

^O,

f(2) = 2vd,lf'@)l < 2,Yx e

R.

Bi6trhng

tap t6t ch cdc

gi6tri

_cria

tich

phdn

k,

^{x) dx}

li khoing (a;b),

tinh b

-

^a

D.2.

C

B

D

M

I

cau 45' c6

_{3 h6p} dung bi, h6p thrl nhAt dung 10

bi

xanh, hQp thrl hai dung ₅

bi

xanh

vi

5

bi

d6, h6p

thrl

ba drrng ₁₀

bi d6' Ngrrdi

ta chon ng6u nhion

m6t

h6p, _sau d6 b6c ngau nhi6n ₂

vi6n bi

tt

h6p d5

thi

drloc c6 2

bi miu

xanh.

H6i

n6u ti6p tuc b6c th6m 1 vi6n

bi

nfra d hop d5 (hai

bi

da

o:t ti{u"

d6 kh6ng dugc

tri l4i

vho h6p)

thi

xr{c su6t b6c _dudc

bi

xanh b}ing bao nhi6u?

A.

A-

G n.il c.;

".r;

cfiu 46'

Cho a

li m6t

s6 nguy6n khdc kh6n g vir b

li

m6r s5 thuc _drrong th6a _{man ab2}

= log2b.

H6i

s6

nio ti

s6 trung

vi

trong _ddy 0,

t,a,b,|.t

A.a- B.b. c.t. o.1

cda

47

' cho

^hinh ch6p ddu s

'ABC c6

tAS

B =

^30o.

M6t

^mdt

phing

_{thay ddi} b _qua

A

c6t

c6c

canh 's'B

vi 'sc

lAn

hldt tai M

vd'N.

Tinh ti

s6 ttrd

tich

cria cric

kh6i

ch6p

s.AMN

vit

s.ABCkhi

_chu

vi tam

gidc

AMN

dat

gi|tri

_{nh6 nh6t.}

..:(r5- r)

4

cAu 4g.

Cho

him s5 f(xl -

^x

-

^{m2 + m}

gid,t4Ldnnh6t.u,;;;';;,r.,i,il;::::'1,3'il:;:;,il.#;,H,'#;::^Y"

trl cria tdp hop _S.

E. -1 2 B. u. r. r. c. u.u. o. o. 1.

4 CAu

49. C0 tiltci

bao

nhi6u

cdp c6cs5 nguyOn

(x;y)

_{th6a mdn}

logr(* -

^2x

+

a:+ 11

5

4.2.

8.2(V3 - ,)

B.6.

o.z(z- 16)

v\+t <1?

c.4.

^1og2@2

D. +y2-l)

5.

C6u

50.

Cho

him

s6

/(x)

^c6

bing

bi6n thi6n nhu sau.

56

A.5. nghi.m

thu6c _nrla

kho,ng 8.4. (-m; 2,2orcria

_phuong

c.3. trinh zf (f(2x- D.2.

₁₎₎

+ 3 = 0li

x -oo -2

^J

foo

+0

0

f(x)

⁵

I

-oo

³