Cô ngọc huyền LB đề KSCL cuối HK II lớp 11

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TOÁN 12

SEASON 2023
___/___/___

H TH

O

TOÁN 12 SEASON 2023
KH O SÁT CH
NG
CU I H C KÌ II L P 11 2K5 XPS

TỐN
Phiên b n ghi chép

M: _______________
BON
(vi t t t: the Best Or Nothing).
Cơ mong các trị ln kh c c t
ghi tâm khí ch t BONer:

"N u tơi quy t làm gì, tơi s làm
nó m t cách th t ngo n m c,
ho c tơi s khơng làm gì c .
QUICK NOTE

Th i gian làm bài: 90 phút, không k th

BON 01 Dãy s nào trong các dãy s

*

A. un : un

3n, n

C. un : un

3n 1, n

i

.
*

.

t c p s nhân?

B. un : un

3 n, n

D. un : u1

3n , n

*
*

.

.

L I GI I
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Itt

3hỄ 3

Chỉ

const

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BON 02 Cho m t c p s nhân có u1 5, u6 160 . Tìm cơng b i c a c p s nhân?
A. 3 .

B. 2 .

L I GI I

46

C. 4 .

D. 2 .

595 160
95 32

4195

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

g

2

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BON 03 Cho c p s nhân un có cơng b

O

u1 là

A. u1

1
.
6

B. u1

L I GI I

µ

1
.
16

C. u1

_14

ai9

u2

1
.
2

1
, u4
4

4 . Giá tr c a

1

.
16

D. u1

92 16

9 4
9 4 cl

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Uq 4193 4

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ur

f

uq.nl

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BON 04
2
A. lim
3

0?
n

.

L I GI I

5
B. lim
3

kim
g
kim

n

6
C. lim
5

.

0

nếu

n

D. lim 3n .

.

Glc 1

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3

0

vì 131

1

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Ib page "H c Tốn cơ Ng c Huy n LB"

c

1

TOÁN 12
QUICK NOTE

BON 05 Giá tr c a A lim
A.

.

B.

L I GI I

n2

4n n b ng

.

0D. 2 .

C. 3 .

nhân liên hợp

a

e

Dạng

SEASON 2023

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Ề

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

1h44am

n

BON 06 Cho hình chóp S.ABC
SA vng góc v

S

A. BC

ABC là tam giác cân t i A , c nh bên
m BC , J
m BM. Kh
nh

M

SAC .

B. BC

kin VttfTt1

n

SAM .

C. BC

SAJ .

D. BC

SAB .

L I GI I
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

AABC cân tại A
ASAB DSAC cgc

AMFBC

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

t

n

1

g

Ễµ

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

c

SB 10

ASBCcân tags

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

SMTBC
BCTSM BetAM

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

BCHSAM

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

SM AM C SAM

ggynAm

µg

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

BON 07
A.

lim xk là

k

x

.

B.

.

D. x .

C. 0 .

L I GI I
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BON 08 lim
x

A.
O

.

2 x5

5x 4

3x 2

2 b ng

B. 0

C. 2 .

D.

.

L I GI I

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

ỵỵỵµ ỵ ỵ

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2

.

x 1
b ng
x 2
B.

.

C. 3 .

SEASON 2023

D. 0 .

L I GI I

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

tdtt

ftp.ztxtt

70

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s2t

to x 0t
X 2

1 fgmjf.tt

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x 2
PhácÐồtoán

fI

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tuấnEBOOK
Quyếthạ lođi HKII

Dựng

CPHoá 660trang

BON 10

buổi live chiasẻ
Dự thi n Sau
t i x 1?
H

Hàm s

A. y x2

3x 5 .

O

B. y

x

2

x 2
.
x 1

x 1
.
x 2

C. y

x 4
.
x2 1

D. y

L I GI I

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x2

BON 11

Cho hàm s

5x 6
,x 2
.
x 2
m
,x 2

f x

hàm s liên t c t i x0

Tìm m
A. 2.

2.

B. 1.

L I GI I

0

C. 2.

D. 1.

Ðể kcs bên t.ec thì

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

D

ftp.zflxkfk

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225.46
2 2 0

0

TOI

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fygfaaef.gg

fuỷmz

ỀfỄ _YỂM

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2 3

1

1

m

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BON 12

Ít

A.

x

C.

x

Ch n kh

1
2 x
2

L I GI I

x

, x

nh sau:
.

