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ÿmçF W©Q PÛL WX«Q QrQ FK·QJ QKóQJ ÿm KRjQ WKjQK NÃ KR¥FK VßP WX«Q Pj FzQ YmçW PíF

NÃ KR¥FK W©Q 7tQK PíF NÃ KR¥FK ÿm ÿÏQK

Bài 7 0ÝW QJmáL ÿL [H ÿ¥S Wï $ 3+ª1 ÿÃQ % WURQJ PÝW WKáL JLDQ ÿm ÿÏQK KL FzQ FiFK % P QJmáL

ÿy QK±Q WK©\ UµQJ VÁ ÿÃQ % FK±P QñD JLá QÃX JLó QJX\rQ Y±Q WÕF ÿDQJ ÿL QKmQJ QÃX W

QJ Y±Q WÕF

WKrP PK WKu VÁ WßL ÿtFK VßP KkQ QñD JLá 7tQK Y±Q WÕF FëD [H ÿ¥S WUHQ TXmQJ ÿmáQJ ÿm

ÿL O~Fÿ«X

Bài 8 +DL WÙ F{QJ QKkQ OjP FKXQJ WURQJ JLá VÁ KRjQ WKjQK [RQJ F{QJ YLËF ÿm ÿÏQK +Ñ Oàm

FzQ O¥L WURQJ JLá +ÓL WÙ WKí KDL OjP PÝW PuQK WKu VDX EDR OkX VÁ KRjQ WKjQK F{QJ YLËF

')QJ 7q JLiF QaL WLGS

1

&KR ÿmáQJ WUzQ 25 Yj PÝW ÿLÇP 6 QµP ErQ QJRjL ÿmáQJ WUzQ 7ï 6 YÁ KDL WLÃS WX\ÃQ 6$ 3+ª1

Yj 6% YßL ÿmáQJ WUzQ $ 3+ª1 Yj % Oj KDL WLÃS ÿLÇP 9Á ÿmáQJ WK·QJ D ÿL TXD 6 Yj F³W ÿmáQJ WUzQ W¥L KDL ÿLÇP 0 1 0 QµP JLóD 6 Yj 1

a CMR: SO AAB

E *ÑL + Oj JLDR ÿLÇP FëD 62 Yj $ 3+ª1 % , Oj WUXQJ ÿLÇP FëD 01 +DL ÿmáQJ WK·QJ 2, Yj $ 3+ª1 % F³W

Trang 7

F &KíQJ PLQK UµQJ 2,2( 5 2

2

&KR 25 7ï ÿLÇP 3 QµP QJRjL ÿmáQJ WUzQ N¿ FiF WLÃS WX\ÃQ 3$ 3+ª1 3% $ 3+ª1 % Oj KDL WLÃS ÿLÇP

Yj N¿ ÿmáQJ NtQK $ 3+ª1 & FëD ÿmáQJ WUzQ

D &05 3$ 3+ª1 2% QÝL WLÃS

E &KíQJ PLQK 32 %& &KR 235 WtQK JyF $ 3+ª1 2% Yj GLËQ WtFK KuQK TX¥W WUzQ $ 3+ª1 2% íQJ YßL FXQJ QKÓ $ 3+ª1 %

3

&KR 25 Fy KDL ÿmáQJ NtQK $ 3+ª1 % Yj &' YX{QJ JyF YßL QKDX *ÑL 0 Oj PÝW ÿLÇP W \ ê WKXÝFQJ SKmkQJ Fy G¥QJ D[ E[ F D 

FXQJ QKÓ $ 3+ª1 & 1ÕL 0% F³W &' ã 1

D &KíQJ PLQK WLD 0' Oj WLD SKkQ JLiF JyF AMB

E &KíQJ PLQK WDP JLiF %20 Yj %1$ 3+ª1 ÿ×QJ G¥QJ Yj WtFK %0%1 NK{QJ ÿÙL

F &KíQJ PLQK 210$ 3+ª1 QÝL WLÃS

4

&KR WDP JLiF $ 3+ª1 %& YX{QJ W¥L $ 3+ª1 ÿmáQJ FDR $ 3+ª1 + 9Á ÿmáQJ WUzQ WkP 2 ÿmáQJ NtQK $ 3+ª1 + F³W

