Infographic chinh phục kỳ thi THPT Quốc gia môn Toán

Page 1

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

3+ʓ1 Òʍ, 6ʽ V *,ʏ, 7 &+ &+8< 1 Òʭ D < 6ʽ *,ˇ, +ʍ1 ..........................................................................2 &K̐ Ó˪ 'ã\ V˺ .............................................................................................................................................. 5 &K̐ Ó˪ &ˎS V˺ F̂QJ FˎS V˺ QK¤Q .............................................................................................................. 8 &K̐ Ó˪ *L̄L KˊQ ......................................................................................................................................... &K̐ Ó˪ +¢P V˺ OL¬Q W̎F .............................................................................................................................

&+8< 1 Òʭ Òʍ2 + 0 ˴ 9, 3+ 1 ˴ 7 &+ 3+ 1 ..............................................23 &K̐ Ó˪ ÒˊR K¢P ̰ 9L SK¤Q ...................................................................................................................... &K̐ Ó˪ 1JXy¬Q K¢P ................................................................................................................................. &K̐ Ó˪ 7¯FK SK¤Q ...................................................................................................................................... &K̐ Ó˪ ̑QJ G̎QJ W¯FK SK¤Q .....................................................................................................................

&+8< 1 Òʭ .+ʏ2 6 7 V ˕1* 'ˑ1* + 0 6ʽ ...............................................64 &K̐ Ó˪ 7®P W˖S [£F Ó˴QK W¯QK JL£ WU˴ F̐D K¢P V˺ ................................................................................... &K̐ Ó˪ 6̚ ÓńQ ÓL˰X F̐D K¢P V˺ W¯QK FK˞Q Oˤ F̐D K¢P V˺ .................................................................... &K̐ Ó˪ &̚F WU˴ F̐D K¢P V˺ ....................................................................................................................... &K̐ Ó˪ *L£ WU˴ ŌQ QKˎW JL£ WU˴ QK˸ QKˎW ................................................................................................... &K̐ Ó˪ 7L˰P F˖Q F̐D Ó˼ WK˴ K¢P V˺ ........................................................................................................ &K̐ Ó˪ Ò˼ WK˴ K¢P V˺ .............................................................................................................................

&+8< 1 Òʭ + 0 6ʽ 0Ī ˴ + 0 6ʽ L2*$5,7 ............................................... &K̐ Ó˪ +¢P V˺ Pī ̰ K¢P V˺ ORJDULW ..................................................................................................... &K̐ Ó˪ 3KņńQJ WU®QK Pī ̰ EˎW SKņńQJ WU®QK Pī SKņńQJ WU®QK ORJDULW ̰ EˎW SKņńQJ WU®QK ORJDULW ......................................................................................... &K̐ Ó˪ &£F E¢L W˖S O¥L VXˎW .....................................................................................................................

&+8< 1 Òʭ 6ʽ 3+˕& ................................................................................... CK̐ Ó˪ &£F SK«S WR£Q Fń EˌQ WU¬Q W˖S V˺ SK̒F .................................................................................... &K̐ Ó˪ 7®P V˺ SK̒F WK˸D P¥Q ÓL˪X NL˰Q FKR WUņ̄F ............................................................................... &K̐ Ó˪ 7˖S ǨS ÓLˬP ELˬX GLˮQ V˺ SK̒F ................................................................................................

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

&K̐ Ó˪ &ÅQ E˖F KDL SKņńQJ WU®QK E˖F KDL F̐D V˺ SK̒F ........................................................................ &K̐ Ó˪ &̚F WU˴ F̐D V˺ SK̒F .....................................................................................................................

&+8< 1 Òʭ 7ˁ +ˏ3 ˴ ; & 68ʑ7 ˴ 7+ʽ1* . ................................................. &K̐ Ó˪ 7K˺QJ N¬ ...................................................................................................................................... &K̐ Ó˪ +R£Q Y˴ W˾ ǨS FK˲QK ǨS .......................................................................................................... &K̐ Ó˪ 1K˴ WK̒F 1LX WńQ .......................................................................................................................... &K̐ Ó˪ ;£F VXˎW .......................................................................................................................................

&+8< 1 Òʭ & 1* 7+˕& /Ņˏ1* *, & ˴ + 0 6ʽ /Ņˏ1* *, & ˴ 3+ŅŃ1* 75 1+ /Ņˏ1* *, & ............................................................................... &K̐ Ó˪ &¶QJ WK̒F Oņ̌QJ JL£F .................................................................................................................. &K̐ Ó˪ +¢P V˺ Oņ̌QJ JL£F ...................................................................................................................... &K̐ Ó˪ 3KņńQJ WU®QK Oņ̌QJ JL£F .............................................................................................................

&+8< 1 Òʭ 0ʳ1+ Òʭ 7ʙ3 +ˏ3 ......................................................................243 &K̐ Ó˪ 0˰QK Ó˪ ....................................................................................................................................... &K̐ Ó˪ 7˖S ǨS Y¢ F£F SK«S WR£Q WU¬Q W˖S ǨS .....................................................................................

&+8< 1 Òʭ 3+ŅŃ1* 75 1+ +ʳ 3+ŅŃ1* 75 1+ %ʑ7 Òʟ1* 7+˕& %ʑ7 3+ŅŃ1* 75 1+ ............................................................................................ &K̐ Ó˪ 3KņńQJ WU®QK Y¢ K˰ SKņńQJ WU®QK E˖F QKˎW F£F SKņńQJ WU®QK TX\ Y˪ SKņńQJ WU®QK E˖F QKˎW E˖F KDL SKņńQJ WU®QK WU»QJ SKņńQJ SKņńQJ WU®QK FK̒D GˎX JL£ WU˴ WX\˰W Ó˺L SKņńQJ WU®QK Y¶ W˲ ........ &K̐ Ó˪ %ˎW Ó˜QJ WK̒F EˎW SKņńQJ WU®QK ................................................................................................

3+ʓ1 + 1+ +ʹ& &+8< 1 Òʭ + 1+ +ʹ& .+ 1* *,$1 ................................................................ 264 &K̐ Ó˪ 4XDQ K˰ VRQJ VRQJ ..................................................................................................................... &K̐ Ó˪ 4XDQ K˰ YX¶QJ JµF ..................................................................................................................... &K̐ Ó˪ *µF ............................................................................................................................................... &K̐ Ó˪ .KRˌQJ F£FK ...............................................................................................................................

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

&+8< 1 Òʭ .+ʽ, Ò$ ',ʳ1 ˴ 0ʣ7 &ʓ8 ˴ 0ʣ7 75ˑ 0ʣ7 1 1 ........................ &K̐ Ó˪ .K˺L ÓD GL˰Q ................................................................................................................................ &K̐ Ó˪ 7Kˬ W¯FK K®QK FKµS ̰ K®QK OÅQJ WU̎ ............................................................................................. &K̐ Ó˪ 7Kˬ W¯FK GL˰Q W¯FK NK˺L QµQ ̰ NK˺L WU̎ NK˺L FːX ......................................................................

&+8< 1 Òʭ 9(&7Ń V ˕1* 'ˑ1* ....................................................................324 &K̐ Ó˪ 9HFWR Y¢ F£F SK«S WR£Q Y˪ YHFWR ............................................................................................... &K̐ Ó˪ 7¯FK Y¶ Kņ̄QJ F̐D KDL YHFWR ...................................................................................................... &K̐ Ó˪ +˰ WK̒F Oņ̌QJ WURQJ WDP JL£F ....................................................................................................

&+8< 1 Òʭ 3+ŅŃ1* 3+ 3 7ʹ$ Ò˅ 7521* 0ʣ7 3+ʟ1* ................................. &K̐ Ó˪ 3KņńQJ WU®QK Óņ̆QJ WK˜QJ ......................................................................................................... &K̐ Ó˪ 3KņńQJ WU®QK Óņ̆QJ WU´Q ............................................................................................................ &K̐ Ó˪ 3KņńQJ WU®QK HOLS .........................................................................................................................

