Mn : Toan Lp 8

Thi gian: 120 phut ( khng k thi gian giao )

Bai 1: ( 1,5 im) Thc hin phep tinh:

a) 216 ( 2 + 1)(22 + 1)(24 + 1)(28 + 1)

b) ( 2x3 26x 24) : ( 2x 8)

c)

O

D

A

B

C

M

Bai 2: ( 2 im) Phn tich cac a thc sau thanh nhn t:

a) (xy + 1)2 2(x + y)2

b) 3x2 + 11x + 6

c) x2 + 2xy + y2 3x 3y 10

Bai 3: (2 im) a) Xac inh cac h s a va b sao cho a thc 2x3 + ax + b chia cho x + 1 d -6, chia cho x 2 d 21

b) Tim gia tri nho nht cua biu thc

2

2

421

xx

A

x

-+

=

Bai 4:(1 im) Cho 3a2 + b2 = 4ab. Tinh gia tri cua biu thc

ab

P

ab

-

=

+

Bai 5: ( 2,5 im) Cho hinh ch nht ABCD, H va I ln lt la hinh chiu cua B va D trn AC, goi M, O, K ln lt la trung im cua AH, HI va CD.

a) Chng minh: B va D i xng qua O

b) Chng minh: BM

^

MK

Bai 6: ( 1 im) Cho hinh binh hanh ABCD. M la mt im bt ki trn canh CD. AM ct BD O. Chng minh rng: SABO = SDMO + SBMC

---------------Ht---------------

UBND HUYN KIM SN

HNG DN CHM THI CHN HSG

PHONG GIAO DUC VA AO TAO

MN: TOAN 8

AP AN

IM

Bai 1

( 1,5 )

(Mi y 0,5 )

a) 216 ( 2 + 1)(22 + 1)(24 + 1)(28 + 1)

=216 (2 1)( 2 + 1)(22 + 1)(24 + 1)(28 + 1)

=216 ( 22 - 1)(22 + 1)(24 + 1)(28 + 1)

=216 (24 - 1)(24 + 1)(28 + 1)

=216 (28 - 1)(28 + 1)

=216 (216 - 1)

= 1

0,125

0,125

0,125

0,125

b) ( 2x3 26x 24) : ( 2x 8)

t phep chia:

Vy: ( 2x3 26x 24) : ( 2x 8) = x2 + 4x + 3

0,25

0,25

(

)

22

11

):2:

12()

..

2()

.

1

xyxy

cxy

yxyxy

xyxyy

xyxyxyxy

xyxyy

xyxyxy

x

-

-+--

--

=-

+-

--

=-

-

-

=

0,125

0.125

0,25

Bai 2:

( 2 )

a) (xy + 1)2 2(x + y)2

=( xy + 1)2 -

(

)

2

2.

xy

+

=[ xy + 1 +

2

.(x + y)].[xy + 1 -

2

.(x + y)]

0,25

0,25

b) 3x2 + 11x + 6

= (3x2 + 9x )+ (2x + 6)

= 3x( x + 3) + 2(x + 3)

= (x+ 3)(3x + 2)

0,25

0.25

0,25

c) x2 + 2xy + y2 3x 3y 10

= (x2 + 2xy + y2 ) (3x + 3y) 10

=( x + y)2 3(x + y) 10

=[ ( x + y)2 + 2(x + y)] [5(x + y) + 10]

=(x + y) (x + y + 2) 5(x + y + 2)

=(x + y + 2)(x + y 5)

0,125

0,125

0,25

0,25

Bai 3:

(2 )

a) a thc 2x3 + ax + b chia cho x + 1 d -6 => - a + b = -4 (1)

a thc 2x3 + ax + b chia cho x - 2 d 21 => 2a + b = 5 (2)

T (1) va (2), suy ra a = 3; b= -1

0,25

0,25

0,5

b) Ta co:

2

2

22

42121

442

xx

Ayy

xxx

-+

==-+=-+

( vi y =

1

x

)

A= (y2 2y + 1) +3 = (y 1)2 + 3 3 vi moi gia tri cua y

Vy: GTNN cua A bng 3 khi y 1 = 0

y = 1

x = 1

0,25

0,5

0,25

Bai 4:

(1 )

iu kin: a -b

T g/t : 3a2 + b2 = 4ab

4a2 4ab + b2 a2 = 0

( 2a b)2 a2 = 0

( 3a b)(a b) = 0

a = b/3 hoc a = b ( tm)

+) Nu a = b/ 3 thi P = -1/2

+) Nu a = b thi P = 0

0,125

0,125

0,125

0,125

0,25

0,125

0,125

Bai 5:

( 2,5 )

(

)

11

:2:

xyxy

xy

yxyxy

-

-+--

Ve hinh ung cho cu a)

0,25

a)-Chng minh t giac BHDI la hinh binh hanh

-co O la trung im cua HI (gt) => O la trung im cua BC

=> B va D i xng qua O

0.75

b) Qua M, ke ng thng song song vi AB ct BH tai N

=> MN

^

BC, va N la trung im cua BH

=> MN la ng trung binh cua tam giac AHB

=> MN // AB va MN = AB

* Chng minh t giac MNCK la hinh binh hanh => CN//KM (1)

* Tam giac BMC co N la trc tm => CN

^

BM (2)

T (1) va (2) suy ra BM

^

MK

0,5

0,5

0,5

Bai 6:

( 1 )

N

O

A

B

D

C

I

H

M

K

-Chng minh: SADB = SAMB => SADO = SBOM (1)

-Chng minh: SADB = SBCD

=>SDAO + SAOB = SDOM + SBOM + SBMC(2)

T (1) va (2) Suy ra S ABO = SDOM +SBCM

0,25

0,25

0,25

0,25

_1412275893.unknown

_1412278677.unknown

_1412280122.unknown

_1412280488.unknown

_1412280500.unknown

_1412337764.unknown

_1412280251.unknown

_1412278735.unknown

_1412278477.unknown

_1412278527.unknown

_1412278251.unknown

_1412275400.unknown

_1412275542.unknown

_1412274335.unknown