, x 0.

lương

x

0

x

D.

Nuts

1

B.

x

, x 0.

1
2 x

, x 0.

ú

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Ib page "H c Tốn cơ Ng c Huy n LB"

c

3

TOÁN 12
QUICK NOTE

BON 13

o hàm c a hàm s y

3
7
sin 5x
cos6 x 2021x là
2
3
15
cos 5x 14sin 6 x 2021 .
2
D. 3cos5x 7sin6x 2021 .

3
cos 5x 42sin 6 x 2021 .
2
C. 15cos5x 7sin6x 2021x .

0

A.

L I GI I

sina.cl Eukx cosUcx
fcosucxDIatx sinucx

SEASON 2023

B.

XÝ

ý

3zsin5X tg.co6 1 2021

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

tg.f6x f sin6 7

3z.l5Y cos5Y

2021

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TỆ cos 5 X

14 x hoi 6

2021

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

BON 14

2

A. y

x 1

2

x 1

L I GI I

2

3

B. y

.

x 1

1

C. y

HxTÉỀ

3x 5
là
x 1

o hàm c a hàm s y

3x 5
x 1

O

Ht

t

.

1

D. y

.

3x 5

x 1

2

x 1

3x 5
x 1

2

.

ỄapẸ

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t

ưgf

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i

IXHỶFỀ

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O

D. y

20 x 26 .

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PITI tiếp tuyến của đths g fcx tạiMả hoànhđợxo
t
là
to
fka
y fkxo
2
2 3 2 EM2
27 2 s 3
9x

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fKA

Cứ

ft

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fk

2

3

2

t 2

14

a

20

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y

2

20.1

t C 14

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g

20

1 26

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Ib page "H c Tốn cơ Ng c Huy n LB"

c

4

TOÁN 12
QUICK NOTE

BON 16
A. y

th hàm s y x3

Ti p tuy n c
3x 7 .

B. y

3x2

2 có h s góc k

3 có

3xa 6 X

fhx
C. y

3x 7 .

SEASON 2023

D. y
O

3x 1 .

3x 1 .

L I GI I
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

fka

y

X Xo

tflxo

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hsg k
3
ÐK 3
fhxo
P 3.12 2
fll

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3 0 66

3

Xo

L

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4

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3 x 1

3

y

Ca

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

1

ga

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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BON 17
th ng y
A. y
C. y

YỀỀẮỀẮ
YE

2h17 1 1

a

X 1

L

ấy

Các ti p tuy n c

O3x

th hàm s

o_O

15

3x 1 , y

3x 7 .

3x 1 .

L I GI I

2x 1
, song song v
x 1

y

Mxo yo là tiếp đi

B. y

3x 1 , y

D. y

3x 11 , y

hat

1

ng

3x 11 .

3x 5 .

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

yn fKICX xoltfcxd.CA
3
a
15
faxon
y

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3

3

ỂT

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________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

ha 1

2

1

1Xo

1

1

1

1

fate
20

x3

2x , giá tr c a f

D

y

3

1 Hũ

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

BON 18

Cho hàm s

OA. 6 .

f x
B. 8 .

1 b ng

C. 3 .

D. 2 .

L I GI I

d

IX ề1

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

fkx
f
f

13

2

71 3 2
k 34

2

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fix6.1

2

E 3 2x

6x

b ng

B. n 1 ! .

C. n 1 .

D. n ! .

L I GI I
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

ÐYE

xn

s

nxn 1
nxml

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MẾN Ễ

y g
yỰ y

n

nu

Ể

ẫỈNm1

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1

Nh 1

xmÝ

Mn 1

n 2

xn 3

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yỄẲCn 1 Ch 2

t

cn

me

xem x

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ỳn

nt

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BON 20 Ch n kh
A.

ng th ng cùng song song v i m t m t ph ng thì song song v i nhau.

B. Hai m t ph ng cùng song song v i m t ph ng th ba thì chúng song song.
C. Hai m t ph ng khơng song song thì c t nhau.

0

D. Hai m t ph ng phân bi t cùng song song v i m t ph ng th ba thì chúng

song song.

L I GI I
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BON 21

ABC.A B C . G i M , N l

BB và CC . G i
A.

AB .

L I GI I

mc a

là giao tuy n c a hai m t ph ng AMN và A B C . Kh ng

0B.