&+8< 1 Òʭ 3+ŅŃ1* 3+ 3 7ʹ$ Ò˅ 7521* .+ 1* *,$1 ................................362 &K̐ Ó˪ +˰ WU̎F W˶D Ó̂ 2[\] .................................................................................................................... &K̐ Ó˪ 3KņńQJ WU®QK PˠW SK˜QJ ............................................................................................................ &K̐ Ó˪ 3KņńQJ WU®QK PˠW FːX ................................................................................................................. &K̐ Ó˪ 3KņńQJ WU®QK Óņ̆QJ WK˜QJ ......................................................................................................... &K̐ Ó˪ &£F E¢L WR£Q OL¬Q K˰ JL̘D Óņ̆QJ WK˜QJ PˠW SK˜QJ PˠW FːX Y¢ ̒QJ G̎QJ SKņńQJ SK£S W˶D Ó̂ WURQJ NK¶QJ JLDQ Y¢R F£F E¢L WR£Q WKˬ W¯FK ........................

&+8< 1 Òʭ 3+ 3 'ˉ, + 1+ ˴ 3+ 3 Òʿ1* Dʍ1* ............................................ &K̐ Ó˪ 3K«S W˴QK WL˨Q .............................................................................................................................. &K̐ Ó˪ 3K«S Ó˺L [̒QJ WU̎F Ó˺L [̒QJ W¤P .............................................................................................. &K̐ Ó˪ 3K«S TXDy .................................................................................................................................... &K̐ Ó˪ 3K«S Y˴ W̚..................................................................................................................................... &K̐ Ó˪ 3K«S Ó˼QJ GˊQJ ..........................................................................................................................

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

$ή0) 0*θ0 &ά0) ȀϞ 6*ϖ *ȅ/ 5Ϝ $θ% $# ҤƵ Ă ҤƵ '

a!0

a 0

:ȩV RJ PI VTȬPJ y ' 0

' !0

' 0

' 0

,1)2*5$3+,& &+1+ 3+̍& .̛ 7+, 7+37 48˹& *,$ 0 1 72 1

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

*ȅ/ 5Ϝ $θ% $Ϝ0 64ț0) 2* 0) &αW C

a!0

a 0

&αW CD

ab 0

ab t 0

*ȅ/ 5Ϝ $θ% 0*ΰ6 64ȏ0 $θ% 0*ΰ6

ad bc ! 0

ad bc 0

&+8< 1 Ò˩ .+ˋ2 6 7 9 ̑1* '̍1* + 0 6˹

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

%*ϲ Ȁό 6ȑ/ 6θ2 :Ȇ% Ȁϖ0* 6Ȓ0* )+Ȇ 64ϖ %ϲ# *ȅ/ 5Ϝ & & 'ˉ1* % , 7˕3 &έPI 6ȬO VιR ZȡE ЄϗPJ EϳC JȠO Uϝ

3x x

2

9¯ G̎ 7Uņ̆QJ /ņńQJ 7K˨ 9LQK ̰ +¢ 1̂L 6ιR ZȡE ЄϗPJ EϳC JȠO Uϝ y # 0;3 .

% \ 5 ^0;3`.

$ \.

3 2

& f;0 3; f .

̽ +ņ̄QJ G˔Q JLˌL ȀKύW MKϓP 3 x x 2 ! 0 0 x 3. 8ι[ VιR ZȡE ЄϗPJ EϳC JȠO Uϝ NȠ & x 0;3 . &K˶Q $ 9¯ G̎ 7U¢ 9LQK 6ιR ZȡE ЄϗPJ EϳC JȠO Uϝ y

VCP x NȠ

­S ½ $ \ 5 ® kS , k ] ¾ .

# \ 5 ^0`.

¯2 & \ 5 ^kS , k ]`.

% \. ̽ +ņ̄QJ G˔Q JLˌL *ȠO Uϝ y

VCP x ZȡE ЄϗPJ MJK XȠ EJϕ MJK EQUZ z x z

­S ½ 8ι[ x \ 5 ® kS , k ] ¾ . 2 ¯ ¿ &K˶Q %

S 2

9¯ G̎ 6ȬO VαV Eί EȡE IKȡ VTϗ EϳC VJCO Uϝ O ЄϏ JȠO Uϝ y # m d 20.

$ m 20.

¿

kS k ]

x m

ZȡE ЄϗPJ VTȪP \ . x 8x m 4 % m t 20. & m ! 20. 2

̽ +ņ̄QJ G˔Q JLˌL *ȠO Uϝ y

&K˶Q '

x m 2

x 8x m 4

ZȡE ЄϗPJ VTȪP \ MJK XȠ EJϕ MJK x 2 8 x m 4 ! 0, x \. ­ 1! 0 ® m ! 20. ¯20 m 0

,1)2*5$3+,& &+1+ 3+̍& .̛ 7+, 7+37 48˹& *,$ 0 1 72 1

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

&έPI 6ȭPJ IKȡ VTϗ EϳC JȠO Uϝ 9¯ G̎ 6̈ .L¬Q *LDQJ %JQ JȠO Uϝ f x

# 8.

$

3 . 2

̽ +ņ̄QJ G˔Q JLˌL 6JC[ x 1 XȠQ JȠO Uϝ f x

2 x

2

3

3 x 1 2 -JK ЄȲ IKȡ VTϗ EϳC f 1 DνPI DCQ PJKȪW! 2

% 6 6.

3

2x 2 3x 1 2 VC EȲ f 1

& 6 3.

3

2.12 3.1 1 2

6 6.

8ι[ f 1 6 6. &K˶Q & 9¯ G̎ %JQ JȠO Uϝ f x x 3 5 x 2 x 16 6ȭPJ IKȡ VTϗ EϳC DKϏW VJϵE f 2 f 1 . # 3. $ 26. % 23. & 7.

̽ +ņ̄QJ G˔Q JLˌL 6JC[ x 2 XȠQ JȠO Uϝ f x x 3 5 x 2 x 16 VC EȲ f 2 23 5.22 2 16 26. 6JC[ x

1 XȠQ JȠO Uϝ f x

x 3 5 x 2 x 16 VC EȲ f 1 1 5. 1 1 16 23. 3

2

8ι[ f 2 f 1 26 23 3. &K˶Q $ 9¯ G̎ ȀKϏO PȠQ UCW ЄȢ[ MJȳPI VJWϥE Єϟ VJϗ JȠO Uϝ y # 1; 2 .

$ 2; 7 .

x 4 x 2 !

% 0; 1 .

& 1;2 .

• +ņ̄QJ G˔Q JLˌL 6JC[ x 1 VC EȲ y

2 ȀKϏO 1; 2 VJWϥE Єϟ VJϗ JȠO Uϝ

6JC[ x 2 VC EȲ y

7 ȀKϏO 2; 7 VJWϥE Єϟ VJϗ JȠO Uϝ

6JC[ x 0 VC EȲ y

1 ȀKϏO 0; 1 VJWϥE Єϟ VJϗ JȠO Uϝ

6JC[ x

2 z 2 ȀKϏO 1;2 MJȳPI VJWϥE Єϟ VJϗ JȠO Uϝ

1 VC EȲ y

&K˶Q '

&+8< 1 Ò˩ .+ˋ2 6 7 9 ̑1* '̍1* + 0 6˹

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

0

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

%*ϲ Ȁό 0*ϖ 6*ϴ% 0+7 6 0 & & 'ˉ1* % , 7˕3 &έPI :ȡE ЄϗPJ Jϓ Uϝ Uϝ JέPI VTQPI MJCK VTKϏP

2J PI RJȡR IKίK %ȳPI VJϵE a b

n

n

¦C a k

k n

n k

bk

Cn a n Cn a n b Cn a n b Cnk an k b k Cnn b n

5ϝ JέPI VϡPI SWȡV VTQPI MJCK VTKϏP NȠ Tk Cnk an k b k d k d n /WϝP VȬO Jϓ Uϝ EϳC Z VTQPI MJCK VTKϏP PJϗ VJϵE 0GYVQP VC NȠO PJ UCW $ ϧE 8KϋV Uϝ JέPI VϡPI SWȡV VTQPI MJCK VTKϏP $ ϧE &ϽC XȠQ Uϝ Oʛ EϳC DKϋP x ЄϏ VȬO k $ ϧE 6JC[ k XȠQ Jϓ Uϝ

