33
,0Ө&7,Ç8
6DXNKLKӑF[RQJEjLQj\+6FyNKҧ QăQJ
1. VӅ NLӃQWKӭF:
– 1KұQELӃWÿѭӧFNKiLQLӋPEҩWSKѭѫQJWUuQKEұFQKҩWPӝWҭQQJKLӋPFӫDEҩWSKѭѫQJWUuQK
EұFQKҩWPӝWҭQ
– *LҧLÿѭӧFEҩWSKѭѫQJWUuQKEұFQKҩWPӝWҭQ
2. VӅ QăQJOӵF:
1ăQJOFFKXQJ 1ăQJOӵFWӵ FKӫWӵ hӑFYj1ăQJOӵFJLDRWLӃSKӧSWiF0ӛL+6WKӵFKLӋQ
FiFKRҥWÿӝQJ.KiPSKiYj7KӵFKjQKVDXÿyWKDPJLDKRҥWÿӝQJQKyPWURQJ
KRҥWÿӝQJ.KiPSKiWuPUDNLӃQWKӭFPӟLÿӏQKQJKƭDEҩWSKѭѫQJWUuQKVӱ GөQJÿѭӧF
WtQKFKҩWEҩWSKѭѫQJWUuQKWURQJJLҧLEҩWSKѭѫQJWUuQK
1ăQJOFWRiQKF 1ăQJOӵFJLҧLTX\ӃWYҩQÿӅ WRiQKӑFYj1ăQJOӵFWѭGX\OұSOXұQ
WRiQKӑF+6GQJWtQKFKҩWEҩWSKѭѫQJWUuQKÿӇ WKӵFKLӋQJLҧLEҩWSKѭѫQJWUuQKWURQJKRҥWÿӝQJ
7KӵFKjQK*LҧLEҩWSKѭѫQJWUuQKWURQJKRҥWÿӝQJ9ұQGөQJ
3. VӅ phҭPFKҩW:
7UiFKQKLӋPYjFKăPFKӍ+6FyWUiFKQKLӋPWURQJKRҥWÿӝQJQKұQELӃWEҩWSKѭѫQJWUuQK
YұQGөQJFiFWtQKFKҩWEҩWSKѭѫQJWUuQKÿӇ JLҧLEҩWSKѭѫQJWUuQK.KLKRҥWÿӝQJQKyPNK{QJ
ÿә OӛLFKREҥQWӵ QKұQVDLVyWWURQJTXiWUuQKWKӵFKLӋQQKLӋPYө
,,7+,ӂ7%ӎ 'Ҥ<+Ӑ&9¬+Ӑ&/,ӊ8
ĈӕLYӟLJLiRYLrQ 6*.6*9.+%'
ĈӕLYӟLKӑFVLQK 6*.ÿӗ GQJKӑFWұS
,,,7,ӂ175Î1+'Ҥ<+ӐC
+RҥWÿӝQJ.KӣLÿӝQJ
a) MөFWLrX *L~S+6WLӃSFұQKӋ WKӭFOjEҩWSKѭѫQJWUuQKEұFQKҩWPӝWҭQJӧLVӵ WzPz
Wӯ hӋ WKӭFGүQÿӃQEjLKӑFYӅ EҩWSKѭѫQJWUuQKEұFQKҩWPӝWҭQ
E1ӝLGXQJ 7KӵFKLӋQYLӃWKӋ WKӭFÿӇ WuPVӕ OѭӧQJFk\[DQKFҫQWUӗQJWKrPFӫDOӟS$
7ӯ ÿyWLӃSFұQEҩWSKѭѫQJWUuQKEұFQKҩWPӝWҭQ
F6ҧQSKҭP +6FyWKӇ ELӇXGLӉQ Vӕ OѭӧQJ Fk\ [DQK FҫQ WUӗQJ WKrP FӫDOӟS $ Oj
[t
G7ә FKӭFWKӵFKLӋQ
* *9FKX\QJLDRQKLPYKFWS *9\rXFҫX+6ÿӑFÿӅ YjTXDQViWKRҥWÿӝQJ.KӣLÿӝQJ
YjYLӃWKӋ WKӭFWKӭFELӇXGLӉQVӕ OѭӧQJFk\[DQKFҫQWUӗQJWKrPFӫDOӟS$
%jL 2. BẤT PHƯƠNG TRÌNH BẬC NHẤT MỘT
Ẩ
N
Thời gian thực hiện: 4 tiết
$.+Ӣ,Ĉ
Ӝ
NG
34