BC .

C.

AC .

AA .

D.

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Á

c

MNCCAMN

AHMM.ME

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

BÚC ABU

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B

A

_µ

MNHBÚ

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C

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

B

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Ib page "H c Tốn cơ Ng c Huy n LB"

c

6

TỐN 12

SEASON 2023

BON 22 Trong các m

QUICK NOTE

1
BC thì B
2

A. N u AB

ị

B. Vì AB

mc

2 AC 5 AD nên b

C. T

AB

D. T

AB 3 AC ta suy ra BA

n AC .

m A, B, C , D cùng thu c m t m t ph ng.

3 AC ta suy ra CB

AC.

3CA.

L I GI I
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

L

Asai

b

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

a

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

À

TE

a

2Ẩc 5ẨD

theo

đly

vềsự đpcủa 3reto

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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BON 23 Cho hình l

nh góc gi a c

ABCD.EFGH

AB và DH .

A. 45 .

A

D

B. 90 .

C. 120 .

D. 60 .

L I GI I
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

g

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

F

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

F

G

BON 24 Kh
A.
nhau.
B.
nhau.
C.

ng th ng phân bi t cùng song song v

ng th ng th ba thì song

song v i nhau.
D.

ng th ng cùng song song v

ng th ng th ba thì vng góc v i

nhau.

L I GI I
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Ib page "H c Tốn cơ Ng c Huy n LB"

c

7

TỐN 12
QUICK NOTE

BON 25 Tìm m
A. m 0 .

L I GI I

hàm s

f x

0B. m

2.

SEASON 2023

x2 x
khi x 1
liên t c t i x 1 .
x 1
m 1 khi x 1

0

1tẪ
C. m

1.

D. m 1 .

Ðể kt liêntục tựx
HIỆN fact fa m 1

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f

fig

tan

ftp.axt

fgin1xYyI

fyI

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1

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từ

m 1 d

và

L

m

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BON 26 Tìm t t c các giá tr c a m
1 x
x
1 x
m
1 x

f x

A. m

1.

L I GI I

1 x

hàm s
khi x 0

liên t c t i x 0 .
khi x 0

B. m 1 .

Ðể hbltu.tn

C. m
0

2.

x o

thì

D. m 0 .

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

fffdfcx
ftp.flxli
A

flo

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

m 1

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Ð

mtt

ftp.kxtn fggfcmthf

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

mt tíaf
ftp.I

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itmTxT

xFotrFr

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ỵ

g

m

BON 27

i ta thi t k m t cái tháp g m 11 t ng. Di n tích b m t trên c a

m i t ng b ng n a di n tích c a m t trên c a t
trên c a t ng 1 b ng n a di n tích c

i và di n tích m t

tháp (bi t di n tích c a

tháp là

12288 m2 ). Tính di n tích m t trên cùng.

O

B. 6m 2 .

A. 8m 2 .

L I GI I

C. 12m 2 .

D. 10m 2 .

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

AN cơng hội

g

f

ỵz

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Stating

11

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1

12288

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42 41.911

12288

f

11

6

4

B.

5
.
4

5
.
4

C.

D. 2 .

L I GI I
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t.IM

f EdYn atII

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nhân lên hợp

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ftp.jlx fxFD

xtFtL

fffIp

fI
yyf XtfxFaxtE
g

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a

f.gg

g

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g

yyg.gg

2

L

1

0

x

1h loại

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µ

l

m

tdxt 170 tx O

m 1

1

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VN

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Mc 1

flo

1

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ftp.gpfkd

D

7

a saocho

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fcotflaK T.no

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A. a 2 .

L I GI I

SEASON 2023

C. 2 a 3 .

KẻBHtsctai.tt

n SC b ng

B

D. a 3 .

tim BH

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

BHndlB.sc

ba

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

u

AI

f

BCIAB

ASBCvây

BCTSB

tại Bcóckao BA

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

BCISA

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c

nao

a'i

8B BC

BU B BC

ỀỂỀ

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ysmpT

se

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2a sn

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BON 32 B n Ng c th m t qu bóng cao su t
m i l n ch

t qu bóng l i n y lên m

cao 20 m so v i m

cao b ng b n ph

c. Bi t r ng qu bóng ln chuy
ng qu

cao l n

ng vng góc v i m
c (t

2B chiase'tIBoxPhac'Ðổ

t,

t. T ng

lúc th

n lúc bóng

khơng n y n a) là
A. 180 m .