8ȭ Fϱ OKPJ JϙC 9¯ G̎ Ò˪ WKL 7+374* *ϓ Uϝ EϳC x 5 VTQPI MJCK VTKϏP x x 6 x 8 NȠ #

$

%

&

• +ņ̄QJ G˔Q JLˌL 5ϝ JέPI VϡPI SWȡV VTQPI MJCK VTKϏP x x 6 NȠ xC6k x 6 k k

C6k 6 k k x 7 k

5ϝ JέPI VϡPI SWȡV VTQPI MJCK VTKϏP x 8 NȠ

­7 k 5 ­k 2 ® ȀϏ VȬO Jϓ Uϝ EϳC x 5 VJȬ k XȠ i RJίK VJϛC OȣP ® ¯8 i 5 ¯i 3 *ϓ Uϝ EϳC x 5 VTQPI MJCK VTKϏP x x 6 x 8 NȠ C6 C8 &K˶Q $ 9¯ G̎ Ò˪ PLQK K˶D F̐D %̂ 8ϧK P NȠ Uϝ PIW[ȪP F PI VJϛC OȣP Cn Cn

55 Uϝ JέPI MJȳPI EJϵC

n

2 · § x VTQPI MJCK VTKϏP EϳC DKϏW VJϵE ¨ x 3 2 ¸ DνPI x ¹ © # $ %

&

• +ņ̄QJ G˔Q JLˌL :ȡE ЄϗPJ P 6C EȲ Cn Cn

n

ªn n n n n « 2 ¬n

8Ȭ n NȠ Uϝ PIW[ȪP F PI PȪP n

§ 2 · k

x k ¨ 2 ¸ 5ϝ JέPI VϡPI SWȡV VTQPI MJCK VTKϏP NȠ C ©x ¹

k k C k x k

,1)2*5$3+,& &+,1+ 3+̍& .̛ 7+, 7+37 48˹& *,$ 0 1 72 1

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

5ϝ JέPI MJȳPI EJϵC x VTQPI MJCK VTKϏP ϵPI XϧK k VJϛC OȣP k k 6 6 5ϝ JέPI MJȳPI EJϵC x VTQPI MJCK VTKϏP NȠ C

&K˶Q ' 9¯ G̎ 7Uņ̆QJ &KX\¬Q ÒˊL K˶F 9LQK 6ȬO Jϓ Uϝ EϳC x 3 UCW MJK MJCK VTKϏP XȠ TȷV IϙP EȡE Є P VJϵE 9

§ · ЄϟPI FέPI EϳC ¨ x x 2 ¸ x z

©x ¹ # $

%

&

̽ +ņ̄QJ G˔Q JLˌL ©x

6C EȲ §¨ x x 2 ·¸ ¹

9

ª º « x x » ¬x ¼

§ · C9k ¨ ¸ ¦ ©x¹ k 9

9

k

9 k

¦¦ C C k i

k 9

i k

9

§ · C9k ¨ ¸ ¦ ©x¹ k 9

k

x k ¦ Cki x

9 k

k i

x k x

k

i

i

k i

i x 3k i 9

­ k i ­i k ® 5ϝ JέPI MJȳPI EJϵC x VTQPI MJCK VTKϏP VJȬ k XȠ i VJϛC OȣP ® ¯ d i d k d ¯ d i d k d 8Ȭ k EJKC JϋV EJQ PȪP i EJKC JϋV EJQ i k

6JϛC OȣP

3 5 6JϛC OȣP

6 6 6JϛC OȣP

9 7 .QέK

%ȡE Dϥ Uϝ i k VJϛC OȣP NȠ *ϓ Uϝ EϳC x 3 NȠ C C C C C C

&K˶Q & 9¯ G̎ 7Uņ̆QJ &KX\¬Q /¬ 4X¿ Ò¶Q ̰ ÒL˰Q %L¬Q 6TQPI MJCK VTKϏP x XϧK Uϝ Oʛ VȿPI FγP Jϓ Uϝ EϳC Uϝ JέPI ЄϵPI EJȭPJ IKϻC NȠ

# C

$ C

% C

9 & 9 C

̽ +ņ̄QJ G˔Q JLˌL 6C EȲ Uϝ JέPI ЄϵPI IKϻC EϳC MJCK VTKϏP NȠ Uϝ JέPI ϵPI XϧK k x

0ȪP Uϝ JέPI ЄϵPI IKϻC NȠ C

C x

11 8ι[ Jϓ Uϝ EϳC Uϝ JέPI ЄϵPI IKϻC C11 20 .3

&K˶Q $

&+8< 1 Ò˩ 7˽ +̋3 ; & ;8ˍ7 7+˹1* .

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

&έPI $ȠK VQȡP VȭPJ VϡPI IKȡ VTϗ DKϏW VJϵE EJQ VT ϧE UϹ FϱPI MJCK VTKϏP PJϗ VJϵE 0GYVQP

8ȭ Fϱ OKPJ JϙC 9¯ G̎ )Kȡ VTϗ EϳC DKϏW VJϵE P

C C C C NȠ

# P

$ P

% P

& P

̽ +ņ̄QJ G˔Q JLˌL 6C PJιP VJα[ EȡE Uϝ JέPI ЄύW EȲ FέPI

VJȬ

%JϙP a b P

C C C C

&K˶Q $ 9¯ G̎ 6ȭPJ IKȡ VTϗ DKϏW VJϵE P

# P

$ P

k C C C C XϧK k N d k d

% P

2

& P

2

̽ +ņ̄QJ G˔Q JLˌL k

d k d 6C PJιP VJα[ EȡE Uϝ JέPI ЄύW EȲ FέPI C

6C EȲ 6TϷ JCK Xϋ EJQ PJCW

8ι[ P

&K˶Q % 9¯ G̎ 6ȭPJ IKȡ VTϗ DKϏW VJϵE P

# P

$ P

C C C C C C

% P

& P

2

̽ +ņ̄QJ G˔Q JLˌL 6C EȲ i

C C i C i C i

C C C C C C i C C C C C

/Ƞ i

8ι[ P

i i

i

C C C C C C

&K˶Q $

,1)2*5$3+,& &+,1+ 3+̍& .̛ 7+, 7+37 48˹& *,$ 0 1 72 1

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

&έPI $ȠK VQȡP VȭPJ VϡPI IKȡ VTϗ DKϏW VJϵE EJQ VT ϧE UϹ FϱPI ЄέQ JȠO VȭEJ RJȢP

8ȭ Fϱ OKPJ JϙC C C C EȲ IKȡ VTϗ NȠ

9¯ G̎ 6ϡPI T

#

$ %

&

̽ +ņ̄QJ G˔Q JLˌL :ȩV MJCK VTKϏP

x

C C x C x C x C x

.α[ ЄέQ JȠO JCK Xϋ EϳC VC Є ϯE

x

C C x C x C x

.α[ ЄέQ JȠO JCK Xϋ EϳC VC Є ϯE

x

C C x C x

%JϙP x VJC[ XȠQ VC Є ϯE

T &K˶Q $

C C C C 9¯ G̎ 6ϡPI S C DνPI #

$

%

&

̽ +ņ̄QJ G˔Q JLˌL :ȩV MJCK VTKϏP .α[ VȭEJ RJȢP VϷ ЄϋP JCK Xϋ EϳC VC Є ϯE

³ x

dx

³ x

dx

C C C C C S

S

&K˶Q &

&+8< 1 Ò˩ 7˽ +̋3 ; & ;8ˍ7 7+˹1* .

