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vii
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1
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1. 7tQKFҩp thiӃt
Mӝt trong nhӳng nhiӋm vө cӫDP{QWRiQOjSKiWWULӇQQăQJOӵFWUtWXӋ chung
cho hӑc sinh, bao gӗPWѭGX\WUӯXWѭӧng, khҧ QăQJWѭӣQJWѭӧQJNK{QJJLDQ
Wѭ GX\ ORJLFWѭ GX\ ELӋn chӭQJ« 7URQJ ÿyYLӋF UqQOX\ӋQ FiF WKDR WiF Wѭ
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nhiӋm vө quan trӑng. Thұt vұ\YuWURQJTXiWUuQKKӑc tұSP{QWRiQKӑc sinh
phҧL WKѭӡQJ [X\rQ WKӵc hiӋn nhӳQJ WKDR WiF Wѭ GX\ ÿһc biӋW Oj ÿӕi vӟL TXi
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nhӳQJWKDRWiFWѭGX\QyLWUrQTheo &K˱˯QJWUuQKJLiRGͭc ph͝ WK{QJQăP
2018 P{Q 7RiQJyS SKҫQKuQKWKjQK UqQ OX\ӋQ YjSKiW WULӇn cho hӑc sinh
QăQJOӵFWRiQKӑc bao gӗPFiFWKjQKSKҫn chӫ yӃXFѫEҧQQăQJOӵFWѭGX\
YjOұp luұQWRiQKӑFQăQg lӵFP{KuQKKyDWRiQKӑFQăQJOӵc giҧi quyӃt vҩn
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tiӋn hӑFWRiQ7ҥi bұc hӑc trung hӑc phә WK{QJQăQJOӵFWѭGX\WKӇ hiӋn ӣ chӛ
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VRViQKSKkQWtFKWәng hӧSÿһc biӋWKyDNKiLTXiWKyDWѭѫQJWӵ, quy nҥp,
diӉn dӏch ( Bӝ *LiRGөFYjĈjRWҥo (2018), &K˱˯QJWUuQKJLiRGͭc ph͝ WK{QJ
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WKiQJQăP 2018 cӫa Bӝ 7Uѭӣng Bӝ *LiRGөFYjĈjRWҥo).
Ӣ WUѭӡng phә WK{QJGҥy hӑFP{Q7RiQOjPӝt hoҥWÿӝQJWRiQKӑFFy
thӇ xem viӋc giҧLWRiQOjKuQKWKӭc chӫ yӃu cӫa hoҥWÿӝQJWRiQKӑFFiFEjL
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2
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WUѭӡQJ7+37WUrQÿӏDEjQQJKLrQFӭu.
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cӫa sӵ vұt, hiӋQWѭӧng.
3
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hiӋn ra quy luұt cӫa sӵ vұt bҵQJ FiF KuQK WKӭF QKѭ ELӇX WѭӧQJ SKiQ
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TXiWKyDWUӯXWѭӧQJKyD.
Trong TXiWUuQKdҥy hӑc P{Q7RiQYLӋFUqQOX\ӋQFiFWKDRWiFWѭGX\
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vұn dөng kiӃn thӭFÿmKӑFYjRgiҧi quyӃWFiFYҩQÿӅ trong thӵc tiӉQĈӇ UqQ
luyӋQYjSKiWWULӇn WѭGX\ cho hӑFVLQKJLiRYLrQFҫn tҥo nhӳng WuQKKXӕQJFy
vҩQÿӅFkXKӓLFyWtQKJӧi mӣ ÿӇ FiFHPWӯQJEѭӟc WѭGX\, suy luұn trong
TXiWUuQKJLҧi quyӃt vҩQÿӅ.
