BDT chinh phuc diem cao mon toan lop 11 tap 2(sdt)

2)565.Ȫ8ȿP*KϓP
%JϳDKȪP
0IW[ϑP0IϙE%JK0IW[ϑP8ȿPȆK0IW[ϑP*QȠPI8KϓV0IW[ϑP6Jϗ6JλO
0IW[ϑP8ʛ/KPJ2JCP:WȢP&—•PI0IW[ϑP*ϻW$λE0IW[ϑPȀϣ%JKϋP

TOÁN
7|3

NHÀ XUẤT BẢN ĐẠI HỌC QUỐC GIA HÀ NỘI


/¢,1Œ,ôp8
7RiQKӑFOjPӝWWURQJQKӳQJP{QNKRDKӑFWӵQKLrQQҵPWURQJFKѭѫQJWUuQKJLiRGөFSKәWK{QJӣ9LӋW
1DPWӯEұF7LӇXKӑFÿӃQ7+379ӅPһWNLӃQWKӭFWRiQKӑFFXQJFҩSFKRFiFHPF{QJFөÿӇWtQKWRiQYjWLӃQ
KjQKQJKLrQFӭXFiFP{QKӑFNKiFQKѭ9ұWOt+yDKӑF9ӅPһWNƭQăQJKӑFWRiQJL~SFiFHPUqQOX\ӋQ
NKҧQăQJWѭGX\VX\OXұQO{JLFVX\QJKƭPҥFKOҥFÿӗQJWKӡLJySSKҫQKuQKWKjQKYjSKiWWULӇQNƭQăQJJLҧL
TX\ӃWYҩQÿӅWURQJFXӝFVӕQJ
9ӟLÿһFWKP{QKӑFÿzLKӓLFyQӅQWҧQJNLӃQWKӭFYjNƭQăQJWKұWYӳQJFKҳFFK~QJW{LOX{QWUăQWUӣWuPUD
QKӳQJSKѭѫQJSKiSWӕLѭXQKҩWJL~SFiFHPWLӃSFұQYjKӑFWұSYӟLWRiQKӑFĈѭӧFÿ~FU~WWӯNLQKQJKLӋP
JLҧQJGҥ\YjQJKLrQFӭXFiFҭQSKҭPFҧWURQJYjQJRjLQѭӟFFXӕQViFK%tTX\ӃWFKLQKSKөFÿLӇPFDR
7RiQ+uQKKӑFÿѭӧFFK~QJW{LWKLӃWNӃQKҵPKӛWUӧWӕLÿDFiFWKҫ\F{YjFiFHPKӑFVLQKWURQJTXiWUuQK
KӑFWұS{QOX\ӋQNLӇPWUDYjÿiQKJLiNLӃQWKӭF

TOÁN

11

+Ӌ WKӕQJ NLӃQ WKӭF EiP ViW FKѭѫQJ
WUuQKKӑFWUrQOӟS

7KHRViWKӛWUӧFiFHPKӑFWұSWUrQOӟS
{QWұSNLӇPWUDÿiQKJLiNӏSWKӡL

0өFWLrXU}UjQJWKHRWӯQJEjL

*L~SFiFHPFyFiLQKuQWәQJTXiWÿһW
UDPөFWLrXÿӇÿҥWÿѭӧFWUѭӟFNKLKӑF

/tWKX\ӃWWUuQKEj\FKLWLӃWNӃWKӧSVѫ
ÿӗKӋWKӕQJKyDOҥLNLӃQWKӭF

7UuQKEj\NLӃQWKӭFFKLWLӃWOtJLҧLÿҫ\ÿӫ
JL~S FiF HP KLӇX VkX VDX ÿy KӋ WKӕQJ
KyDOҥLÿӇFiFHPWKҩ\U}ÿѭӧFVӵO{JLF
FӫD NLӃQ WKӭF QKӳQJ NLӃQ WKӭF WUӑQJ
WkPFҫQQKӟ

%jL WұS ÿѭӧF SKkQ GҥQJ FKL WLӃW WKjQK
FiF EjL WRiQ NLӇX FkX KӓL WKѭӡQJ JһS
Fy SKѭѫQJ SKiS JLҧL FKL WLӃW WKHR WӯQJ
EѭӟFYjFiFYtGөPLQKKӑD

*L~SFiFHPQKұQELӃWÿѭӧFWӯQJGҥQJ
EjLNLӇXKӓLYjFiFKWѭGX\ÿӇJLҧLGҥQJ
EjLNLӇXKӓLÿy

+ӋWKӕQJFiFPҽRJLҧLNLQKQJKLӋPOjP
EjLOӛLVDLFҫQWUiQKNLӃQWKӭFEәVXQJ
YjFiFFK~êÿLNqPYӟLFiFYtGө