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

%*ϲ Ȁό :Ȇ% 57ΰ6 & & 'ˉ1* % , 7˕3 8ȭ Fϱ OKPJ JϙC 9¯ G̎ 7Uņ̆QJ &KX\¬Q +ˊ /RQJ ̰ 4XˌQJ 1LQK %Ȳ VJχ Є ϯE ЄȡPJ Uϝ $ϝE PIηW PJKȪP VJχ 6ȭPJ ZȡE UWαV ЄϏ VȭEJ Uϝ IJK VTȪP VJχ DϝE Є ϯE NȠ OϥV Uϝ Nχ

# 2

7 $ 9

%

5

&

2 9

̽ +ņ̄QJ G˔Q JLˌL 6TQPI VJχ Є ϯE ЄȡPJ Uϝ EȲ VJχ Uϝ Nχ VJχ Uϝ EJρP 2 EȡEJ %JϙP PIηW PJKȪP VJχ VϷ VJχ EȲ C ȀϏ VȭEJ Uϝ IJK VTȪP VJχ DϝE Є ϯE NȠ OϥV Uϝ Nχ VJȬ Eί VJχ DϝE Є ϯE ЄύW NȠ Uϝ Nχ 5ϝ EȡEJ DϝE VJχ Nχ NȠ C52 EȡEJ C2 2 &Q ЄȲ ZȡE UWαV EγP VȬO NȠ 25 C 9 &K˶Q ' 9¯ G̎ 7Uņ̆QJ 1JX\ˮQ +X˰ 3K¼ <¬Q )KGQ JCK EQP UȷE UλE EȢP ЄϝK XȠ ЄϟPI EJαV 6ȭPJ ZȡE UWαV DKϋP Eϝ ũ6ϡPI Uϝ EJαO ZWαV JKϓP NȠ Ū #

7 36

$

6

%

9

&

5 36

̽ +ņ̄QJ G˔Q JLˌL 6C EȲ ȀϏ VϡPI Uϝ EJαO ZWαV JKϓP MJK IKGQ JCK EQP UȷE UλE DνPI VJȬ EJαO ZWαV JKϓP VTQPI VϷPI UȷE UλE RJίK NȠ

^ ` ^ ` ^ ` ^ ` ^ `

:ȡE UWαV ZWαV JKϓP i EJαO d i d VTȪP VϷPI UȷE UλE NȠ PJ PJCW XȠ DνPI 6 -JK ЄȲ ZȡE UWαV EγP VȬO NȠ 6 6 6 6 6 6 36 &K˶Q ' 9¯ G̎ 7ˊS &K¯ 7R£Q +˶F 7X˾L 7Uˤ -ϋV SWί b c EϳC XKϓE IKGQ OϥV EQP UȷE UλE EȢP ЄϝK JCK NγP NKȪP VKϋR VTQPI ЄȲ D NȠ Uϝ EJαO ZWαV JKϓP NγP IKGQ VJϵ PJαV E NȠ Uϝ EJαO ZWαV JKϓP NγP IKGQ VJϵ JCK Є ϯE VJC[ XȠQ RJ PI VTȬPJ DιE JCK x 2 bx c 6ȭPJ ZȡE UWαV ЄϏ RJ PI VTȬPJ DιE JCK ЄȲ Xȳ PIJKϓO #

7

$

23 36

%

36

&

&+8< 1 Ò˩ 7˽ +̋3 ; & ;8ˍ7 7+˹1* .

https://m.me/vnGooda

5 36


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

• Hņ̄QJ G˔Q JLˌL :ȡE UWαV ZWαV JKϓP i EJαO d i d MJK IKGQ UȷE UλE DνPI 6 6C EȲ RJ PI VTȬPJ x 2 bx c Xȳ PIJKϓO MJK XȠ EJϕ MJK b2 c c !

6T ϩPI JϯR b c ^ ` EȲ ZȡE UWαV NȠ 6 6

6

b2 b c ^ `

6T ϩPI JϯR b c ^ ` EȲ ZȡE UWαV NȠ 6 6 36 6T ϩPI JϯR b c ^ ` EȲ ZȡE UWαV NȠ 6 6 9 6T ϩPI JϯR b c ^ ` EȲ ZȡE UWαV NȠ -JK ЄȲ ZȡE UWαV EγP VȬO NȠ &K˶Q & 9¯ G̎ 7Uņ̆QJ 1JX\ˮQ +X˰ 3K¼ <¬Q :ϋR PIηW PJKȪP JϙE UKPJ PCO XȠ JϙE UKPJ Pϻ XȠQ PIϟK OϥV DȠP VTȱP EȲ EJϣ PIϟK 6ȭPJ ZȡE UWαV DKϋP Eϝ ũ-JȳPI EȲ JϙE UKPJ Pϻ PȠQ PIϟK EέPJ PJCWŪ #

5

$

2 9

%

5

7 & 9

̽ +ņ̄QJ G˔Q JLˌL 5ϝ EȡEJ ZϋR DέP JϙE UKPJ XȠQ OϥV DȠP VTȱP NȠ Я EȡEJ %ϝ ЄϗPJ OϥV DέP PCO ZϋR DέP PCO EȱP NέK EȲ Я EȡEJ ZϋR %QK DέP PCO PJ XȡEJ PIȿP MJK ЄȲ VC EȲ MJQίPI VTϝPI %JϙP TC MJQίPI VTϝPI VϷ MJQίPI VTϝPI EȲ C6 EȡEJ :ϋR DέP Pϻ XȠQ MJQίPI VTϝPI Єȣ EJϙP EȲ Я EȡEJ

5ϝ EȡEJ ZϋR DέP XȠQ DȠP VTȱP UCQ EJQ MJȳPI EȲ DέP Pϻ PȠQ PIϟK EέPJ PJCW NȠ Я%6 Я EȡEJ :ȡE UWαV ЄϏ MJȳPI EȲ DέP Pϻ PIϟK EέPJ PJCW NȠ &K˶Q $

,1)2*5$3+,& &+,1+ 3+̍& .̛ 7+, 7+37 48˹& *,$ 0 1 72 1

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

% , 7˕3 7˽1* +̋3 &¤X ,' %JQ VιR JϯR / IϟO RJγP VϹ 5ϝ VιR EQP IϟO RJγP VϹ EϳC / NȠ 8 # A

2 $ A

2 % C

& 2

6TȭEJ Єύ VJK VJϹ -ȪPJ )KȡQ &ϱE 3WϝE )KC 868

&¤X ,' 6ȬO Jϓ Uϝ EϳC x VTQPI MJCK VTKϏP x x 3 #

$

%

&

6TȭEJ Єύ VJK VJϹ VT ϩPI %JW[ȪP 6JȡK 0IW[ȪP

&¤X ,' /ϥV JϥR EJϵC SWί EγW IϟO SWί OȠW ZCPJ XȠ SWί OȠW Єϛ %JϙP PIηW PJKȪP ЄϟPI VJϩK SWί EγW VϷ JϥR ЄȲ :ȡE UWαV ЄϏ SWί EγW EJϙP TC EȶPI OȠW DνPI #

7

$

35 22

%

9

&¤X ,' %JQ Uϝ PIW[ȪP F PI P VJϛC OȣP n · § x 2 ¨ ¸ XϧK x z x2 ¹ © #

x

$

%

22

6TȭEJ Єύ VJK VJϹ VT ϩPI ȀϝE $ȬPJ -KύW Ţ ȀϟPI 6JȡR 6ȬO Uϝ JέPI EJϵC VTQPI MJCK VTKϏP x D

x

&

256 x

6TȭEJ Єύ VJK VJϹ VT ϩPI 0IW[ϑP *Wϓ 2Jȷ ;ȪP &¤X ,' 6Ϸ EȡE Uϝ NιR Uϝ VϽ PJKȪP EȲ EJϻ Uϝ ЄȳK OϥV MJȡE PJCW 6ȭPJ ZȡE UWαV ЄϏ Uϝ Є ϯE NιR EJKC JϋV EJQ #

$

% 3

D

6TȭEJ Єύ VJK VJϹ VT ϩPI $C ȀȬPJ Ţ 6JCPJ *ȲC

&¤X ,' %Ȳ DCQ PJKȪW Uϝ EȲ DC EJϻ Uϝ ЄȳK OϥV MJȡE PJCW OȠ EȡE EJϻ Uϝ ЄȲ VJWϥE VιR JϯR ^ ` ! # C93