B. 100 m .

C. 140 m .

L I GI I

D. 80 m .

EBOOkttta.totklI

tốn

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

g.togi8d.c

taig

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o

ggjt

tao.fgp

pháhố

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iii

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củaCSN

silà ton

lùi vơhạn

16

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ứyqỊỆ

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

f

Ig
dý

80Cm

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bong rơi

tổng qng

G

201 20

ftp.itdofgjt

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100 m

Ị

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8

801100

180

BON 33 Cho hình chóp S.ABC có SA vng góc v i m

ABC

góc h p gi a SB và m t ph ng ABC là
A. SBA .
O
L I GI

B. SBC .

I

C. SAB .

D. BSA .

ẦBỨ

BẤM

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

STBĂ

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sin x cos x
x

.

C. 2 cos x .

B. cos x .

L I GI I

D

UN

D.

x

.

1

Ỹ

a UKA

cos x

t.nn.rx.cosfxztinrx.cat
rx

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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x2

BON 35 Hàm s y

O

A. y

x 1

C. y

Ẻ

120

5

1

5

x 1

L I GI I

6

g

6

x 1
x 1

o hàm c p 5 b ng

titan

.

B. y

120

5

x 1

D. y

.

6

1

5

x 1

1

_xt

yk

.

1

6

.

cty

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7

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É F

ử

HÊN Ấm

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ftp

IỆỆỆ
XAY
µẦÝ
a

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ý

Ể

g

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3.

C. m 3 .

mx 13 3

s

D. m 1 .

m

xe

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

a 1

c 2
m

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ft 1

2

HP 2

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m c3

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Ib page "H c Tốn cơ Ng c Huy n LB"

c

11

TOÁN 12
QUICK NOTE

BON 37
A

6; 5 là

O

A. y

f flxoHX x.lt flxo

YỀI Ý fẸ

y

L I GI I

1_

x 2.

fhx

C

C

1
7
.
x
4
2

x 1 và y

C. y x 1 và y

x 2
x 2

SEASON 2023

_1h27

B. y

x 2 và y

2x 1 .

D. y

x 1 và y

1
x
4

1 2

3
.
4

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

x

z

27

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Mxo

tiếp đi
yo là

x.lt

ffzj.cx

y

gtI

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Al 6,5

5

C A

6

Ệg

t

KẸT

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

272

51

4 toto

that 2 Ho 2

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

24

440

0

0

7020
Xo 26

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

HỬ Xo so

y
y

e

1

X

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

TI Xoa

7h

xt

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

D. 45 .

C. 90 .

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

A

cos

AD BC

cos ẨD

ẤO

1

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Ị

m

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

zADIIfp.FI

AD AB.GSDTtB

AD7Ag

ẪtAg M

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

39

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

as

ABB

3

ftpa

600

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Ib page "H c Tốn cơ Ng c Huy n LB"

c

12

TOÁN 12
QUICK NOTE

BON 39 M

ng th ng kh i hành t

ng S (mét

cc

m t nhà ga. Quãng

t hàm s c a th i gian t (giây), hàm s

6t 2 t 3 . Th

S t

SEASON 2023

m t (giây) mà t

n t c v m/s c a chuy

ng

t giá tr l n nh t là
A. t

2s .

B. t

3s .

C. t

4s .

D. t 6s .

L I GI I
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

VA 7 84

2
2
61 63
121 3
3 f 4 19 1 12
342 Tt
12 34 272 E 12 3 0

12

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Ðâu

f 2

0

f

D

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2

.

D.

nghiêng

s

10 a
.
2

nếutang 11

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

hi

tBDta.io

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

AOLBD
AOTBD
BDICSAO
SALBD
SA AO CHAO SANTO1173

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Ặỵ

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

D

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

D

thao

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

c

B

SBDY THAO

SBDINSAO SO

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

1

AKI 80

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Akt HBD

DIA

D LAK

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íỊ

ấỊỆỆ

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Ib page "H c Tốn cơ Ng c Huy n LB"

c

13

TỐN 12
QUICK NOTE

BON 41 Cho kh i chóp S.ABCD

SEASON 2023

ABCD là hình bình hành,

AD 2a, AB a , góc BCD b ng 60 , SB vng góc v i m t ph ng
SB

ABCD ,

a 3 . Tính cos c a góc t o b i SD và m t ph ng SAC .

