De thi tuyen sinh lop 10 mon Tieng Toan 1213

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IBANCH1NH1

sa

GIAo DYC vA DAo

~o

BENTRE

~;o ,

DE CHINHTHUC

DE THI TUYEN SINH LOP 10

TRUNG HQC PHO THONG NAM HQC 2012 - 2013
Mon: ToAN

ThOi gian : 120 phut (khong k~ phat d~)

Cau 1.(4 di~m)

Khong sir dung may tinh cAm tay,

a) Tinh: A =

-

J8 -

2J18

Fa .

b) Giai phuong trinh: X2- 3x - 18

=

{X+2Y =5
c) Giai h~ phirong trinh:

x-y=-1

Cau 2. (5 diem)

Cho phuong trinh: X2- mx

+

m - 3 =0 (1), voi m 1fttham s6.

a) Chung minh rang phirong trinh (1) luon co 2 nghiem phan biet voi moi m.

b) Khi phuong trinh (1) co hai nghiem phan biet Xl va X2,tim cac gia tri cua m

saD cho Xj

+

X2=2XIX2.

c) Tim gia tri nho nhat cua bieu tlurc B =2(X12+xl) - XIX2'

Cau 3. (5 di~m)

Cho cac ham s6 y =x2 co db thi la (P) va y = - X

+

m co db thi la (d), voi m la

tham s6.

a) V6i m

=

2, hay ve (P) va (d) tren cung mot h~ true toa dQ vuong goc (don vi

tren cac true bang nhau) va tim toa dQ cac giao diem cua (P) va (d) bang phep tinh,

b) Tim m d~ (d) c~t (P) tai hai di~m nam v€ hai phia cua true tung.
Cau 4. (6 di~m)

Cho tam giac ABC (AB<AC) co ba goc d€u nhon va nQi ti~p duong tron tam 0,

ban kinh R. Ve dirong kinh AD va duong cao AH (HEBC). Tir B va C ve BI va CK
cung vuong goc voi AD c~t AD IAnhrot tai I va K.

a) Chirng minh ill giac ABHI va tir giac AHKC nQi tiep,

b) Chirng minh: IH II CD.

c) Chirng minh: LlIHK va LlBAC dbng dang.

d) Cho

RAe

=60°. Tinh dien tich cua hinh gioi han boi day BC va cung nho BC

cua dirong tron tam

°

theo R.

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---HET---.'-. SOGIAODVCvABAoT~O
BENTRE

WONG DAN CHAM

'nn TUYEN SINH LOP 10 TRUNG HQC PH6 THONG
NAM HQC 2012 - 2013

Mon: ToAN

DE

CHINH T

RU

e

, CA'

.. au

Caul

a) A =J8 -2.J18 +J50 = ~4.2 -2..)9.2 +..)25.2

=

2 .

J2 -

2

.

3

.

J2

5 .

J2

0,50

---~

--

(2

-

~-

6 -;

S

-)

J2

-

~

--

:]2

--

-

----

-

---

-

--

-

---

--

---

- --

-

--

0 ;

50 ---

-- ----

---

-

---b) Giai phirong trinh: Xl - 3x - 18=O.

~

=

9 - 4.(-18)

=

81>0

~.Ji

=

9 0,50

_.•...- --- --- - -- --- - -_.•.- --_.•._.•..•..•.- - --_.•..•..•..•..•..•._.•..•...•..•..•...._.•..•..•..•._.•..•.-.•..•..•..•..•..•..•._.•._... .•..•..•...•..•.

~

-

.

-

....•..•..•..•.:~-.•..•..•..•..•.

Ph inhcc hie 3+9 6 3-9 1,00 MOlnghl~m

irong tn co ng rem: XI =-2- = ; x2 =-2- =-3 0,50
{X+ 2y =5 (1)

c) Giaih~ phirong trinh:

x- y =-1 (2)

_1_

~

Y_{

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>-~~:

{~

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~:}

_~ _

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J ~~~~ _

V~yh~ co nghiem:

{

X

=

1 0 50

y=2 '

Cho phuong trinh: XL - mx

+

m - 3=0 (1)

a) Taco ~=m2-4(m-3)=m2-4m+12 0,50

::::

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:::::::::

V~yphuong trinh (1) luon co hai nghiem phan biet voi moi 0,50
m.

b) Khi phirong trinh (1) co hai nghiem phan bi~t Xlva X2,

{Xl +X2 =m

theo Viet ta co: 0,50

Xl,X2 =m-3

---,--- --- ---

---Theo

de

bai, ta co x, + X2= 2XIX2¢:} m = 2(m - 3) 0,50

--- --- ---

-¢:}m = 2m - 6 ¢:}m = 6. 0,50

c) Tim gia tri nho nhat cua bieu tlurc B = 2(x,l. + X2l) - X,X2

Ta co B = 2(X12+ xl) - XIX2

= 2[(XI + X2)2- 2XIX2]- XIX2.=2(XI + X2)2- 5XIX2

0,50

---:[---2--- --- ---

-= 2m - 5(m - 3) = 2m - 5m + 15

2 5 5 2 5 2 0,50

=2(m -2·4m)+15=2(m-

4)

-2(4) +15

--- --- ---

-=2(m-~Y+ 95 ~ 95

4 8 8 0,50

--- --- ---

-" " inhc nh" . b','( hu BI' 95 khi 5

V'i}.ygra tn 0 at cua leu t ire a

8

1m

=

4 . 0,50

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Cau3

Cho cac ham so y =x co do thi la (P) va y=-x +m co do

thi la (d),

a) m= 2, ve (P): y = X2

va

(d): y = -x +2 tren cung mot

h~true toa d(>vuong goc.