$ 3

% A93

& 9

6TȭEJ Єύ VJK VJϹ VT ϩPI %JW[ȪP 6JȡK 0IW[ȪP NγP &¤X ,' )Kί UϹ TνPI VTQPI ȀέK JϥK VJϏ FϱE VJϏ VJCQ VϕPJ )KC .CK PȿO EȲ ЄϥK DȲPI ЄȿPI Mȭ VJCO IKC IKίK Є ϯE EJKC VJȠPJ DίPI # $ % & OϣK DίPI IϟO ЄϥK %ȡEJ VJϵE VJK ЄαW PJ UCW 8ȱPI %ȡE ЄϥK VTQPI OϣK DίPI VJK ЄαW XȱPI VTȱP OϥV N ϯV VȭPJ ЄKϏO XȠ EJϙP TC ЄϥK PJαV EϳC OϣK DίPI 8ȱPI ȀϥK PJαV DίPI # IσR ЄϥK PJαV DίPI % ЄϥK PJαV DίPI $ IσR ЄϥK PJαV DίPI & 8ȱPI 6TCPJ IKίK DC *CK ЄϥK VJWC VTQPI DȡP MϋV VTCPJ IKίK PJαV *CK ЄϥK VJλPI VTQPI DȡP MϋV $KϋV TνPI VαV Eί EȡE VTιP ЄαW FKϑP TC VTȪP UȢP XιP ЄϥPI 2NGKMW XȠQ EȡE PIȠ[ NKȪP VKϋR OϣK PIȠ[ VTιP *ϛK $CP Vϡ EJϵE EγP O ϯP UȢP XιP ЄϥPI VTQPI DCQ PJKȪW PIȠ[! #

$

%

&

6TȭEJ Єύ VJK VJϹ VT ϩPI 0IW[ϑP &W Ţ *ϟ %Jȭ /KPJ

&+8< 1 Ò˩ 7˽ +̋3 ; & ;8ˍ7 7+˹1* .

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

&¤X ,' %JQ OϥV ЄC IKȡE ЄύW * EȲ ЄϕPJ 0I ϩK VC NιR OϥV Vϵ IKȡE EȲ ЄϕPJ NȠ ЄϕPJ EϳC *

6ȭPJ Uϝ Vϵ IKȡE Є ϯE NιR VJȠPJ OȠ MJȳPI EȲ EέPJ PȠQ NȠ EέPJ EϳC * #

$

%

&

6TȭEJ Єύ VJK VJϹ VT ϩPI %JW[ȪP *έ .QPI Ţ 3WίPI 0KPJ &¤X ,' /ϥV PI ϩK IϙK ЄKϓP VJQέK PJ PI SWȪP OαV EJϻ Uϝ EWϝK 6ȭPJ ZȡE UWαV ЄϏ PI ϩK ЄȲ IϙK ЄȷPI Uϝ ЄKϓP VJQέK OȠ MJȳPI RJίK VJϹ SWȡ JCK NγP

# 5

$

%

2 & 9

6TȭEJ Єύ VJK VJϹ VT ϩPI 0IW[ϑP &W Ţ *ϟ %Jȭ /KPJ

&¤X ,' /ϥV PJȲO IϟO PCO Pϻ %JϙP PIηW PJKȪP DέP :ȡE UWαV ЄϏ VTQPI DέP Є ϯE EJϙP EȲ Eί PCO NηP Pϻ OȠ PCO PJKύW J P Pϻ NȠ! #

$

%

&

6TȭEJ Єύ VJK VJϹ VT ϩPI 0IW[ϑP *Wϓ 2Jȷ ;ȪP

&¤X ,' %JQ EȡE Uϝ PIW[ȪP k n VJϛC k d n %ȳPI VJϵE PȠQ UCW ЄȢ[ ЄȷPI! # Cnk

nЯ kЯ

$ Cnk

nЯ n k Я

% Cnk

nЯ k Я n k Я

& Cnk

k ЯnЯ n k Я

6TȭEJ Єύ VJK VJϹ VT ϩPI #P .ȣQ Ţ *ίK 2JȱPI n

3· § &¤X ,' 6ȬO Uϝ JέPI MJȳPI EJϵC Z VTQPI MJCK VTKϏP PJϗ VJϵE 0GYVQP ¨ x 2 ¸ x z DKϋV TνPI x¹ © Cn Cn Cn n Cnn n Cnk NȠ Vϡ JϯR EJιR M EϳC P RJγP VϹ

#

$

%

&

6TȭEJ Єύ VJK VJϹ VT ϩPI 6έR %Jȭ 6QȡP *ϙE 6WϡK 6Tχ &¤X ,' %JϙP PIηW PJKȪP OϥV Uϝ EȲ DC EJϻ Uϝ RJȢP DKϓV :ȡE UWαV EϳC DKϋP Eϝ ũ5ϝ EJϙP Є ϯE EȲ FέPI abc VJϛC OȣP ЄKύW MKϓP a ! b ! c Ū NȠ A3 C3 $ #

%

C93

&

A93

6TȭEJ Єύ VJK VJϹ VT ϩPI 6JȡK *ȱC Ţ 0IJϓ #P 2 n

&¤X ,' 8ϧK n NȠ Uϝ PIW[ȪP F PI VJϛC OȣP C C n 2 · § EϳC DKϏW VJϵE ¨ x 3 2 ¸ DνPI x ¹ © #

$ Z

3 n

% Z

Jϓ Uϝ EϳC Uϝ JέPI EJϵC x VTQPI MJCK VTKϏP

&

6TȭEJ Єύ VJK VJϹ VT ϩPI ȀϝE $ȬPJ -KύW Ţ ȀϟPI 6JȡR &¤X ,' %JQ ЄC IKȡE ЄύW EέPJ 5ϝ VCO IKȡE XWȳPI EȲ ЄϕPJ NȠ ЄϕPJ EϳC EϳC ЄC IKȡE DνPI 2 # C

3 $ C

2 % C

2 & C

6TȭEJ Єύ VJK VJϹ VT ϩPI %JW[ȪP Ȁ* 5 2JέO *Ƞ 0ϥK

,1)2*5$3+,& &+,1+ 3+̍& .̛ 7+, 7+37 48˹& *,$ 0 1 72 1

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIᝆN Sà CH QU�

A

B

a x

A, B, C

AB BC AC A1An A1A2 A2A3 ... An 1An

1

5

A

G

ABCD lĂ hĂŹnh bĂŹnh hĂ nh: AB AD AC D C

B

C

G ABC GA GB GC 0 B

A

4

2

a

a b 0.

b

A

3 k 0 ka 0 k a 0

ka ka

324

O

OB OA AB

O, A, B

a

a

M

B

M AB: MA MB O OA OB 2OM

k 0. k 0.

&+Ëż 1‚< Ă’ËŤ 7ÂŒ1 &8Ëš1 6ƒ&+

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

%*ϲ Ȁό 8'%6 8ȅ %Ȇ% 2*Ȏ2 61Ȇ0 8ό 8'%6

& & 'ˉ1* % , 7˕3 &έPI :ȡE ЄϗPJ OϥV XGEV RJ PI J ϧPI EϳC XGEV Єϥ FȠK EϳC XGV JCK XGEV DνPI PJCW

2J PI RJȡR IKίK Ů :ȡE ЄϗPJ OϥV XGEV XȠ ZȡE ЄϗPJ UϽ EȶPI RJ PI EȶPI J ϧPI EϳC JCK XGEV FϽC XȠQ ЄϗPJ PIJɡC Ů &ϽC XȠQ EȡE VȭPJ EJαV JȬPJ JϙE EϳC EȡE JȬPJ Єȣ EJQ ЄϏ VȭPJ Єϥ FȠK EϳC OϥV XGEV Ů *CK XGEV DνPI PJCW MJK EJȷPI EȶPI J ϧPI XȠ EȶPI Єϥ FȠK

8ȭ Fϱ OKPJ JϙC 9¯ G̎ %JQ PIʛ IKȡE ABCDE %Ȳ DCQ PJKȪW XGEV MJȡE XGEV MJȳPI EȲ ЄKϏO ЄγW XȠ ЄKϏO EWϝK NȠ ЄϕPJ EϳC PIʛ IKȡE! #