$ 3+ª1 % Yj $ 3+ª1 & O«Q OmçW ã , Yj

D &KíQJ PLQK $ 3+ª1 ,+ Oj KuQK FKó QK±W

b CKíQJ PLQK , = HB.HC2

F &KíQJ PLQK %,.& QÝL WLÃS

G , Oj WLÃS WX\ÃQ FëD ÿmáQJ WUzQ QJR¥L WLÃS WDP JLiF +.&

5

7ï PÝW ÿLÇP $ 3+ª1 ã QJRjL ÿmáQJ WUzQ 25 YÁ WLÃS WX\ÃQ $ 3+ª1 % Yj FiW WX\ÃQ $ 3+ª1 01 FëD ÿmáQJ WUzQ 25 % WKXÝF FXQJ OßQ 01 *ÑL , Oj WUXQJ ÿLÇP FëD Gây MN

D&KíQJ PLQK UµQJ $ 3+ª1 ,2% Oj Wí JLiF QÝL WLÃS

E&KíQJ PLQK UµQJ $ 3+ª1 % = AM.AN2

F %LÃW $ 3+ª1 % 5 7tQK FKX YL ÿmáQJ WUzQ QJR¥L WLÃS Wí JLiF $ 3+ª1 ,2% WKHR 5

6

.¿ %0 F³W ÿmáQJ WUzQ W¥L ÿLÇP ' máQJ WK·QJ '$ 3+ª1 F³W ÿmáQJ WUzQ W¥L 6

a &KíQJ PLQK $ 3+ª1 %&' QÝL WLÃS

b &KíQJ PLQK JyF $ 3+ª1 %' EµQJ JyF $ 3+ª1 &'

F &KíQJ PLQK &$ 3+ª1 Oj WLD SKkQ JLiF FëD JyF 6&%

G %LÃW $ 3+ª1 %D JyF %&$ 3+ª1 EµQJ ÿÝ 7tQK WKÇ WtFK KuQK QyQ ÿmçF W¥R WKjQK NKL TXD\ WDP JLiF YX{QJ %$ 3+ª1 & TXDQK F¥QK JyF YX{QJ $ 3+ª1 & FÕ ÿÏQK

7

&KR WDP JLiF $ 3+ª1 %& Fy ED JyF QKÑQ QÝL WLÃS ÿmáQJ WUzQ WkP 2 máQJ WK·QJ YX{QJ JyF YßL

%& W¥L % F³W 2 W¥L 0 Yj F³W ÿmáQJ WK·QJ $ 3+ª1 & W¥L ' *ÑL 1 Oj ÿLÇP ÿÕL [íQJ FëD 0 TXD %&

$ 3+ª1 % F³W &1 W¥L (

D &KíQJ PLQK UµQJ ED ÿLÇP 0 2 & WK·QJ KjQJ

E &KíQJ PLQK '$ 3+ª1 '& '0'%

F &KíQJ PLQK EÕQ ÿLÇP $ 3+ª1 ' ( 1 WKXÝF PÝW ÿmáQJ WUzQ

G &KR ELÃW $ 3+ª1 % $ 3+ª1 & &KíQJ PLQK UµQJ JyF %1& EµQJ KDL O«Q JyF %'&

8 &KR WDP JLiF $ 3+ª1 %& YX{QJ W¥L $ 3+ª1 $ 3+ª1 % $ 3+ª1 & ÿmáQJ FDR $ 3+ª1 + 7UrQ ÿR¥Q +& O©\ ÿLÇP ' VDR FKR +' +% YÁ &( YX{QJ JyF YßL $ 3+ª1 ' ( WKXÝF $ 3+ª1 '

D &KíQJ PLQK $ 3+ª1 +&( QÝL WLÃS [iF ÿÏQK WkP 2 FëD ÿmáQJ WUzQ QJR¥L WLÃS Wí JLiF $ 3+ª1 +&(

E &KíQJ PLQK &+ Oj WLD SKkQ JLiF FëD JyF $ 3+ª1 &(

9

&KR WDP JLiF $ 3+ª1 %& JyF % Yj JyF & QKÑQ &iF ÿmáQJ WUzQ ÿmáQJ NtQK $ 3+ª1 % $ 3+ª1 & F³W QKDX W¥L ' 0ÝW

ÿmáQJ WK·QJ TXD $ 3+ª1 F³W ÿmáQJ WUzQ ÿmáQJ NtQK $ 3+ª1 % $ 3+ª1 & O«Q OmçW W¥L ( Yj )

a) &KíQJ PLQK % & ' WK·QJ KjQJ

b) &KíQJ PLQK % & ( ) QµP WUrQ PÝW ÿmáQJ WUzQ

10 &KR WDP JLiF $ 3+ª1 %& YX{QJ ã $ 3+ª1 Yj PÝW ÿLÇP ' QµP JLóD $ 3+ª1 Yj % máQJ WUzQ ÿmáQJ NtQK %' F³W %& W¥L