Bang mot

s6

gia tri:

-

;1

-

-_:--_~_1----:----:---:--1,00

-"(

d

)"

di

-

q~a

-

(

0 ; -

i

"j~

~

-

(i

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;

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oj

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----

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O;St)

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D6

till

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---

-

-Y

y={l

0,50 (P)

0,50 (d)

-2

y=-:x+2

-

* -

XAe

-

diiili

-

tQa

-

d~

-

giao

-

di6m

-

c~a-

CP)" ~~

-

cdj

-

b~ng ph~p

-

ifllil

:-- -

--

-

--- ----

--

----

-

---

---Phuong trinh hoanh d(>giao diem cua (P) va (d) la:

<=>X2

=

-x+2<=> X2 +X - 2

=

0 0,50

.

-, ~~

;.

~

~.

~

.;~

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.

o~ [:

:

.

: ~~

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.

I

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:

· ~2

e

::

·

~·

~

···

.

...

~:~

.. .

..

---,---._.--- --- ---

--V~ycac giao diem la: ( 1; 1) va (-2; 4). 0,50

b) Tim m de (d) cat (P) tai hai diem nam ve hai phia cua

true tung

Phuong trinh hoanh d(>giao di~m cua (P) va (d) la

X2 +x-m

=

0 (*).

(d) c~t (P) tai hai di~m nam v€ hai phia cua true tung thi (*)

phai co 2 nghiem phan bi~t trai

dfru

<=> a.c<O

<=> l.(-m) < 0 <=>m>O 0,50

6,00<1

Cau4

0,50 (e)

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a) Chirng minh tir giac ABHI va ill giac AHKC nQi tiep

Ta co:

AiiB

=

AiB

=

900 (hoac

AiiC

=

AKC

=

900) (gt) 0,50
Nen cac goc

AiiB

AiB

cung nhin AB duoi mot goc

vuong

(AiiC

AKC

cung nhin AC diroi mQt goc vuong)

_Y~X:

Jft:

_

g~~~_

~~~~_

{h~~~

_tf!_

g~~~

_@_~~ __

~9~_

!!~J?)

:

~

_

Ttrong tv : Tu giac AHKC (ho~c ill giac ABHI nQi tiep). 0,50
0,50

b) Chung minh: IH // CD

Ta co

Aiii

=

1800 (nr giac ABHI nQi tiep)

-- -- - -- 050

_

M_~

_!!!li

.

t.

!!!~_::

_

?

_

!

Q~__

~~J?__

~~!!_::

J!!!(

< ~)

~

_

Lai co

Aiii

AiiC

(goc nQi tiep cua (0» (2)

---

----

-

~~~~--

---

----Tir (1)va (2) ta co

JiiK

=

AiiC

nen IHI/CD 0,50

c) Chung minh: ~IHK va ~BAC dong dang
Ta co

Aiii

JiiK

(cmt)

_

y~

__

1f!j

_

::

_

1XH

__

(~l!~g

_

~~~

_

~~~g

_

A~J

~~~~

_

Nen ~ IHK - ~ BAC (g.g) 0,50

d) Tinh dien tich cua hinh (vien phdn BDC) theo ban kinh
R cua dirong tron tam O.

Theo de bai

BAC

=60° ~

roc

=120°(goc nQi tiep bang
mra goc 6 tam).

Tir 0 ve OM.l Be (M E BC) M la trung diem cua BC (ban

kinh vuong goc voi day) va

RoM

=60°, nen MOM la

, ., d}. ( 'BMl';I , A BM

R

.

J3

nua tam gIaC eu co a uucrng cao nen = -- ~

BC =

R

.

J3),

OM= R .

S - nR2n - nR21200. nR2 (d d)

quat DOC - 3600 - 3600 = -3- v t 0,50

--- --- - -- - - -- -- -1- -

-ji

---

-

;i --

--

-ji

2

-;j3

- ---

-

---

-

--

----

-

--

-

--

---

-

- --

-

--

-- --

-

---- - --

-

-- --

--

---

-

--

--SflOBC =

2

.

'

2·

R 3 - -4- (dvdt) 0,50

SBIC =Squ,tDOC - SflOBC

nR2 R2

.

J3

R2

= - - --

=

(4n-3.J3)- (dvdt)

3 4 12

L-__~ _

0,50

I) Neu hoc sinh him bai khong theo huang ddn cham nhung dung vdn cho dti diem
theo tung cau,

2) Hoc sinh co the dung may tinh cAm tay (cac loai may tinh diroc phep dem vao
phong thi) de lam bai neu de bai khong yeu cAu giai theo phuong phap nao.

</div>

De thi tuyen sinh lop 10 mon Tieng Toan 1213

IBANCH1NH1

sa

GIAo DYC vA DAo

~o

DE CHINHTHUC

-

J8 -

2J18

Fa .

=

+

+

+

=

<i>RAe</i>

°

DE

CHINH T

RU

e

=

2

.

J2 -

<i>2</i>

<i>.</i>

<i>3</i>

<i>.</i>

<i>J2</i>

5

.

J2

---~

--

(2

-

~-

6

-;

S

-)

J2

-

~

--

:]2

--

-

----

-

---

-

--

-

-

---

--

---

---

- --

-

--

0

;

50

---

-- ----

---

-

~

=

=

<i>~.Ji</i>

=

~

-

.

-

_1_