A.

1
.
4

B.

3
.
2

15

.
4

0
C.

D.

3
.
4

L I GI I
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

D HAC

nin SDTGACI

qúvểkk

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

8D Ok

ỊỊ

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

DIDISAC

BH

BA.BG

atf

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

BE BHHB

a

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

VBHfgp.TT

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

từ

à

i

14

caa

tff.IE

19 9

B. T

f x

8

x 5

5

3.
O

.

11
.
18

C. T

L I GI I

13
.
36

13
.
18

D. T

fff

57 0

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

II HẾT

3

hữu hạn

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Ừ

X5

35

2

gửihạnhữu hạn thì
87 0

ffgfffmtt.lt

19 27

ỂẲỀỀẲ

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

KỂ

stfu

g

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

thơ

VỀ.tt ttfpF

gTt3

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Ib page "H c Tốn cơ Ng c Huy n LB"

c

14

J

3 1817
25 7

RẤT

3

TẾ

tg

BẾT

2

TOÁN 12
QUICK NOTE

BON 43 Cho hàm s
2f2 x

7f x

hàm s g x

15

x

khi x 1

x 1
mx 2

A. m 24 .

th a mãn lim

f x liên t c trên

SEASON 2023

f x

1

5

2. Tìm m

x 1

hữuhạn

liên t c t i x 1 ?

t

khi x 1
C. m 26 .

B. m 25 .

ỀỄ5

D. m 27 .

L I GI I
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Hs liên tục tại

1 thì Ðt
m.tt 2 mt 2
9117
a

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Ðfỵỷ

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

d

fkA tflxt

15

f.gg 2fcxtt3 fcxt5
x D
C2fU t3J

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

gfg.my

x 1

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

ftp.gld

Ht3J.fffI1I

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2.51 3

2

26

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

từ

và

26

mt 2

mi

24

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

BON 44 Cho hình chóp S.ABCD có ABCD là hình vng c nh a; SA a;
ABCD . Kho ng cách gi

SA

O
A.

a 6
.
6

ng th ng chéo nhau SC; BD b ng

B. a 6 .

C. a 3 .

L I GI I

dao

D. a.

BD

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

s

a

SGCK
BDH la
dlBD.SC D D la
D 0 la
DIA a

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

AOMat fc.li

ftp.t
dunk

Ap Ừ

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

B

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

ỮẲ

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

111AM

1a.AkjazB

xe

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

p

f

fµt

Atef

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Ib page "H c Tốn cơ Ng c Huy n LB"

c

15

TOÁN 12
QUICK NOTE

ax 2

BON 45 Cho 2 s th c a, b và hàm s f x

bx 1

x2

1
.
4

A. T

t Nhậnxét Hàmsốliên tuc
trêncác
khoang tai2 và12 to

a b bi t r ng hàm s

khi x 2

.

nh c a nó.

1
.
8

C. T

L I GI I TXÐ D M
ti Hànsó

2

c trên t

1
.
4

B. T

khi x 2

2x a 2 x x 1
x 2

Tính t ng T

SEASON 2023

1
.
8

D. T

Hànsố liêntụctại x 2

liênlục Nh

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

figg fix
ftp.flx ftd

flx ftL

ftp.g

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

a 22 t b 2 1
2
fff.mg Xe_2x tat

4at dbt 1

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

t

fffmjtflxt

XFẤ

Nhân hợpdạng
luyện

2

2 2

Ltlx N

I

XE

t.ttatt iaxxr.it

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fygg.fr

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Từnhận xét ta thấy để7giớihạnhữuhạncủa hàn số

tại a 2 thừa O

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Khiđó

fyfyfxhfgizf.FI xf.f

d

1

f

d.d2t2T

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Mà ftp.gglx 2

dođóđể

thì

Ề t.IE 1

nam

2

ftp.f

ai O

đang

0

hữuhạn Vậy từ

và

i

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

y

g

tao26 1

E 18

fabi 118

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

at

BON 46
tuy n c

34

y x3 3x2

C . Tìm M thu c C

2

th hàm s t i M

A. M 1;0 .

L I GI I

B. M

Ðặt fact X
ti Goi M xo

ti p

.
C. M

1;0 .

3Ỹ

D. M 0;1 .

2;0 .