( &iF ÿmáQJ WK·QJ &' $ 3+ª1 ( O«Q OmçW F³W ÿmáQJ WUzQ W¥L FiF ÿLÇP WKí KDL ) * &KíQJ PLQK

D 7DP JLiF $ 3+ª1 %& ÿ×QJ G¥QJ YßL WDP JLiF EBD

Trang 8

F $ 3+ª1 & VRQJ VRQJ YßL )*

G &iF ÿmáQJ WK·QJ $ 3+ª1 & '( Yj %) ÿ×QJ TX\

11

&KR WDP JLiF $ 3+ª1 %& QÝL WLÃS ÿmáQJ WUzQ WkP 2 0 Oj PÝW ÿLÇP WUrQ FXQJ $ 3+ª1 & NK{QJ FKíD %

N¿ 0+

YX{QJ JyF YßL $ 3+ª1 & 0 YX{QJ JyF YßL %&

a) &KíQJ PLQK Wí JLiF 0+.& Oj Wí JLiF QÝL WLÃS b) &KíQJ PLQK JyF $ 3+ª1 0% JyF +0

c &KíQJ PLQK' $ 3+ª1 0% ÿ×QJ G¥QJ YßL' HMK

12.

&KR ÿmáQJ WUzQ WkP 2 Yj ÿLÇP $ 3+ª1 QµP QJRjL ÿmáQJ WUzQ ÿy 9Á FiF WLÃS WX\ÃQ $ 3+ª1 % $ 3+ª1 &

Yj FiW WX\ÃQ

$ 3+ª1 '( WßL ÿmáQJ WUzQ % Yj & Oj WLÃS ÿLÇP *ÑL + Oj WUXQJ ÿLÇP FëD '(

a)

&KíQJ PLQK $ 3+ª1 % + 2 & F QJ WKXÝF PÝW ÿmáQJ WUzQ ;iF ÿÏQK WkP FëD ÿmáQJ WUzQQJ SKmkQJ Fy G¥QJ D[ E[ F D  ÿy

b) &KíQJ PLQK +$ 3+ª1 Oj WLD SKkQ JLiF FëD JyF %+&

c) *ÑL , Oj JLDR ÿLÇP FëD %& Yj '( &05 $ 3+ª1 % = AI.AH2 d) %+ F³W 2 ã &KíQJ PLQK UµQJ $ 3+ª1 ( VRQJ VRQJ &

,,, 0`7 6X H 7+$ 3+ª1 0 +*2

Ä 1

Câu 1 ÿLÇP &KR SKmkQJ WUuQK [ +2 3 x +1 2= 0 (1)

D &KíQJ PLQK UµQJ SKmkQJ WUuQK OX{Q Fy KDL QJKLËP SKkQ ELËW

E *ÑL x , x Oj KDL QJKLËP FëD SKmkQJ WUuQK +m\ WtQK WÙQJ 1 2

1 2

x x

Câu 2 ÿLÇP &KR KjP VÕ \ -2x 2

a) 7uP FiF ÿLÇP WKXÝF ÿ× WKÏ KjP VÕ Fy WXQJ ÿÝ EµQJ -16

b) 7uP FiF ÿLÇP WKXÝF ÿ× WKÏ KjP VÕ Fy KRjQK ÿÝ EµQJ WXQJ ÿÝ

Câu 3 ÿLÇP *L§L EjL WRiQ VDX EµQJ FiFK O±S SKmkQJ WUuQK

0ÝW QKyP KÑF VLQK WKDP JLD ODR ÿÝQJ FKX\ÇQ WK QJ ViFK YÅ WKm YLËQ FëD WUmáQJQJ SKmkQJ Fy G¥QJ D[ E[ F D 

ÃQ EXÙL ODR

ÿÝQJ Fy KDL E¥Q EÏ ÕP NK{QJ WKDP JLD ÿmçF Yu Y±\ PÛL E¥Q SK§L FKX\ÇQ WKrP WK QJ QóD QJ SKmkQJ Fy G¥QJ D[ E[ F D  PßL KÃW VÕ ViFK F«Q FKX\ÇQ +ÓL VÕ KÑF VLQK FëD QKyP ÿy"