$

% 14

&

• +ņ̄QJ G˔Q JLˌL

JJJG JJJG *CK ЄKϏO RJȢP DKϓV EJοPI JέP A B VC ZȡE ЄϗPJ Є ϯE JCK XGEV MJȡE XGEV MJȳPI NȠ AB BA /Ƞ VϷ PȿO ЄϕPJ A B C D E EϳC PIʛ IKȡE VC EȲ 10 EσR ЄKϏO RJȢP DKϓV FQ ЄȲ EȲ XGEV VJϛC OȣP [ȪW EγW DȠK VQȡP

&K˶Q $ 9¯ G̎ %JQ JȬPJ XWȳPI ABCD EȲ VȢO O EέPJ a )ϙK M NȠ VTWPI ЄKϏO EϳC AB 6ȭPJ Єϥ FȠK EϳC JJJG XGEV MD JJJG a 15 JJJG a 5 JJJG a 5 JJJG a 5 # MD $ MD % MD & MD 2 3 2 4 • +ņ̄QJ G˔Q JLˌL ȆR FϱPI ЄϗPJ Nȭ 2KVCIQ VTQPI VCO IKȡE XWȳPI MAD VC EȲ 2

DM 2

§a· 2 ¨ ¸ a 2 © ¹ a 5 2

AM 2 AD 2

JJJG 8ι[ MD

MD

5a 2 DM 4

a 5 2

&K˶Q & 9¯ G̎ %JQ VCO IKȡE ABC EȲ VTϽE VȢO H, D NȠ ЄKϏO ЄϝK ZϵPI XϧK B SWC VȢO O EϳC Є ϩPI VTȱP PIQέK VKϋR VCO IKȡE ABC -JοPI ЄϗPJ PȠQ UCW ЄȢ[ NȠ ЄȷPI! JJJG JJJG JJJG JJJG JJJG # HA CD XȠ AD CH $ HA JJJG JJJG JJJG JJJG JJJG % HA CD XȠ AC HD & HA

JJJG JJJG JJJG CD XȠ AD HC JJJG JJJG JJJG JJJG JJJG CD XȠ AD HC XȠ OB OD

&+8< 1 Ò˩ 9(&7Ń 9 ̑1* '̍1*

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ • +ņ̄QJ G˔Q JLˌL

8Ȭ D ЄϝK ZϵPI XϧK B SWC O PȪP D VJWϥE Є ϩPI VTȱP VȢO O &Q ЄȲ AD __ CH EȶPI XWȳPI IȲE XϧK AB A

AH __ CD EȶPI XWȳPI IȲE XϧK BC

D

5W[ TC ADCH NȠ JȬPJ DȬPJ JȠPJ JJJG JJJG 8ι[ HA CD XȠ

O

&K˶Q %

H B

C

&έPI %JϵPI OKPJ ЄοPI VJϵE XGEV

2J PI RJȡR IKίK ȀϏ EJϵPI OKPJ OϥV ЄοPI VJϵE XGEV VC VJ ϩPI UϹ FϱPI EȡE RJȩR DKϋP ЄϡK Xϋ PȠ[ VJȠPJ Xϋ MKC DKϋP ЄϡK V PI Є PI DKϋP ЄϡK JCK Xϋ EȶPI DνPI OϥV ЄέK N ϯPI VTWPI IKCP Chú ý: 0ϋW JCK Xϋ NȠ RJȩR EϥPI VTϷ EȲ EȶPI Uϝ N ϯPI XGEV VJȬ VC FȶPI SW[ VλE DC ЄKϏO G 0ϋW Xϋ VTȡK NȠ VϡPI EϳC PJKύW XGEV Xϋ RJίK NȠ XGEV 0 VJȬ DKϋP ЄϡK Xϋ VTȡK VJȠPJ VϡPI EȡE EσR XGEV ЄϝK PJCW

8ȭ Fϱ OKPJ JϙC 9¯ G̎ %JQ ЄKϏO A, B, C, D, E, F ȀοPI VJϵE PȠQ UCW ЄȢ[ ЄȷPI! JJJG JJJG JJG JJJG JJG JJJG G JJJG JJJG JJG JJJG JJG JJJG JJJG # AB CD FA BC EF DE 0 $ AB CD FA BC EF DE AF JJJG JJJG JJG JJJG JJG JJJG JJJG JJJG JJJG JJG JJJG JJG JJJG JJJG % AB CD FA BC EF DE AE & AB CD FA BC EF DE AD • +ņ̄QJ G˔Q JLˌL JJJG JJJG JJG JJJG JJG JJJG AB CD FA BC EF DE

JJJG

JJJG

JJJG

JJJG

JJG

JJG

AB BC CD DE EF FA

JJJG JJJG JJG G AC CE EA 0

&K˶Q $ 9¯ G̎ %JQ Vϵ IKȡE ABCD )ϙK I J NγP N ϯV NȠ VTWPI ЄKϏO EϳC AB XȠ CD O NȠ VTWPI ЄKϏO EϳC IJ -JοPI ЄϗPJ PȠQ UCW ЄȢ[ NȠ ЄȷPI! JJJG JJJG JJJG JJJG JJG # AC BD IJ $ AC BD • +ņ̄QJ G˔Q JLˌL

JJJG 6JGQ SW[ VλE DC ЄKϏO VC EȲ AC JJJG JJG JJG JJJG 6 PI VϽ EȲ BD BI IJ JD

JJJG JJJG JJG 1 JJG IJ % AC BD 3IJ 2

JJG JJG JJJG AI IJ JC

JJG JJG G ­° AI BI 0 /Ƞ I J NγP N ϯV NȠ VTWPI ЄKϏO EϳC AB CD PȪP ® JJJG JJJG G °̄JC JD 0 JJJG JJJG JJG %ϥPI XȠ VJGQ Xϋ XȠ ȡR FϱPI VC Є ϯE AC BD 2IJ

&K˶Q '

JJJG JJJG JJG & AC BD 2IJ

A

B

I

O D

J

C

&+˿ 1 < Ò˫ 7 1 &8˹1 6 &+

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

JJJG JJJG 9¯ G̎ %JQ Vϵ IKȡE ABCD VTȪP EέPJ AB CD Nα[ NγP N ϯV EȡE ЄKϏO M N UCQ EJQ 3 AM 2 AB XȠ JJJG JJJG JJJG JJJG JJJJG DN DC 6ȭPJ XGEV MN VJGQ JCK XGEV AD BC JJJJG 1 JJJG 1 JJJG JJJJG 1 JJJG 2 JJJG AD BC AD BC # MN $ MN 3 3 3 3 JJJJG 1 JJJG 2 JJJG JJJJG 2 JJJG 1 JJJG AD BC AD BC % MN & MN 3 3 3 3 • +ņ̄QJ G˔Q JLˌL JJJJG JJJG JJJG JJJG JJJJG JJJG JJJG JJJG 6C EȲ MN MA AD DN XȠ MN MB BC CN JJJJG JJJG JJJG JJJG JJJG JJJG JJJG 5W[ TC 3 MN MA AD DN 2 MB BC CN JJJG JJJG JJJG JJJG JJJG JJJG MA MB AD BC DN CN JJJG JJJG G JJJG JJJG G 6JGQ DȠK TC VC EȲ MA 2 MB 0 XȠ DN CN JJJJG JJJG JJJG JJJJG 1 JJJG 2 JJJG AD BC 8ι[ MN AD BC MN 3 3 &K˶Q &

9¯ G̎ %JQ VCO IKȡE ABC EȲ VTϽE VȢO H XȠ VȢO Є ϩPI VTȱP PIQέK VKϋR O -JοPI ЄϗPJ PȠQ UCW ЄȢ[ NȠ ЄȷPI! JJJG JJJG JJJG # HA HB HC JJJG JJJG JJJG % HA HB HC