Sӕ phӭFWURQJViFKJLiRNKRDOӟSOjPӝt trong nhӳng nӝi dung quan
trӑQJWURQJFKѭѫQJWUuQKWRiQ7+37. Sӕ phӭFOjPӝt trong nhӳQJSKiWKLӋn
lӟn cӫDQKjWRiQKӑc Gau ± [ѫ
Trong nhӳQJQăPJҫQÿk\QӝLGXQJWKLĈҥi hӑc- &DRÿҷQJYjFiFNǤ
thi chӑn hӑc sinh giӓi nӝi dung Sӕ phӭFOjPӝt trong nhӳng nӝLGXQJ\rXcҫu
WKtVLQKSKҧi thӵc hiӋQWURQJFiFEjLWKLP{Q7RiQ.Qua thӵc tiӉn giҧng dҥ\Yj
kiӇPWUDÿiQKJLiNӃt hӧSÿLӅXWUDWKHRG}LNӃt quҧ WKLĈҥi hӑF&DRÿҷng cӫa
FiFNKyDJҫQÿk\, FK~QJW{LQKұn thҩy phҫn lӟQFiFWKtVLQKÿӅu hҥn chӃ trong
viӋc xӱ OêFiFQӝLGXQJOLrQTXDQÿӃn chӫ ÿӅ Qj\Fө thӇ OjNK{QJOjPÿѭӧc
hoһFOjPNK{QJWUӑn vҽn nӝLGXQJÿӅ thi vӅ Sӕ phӭFPjWKӵc tiӉQFK~QJW{L
nhұn thҩy nӝLGXQJQj\OjNK{QJTXiNKy
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VLQKFiFQӝi dung sau:
- Cӫng cӕ YjPӣ rӝng nhӳng kiӃn thӭFPjKӑFVLQKÿmWLӃSWKXÿѭӧc
TXDP{QKӑc ӣ WUrQOӟSÿӇ biӃt vұn dөQJViQJWҥRYjRFiFFkXKӓLOLrQTXDQ
- 5qQOX\ӋQFiFNӻ QăQJFѫEҧn cҫn thiӃt nhҵPQkQJFDRQăQJOӵFWѭ
GX\YjWKiLÿӝ WtFKFӵc cӫa hӑc sinh trong hӑc tұp.
4
- GiҧLÿѭӧFFiFEjLWRiQQkQJFDRWURQJFiFÿӅ thi THPT Quӕc gia Yj
FiFEjLWRiQWURQJFiFNǤ WKLNKiF
- TұSFKRFiFHPWKyLTXHQWѭGX\ViQJWҥRYjYұn dөng linh hoҥWFiF
kiӃn thӭc hӑFWURQJFKѭѫQJWUuQKSKә WK{QJQyLFKXQJYjNLӃn thӭc kӻ QăQJ
vӅ Sӕ phӭFQyLULrQJÿӇ giҧi quyӃWFiFYҩQÿӅ PjWKӵc tӃ ÿDQJÿzLKӓi.
2. Mөc WLrX QJKLrQFӭu cӫa luұQYăQ
- MөFÿtFKQJKLrQFӭu: ;k\Gӵng hӋ thӕng FiFJyLEjLWұp vӅ chӫ ÿӅ
sӕ phӭFYjÿӅ xuҩt mӝt sӕ biӋQSKiSNKDLWKiFVӱ dөng nhҵPUqQOX\Ӌn cho
hӑc sinh mӝt sӕ WKDRWiFWѭGX\
3. NhiӋm vө QJKLrQFӭu
- HӋ thӕQJKyDFѫVӣ OêOXұQYjWKӵc tiӉn vӅ dҥy hӑc chӫ ÿӅ sӕ phӭc
trong dҥy hӑF7RiQ7+37
- 5qQ OX\Ӌn mӝt sӕ WKDR WiF Wѭ GX\ FKR KӑF VLQK WK{QJ TXD viӋc [k\
dӵQJFiFJyLEjLWұp.
- 1JKLrQFӭu mөFWLrXQӝLGXQJFKѭѫQJWUuQKbӝ P{Q7RiQ7+37QyL
chung, nӝi dung dung chӫ ÿӅ sӕ phӭc QyL ULrQJ OjP U} ѭX WKӃ cӫa chӫ ÿӅ
7RiQKӑFQj\WURQJYLӋc SKiWWULӇQWѭGX\cho hӑc sinh.
- ;iFÿӏnh ÿѭӧc ÿӏQKKѭӟQJFiFQJX\rQWҳFOjPFăQFӭ ÿӇ tӯ ÿy[k\
dӵQJFiFELӋQSKiSEӗLGѭӥQJQăQJOӵc YjSKiWWULӇQWѭGX\.
- ĈӅ xuҩt mӝt sӕ biӋQSKiSÿӇ bӗLGѭӥQJQăQJOӵc WѭGX\ cho hӑc sinh
WK{QJTXDGҥy hӑc vӅ chӫ ÿӅ sӕ phӭc.
- Thӵc hiӋn thӱ nghiӋPÿӇ khҷQJÿӏnh WtQKNKҧ WKLYjKLӋu quҧ cӫa Luұn
YăQ
4. ĈӕLWѭӧng YjSKҥPYLQJKLrQFӭu
ĈӕLWѭӧQJQJKLrQFӭu
-.KiFKWKӇ QJKLrQFӭu: 4XiWUuQKGҥy hӑc chӫ ÿӅ Sӕ phӭc cho hӑc sinh
lӟp 12.
- Nhӳng biӋQSKiSWKӵc hiӋQiSGөng trong hӑc tұSYjJLҧng dҥy phҫn
5
Sӕ phӭc ӣ 7RiQlӟp WURQJWUѭӡng THPT.