2

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Ẻ 3 042 là tiếpđiểncủatiếptuyến

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

với ÐTHS c

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3 2 6X

ý

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Ð Hệ sốgả tiếptuyến của

tại

M là

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

f fkxd

hà 6 0

3

2

11

3

3

1

33 3

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

f Vậy

hệsógoccnhỏnhất bằng

3

khi xo 1

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

M 1 0

B

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

. Giá tr c a a2
16

SEASON 2023

b2 là

C. 20 .

D. 10 .

L I GI I
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

lýgả
Nếu

t Do ftp.txhtax

x b

là giớihạnhữu hạn

f

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

ftp.ltthuct LFO

X

1

2X

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1 0

egg.ca 2

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Dạng

g

a

ftp.glTử

nên

vô

thức1 0

lý

nên ftp.zdxttax

x b
4242at 6 2 6 0
flot.se

0

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

b

2

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

fotda
efyggfxtaxtT
lx. K

feotda td

fy.iggdxhtaxtT x

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2x

Xlx 2

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

axỊỀỄừa_f

h

ro
sfgigfxkaxt6
x4axtTtVeotTa
2 xlx.LK

mỷµ

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dX

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ỬỂỀ

Ề

a

Ềf

nỨỂỂỄ

FìỬ

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F

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

dtdta

at 9

ty

f

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24da16 Y10fr

Motta

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Từ

at9

và

quota 8n

BON 48 Gi i h n lim

và b 0 .

3

116

12
3

11
n
5n 2

a

2

7

ãt BỊ 13

3 b L

a
a
v i là phân s t i gi n
b
b

có k t qu

a 2b có k t qu

A. 11.

B. 6.

C. 7.

D. 13.

L I GI I
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Ốt

kim

nt

kim TẦM

n

MẤT

thin

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

5h 2

5h 2

5h 2

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

kim

7h

t 11

ẤM

ỄfntỀ

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5hta

TẨY

tết

ntn

Ì

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Tu
5tnI ffFftYpt1n1

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ga
b

1

at

2b

tt 2.5 11

B

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

g

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________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Ib page "H c Tốn cơ Ng c Huy n LB"

c

17

TỐN 12

SEASON 2023

BON 49 M t hình vng ABCD có c nh b ng 1, có di n tích là S1 . N i b n

QUICK NOTE

m A1 , B1 ,C1 , D1 l

t c a b n c nh AB, BC,CD, DA

vng A1 B1C1 D1 có di n tích là S 2
tích là S 3 . C

m A2 , B2 , C2 , D2 l n

n ib

t c a b n c nh A1 B1 , B1C1 , C1 D1 , D1 A1

c hình

c hình vng A2 B2C 2 D2 có di n
c các di n tích S4 , S5 , S6 ,...Sn . Tính

ti p t

lim S1 S2 S3 ... Sn ?
A. 1.

B. 2.

C.

1
.
2

1
.
4

D.

L I GI I
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

An

A

A

HAI ỀỮ L

G _A BE f E 14

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

B

C

Ba

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________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

A B

AaBỹI

KỂ Ệ

E

4 AsBI tr

18

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A tx.it nai

h

Ữ ff

tới

HEN

n 32

a

kim

HỴẪ

ffqz2

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

BON 50 Cho các hàm s y

Ưmy

Sn_LAMBa

8 x 5.

A. y 8 x 9.

D fC7
th l

22

0

B. y 12x 3.

C. y 24 x 27.

L I GI I

D. y

4 x 1.

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

thânhỏi PTtứftuyến của

g flat 2 13 9 7

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A

y _gkxo

H

tgcxo

tiếpđi C

2

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ffxhtd
c
X 2
6

ldxt27
gtxt
944

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A

y

f

tf

6747

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tim
5 Dữkiện 1 PTHcủa tai A là yadxt3 tn
a
Aý yn fkU.hr 2 2tfk 142 X 21121127
tin

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dtttD

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2 3

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ff2192

ẤRK2
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f'k7 fffM
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2447

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ty

tại Blày

15

2147 1

Thay

X

x

27tf1fk7
t

7

4147

tfft

X 2

8

Ấtkq

ltfoth.gg
vào

f fa

21

bfttllxtttff7
y 6.4
hr 2 t 21
24

27

Cô ngọc huyền LB đề KSCL cuối HK II lớp 11

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