7UX\ӅQWKөFKRFiFHPQKӳQJNLQKQJKLӋP
FӫDFiFWiFJLҧQKLӅXQăPGҥ\KӑFJL~S
FiFHPQҳPYӳQJNLӃQWKӭFPӟL{QWұS
OҥLNLӃQWKӭFFNJNKLFҫQ

+Ӌ WKӕQJ ÿӅ NLӇP WUD  SK~W  SK~W
KӑFNuEiPViWWKHRTXiWUuQKKӑF

+ӛWUӧFiFHP{QWұSÿ~QJWKӡLÿLӇPÿӇ
WӵWLQNKLOjPFiFEjLNLӇPWUDWUrQOӟS


&ҩXWU~FFөWKӇFӫDFXӕQViFKQKѭVDX
3KҫQ1ӝLGXQJNLӃQWKӭF
TURQJÿySKҫQÿѭӧFFKLDWKjQKFiFQӝLGXQJOӟQVDX


&KѭѫQJ3KpSGӡLKuQKYjSKpSÿӗQJGҥQJWURQJPһWSKҷQJ



&KѭѫQJĈѭӡQJWKҷQJYjPһWSKҷQJWURQJNK{QJJLDQTXDQKӋVRQJVRQJ



&KѭѫQJ9HFWѫWURQJNK{QJJLDQTXDQKӋYX{QJJyFWURQJNK{QJJLDQ

3KҫQĈӅNLӇPWUD
3KҫQĈiSiQ
9ӟLQKӳQJѭXÿLӇPFӫDFXӕQViFKFK~QJW{LPRQJUҵQJ%tTX\ӃWFKLQKSKөFÿLӇPFDR7RiQ+uQKKӑF

VӁÿHPÿӃQFKRFiFHPKӑFVLQKQJXӗQFҧPKӭQJKӑFWұSÿӗQJKjQKFQJFiFHPWURQJKjQKWUuQKFKLQK
SKөFWULWKӭFYjOjQJXӗQWjLOLӋXWKDPNKҧRKӳXtFKFKRFiFEҥQÿӗQJQJKLӋSWURQJTXiWUuQKJLҧQJGҥ\
7URQJTXiWUuQKELrQVRҥQFK~QJW{LNK{QJWKӇWUiQKNKӓLQKӳQJWKLӃXVyWNK{QJPRQJPXӕQUҩWPRQJVӁ
QKұQÿѭӧFQKӳQJÿyQJJySTXêEiXWӯEҥQÿӑFJҫQ[DFiFWKҫ\F{FNJQJQKѭFiFHPKӑFVLQKWKkQPӃQÿӇ
FK~QJW{LKRjQWKLӋQFXӕQViFKKѫQWURQJQKӳQJOҫQWiLEҧQWLӃSWKHR
;LQFKkQWKjQKF̻P˿Q


/¢,&l0¡1
6DXWKӡLJLDQGjLQӛOӵFWULӇQNKDLWUѭӟFVӵFKӡÿyQFӫDFiFHPKӑFVLQKYjEҥQÿӑFPӑLPLӅQ7әTXӕF
FXӕQViFK%tTX\ӃWFKLQKSKөFÿLӇPFDR7RiQ+uQKKӑFÿmFKtQKWKӭFSKiWKjQK0ӛLFXӕQViFKUD
ÿӡLOjWKjQKTXҧFӫDFҧPӝWWұSWKӇOӟQPҥQKWURQJÿyNK{QJWKӇWKLӃXF{QJODRFӫDFiFWKҫ\F{JLiR±QKӳQJ
QJѭӡLWUӵFWLӃSFKҩSE~WYLӃWQrQFXӕQViFK9ӟLWҩWFҧWkPKX\ӃWWLQKKRDÿѭӧFWtFKONJ\VѭXWҫPWURQJVXӕW
TXiWUuQKJLҧQJGҥ\FiFWKҫ\F{ÿmWUӣWKjQKQKӳQJ³QJѭӡLWUX\ӅQOӱD´WKҫPOһQJFKRFiFHPKӑFVLQKTXD
WӯQJWUDQJViFK
&{QJW\&әSKҫQ&&*URXS7RjQ&ҫX[LQÿѭӧFJӱLOӡLFҧPѫQFKkQWKjQKYjVkXVҳFÿӃQFiFWKҫ\F{