6
4.2 PhҥPYLQJKLrQFӭu
VӅ mһWOtOXұQFK~QJW{LFKӫ yӃu tұSWUXQJYjRQJKLrQFӭu viӋc khai
WKiFYjVӱ dөng hӋ thӕQJEjLWұp sӕ phӭc nhҵPUqQOX\Ӌn cho hӑc sinh lӟp 12
nhӳQJWKDRWiFWѭGX\QKѭSKkQWtFKWәng hӧSNKiLTXiWKyDWѭѫQJWӵ KyD
Yjÿһc biӋWKyD
VӅ khҧRViWWKӵc trҥQJFK~QJW{LFKӍ QJKLrQFӭXFKѭѫQJWUuQKWUrQÿӏa
EjQ+X\ӋQ7DP1{QJYjPӝt sӕ WUѭӡQJ7+37OkQFұn cӫa tӍQK3K~7Kӑ.
5. Giҧ thuyӃt khoa hӑc
NӃXNKDLWKiFYjVӱ dөng hiӋu quҧ hӋ thӕng FiFJyLEjLWұp sӁ JySSKҫn
SKiWWULӇn WѭGX\ cho hӑc sinh bҧRÿҧm thӵc hiӋn tӕt mөFWLrXGҥy hӑc.
63KѭѫQJSKiSQJKLrQFӭu
- 3KѭѫQJSKiSQJKLrQFӭXOtOXұQ7uPKLӇXQJKLrQFӭXJLiRWUuQKWjL
liӋXYӅFKX\rQÿӅsӕ phӭcFiFViFKWKDPNKҧRYjFiFWjLOLӋXNKiFOLrQTXDQ
ÿӃQÿӅWjL
-3KѭѫQJSKiSÿLӅXWUDTXDQViW.KҧRViWWKӵFWUҥQJGҥ\Kӑc giҧLWRiQ
sӕ phӭc ӣ WUѭӡng THPT hiӋn nay.
éQJKƭDvӅ mһt OtOXұQYjWKӵc tiӉn
éQJKƭDvӅ mһt OtOXұn
LuұQYăQÿmÿѭDUDFiFKNKDLWKiFYjVӱ dөng hӋ thӕQJEjLWұSWRiQKӑc
trong dҥy hӑc chӫ ÿӅ sӕ phӭc cho hӑc sinh lӟp 12 nhҵPUqQOX\ӋQSKiWWULӇn
cho hӑc sinh lӟSFiFWKDRWiFWѭGX\
éQJKƭD vӅ mһt thӵc tiӉn
LuұQYăQOjWjLOLӋu tham khҧo hӳXtFKKӛ trӧ JLiRYLrQFiFKWKӭc khai
WKiFVӱ dөng hӋ thӕQJEjLWұSWRiQQyLFKXQJKӋ thӕQJEjLWұp vӅ chӫ ÿӅ Sӕ
phӭFQyLULrQJWURQJGҥy hӑFP{QWRiQQKҵPUqQOX\ӋQSKiWWULӇn cho hӑc sinh
lӟSFiFWKDRWiFWѭGX\
7
NӜI DUNG 9¬3+ѬѪ1*3+È31*+,Ç1&ӬU
&+ѬѪ1*0ӜT SӔ VҨ1Ĉӄ Vӄ &Ѫ6Ӣ /é/8ҰN
9¬7+ӴC TIӈN
1.1. Lӏch sӱ cӫa vҩQÿӅ QJKLrQFӭu
1KѭFK~QJWDÿmELӃt tѭGX\7'Ojmӝt TXiWUuQKQKұn thӭc, phҧQiQK
nhӳng thuӝF WtQK chung bҧn chҩt, nhӳng mӕi quan hӋ Fy WtQK chҩt quy luұt
cӫa sӵ vұt, hiӋQWѭӧng >>@+RjQJ3Kr7ӯ ÿLӇn tiӃng ViӋt. NXB Khoa
hӑF[mKӝi.]. &yWKӇ QyL 7'OjJLDLÿRҥn cao cӫa nhұn thӭc, QyÿLVkXYjREҧn
chҩWYjchӍ UDFiF quy luұt cӫa sӵ vұt hiӋQWѭӧng bҵQJFiFKuQKWKӭFQKѭELӇu
WѭӧQJSKiQ ÿRiQVX\OtĈӕLWѭӧng cӫDWKDRWiF7'OjQKӳQJKuQKҧnh, biӇu
WѭӧQJNtKLӋX&iFWKDRWiF7'FKӫ yӃu gӗPSKkQWtFKWәng hӧSVRViQK
WѭѫQJWӵNKiLTXiWKyDWUӯXWѭӧQJKyD
.KiLQLӋm vӅ FiFWKDRWiFWѭGX\ÿѭӧFÿӅ cұSÿӃn trong nhiӅXWjLliӋu
vӅ SKѭѫQJSKiSGҥy hӑFYjWKӵFKjQKJLҧLWRiQ>@>@
&yQKLӅXQKjJLiRGөFÿmQJKLrQFӭu vӅ WѭGX\QyLFKXQJWѭGX\WRiQ
hӑF QyL ULrQJ WURQJ Vӕ ÿy WLrX ELӇX Yj TXHQ WKXӝF Oj 3RO\D Trong dҥy hӑc
7RiQYLӋFUqQOX\ӋQFiFWKDRWiF7'FKR+6FyYDLWUzTXDQWUӑQJOjFѫVӣ ÿӇ
QJѭӡi hӑc nҳm vӳQJYjELӃt vұn dөng kiӃn thӭFÿmKӑFYjRWKӵc tiӉn. 9uYұy
vҩQ ÿӅ UqQOX\ӋQ FiF WKDRWiF 7' FKR KӑF VLQK ÿmWKXK~WVӵ TXDQWkP Fӫa
nhiӅXWiFJLҧ7KHRÿyFiFWiFJLҧ ÿmÿӅ xuҩt nhӳng giҧLSKiSFiFKWKӭFUqQ
luyӋn cho HS mӝt sӕ WKDRWiFWѭGX\WK{QJTXDGҥy hӑFFiFFKӫ ÿӅ hoһFFiF
nӝLGXQJWRiQKӑc cө thӇ.