* +6WKFKLQQKLPYKFWS&iFQKyP +6WKӵFKLӋQWUҧ OӡLFkXKӓLKRҥWÿӝQJ.KӣLÿӝQJ
EҵQJFiFKWKӇ KLӋQVӕ Fk\WUӗQJWKrPFӝQJYӟLSKҧLOӟQKѫQKRһFEҵQJ
* %iRFiRNWTXKRWÿQJYjWKROXQ: *9FKRQKyP+6[XQJSKRQJJKLNӃWTXҧ
WUrQEҧQJQKyP+6NKiFQKұQ[pW
* KWOXQQKQÿQK: *9QKұQ[pWFkXWUҧ OӡLFӫD+6YjFKӕWOҥL[t
.KiLQLӋPEҩWSKѭѫQJWUuQK
+RҥWÿӝQJ.KiPSKi
a) MөFWLrX +6SKiWELӇXÿѭӧFÿӏQKQJKƭDEҩWSKѭѫQJWUuQK
ENӝLGXQJ 1KyP+6ÿӑFÿӅ EjLYjWUҧ OӡLFkXKӓLWURQJKRҥWÿӝQJ.KiPSKi6DXÿy
U~WUDÿӏQKQJKƭDEҩWSKѭѫQJWUuQK
F6ҧQSKҭP
+RҥWÿӝQJ.KiPSKi[t
G7ә FKӭFWKӵFKLӋQ
*9FKX\QJLDRQKLPYKFWS *9\rXFҫXFiFQKyP+6ÿӅ EjLYjWUҧ OӡLFkXKӓL
WURQJKRҥWÿӝQJ.KiPSKi
+6WKFKLQQKLPYKFWS
– &iFQKyP+6TXDQViWWKӵFKLӋQKRҥWÿӝQJ.KiPSKi
– *9WәQJTXiWOrQFiFKӋ WKӭFWѭѫQJWӵ FӫDKRҥWÿӝQJ.KiPSKiWӯ ÿy\rXFҫX+6
SKiWELӇXÿӏQKQJKƭDEҩWSKѭѫQJWUuQK
%iRFiRNWTXKRWÿQJYjWKROXQ
– ĈҥLGLӋQQKyP+6OrQEҧQJJKLÿiSiQWURQJKRҥWÿӝQJ.KiPSKi
– +6SKiWELӇXÿӏQKQJKƭDEҩWSKѭѫQJWUuQK
.WOXQQKQÿQK
– *9ÿiQKJLiNӃWTXҧ OjPYLӋFFӫD+6TXDKRҥWÿӝQJ.KiPSKi
– *9WUuQKEj\9tGө
+RҥWÿӝQJ: 7KӵFKjQK
a) MөFWLrX
– Sӱ GөQJÿӏQKQJKƭDEҩWSKѭѫQJWUuQK EұFQKҩWPӝWҭQQKұQELӃWFiFEҩWSKѭѫQJWUuQK
EұFQKҩWPӝWҭQ WURQJ KRҥWÿӝQJ 7KӵFKjQK
– 7uPQJKLӋPFӫDEҩWSKѭѫQJWUuQK EұFQKҩWPӝWҭQWURQJ KRҥWÿӝQJ 7KӵFKjQK
E1ӝLGXQJ+6WKӵFKLӋQ KRҥWÿӝQJ 7KӵFKjQKFKӍ UDFiFEҩWSKѭѫQJWUuQKEұFQKҩW
PӝWҭQWuPPӝWVӕ OjQJKLӋPYjNK{QJOjQJKLӋPFӫDEҩWSKѭѫQJWUuQKEұFQKҩWPӝWҭQ
F6ҧQSKҭP
+RҥWÿӝQJThӵFKjQK&iFEҩWSKѭѫQJWUuQKEұFQKҩWPӝWҭQOj[–[d
+RҥWÿӝQJThӵFKjQK[ OjPӝWQJKLӋPFӫDEҩWSKѭѫQJWUuQK
[ –NK{QJOjQJKLӋPFӫDEҩWSKѭѫQJWUuQK
ҩ
%. .+È03+È– 7+Ӵ&+¬1+–VҰ1'ӨNG
G7ә FKӭFWKӵFKLӋQ
*9FKX\QJLDRQKLPYKFWS *9\rXFҫX+6ÿӑFYjWKӵFKLӋQ KRҥWÿӝQJ 7KӵFKjQK