3*676/r9ăQ+LӋQ
&KͿELrQ


*L̻QJYLrQ.KRD7RiQ7LQ7Ú͵QJĈ̹LKͥF6́SK̹P+j1ͱL

1JX\ӉQ1JӑF&KL

1JX\ӉQ9ăQÈL

*LiRYLrQ7RiQ
7UXQJWkP7RiQ7UXQJ+Rj1KkQ&KtQK

*LiRYLrQ7RiQ
+͟WKͩQJJLiRGͽFWUΉFWX\͗Q7ROLKDYQ

1JX\ӉQ+RjQJ9LӋW

1JX\ӉQ7Kӏ7KҳP

*LiRYLrQ7RiQ
+͟WKͩQJJLiRGͽFWUΉFWX\͗Q7ROLKDYQ

*LiRYLrQ7RiQ
7Ú͵QJĈjR'X\7΃+j1ͱL

1JX\ӉQ9NJ0LQK

3KDQ;XkQ'ѭѫQJ

*LiRYLrQ7RiQ
7UXQJWkP$(PDUWKHGXFDWLRQ

*LiRYLrQ7RiQ
7Ú͵QJĈjR'X\7΃+j1ͱL

1JX\ӉQ+ӳX%ҳF

1JX\ӉQĈӛ&KLӃQ

*LiRYLrQ7RiQ
7UXQJWkP$(PDUWKHGXFDWLRQ

*LiRYLrQ7RiQ
7Ú͵QJĈjR'X\7΃+j1ͱL

&K~QJW{LKLYӑQJVӁOX{QQKұQÿѭӧFQKӳQJêNLӃQÿyQJJySWkPKX\ӃWWұQWuQKFӫDFiFWKҫ\F{ÿӇFK~QJ
W{LFyWKӇKRjQWKLӋQKѫQQӳDQӝLGXQJFXӕQViFKYӅNLӃQWKӭFFKX\rQP{QKRjQWKjQKVӭPӋQKFDRFҧFӫD
PuQKOjQJѭӡLÿӗQJKjQKFQJFiFHPKӑFVLQKWUrQFRQÿѭӡQJKӑFYҩQ
;LQWUkQWUͥQJF̻P˿Q



+›£1*'s1ô&6k&++,…848l
%tTX\ӃWFKLQKSKөFÿLӇPFDR7RiQ+uQKKӑFOjFXӕQViFKFySKѭѫQJSKiSWUuQKEj\NLӃQWKӭFY{
FQJÿһFELӋWĈӇJL~SFiFHPVӱGөQJKLӋXTXҧYjNKDLWKiFWULӋWÿӇQKӳQJѭXÿLӇPFӫDFXӕQViFKQKyPWiF
JLҧ[LQFKLDVҿYӟLFiFHPEtTX\ӃWVӱGөQJFXӕQViFK



0š&/š&














1ӝLGXQJ

ĈiSiQ

3+Ҫ11Ӝ,'81*.,ӂ17+Ӭ& 
&KѭѫQJ3KpSGӡLKuQKYjSKpSÿӗQJGҥQJWURQJPһWSKҷQJ  
%jL3KpSELӃQKuQK±SKpSWӏQKWLӃQ  
%jL3KpSTXD\  
%jL.KiLQLӋPSKpSGӡLKuQK±KDLKuQKEҵQJQKDX  
%jL3KpSYӏWӵ  
%jL3KpSÿӗQJGҥQJ  

&KѭѫQJĈѭӡQJWKҷQJYjPһWSKҷQJWURQJNK{QJJLDQ
4XDQKӋVRQJVRQJ  
%jLĈҥLFѭѫQJYӅÿѭӡQJWKҷQJYjPһWSKҷQJ  
%jL+DLÿѭӡQJWKҷQJFKpRQKDXYjKDLÿѭӡQJWKҷQJVRQJVRQJ  
%jLĈѭӡQJWKҷQJVRQJVRQJYӟLPһWSKҷQJ  
%jL0һWSKҷQJVRQJVRQJYӟLPһWSKҷQJ  

&KѭѫQJ9HFWѫWURQJNK{QJJLDQ
4XDQKӋYX{QJJyFWURQJNK{QJJLDQ  
%jL9HFWѫWURQJNK{QJJLDQ±KDLÿѭӡQJWKҷQJYX{QJJyF  
%jL*yF 
%jLĈѭӡQJWKҷQJYX{QJJyFYӟLPһWSKҷQJ±KDLPһWSKҷQJYX{QJJyF  
%jL.KRҧQJFiFK  

3+Ҫ1Ĉӄ.,ӆ075$ 
3+Ҫ1ĈÈ3È1

ĈiSiQSKҫQ 
ĈiSiQSKҫQ 




&+›¡1* 1
3+|3'¢,+†1+9j3+|3%,‚1'n1*
7521*0z73+x1*
%j,3+|3%,‚1+†1+3+|37Š1+7,‚1

1
2

12

1

1ҳPÿѭӧFÿӏQKQJKƭDSKpSELӃQKuQKPӝWVӕWKXұWQJӳYjNtKLӋXOLrQTXDQ

2

1ҳPÿѭӧFÿӏQKQJKƭDSKpSWӏQKWLӃQ

3

%LӃWYӁҧQKYj[iFÿѭӧFҧQKFӫDPӝWKuQKTXDSKpSWӏQKWLӃQ

4

1ҳPÿѭӧFWtQKFKҩWFӫDSKpSWӏQKWLӃQ

%LӃWYұQGөQJÿӏQKQJKƭDYjWtQKFKҩWFӫDSKpSELӃQKuQKYjSKpSWӏQK
WLӃQÿӇ[iFÿӏQKҧQKFӫDPӝWÿLӇPPӝWÿѭӡQJWKҷQJFKRWUѭӟF
%LӃWYұQGөQJSKpSWӏQKWLӃQÿӇJLҧLPӝWVӕEjLWRiQYӅTXӻWtFK