Trong [1], QKyPWiFJLҧ NguyӉQ7KDQK+ѭQJ1J{7QJ1KkQÿmFKӍ
ra nhӳQJFiFKWKӭFÿӇ UqQOX\Ӌn cho hӑc sinh mӝt sӕ WKDRWiFWѭGX\SKkQWtFK
YjWәng hӧSWѭѫQg tӵ KyDNKiLTXiWKyDYjÿһc biӋWKyDVRViQKWK{QJTXD
dҥy hӑFFKѭѫQJ³7ӭ JLiF´7RiQӣ WUѭӡng trung hӑFFѫVӣ.
8
7KHRWiFJLҧ /r3KѭѫQJ>@FNJQJÿmSKkQWtFKQKӳQJFѫVӣ khoa hӑc cӫDFiF
WKDRWiFWѭGX\WKӵc tiӉn viӋFUqQOX\ӋQYjWKӵc hiӋQFiFWKDRWiFQj\FӫDJLiR
YLrQYjKӑc sinh ӣ WUѭӡQJ7+37ÿӅ xuҩWTX\WUuQKWKӵc hiӋQWKDRWiFSKkQ
WtFK- tәng hӧSTX\WUuQKWKӵc hiӋQWKDRWiFWUӯXWѭӧQJKyD- NKiLTXiWKyDÿӅ
xuҩt 7 biӋQSKiSVѭSKҥm nhҵPUqQOX\ӋQFiFWKDRWiFWѭGX\FKRKӑc sinh.
1.2. 7ѭGX\
.KiLQLӋPYjÿһFÿLӇm cӫDWѭGX\
7ѭGX\OjPӝWTXiWUuQKWkPOêSKҧQiQKQKӳng thuӝFWtQKEҧn chҩt, nhӳng
mӕLOLrQKӋ YjTXDQKӋ ErQWURQJFyWtQKTX\OXұWFӫDVӵ vұt, hiӋQWѭӧng trong
hiӋn thӵF NKiFK TXDQ Pj WUѭӟF ÿy WD FKѭD ELӃt. Theo Tӯ ÿiӇn TiӃng ViӋW
³7ѭGX\OjJLDLÿRҥQFDRFӫDTXiWUuQKÿLVkXYjR FiLEҧn chҩWYjSKiWKLӋn ra
quy luұWFӫDVӵ vұt bҵng nhӳQJKuQKWKӭFQKѭELӇu WѭӧQJSKiQÿRiQYjVX\
Oê´ Ӣ mӭFÿӝ nhұn thӭc cҧPWtQKFRQQJѭӡi mӟi chӍ phҧQiQKFiFWKXӝFWtQK
ErQ ngojLQKѭKuQKGiQJPjXVҳF«OjQKӳng thuӝFWtQKFyWKӇWKD\ÿәLYj
nhұn thӭc ÿѭӧc bҵQJFiFJLiFTXDQNKLVӵ vұt, hiӋQWѭӧQJÿDQJWUӵc tiӃp WiF
ÿӝng. Nҧ\VLQKWUrQ FѫVӣ nhұn thӭc cҧPWtQKYjYѭӧt xa giӟLKҥQFӫDnhұn
thӭc cҧPWtQKWѭGX\SKҧQiQK nhӳng thuӝFWtQKEҧn chҩWErQWURQJQKӳng
mӕL OLrQ KӋ Fy WtQK TX\ OXұW FӫD KjQJ ORҥW sӵ vұt, hiӋQ Wѭӧng (nhӳng thuӝc
WtQKQKӳng mӕLOLrQKӋ, quan hӋ Qj\OjQKӳQJÿһc ÿLӇm gҳQOLӅQYӟi sӵ vұt,
hiӋQWѭӧng), nhӳQJFiLPjEҵQJFiFJLiFTXDQYjSKѭѫQJ thӭc nhұn thӭc cҧm
WtQKFRQQJѭӡLFKѭDWKӇ phҧQiQKÿѭӧc. MһWNKiFӣ mӭFÿӝ nhұn thӭc cҧm
WtQKFRQQJѭӡi chӍ phҧQiQKFiLÿDQJFyWURQJKLӋQWҥLWUӵc tiӃSWiFÿӝQJYjR
JLiFTXDQWDÿӃQWѭGX\FRQQJѭӡLKѭӟQJYjRYLӋFWuPNLӃPFiLPӟLFiLEҧn
chҩWFiL NKiLTXiWQKӳQJFiLPjFRQQJѭӡLFKѭDELӃWFRQQJѭӡi cҫn phҧLWuP