Câu 4 ÿLÇP 7DP JLiF 2$ 3+ª1 % YX{QJ W¥L 2 2% JyF $ 3+ª1 2% 3004XD\ WDP JLiF ÿy PÝW YzQJ TXDQK F¥QK JyF YX{QJ 2$ 3+ª1 WD ÿmçF PÝW KuQK Ju" 7tQK GLËQ WtFK [XQJ TXDQK FëD KuQK

ÿmáQJ WUzQ ÿmáQJ NtQK 0& ¿ %0 F³W ÿmáQJ WUzQ W¥L ' máQJ WK·QJ '$ 3+ª1 F³W ÿmáQJ WUzQ W¥L 6

&KíQJ PLQK UµQJ

a) $ 3+ª1 %&' Oj PÝW Wí JLiF QÝL WLÃS b) Góc ABD = góc ACD

c) &$ 3+ª1 Oj WLD SKkQ JLiF FëD JyF 6&%

Ä

Câu 1: ÿLÇP

5~W JÑQ ELÇX WKíF $ 3+ª1 3 1 1 27 2 3

Câu 2: ÿLÇP

&KR KË SKmkQJ WUuQK3x 2y 6

mx y 3

w

tw + = w

v

E *L§L KË SKmkQJ WUuQK NKL P

Câu 3: ÿLÇP

Trang 9

+DL YzL QmßF F QJ FK§\ YjR EÇ WKu JLá ÿ«\ EÇ 1ÃX PÛL YzL FK§\ PÝW PuQK FKR ÿ«\ EÇQJ SKmkQJ Fy G¥QJ D[ E[ F D  WKu YzL WKí KDL F«Q QKLÅX KkQ YzL WKí QK©W Oj JLá 7tQK WKáL JLDQ PÛL YzL FK§\ PÝW PuQK ÿ«\ EÇCâu 4: ÿLÇP

&KR WDP JLiF $ 3+ª1 %& YX{QJ W¥L $ 3+ª1 Fy , Oj WUXQJ ÿLÇP FëD $ 3+ª1 & 9Á ,' YX{QJ JyF YßL F¥QK KX\ÅQ

BC, (DÌ %& &KíQJ PLQK $ 3+ª1 % = BD ± CD2 2 2

Câu 5: ÿLÇP

&KR WDP JLiF $ 3+ª1 %& Fy JyF QKÑQ QÝL WLÃS WURQJ ÿmáQJ WUzQ WkP 2 FiF ÿmáQJ Fao AD, BK FëD WDP JLiF J»S QKDX W¥L + *ÑL ( ) WKHR WKí Wõ Oj JLDR ÿLÇP WKíF KDL FëD %2 Yj % NpR GjL YßLÿmáQJ WUzQ 2

D &KíQJ PLQK ()$ 3+ª1 &

E *ÑL , Oj WUXQJ ÿLÇP FëD $ 3+ª1 & &KíQJ PLQK ÿLÇP + , ( WK·QJ KjQJ Yj 2, 1

2BH

Câu 6: ÿLÇP

P = bc ac ab

a + b + c

Ä

Câu1: &KR SKmkQJ WUuQK E±F KDL [ - 22 3 x 1 0Yj JÑL KDL QJKLËP FëD SW Oj [ và x K{QJ JL§L1 2

pt, tính giá tUÏ FëD FiF ELÇX WKíF VDX

a) x + x1 2 b) x x1 2 c) x12+ x22

Câu 2: D 9LÃW F{QJ WKíF WtQK WKÇ WtFK FëD KuQK WUéFy JKL U} FiF Nt KLËX WURQJ F{QJ

WKíF E &KR KuQK FKó QK±W $ 3+ª1 %&' Fy F¥QK $ 3+ª1 % D %& D 7tQK WKÇ WtFK KuQK VLQK UD NKL TXD\3

KuQK FKó QK±W PÝW YzQJ TXDQK F¥QK $ 3+ª1 %

Câu 3: &KR KjP VÕ \ -2x 2

c) 7uP FiF ÿLÇP WKXÝF ÿ× WKÏ KjP VÕ Fy WXQJ ÿÝ EµQJ -16

d) 7uP FiF ÿLÇP WKXÝF ÿ× WKÏ KjP VÕ FiFK ÿÅX KDL WUéF WR¥ ÿÝ

Câu 4 0ÝW WKñD UXÝQJ KuQK WDP JLiF Fy GLËQ WtFK P 7tQK F¥QK ÿi\ FëD WKñD UXÝQJ ÿy