JJJG 4HO 2 JJJG HO 3

JJJG JJJG JJJG JJJG $ HA HB HC 2HO JJJG JJJG JJJG JJJG & HA HB HC 3HO

• +ņ̄QJ G˔Q JLˌL JJJG JJJG JJJG JJJG 6C VJα[ HA HB HC 2HO PϋW VCO IKȡE ABC NȠ VCO IKȡE XWȳPI 0ϋW VCO IKȡE ABC MJȳPI XWȳPI -JK ЄȲ IϙK D NȠ ЄKϏO ЄϝK ZϵPI EϳC A SWC O -JK ЄȲ VC EȲ BH __ DC XȬ EȶPI XWȳPI IȲE XϧK AC /σV MJȡE BD __ CH XȬ EȶPI XWȳPI IȲE XϧK AB &Q ЄȲ BDCH NȠ JȬPJ DȬPJ JȠPJ 6JGQ SW[ VλE JȬPJ DȬPJ JȠPJ VC EȲ JJJG JJJG JJJG HB HC HD

JJJG JJJG JJJG /σV MJȡE XȬ O NȠ VTWPI ЄKϏO EϳC AD PȪP HA HD 2HO

JJJG JJJG JJJG JJJG 6Ϸ XȠ UW[ TC HA HB HC 2HO &K˶Q % &έPI :ȡE ЄϗPJ OϥV ЄKϏO VJϛC OȣP OϥV ЄοPI VJϵE XGEV EJQ VT ϧE

2J PI RJȡR IKίK

JJJG Ů ȀϝK XϧK Jϓ VJϵE XGEV VC VJ ϩPI DKϋP ЄϡK Xύ FέPI OM

G G k v VTQPI ЄȲ k NȠ Uϝ VJϽE VJC[ ЄϡK O XȠ v Єȣ

Є ϯE ZȡE ЄϗPJ Ů ȀϝK XϧK Jϓ VJϵE Xύ Єϥ FȠK

JJJG 4ȷV IϙP Jϓ VJϵE Єȣ EJQ Xύ FέPI OM

R XϧK O Eϝ ЄϗPJ R NȠ Єϥ FȠK EJQ VT ϧE 0J Xι[ VιR JϯR EȡE ЄKϏO M NȠ

&+8< 1 Ò˩ 9(&7Ń 9 ̑1* '̍1*

https://m.me/vnGooda


GOODA.VN - THU VI ỆN SÁCH QUÝ

http://sach.gooda.vn/infographic

Ȁ ϩPI VTȱP VȢO O DȡP MȭPJ R PϋW R ! 0 ȀKϏO O PϋW R 0 + PϋW R 0

JJJG 4ȷV IϙP Jϓ VJϵE Єȣ EJQ Xύ FέPI MA

JJJG MB XϧK A B NȠ JCK ЄKϏO RJȢP DKϓV Eϝ ЄϗPJ -JK ЄȲ VιR JϯR EȡE ЄKϏO

M NȠ VTWPI VTϽE EϳC ЄQέP VJοPI AB

8ȭ Fϱ OKPJ JϙC JJJG JJJG JJJG G 9¯ G̎ 0ϋW MA MB MC 0 VJȬ MJοPI ЄϗPJ PȠQ F ϧK ЄȢ[ ЄȷPI! # M NȠ ЄϕPJ EϳC JȬPJ DȬPJ JȠPJ MCBA

$ M NȠ ЄϕPJ EϳC JȬPJ DȬPJ JȠPJ MCAB

% M NȠ VTϙPI VȢO EϳC VCO IKȡE ABC

& M NȠ ЄϕPJ EϳC JȬPJ DȬPJ JȠPJ MACB

• +ņ̄QJ G˔Q JLˌL JJJG JJJG JJJG G JJJG JJJG G JJJG 6C EȲ MA MB MC 0 BA MC 0 MC

JJJG AB

8ι[ M NȠ ЄϕPJ EϳC JȬPJ DȬPJ JȠPJ MCBA &K˶Q $ 2JȢP VȭEJ RJ PI ȡP PJKϑW 2J PI ȡP $ 5CK FQ EJW[ϏP Xϋ MJȳPI ЄϡK FαW JJJG JJJG JJJG G JJJG JJJG G JJJG JJJG MA MB MC 0 BA MC 0 MC BA JJJG JJJG JJJG G 2J PI ȡP % 5CK FQ PJγO XϧK ЄοPI VJϵE MA MB MC 0 JJJG JJJG JJJG G JJJG JJJG JJJG G JJJG JJJG 2J PI ȡP & 5CK FQ FȶPI UCK SW[ VλE EϥPI MA MB MC 0 MA MC MB 0 AC MB JJJG JJJG JJJG JJJG 9¯ G̎ %JQ VCO IKȡE ABC 6ιR JϯR EȡE ЄKϏO M VJϛC OȣP MB MC BM BA NȠ # Є ϩPI VJοPI AB

% Є ϩPI VTȱP VȢO A DȡP MȭPJ BC

$ VTWPI VTϽE ЄQέP BC

& Є ϩPI VJοPI SWC A XȠ UQPI UQPI XϧK BC

• +ņ̄QJ G˔Q JLˌL 6C EȲ

/Ƞ A B C Eϝ ЄϗPJ PȪP VιR JϯR ЄKϏO M NȠ Є ϩPI VTȱP VȢO A DȡP MȭPJ BC &K˶Q & 9¯ G̎ %JQ VCO IKȡE ЄύW ABC EέPJ a $KϋV TνPI VιR JϯR EȡE ЄKϏO M VJϛC OȣP ЄοPI VJϵE JJJG JJJG JJJG JJJG JJJG 2MA 3MB 4MC MB MA NȠ Є ϩPI VTȱP Eϝ ЄϗPJ EȲ DȡP MȭPJ R 6ȭPJ DȡP MȭPJ R VJGQ a a a a a # r $ r % r & r 3 9 2 6 • +ņ̄QJ G˔Q JLˌL )ϙK G NȠ VTϙPI VȢO EϳC VCO IKȡE ABC 6C EȲ

JJG JJG JJG G JJG JJG JJG JJG JJG G XϧK I NȠ ЄKϏO UCQ EJQ 2IA 3IB 4IC 0 IA IB IC IC IA

&+˿ 1 < Ò˫ 7 1 &8˹1 6 &+

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

/Ƞ G NȠ VTϙPI VȢO EϳC VCO IKȡE ABC PȪP JJG JJG JJG G JJG JJG JJG G JJG JJJG -JK ЄȲ IG IC IA IG AI IC IG CA JJJG JJJG JJJG JJJG JJJG JJG JJG JJG JJG JJJG &Q ЄȲ MA MB MC MB MA MI IA IB IC AB MI

AB

8Ȭ I NȠ ЄKϏO Eϝ ЄϗPJ VJϛC OȣP PȪP VιR JϯR EȡE ЄKϏO M EγP VȬO NȠ Є ϩPI VTȱP VȢO I DȡP MȭPJ r &K˶Q %

JJJG JJJG JJJG 9¯ G̎ %JQ 'ABC 6ιR JϯR EȡE ЄKϏO M VJϛC OȣP MA 2MB MC

AB 9

a 9

JJJG kBC ( k NȠ Uϝ VJC[ ЄϡK k z 0 NȠ

# Є ϩPI VTWPI VTϽE EϳC ЄQέP VJοPI BC $ Є ϩPI VTWPI DȬPJ EϳC 'ABC ϵPI XϧK EέPJ BC % Є ϩPI VTȱP Є ϩPI MȭPJ BC & Є ϩPI VTȱP Є ϩPI MȭPJ AB • +ņ̄QJ G˔Q JLˌL JJJG JJJG JJJG JJJG JJJG JJJG JJJG JJJG JJJG 6C EȲ MA 2MB MC kBC MA MB MB MC kBC JJG 1 k JJJG JJJG JJG JJJG JJJG JJG CB IM EȶPI RJ PI CB Eϝ ЄϗPJ 2MI CB kBC ( I NȠ VTWPI ЄKϏO EϳC AB ) IM 2 8ι[ VιR JϯR EȡE ЄKϏO M NȠ Є ϩPI VJοPI ' SWC I NȠ ' __ BC VϵE NȠ Є ϩPI VTWPI DȬPJ EϳC 'ABC ϵPI XϧK