kiӃP Yj Qҳm ÿѭӧF ÿӇ tiӃp tөc nhұn thӭc, cҧL WҥR Yj ViQJ WҥR WKӃ giӟi. 1Kѭ
vұ\WѭGX\JL~SFRQQJѭӡi nҳPÿѭӧc bҧn chҩWYjTX\OXұt vұQÿӝQJFӫD tӵ
QKLrQ[mKӝLYjFRQQJѭӡLWѭGX\FyWiFGөng cҧLWҥROҥLWK{QJWLQQKұn thӭc
cҧm WtQK OjP FKR FK~QJ Fy ê QJKƭD KѫQ WURQJ FXӝc sӕQJ Wѭ GX\ Yұn dөng
9
nhӳQJFiLÿm biӃWÿӇ ÿӅUDJLҧLSKiSJLҧi quyӃt nhӳQJFiLWѭѫQJWӵ. 7ѭGX\
WRiQ KӑF ÿѭӧc hiӇX Oj TXi WUuQK QKұn thӭc, phҧQ iQK QKӳng thuӝF WtQK bҧn
chҩWSKiWKLӋn ra nhӳng mӕi quan hӋ ErQWURQJFyTX\OXұWFӫDFiFÿӕLWѭӧng
WRiQKӑFPjWUѭӟFÿyWDFKѭDELӃt. Sҧn phҭPFӫDWѭGX\WRiQKӑFOjQKӳng
NKiL niӋm, nhӳQJÿӏQK OêTX\ WҳFSKѭѫQJ SKiSVX\ OXұQ«PDQJWtQKNKiL
TXiWWtQK trӯXWѭӧQJFDRFy WtQKNKRDKӑFWtQKORJLFFKһt chӁFiFWULWKӭFFy
mӕi quan hӋ mұt thiӃWYjKӛ trӧ lүQQKDXÿѭӧc biӇXÿҥWFKӫ\Ӄu bҵQJQJ{Q
ngӳ viӃWNêKLӋu, biӇu thӭFF{QJWKӭF«
Theo NguyӉQ %i .LP YLӋF Gҥ\ KӑF WRiQ NK{QJ FKӍ dӯQJ OҥL ӣ chӛ chӍ ÿӇ
QJѭӡi hӑF Oƭnh hӝL ÿѭӧc tri thӭF WRiQ KӑF UqQ OX\ӋQ ÿѭӧF FiF Nӻ QăQJ Nӻ
xҧRPjÿzL hӓLNK{QJQJӯQJQkQJFDR\rXFҫXÿӇWK~Fÿҭy sӵ SKiWWULӇQFӫD
QJѭӡi hӑc, buӝc hӑ phҧLWtFKFӵFVX\QJKƭSKҩQÿҩu nhҵPÿҥWÿѭӧc mөFWLrX
ÿӗng thӡLTXDÿyKuQK WKjQKYjUqQOX\Ӌn FKRQJѭӡi hӑc nhӳQJSKѭѫQJSKiS
VX\QJKƭSKѭѫQJSKiSWѭGX\ YjSKѭѫQJSKiSOjPYLӋc khoa hӑF3KiWWULӇn
WѭGX\WRiQKӑFFKRQJѭӡi hӑFOjPӝt OƭQKYӵc vӯa rӝng lӟn, vӯDNKyNKăQ
QJѭӡLJLiRYLrQGҥ\WRiQFҫn phҧi biӃWWtFKONJ\ kiӃn thӭFU~WNLQKQJKLӋm mӝt
FiFKWKѭӡQJ[X\rQYjOkXGjLÿӇ tӯ ÿyYӳQJYjQJKѫQ YӅFKX\rQP{QQJKLӋp
vөFyQKӳng biӋQSKiSUqQOX\ӋQYjSKiWWULӇQWѭGX\WRiQ hӑc mӝWFiFKWKtFK
hӧp cho tӯQJORҥL+6WURQJTXiWUuQKJLҧQJGҥ\>@ Theo NguyӉn Duy Thuұn
WKuYLӋFUqQOX\ӋQYj SKiWWULӇQWѭGX\FKR+6Yj mӝt nhiӋm vө quan trӑng
trong sӵ nghiӋSJLiRGөFÿһc biӋWOjWURQJTXiWUuQKGҥ\ hӑFWRiQ1ySKҧi trҧi
qua mӝWTXiWUuQKWKѭӡQJ[X\rQYұn dөQJFiFTX\WҳFWѭGX\ FѫEҧn mӝWFiFK