ELÃW

2 UµQJ QÃX W QJ F¥QK ÿi\ WKrP P Yj JL§P FKLÅX FDR WmkQJ íQJ ÿL P WKu GLËQ WtFK FëD Qy NK{QJWKD\ ÿÙL

Câu 5: &KR KuQK YX{QJ $ 3+ª1 %&' ÿLÇP ( WKXÝF F¥QK %& ( % ( & 4XD % NÁ ÿmáQJ WK·QJ YX{QJ  JyF YßL '( ÿmáQJ WK·QJ Qj\ F³W FiF ÿmáQJ WK·QJ '( Yj '& WKHR WKí Wõ ã + Yj

a) &05 7í JLiF %+&' Oj Wí JLiF QÝL WLÃS

b) 7tQK VÕ ÿR JyF &+

c) &KíQJ PLQK &.' +.%

Ä 4

Câu 1: ÿLÇP

D 5~W JÑQ ELÇX WKíF $ 3+ª1 5 5

+ +

b/ &KíQJ PLQK ÿ·QJ WKíF a b 2b 1

a b

a- b- a+ b- - = YßL D ñ0; a ñ 0 và a ï b

Câu 2: ÿLÇP

*L§L SKmkQJ WUuQK [ + 3x ± 108 = 02

Câu 3: ÿLÇP

0ÝW FD Q{ FK¥\ WUrQ V{QJ [X{L GzQJ NP Yj QJmçF GzQJ NP WKáL JLDQ F§ ÿL Yj YÅ KÃW JLá +m\ WuP Y±Q WÕF FD Q{ WURQJ QmßF \rQ O»QJ ELÃW UµQJ Y±Q WÕF FëD QmßF FK§\ Oj NPK

Trang 10

&KR WDP JLiF ÿÅX $ 3+ª1 %& Fy ÿmáQJ FDR $ 3+ª1 + 0 Oj ÿLÇP E©W Nä WUrQ F¥QK %& 0 không trùng YßL % Yj & *ÑL 3 4 WKHR WKí Wõ Oj FKkQ FiF ÿmáQJ YX{QJ JyF NÁ Wñ 0 ÿÃQ $ 3+ª1 % Yj $ 3+ª1 & 2 Oj WUXQJÿLÇP FëD $ 3+ª1 0 &KíQJ PLQK UµQJ

D &iF ÿLÇP $ 3+ª1 3 0 + 4 F QJ QµP WUrQ PÝW ÿmáQJ WUzQQJ SKmkQJ Fy G¥QJ D[ E[ F D 

E 7í JLiF 23+4 Oj KuQK Ju"

Câu 5: ÿLÇP

&KR D E Oj FiF VÕ GmkQJ &KíQJ PLQK UµQJ

a b

+

Ä

Bài 1 *L§L SKmkQJ WUuQK Yj KË SKmkQJ WUuQK VDX ÿ

a)

¯

®

-5 3

3 2

y x

b) x ± (2 3 5)x 15 1 0

Bài 2 Cho parabol (P): y = 2

4

1

x Yj ÿmáQJ WK·QJ G \ [ - 1

D 9Á 3 Yj G WUrQ F QJ PÝW P»W SK·QJ WÑD ÿÝ ÿQJ SKmkQJ Fy G¥QJ D[ E[ F D 

E ;iF ÿÏQK WÑD ÿÝ FiF JLDR ÿLÇP FëD 3 Yj G EµQJ SKpS WtQK ÿ

Bài 3: 7tQK FKX YL KuQK FKó QK±W ELÃW UµQJ FKLÅX GjL KkQ FKLÅX UÝQJ P Yj GLËQ WtFK

Oj Bài 4 &KR ÿmáQJ WUuQ 25 Yj PÝW ÿLÇQ $ 3+ª1 QµP QJRjL ÿmáQJ WUzQ VDR FKR 2$ 3+ª1 5 9Á FiF WLÃS

WX\ÃQ $ 3+ª1 % $ 3+ª1 & YßL 2 % & Oj FiF WLÃS ÿLÇP $ 3+ª1 2 F³W %& W¥L +

D &KíQJ PLQK Wí JLiF $ 3+ª1 %2& QÝL WLÃS

E &KíQJ PLQK $ 3+ª1 2 YX{QJ JyF YßL %& W¥L +

F 7tQK GLËQ WtFK Wí giác ABOC theo R

³&K~F HP {Q WkS WYW´

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