+6WKFKLQQKLPYKFWS 0ӛL+6WKӵFKLӋQQKұQELӃWFiFEҩWSKѭѫQJWUuQK
EұFQKҩWPӝWҭQWURQJKRҥWÿӝQJ7KӵFKjQKYjFKӍ UDPӝWVӕ OjQJKLӋPNK{QJOjQJKLӋP
FӫDEҩWSKѭѫQJWUuQKEұFQKҩWPӝWҭQWURQJ KRҥWÿӝQJ 7KӵFKjQK
%iRFiRNWTXKRWÿQJYjWKROXQ &KӑQ+6EҩWNuOҫQOѭӧWOrQEҧQJWUuQKEj\
KRҥWÿӝQJ7KӵFKjQK+6NKiFQKұQ[pW
.WOXQQKQÿQK *9QKұQ[pWÿiQKJLiEjLOjPFӫD+6TXD KRҥWÿӝQJ 7KӵFKjQK2
VRYӟLÿiSiQÿ~QJ*ӧLêPӣUӝQJFKR+6WѭGX\NKiFKѫQWURQJKRҥWÿӝQJ7KӵFKjQK
FKӍ UDFiFQJKLӋPNKiFQKDX
2. *LҧLEҩWSKѭѫQJWUuQKEұFQKҩWPӝWҭQ
+RҥWÿӝQJ.KiPSKi
a) MөFWLrX: +6FKӍ UDÿѭӧFGӵDYjRWtQKFKҩWEҩWÿҷQJWKӭFWDYұQGөQJYjRJLҧLEҩW
SKѭѫQJWUuQKEұFQKҩWPӝWҭQ
E1ӝLGXQJ+6KRҥWÿӝQJQKyPFQJWKҧROXұQKRjQWKjQKKRҥWÿӝQJ.KiPSKi
F6ҧQSKҭP
– +RҥWÿӝQJKKiPSKi: D[!–E[!
2
F[t
2
3
GTә FKӭF WKӵFKLӋQ:
*9FKX\QJLDRQKLPYKFWS *9FKR+6KRҥWÿӝQJQKyPWKӵFKLӋQKRҥWÿӝQJ
.KiPSKi
+6WKFKLQQKLPYKFWS
– +6TXDQViWÿӅEjLYjWKӵFKLӋQKRҥWÿӝQJ.KiPSKi*9KѭӟQJGүQ+6VӱGөQJ
WtQKFKҩWFӫDEҩWÿҷQJWKӭF
– +6U~WUDWtQKFKҩWFӫDEҩWSKѭѫQJWUuQK
%iRFiRNWTXKRWÿQJYjWKROXQ
– +6OrQEҧQJGiQNӃWTXҧ KRҥWÿӝQJ.KiPSKiFiFQKyPNKiFQKұQ[pWFKpRQKDX
– +6U~WUDFiFWtQKFKҩWFӫDEҩWSKѭѫQJWUuQKWtQKFKҩWFӝQJWtQKFKҩWQKkQ
.WOXQQKQÿQK:
– *9QKұQ[pWÿӕLFKLӃXNӃWTXҧ KRҥWÿӝQJ.KiPSKiFӫD+6YӟLVҧQSKҭP
– *9NӃWOXұQFiFWtQKFKҩWFӫDEҩWSKѭѫQJWUuQK
– *9OҫQOѭӧWWUuQKEj\9tGө
+RҥWÿӝQJ: ThӵFKjQK
a) MөFWLrX ÈSGөQJWtQKFKҩWEҩWSKѭѫQJWUuQKJLҧLÿѭӧFFiFEҩWSKѭѫQJWUuQKEұFQKҩWPӝWҭQ
E1ӝLGXQJ +6ÿӑFYjWKӵFKLӋQKRҥWÿӝQJ7KӵFKjQK
F6ҧQSKҭP
+RҥWÿӝQJThӵFKjQKD[
3
E[d –
3
+RҥWÿӝQJThӵFKjQK[!–
G7ә FKӭFWKӵFKLӋQ
*9 FKX\Q JLDR QKLP Y KF WS *9\rXFҫX+6ÿӑFYjWKӵFKLӋQ KRҥW ÿӝQJ
7KӵFKjQK
+6WKFKLQQKLPYKFWS 0ӛL+6JLҧLPӝWEҩWSKѭѫQJWUuQKEұFQKҩWPӝWҭQFӫD