WKtFKKӧp, phҧi xuҩWSKiWWӯ FiFYҩQÿӅGӉ ÿӃn NKyÿLWӯ FiFWUѭӡng hӧSÿѫQ
giҧQ ÿӃn phӭF WҥS SKҧi vұn dөQJ FiF SKѭѫQJ SKiS VX\ OXұn mӝW FiFK OLQK
KRҥW.LӃn thӭFWRiQKӑFÿѭӧc sҳp xӃp theo hӋ thӕQJO{JLFFKһt chӁ YjOLrQ
tөc, tri thӭFWUѭӟFOjPFѫVӣ cho tri thӭFVDXFKRQrQSKҧi hiӇXYjQҳm vӳng
kiӃn thӭFFy kiӃn thӭc mӟLFyFѫVӣ ÿӇ dӵDWUrQÿyPjWѭGX\ÿ~QJÿҳn, hiӇu
biӃWFjQJVkXVҳc, kiӃn thӭFFjQJYӳQJYjQJWKuWѭGX\FjQJFKtQK[iFFjQJ
10
PҥFKOҥF>@ 5qQOX\ӋQYjSKiWWULӇQWѭGX\FKRQJѭӡi hӑFOjPӝt nhiӋm vө
quan trӑng WURQJGҥ\KӑF7RiQKӑFOjP{QNKRDKӑFFyWtQKWUӯXWѭӧng cao
YjWtQKORJLFFKһt chӁ9uYұ\QJѭӡi hӑc phҧLFySKѭѫQJSKiSWѭGX\NKRD
hӑF Yj PDQJ WtQK ViQJ WҥR 0{Q WRiQ Fy QKLӅX WLӅP QăQJ Yj FNJQJ Oj P{L
WUѭӡng tӕt nhҩWÿӇ UqQOX\ӋQYjSKiW triӇQWѭGX\FӫDQJѭӡi hӑF7URQJTXi
WUuQKGҥ\WRiQErQFҥQKYLӋFGҥ\+6FiFKWuP lӡi giҧLEjLWұp nӃXFySKѭѫQJ
SKiSNKDLWKiFKӋ thӕQJEjLWұSFkXKӓi mӝWFiFK WKtFKKӧp dӵDWUrQQKӳng
QJX\rQWҳFFѫEҧn sӁJL~SFiFHPELӃWWuPOӡi giҧLEjLWRiQ bҵQJQKLӅXFiFK
NKiFQKDXNKDLWKiFEjLWRiQWKHRQKLӅXKѭӟQJYjJyFÿӝ NKiF nhau, nhӳQJ
KRҥWÿӝQJQj\VӁ JySSKҫQUqQOX\ӋQYjSKiWWULӇQWѭGX\ӣ +6QkQJ cao chҩt
OѭӧQJGҥ\KӑFÿiSӭQJ\rXFҫXGҥ\KӑFSKiWWULӇn hiӋn nay.
1.2.2. Mӝt sӕ WtQKFKҩWÿһFWUѭQJFӫDWѭGX\
7tQKFyY̭Qÿ͉
.K{QJSKҧLKRjQFҧQKQjRFNJQJJk\ÿѭӧFWѭGX\FRQQJѭӡi. MuӕQNtFKWKtFK
ÿѭӧFWѭGX\SKҧLÿӗng thӡLFyKDLÿLӅXNLӋn:
- 7Uѭӟc hӃt phҧi gһSKRjQFҧQKKD\WuQKKXӕQJFyYҩQÿӅ7uQKKXӕQJFy
vҩQÿӅOjWuQKKXӕng chӭDÿӵng mӝt mөFÿtFKPӟi, vҩQÿӅPӟi, mӝWFiFKWKӭc
giҧi quyӃt mӟL Pj Eҵng vӕn hiӇu biӃW FNJ QKӳQJ SKѭѫQJ WLӋQ FNJ SKѭѫQJ
SKiS KRҥW ÿӝQJ FNJ ÿm Fy PһF G Yүn cҫn thiӃW QKѭQJ NK{QJ ÿӫ Vӭc giҧi
quyӃt vҩQÿӅPӟLÿyÿӇÿҥWÿѭӧc mөFÿtFKPӟLÿyĈӇ nhұn thӭFÿѭӧc con
QJѭӡi phҧL Yѭӧt ra khӓL SKҥP vi nhӳng hiӇu biӃW FNJ Yj ÿL WuP FiL PӟL ÿҥW
mөFÿtFKPӟi, cҫQÿӃn nhӳQJSKѭѫQJSKiSPӟi, tӭFOjSKҧLWѭGX\.
