UBND HUYN THY NGUYN THI HC SINH GII

MN: TON 8Thi gian: 120 pht (khng k thi gian giao )Cu1 (3,0 im):

1) Cho biu thc:

a- Tm iu kin xc nh ca A, ri rt gn A.

b- Tm cc gi tr nguyn ca x A nhn gi tr nguyn.

2) Gii phng trnh:

Cu 2 (2,0 im):

a) Cho a + b + c = 0 v a2 + b2 + c2 = 14

Tnh gi tr ca biu thc B = a4 + b4 + c4b) Tm s nguyn dng n n5+1 chia ht cho n3+1

Cui3 (1,0 im)Cho a l s nguyn. Chng minh rng biu thc:

P= ( a+ 1)( a+2)( a+3)( a+4)+1 l bnh phng ca 1 s nguyn. Cu 4 (1,0 im):

Cho tam gic ABC c din tch S, trung tuyn AM. Gi N l trung im ca AM, BN ct cnh AC ti E, CN ct cnh AB ti F. Tnh din tch t gic AFNE theo S.

Cu 5 (3,0 im):

Cho hnh bnh hnh ABCD. Qua A k mt ng thng tu ct BD, BC, CD ln lt ti E, K, G. Chng minh:

a)

b)

c) Khi ng thng i qua A thay i th tch BK.DG c gi tr khng i.

............................... HT.................................

UBND HUYN KIM SNPHNG GIO DC V O TO

HNG DN CHM THI CHN HSG

MN: TON 8

CuYu cu ni dungim

Cu1

3,0

1a

a- KX:

0,25

0,75

1b

0,25

A nguyn th nguyn hay x+3(4)0,25

Suy ra:

x+3

-4

-2

-1

1

2

4

x

-7

-5

-4

-2

-1

1

V KX: x-20,25

Vy x nhn cc gi tr: -7;-5;-4;-1;1

0,25

2

* Xt khong x phng trnh cho tr thnh: (1)

Vi pt (1) tr thnh: x-3=x+1, v nghim

0,25

Vi pt (1) c nghim x=1 thuc khong ang xt

0,25

* Xt khong x< 0 pt cho tr thnh: (2)

Vi pt (2) c dng: x+3= x+1, v nghim

0,25

Vi pt (2) c nghim x=-2 (khng thuc khong ang xt)

Vy phng trnh cho c tp nghim S =

0,25

Cu2

2 a

Ta c:

0,25

Li c: a+ b+ c = 0

EMBED Equation.3

EMBED Equation.3

0,5

Do :

B = a4+ b4+ c4 = 196-2.49 = 980,25

b

(v )

0,5

Nu n=1 th c 0 chia ht cho 1

Nu n> 1th n-1< n(n-1)+1=n2-n+1 nn (n-1) khng th chia ht cho n2-n+1

Vy gi tr duy nht ca n tm c l 10,5

Cu3

1,0

P= ( a+ 1)( a+2)( a+3)( a+4)+1 = (a

t ata c:

P = x( x+ 2)+1= x+ 2x + 1= (x + 1). Thay a ta c P = ( a

EMBED Equation.3 V a l s nguyn nn ( a

EMBED Equation.3 l s nguyn, do

p =( a

EMBED Equation.3 l bnh phng ca mt s nguyn. Suy ra iu phi chng minh.0,25

0,5

0,25

Cu4

1

V MK//CF 0,25

;

0,25

m

EMBED Equation.30,25

Tng t c:

0,25

Cu5

3

Do BK//AD, nn (1)

0,5

Do AB//DG, nn(2)

0,25

T (1)(2)

0,25

Ta c: (3)

0,25

Tng t: (4)

0,5

Cng tng v ca (3) v (4) ta c:

hay

0,5

t AB=a; AD=b th: v

0,5

Nhn theo tng v ca hai ng thc trn, ta c:

c gi tr khng i0,5

HT

Ghi ch: Hc sinh lm cch khc ng vn cho im ti a

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