KRҥWÿӝQJ7KӵFKjQK
%iRFiRNWTXKRWÿQJYjWKROXQ +6[XQJSKRQJOҫQOѭӧWOrQEҧQJWUuQKEj\
KRҥWÿӝQJ7KӵFKjQK+6NKiFQKұQ[pW
.WOXQQKQÿQK:
– *9QKұQ[pWÿiQKJLiEjLOjPFӫD+6WURQJ KRҥWÿӝQJ 7KӵFKjQKYӟLÿiSiQÿ~QJ
– *9WyPWҳWQKҳFOҥLFiFWtQKFKҩWYjQrXOҥLFiFEѭӟFJLҧLEҩWSKѭѫQJWUuQKEұFQKҩWPӝWҭQ
+RҥWÿӝQJ: VұQGөQJ
a) MөFWLrX ÈSGөQJÿӏQKQJKƭDWKӵFKLӋQELӇXWKӏ EҩWSKѭѫQJWUuQKUӗLWuPQJKLӋPFӫD
EҩWSKѭѫQJWUuQKEұFQKҩWPӝWҭQ
E1ӝLGXQJ+6WKӵFKLӋQKRҥWÿӝQJ9ұQGөQJ
F6ҧQSKҭP
+RҥWÿӝQJVұQGөQJSӕ Fk\[DQKOӟSFҫQWUӗQJWKrPtWQKҩWOjFk\
G7ә FKӭFWKӵFKLӋQ
*9FKX\QJLDRQKLPYKFWS *9\rXFҫX+6ÿӑFYjWKӵFKLӋQ KRҥWÿӝQJ 9ұQGөQJ
+6WKFKLQQKLPYKFWS 0ӛL+6WKӵFKLӋQ KRҥWÿӝQJ 9ұQGөQJ
%iRFiRNWTXKRWÿQJYjWKROXQ &KӑQ+6[XQJSKRQJOrQEҧQJWUuQKEj\
KRҥWÿӝQJ9ұQGөQJ+6NKiFQKұQ[pW
.WOXQQKQÿQK *9QKұQ[pWÿiQKJLiEjLOjPFӫD+6WURQJ KRҥWÿӝQJ 9ұQGөQJ
VRYӟLÿiSiQÿ~QJ
– ;HPOҥLÿӏQKQJKƭDYjQKұQELӃWFiFEҩWSKѭѫQJWUuQKEұFQKҩWPӝWҭQ
– ;HPOҥLFiFWtQKFKҩWFӫDEҩWSKѭѫQJWUuQKYұQGөQJYjRJLҧLFiFEҩWSKѭѫQJWUuQK
EұFQKҩWPӝWҭQ
– +RjQWKjQKEjLWұS
– &KXҭQEӏ EjLPӟL“%jLWұSFXӕLFKѭѫQJ”
,9.ӂ +2Ҥ&+ĈÈ1+*,È
+uQKWKӭF ÿiQKJLi 3KѭѫQJSKiS ÿiQKJLi &{QJFө ÿiQKJLi *KL&K~
– ĈiQKJLiWKѭӡQJ[X\rQ
6ӵ WtFK FӵF FKӫ ÿӝQJ
FӫD +6 WURQJ TXi WUuQK
WKDPJLD[k\GӵQJEjL
6ӵ hӭQJ WK~ Wӵ WLQ
WUiFK QKLӋP FӫD +6 NKL
WKDP JLD FiF KRҥW ÿӝQJ
hӑFWұSFiQKkQJLҧLÿѭӧF
EҩWSKѭѫQJWUuQKEұFQKҩW
PӝWҭQ
7KӵF KLӋQ FiF QKLӋP
Yө hӧSWiFQKyP
– 3KѭѫQJSKiSTXDQViW
*9TXDQViWTXDTXi
WUuQK KӑF WұS FKXҭQ Eӏ
EjLWKDPJLDYjREjLKӑF
*9TXDQViWKjQKÿӝQJ
FNJQJQKѭWKiLÿӝFҧP[~F
FӫD+6
– %iR FiR WKӵF KLӋQ
F{QJYLӋF
– +Ӌ WKӕQJFkXKӓLYj
JLҧLEjLWұS
– 7UDRÿәLWKҧROXұQ
EL
Ӄ
iE
ҩ
KuK
&1+,ӊM VӨ