- Thӭ KDL +RjQ FҧQK FyYҩQ ÿӅSKҧL ÿѭӧF Fi QKkQ QKұn thӭF ÿҫ\ ÿӫ ÿѭӧc
chuyӇQWKjQKQKLӋm vөFӫDFiQKkQWӭc OjFiQKkQSKҧL[iFÿӏQKÿѭӧFFiLJu
(dӳ kiӋQÿmELӃWÿmFKRYjFiLJuFKѭDELӃt (phҧLWuPÿӗng thӡLFyQKXFҫu
ÿӝQJFѫWuPNLӃPQyYjSKҧLFyWULWKӭc cҫn thiӃWÿӇ giҧi quyӃWWUrQFѫVӣ ÿy
WѭGX\Qҧy sinh.
9t Gө .KL Gҥ\ Qӝi dung sӕ phӭc WURQJ EjL ³Sӕ phӭF´ *9 Fy thӇ WҥR WuQK
11
huӕQJFyYҩQÿӅWK{QJTXDEjLWRiQVDX GiҧLSKѭѫQJWUuQKVDXWUrQWұp sӕ
thӵc x2 +1=0. +6FyWKӇ giҧLÿѭӧFQJD\\rXFҫXÿҫXWLrQQKӡ YjRNLӃn thӭc
ÿmELӃt. 7X\QKLrQӣ \rXFҫu thӭ hai khi JLiRYLrQFKRL2= -1ฺ Xuҩt hiӋQWuQK
huӕQJFyYҩQÿӅQKѭYұy HS sӁ WuPNLӃn thӭc mӟLÿӇ giҧi quyӃWEjLWRiQ.
7tQKJLiQWL͇p
ChӭFQăQJFӫDWѭGX\OjÿLYjRFiLEҧn chҩWYjTXDQKӋ FyWtQKTX\OXұWFӫD
KjQJORҥWVӵ vұt, hiӋQWѭӧng, nhӳQJFiLPjWUѭӟFÿyEҵQJFiFJLiFTXDQEҵng
nhұn thӭc cҧPWtQKFKѭDSKҧQiQKÿѭӧc. Do vұ\WѭGX\SKҧQiQKJLiQWLӃp.
7tQKJLiQtiӃSFӫDWѭGX\WKӇ hiӋn:
- 7ѭGX\SKiWKLӋn ra bҧn chҩWFӫDVӵ vұt, hiӋQWѭӧQJYjTX\OXұt giӳDFK~QJ
nhӡ sӱ dөQJF{QJFөSKѭѫQJWLӋQQKѭÿӗng hӗ, nhiӋt kӃPi\PyF«YjFiF
kӃt quҧ nhұn thӭFQKѭTX\WҳFF{QJWKӭc, quy luұW«FӫDORjLQJѭӡLYjNLQK
nghiӋm FӫDFiQKkQPuQK
- 7tQK JLiQ WLӃS FӫD Wѭ GX\ FzQ WKӇ hiӋn ӣ chӛ Qy FzQ ELӇu hiӋQ WURQJ QJ{Q
ngӳ&RQQJѭӡLOX{QGQJQJ{QQJӳ ÿӇ WѭGX\Nhӡ WtQKJLiQWLӃSPjWѭGX\ÿm
mӣ rӝQJ NK{QJ JLӟL KҥQ QKӳng khҧ QăQJ nhұn thӭF FӫD FRQ QJѭӡi.