EέPJ BC &K˶Q %

&+8< 1 Ò˩ 9(&7Ń 9 ̑1* '̍1*

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

(a1; a2) (b1; b2)

a

b

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

%*ϲ Ȁό 6Ȓ%* 8Ș * Ϧ0) %ϲ# *#+ 8'%6

& & 'ˉ1* % , 7˕3 &έPI 6ȭEJ Xȳ J ϧPI EϳC JCK XGEV

2J PI RJȡR IKίK

G G + 2J ng pháp 1: Ȁ C JCK XGEV a, b Xύ EȶPI IϝE ЄϏ ZȡE ЄϗPJ Є ϯE IȲE D

G G

a, b 6Ϸ ЄȲ VȭPJ Є ϯE

2J PI RJȡR 2JȢP VȭEJ VȭEJ Xȳ J ϧPI VJȠPJ PJKύW VȭEJ F ϧK FέPI VϡPI JKϓW PJϩ EȡE SWK VλE XGEV OȠ OϣK VȭEJ Xȳ J ϧPI VJȠPJ RJγP ЄύW VȭPJ Є ϯE

8ȭ Fϱ OKPJ JϙC JJG JJJG JJG JJJG 9¯ G̎ %JQ JȬPJ XWȳPI ABCD EέPJ a 6ȭPJ VȭEJ DA.DC XȠ AB.AC . JJJG JJJG JJG JJJG JJG JJJG JJG JJJG # DA.DC 1, AB.AC a2 $ DA.DC 0; AB.AC 2a2 JJG JJJG JJG JJJG JJG JJJG JJG JJJG % DA.DC 0; AB.AC a2 & DA.DC 1; AB.AC 2a2

• +ņ̄QJ G˔Q JLˌL JJG JJJG JJG JJJG JJG JJJG 6C EȲ DA DC DA DC EQU DA DC a a EQU 0 . JJG JJJG JJG JJJG JJG JJJG AB AC AB AC EQU AB AC a a EQU 0 a2 .

&K˶Q & 9¯ G̎ %JQ %ABC ЄύW EέPJ a 8ω Xύ RJȭC PIQȠK VCO IKȡE EȡE JȬPJ XWȳPI ABMN , BCEF , CAHK 6ȭPJ VȭEJ JJJG JJJG JJJG JJG Xȳ J ϧPI UCW AM.CH XȠ AM.BC . JJJG JJJG JJJG JJG 1 3 2 JJJG JJJG JJJG JJG 1 3 2 $ AM.CH a2 ; AM.BC # AM.CH a2 ; AM.BC a a 2 2 JJJG JJJG JJJG JJG JJJG JJJG JJJG JJG 1 3 2 1 3 2 % AM.CH a2 ; AM.BC & AM.CH a2 ; AM.BC a a 2 2 • +ņ̄QJ G˔Q JLˌL JJJG JJJG JJG JJJG JJJG JJJG JJG JJJG JJG JJJG JJJG JJJG JJJG JJJG 6C EȲ AM.CH AB AN AH AC AB.AH AB.AC AN.AH AN.AC

H

N

a 3 a 2 a 2 a 2 3

a2 2 2 2 2 JJJG JJG JJJG JJG JJJG JJG JJJG JJJG JJJG JJG JJG JJJG JJG 2 AM.BC AN AB AC AB AN.AC AN.AB AB.AC AB JJJG JJJG JJG JJJG JJG AC AN AB AB 2 XȬ AN.AB 0 FQ AN ? AB JJJG JJJG 1 3 2 1 3 2 AM.AC AB 2 a a2 a . 2 2 &K˶Q '

A

K

M

B

C

F

E

&+˿ 1 < Ò˫ 7 1 &8˹1 6 &+

https://m.me/vnGooda


http://sach.gooda.vn/infographic

GOODA.VN - THU VIỆN SÁCH QUÝ

&έPI %JϵPI OKPJ ЄοPI VJϵE PJϩ VȭEJ Xȳ J ϧPI

2J PI RJȡR IKίK Ů ȀϝK XϧK EȡE DKϏW VJϵE Xύ VȭEJ Xȳ J ϧPI VC VJ ϩPI UϹ FϱPI ЄϗPJ PIJɡC JQσE VȭPJ EJαV EϳC VȭEJ Xȳ J ϧPI %Jȷ Ⱥ RJȩR RJȢP VȭEJ XGEV SW[ VλE VTWPI ЄKϏO SW[ VλE JȬPJ DȬPJ JȠPJ Ű JJG 2 JJG JJG Ů ȀϝK XϧK EȡE DKϏW VJϵE Xύ Єϥ FȠK VC VJ ϩPI UϹ FϱPI AB 2 AB AB.AB . W Ⱥ VȭPJ EJαV EϳC EȡE JȬPJ E DίP

8ȭ Fϱ OKPJ JϙC 9¯ G̎ %JQ VCO IKȡE ABC IϙK I NȠ VTWPI ЄKϏO EϳC AB ȀοPI VJϵE PȠQ UCW ЄȢ[ NȠ ЄȷPI! AB 2 AB 2 # CA2 CB 2 2CI2 $ CA2 CB 2 2CI2 2 2 2 AB AB 2 % CA2 CB 2 2CI2

& CA2 CB 2 CI2

2 2

• +ņ̄QJ G˔Q JLˌL 6JGQ SW[ VλE VTWPI ЄKϏO VC EȲ

&K˶Q & 9¯ G̎ %JQ ЄKϏO A, B , C , D DαV MȬ )ϙK O NȠ VTWPI ЄKϏO EϳC AB ȀοPI VJϵE PȠQ UCW ЄȢ[ NȠ UCK! JJG JJG JJG JJG JJJG JJG JJJG JJJG JJJG JJJG # DA.BC DB.CA DC.AB 0 . $ AB CD AB CD AB 2 CD 2 JJJG JJJG JJJG JJJG JJJG JJJG JJJG JJJG JJJG % AB BC AD AB.BC AB.AD & MA.MB OM 2 OA2 XϧK M DαV MȬ

• +ņ̄QJ G˔Q JLˌL

JJG JJG JJG JJG JJJG JJG JJG JJJG JJG JJG JJG JJJG JJJG JJG JJG 6C EȲ DA.BC DB.CA DC.AB DA DC DB DB DA DC DC DB DA JJG JJJG JJG JJG JJG JJG JJG JJJG JJJG JJG JJJG JJG DA.DC DA.DB DB.DA DB.DC DC.DB DC.DA 0 . JJG JJG JJG JJG JJJG JJG 5W[ TC DA.BC DB.CA DC.AB 0

8ι[ # ЄȷPI

&ϑ VJα[ $ ЄȷPI VJGQ JνPI ЄοPI VJϵE % ЄȷPI VJGQ VȭPJ EJαV RJȢP RJϝK XϧK RJȩR EϥPI JJJG JJJG JJJG JJJG JJJG JJJG JJJG 2 JJJG JJJG JJJG JJJG JJJG JJJG 2 JJJG 2 6C EȲ MA.MB MO OA MO OB MO MO OA OB OA.OB MO OA

MO2 OA2 .

8ι[ & UCK &K˶Q ' 0JιP ZȩV 6Ϸ Xȭ Fϱ VC EȲ VJϏ UW[ TC EȡEJ EJϵPI OKPJ DC Є ϩPI ECQ VTQPI VCO IKȡE ЄϟPI SW[ PJ UCW JJG JJG JJJG JJG )ϙK H NȠ IKCQ EϳC JCK Є ϩPI ECQ ZWαV RJȡV VϷ ЄϕPJ A, B -JK ЄȲ HA.BC 0; HC.AB 0 JJG JJG JJJG JJG JJJG JJG 6Ϸ ЄοPI VJϵE

VC EJQ ЄKϏO D VTȶPI XϧK ЄKϏO H VC Є ϯE HA.BC HB.CA HC.AB 0

&+8< 1 Ò˩ 9(&7Ń 9 ̑1* '̍1*

https://m.me/vnGooda


Turn static files into dynamic content formats.

Create a flipbook
Issuu converts static files into: digital portfolios, online yearbooks, online catalogs, digital photo albums and more. Sign up and create your flipbook.