%¬L3K¾SELÄQKÈQKSK¾SWÌQKWLÄQ


, /Ë7+8<ӂ775Ӑ1*7Æ0
3KpSELӃQKuQK

ĈӏQKQJKƭD
4X\WҳFÿһWWѭѫQJӭQJPӛLÿLӇPMFӫDPһWSKҷQJYӟLPӝW
ÿLӇP[iFÿӏQKGX\QKҩW M cFӫDPһWSKҷQJÿyJӑLOjSKpSELӃQ
KuQKWURQJPһWSKҷQJ
.tKLӋX
• 3KpSELӃQKuQKOjFYjYLӃW F  M
M c KD\ M c F  M

.KLÿy M c JӑLOjҧQKFӫDMTXDSKpSELӃQKuQKF
• 1ӃXH OjPӝWKuQKQjRÿyWURQJPһWSKҷQJWKuWDNtKLӋX
H ‘ F (H) OjWұSKӧSFiFÿLӇPҧQKFӫDMWKXӝFH.KLÿyWD QyL
FELӃQKuQKHWKjQKKuQKH ‘KD\H ‘ҧQKFӫDKuQKH ‘TXDSKpS
ELӃQKuQKF
3KpSELӃQKuQKELӃQPӛLÿLӇPMFӫDPһWSKҷQJWKjQKFKtQK
QyÿѭӧFJӑLOjSKpSÿӗQJQKҩW

9tGͽ+uQKFKL͗XFͿDÿL͛P$OrQÿ́͵QJWK͋QJG
OjÿL͛P+.KLÿyWDFySKpSEL͗QKuQKEL͗QÿL͛P

$WKjQK+

)  $


+ ÿ́ͻFJͥLOjSKpSFKL͗XYX{QJJyF

3KpSWӏQKWLӃQ
ĈӏQKQJKƭD
G
7URQJPһWSKҷQJFKRYHFWѫX3KpSELӃQKuQKELӃQPӛLÿLӇPM
JJJJJG G
G
WKjQKÿLӇPM cVDRFKR00 c XJӑLOjSKpSWӏQKWLӃQWKHRYHFWѫX
NtKLӋX7XG

1KѭYұ\ 7XG  0


D
1ӃX7XG  0


JJJJJG
0 c œ 00 c

G
X

7tQKFKҩW

0
 7XG  1


JJJJJJG
0
WKu0
1


JJJJG
01

1KͅQ[pW
‡3KpS WͣQK WL͗Q WKHR YHFW˿NK{QJ FKtQK Oj
SKpSÿͫQJQK̽W
‡3KpSWͣQKWL͗Qÿ́ͻF[iFÿͣQKNKLFyYHFW˿
WͣQK WL͗Q W΁F Oj EL͗W ÿL͛P ÿ̿X ÿL͛P FXͩL FͿD
YHFW˿KR͏FEL͗WḰͳQJYjÿͱGjLFͿDYHFW˿
‡3KpSWͣQKWL͗QE̻RWRjQNKR̻QJFiFKJL·D
KDLÿL͛PE̽WNu

7ӯÿyVX\UD0
1
01
E
3KpSWӏQKWLӃQELӃQ
• ĈѭӡQJWKҷQJWKjQKÿѭӡQJWKҷQJVRQJVRQJKRһFWUQJYӟLQy
• ĈRҥQWKҷQJWKjQKÿRҥQWKҷQJEҵQJQy

• 7DPJLiFWKjQKWDPJLiFEҵQJQy*yFWKjQKJyFEҵQJQy
• ĈѭӡQJWUzQWKjQKÿѭӡQJWUzQFQJEiQNtQK
%LӇXWKӭFWӑDÿӝ

G
7URQJPһWSKҷQJ2[\FKRÿLӇP0  [ \
YjYHFWѫX  D E


&K~ ê 1͗X TXrQ F{QJ WK΁F Qj\ WD FK͡ F̿Q FKR
JJJJJG G
00 c X VX\UDFiFWͥDÿͱẂ˿QJ΁QJE͉QJQKDX

*ӑLÿLӇP 0 c  [ c \ c
OjҧQKFӫDÿLӇP 0  [ \