9t Gө ĈӇ giҧi mӝW EjL WRiQ NK{QJ FKӍ dӵD WUrQ YLӋF +6 [iF ÿӏQK ÿѭӧc
\rXFҫXFӫDEjLWRiQPjFzQSKҧi nhӟ YjVӱ dөQJFiFÿӏQKOêF{QJWKӭc, quy
tҳF«Fy OLrQ TXDQ ÿӃQ EjL WRiQ PӟL Fy WKӇ giҧi quyӃW ÿѭӧF QKDQK FKyQJ GӉ
GjQJ
7tQKWUͳXW˱ͫQJYjNKiLTXiW
7ѭGX\FyNKҧQăQJÿLVkXYjRQKLӅXVӵ vұt, hiӋQWѭӧng nhҵPYҥFKUDQKӳng
thuӝFWtQKFKXQJQKӳng mӕLOLrQKӋ, quan hӋ FyWtQKTX\OXұt giӳDFK~QJ
1yL FiFK NKiF Wѭ GX\ Fy NKҧ QăQJ SKҧQ iQK QKӳng thuӝF WtQK FKXQJ QKҩt,
bҧn chҩt nhҩWFӫDmӝWORҥWÿӕLWѭӧng - tӭFOjWѭGX\SKҧQiQKKLӋn thӵFNKich
quan. 4XiWUuQKÿLÿӃQNKiLTXiWKyDKLӋn thӵFNKiFKTXDQWѭGX\SKҧi trӯu
xuҩt khӓi sӵ vұt, hiӋQWѭӧng nhӳng thuӝFWtQKQKӳng dҩu hiӋu cө thӇFiELӋW
[pWYӅPӝt SKѭѫQJGLӋQQjRÿy- tӭFOjWѭGX\PDQJWtQKWUӯXWѭӧQJÿӇ chӍ giӳ
12
OҥLQKӳng thuӝc WtQKEҧn chҩWFKXQJFKRQKLӅXVӵ vұt hiӋQWѭӧQJ«UӗLWUrQFѫ
sӣ ÿyPjNKiLTXiW7yPOҥLWѭGX\SKҧQiQKFiLEҧn chҩWFKXQJFKRQKLӅX
sӵ vұt hӧSWKjQKPӝt QKyPPӝWORҥLPӝWSKҥPWUÿӗng thӡi trӯu xuҩt khӓi
nhӳng sӵ vұWÿyFiLFө thӇ, FiELӋW'RÿyWѭGX\ÿӗng thӡi vӯDPDQJWtQK
trӯXWѭӧng, vӯDPDQJWtQKNKiLTXiW
7tQKTXDQK͏ ch̿t chͅ vͣLQJ{Qngͷ
7ѭGX\WUӯXWѭӧQJJLiQWLӃSNKiLTXiWNK{QJWKӇ tӗQWҥLErQQJRjLQJ{QQJӳ,
QyQKҩt thiӃWGQJQJ{QQJӳ OjPSKѭѫQJWLӋn. NӃXNK{QJFyQJ{QQJӳ WKuEҧn
WKkQ TXi WUuQK Wѭ GX\ NK{QJ GLӉQ UD ÿӗng thӡL FiF Vҧn phҭP Wѭ GX\ FNJQJ
NK{QJÿѭӧFFKӫthӇ YjQJѭӡLNKiFWLӃp nhұQ1J{QQJӳ cӕ ÿӏQKOҥLFiF NӃt
quҧFӫDWѭGX\YjQKӡ ÿyOjPNKiFKTXDQKyDFK~QJFKRQJѭӡLNKiFYjEҧQ
WKkQFKӫWKӇ WѭGX\Ӣ mӭFÿӝ nhұn thӭc cҧPWtQKFyWKӇ FKѭDFҫQÿӃQQJ{Q
ngӳ vүQFyKuQKҧQKWUrQQmR&zQÿӃQWѭGX\QKҩt thiӃt phҧi sӱ dөQJQJ{Q
ngӳ OjPSKѭѫQJWLӋQYu
- Nhӡ TXiWUuQKQJ{QQJӳ WURQJÿҫu bҧQWKkQFKӫWKӇ mӟLêWKӭFÿѭӧc, nhұn
thӭFÿѭӧFWuQKKXӕQJFyYҩQÿӅ
- TiӃp theo trong diӉn biӃQFӫDTXiWUuQKWѭGX\FRQQJѭӡi sӱ dөQJQJ{QQJӳ
ÿӇ tiӃQ KjQK FiF WKDR WiF SKkQ WtFK WәQJ KӧS VR ViQK NKiL TXiW KyD WUӯu
WѭӧngKyD
- QJ{QQJӳ WKDPJLDYjRTXiWUuQKWѭGX\
- 1J{QQJӳ FzQELӇXÿҥWNӃt quҧ FӫDTXiWUuQKWѭGX\Sҧn phҭP PjWѭGX\
ÿHPOҥLOjQKӳQJNKiLQLӋm, quy luұW«QJ{QQJӳ sӁ OjPNKiFKTXDQKyDYұt
chҩt KyDQyUDNKӓLÿҫXWDÿӇ ta nhұn thӭFQyEҵQJWuPWzLnhӳng tӯ, nhӳng
mӋQKÿӅELӇXÿҥWQy 1KѭYұ\WѭGX\YjQJ{QQJӳ FyPӕi quan hӋ chһt chӁ
vӟL QKDX WX\ QKLrQ QJ{Q QJӳ NK{QJ SKҧL Oj Wѭ GX\ Pj QJ{Q QJӳ chӍ Oj
SKѭѫQJWLӋn.
7tQKTXDQK͏ m̵t thi͇t vͣi nh̵n thͱc c̫PWtQK
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