kim tra 45 pht mn ton 8

MN: TON 8Thi gian: 120 pht (Khng k thi gian giao )Cu 1: (2,5 im) a) Phn tch a thc thnh nhn t:

b) Tm cc s nguyn sao cho: .

c) Tm cc hng s a v b sao cho chia cho d 7; chia cho d 4.

Cu 2: (1,5 im) a) Tnh gi tr biu thc:

A= vi

b) Tm B c gi tr nh nht: vi x>0Cu 3: (2 im)

Chng minh rng: a)

b) Nu l cc s t nhin tha mn: th:

m-n v u l s chnh phng.

Cu 4: (4 im)Gi O l giao im hai ng cho AC v BD ca hnh thang ABCD (AB//CD). ng thng qua O song song vi AB ct AD v BC ln lt ti M v N.

a) Chng minh OM=ON.

b) Chng minh . c) Bit Tnh ?

d) Nu . Chng minh BD > AC.-----------HT-------------

UBND HUYN KIM SNPHNG GIO DC V O TO

HNG DN CHM THI CHN HSGMN: TON 8

Cup nim

1

a/ =

0,5

=

0,25

b/

EMBED Equation.3 . Do l cc s nguyn nn ta c:

TH1: (tha mn) hoc(tha mn)0,25

0,25

TH2: (tha mn) hoc (tha mn)0,5

c/ V chia cho d 7 nn ta c: =

do vi th -1-a+b=7, tc l a-b = -8 (1).0,25

V chia cho d 4 nn ta c: =

do vi th 8+2a+b=4, tc l 2a+b=-4 (2).

0,25

T (1) v (2) suy ra a=-4;b=4.0,25

2a/ Ta c: vi mi nn ta c:0,25

A= =

0,25

Thay vo A ta c: A=

0,25

b/ B==

0,25

=.0,25

Du = xy ra khi .0,25

Vy GTNN ca B l t c khi .

3

a/ t a=2011; b=11; c=2000. Khi ta c a=b+c.

Xt v phi ng thc ta c:

0,25

Thay a=b+c vo

0,25

0,25

Nn .0,25

Vy:

b/Ta c

EMBED Equation.3 (*)0,5

Gi d l CLN(m-n;5m+5n+1)(5m+5n+1)+5m-5n d10m+1 d

Mt khc t (*) ta c:

EMBED Equation.3 d2m d. M 10m+1 d nn 1 dd=10,25

Vy m-n;5m+5n+1 l cc s t nhin nguyn t cng nhau,

tha mn (*) nn chng u l cc s chnh phng.0,25

4

hnh v0,25

a/ Ta c Do MN//DC

EMBED Equation.3

EMBED Equation.3 OM=ON.0,5

0,5

b/ Do MN//AB v CD

EMBED Equation.3 v . Do :

(1)0,25

Tng t: (2)0,25

T (1);(2)

EMBED Equation.3 0,25

EMBED Equation.3 0,25

c/ Hai tam gic c cng ng cao th t s din tch 2 tam gic bng t s gia 2 cnh y tng ng. Do vy: v 0,25

Nhng

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3 nn .

Tng t .Vy

0,5

0,25

d/ H AH, BK vung gc vi CD ti H v K

Do nn H, K nm trong on CD

Ta c .

T gic BCEA l hnh bnh hnh nn BC=AE Vy AD>BC DH>KCDK > CH.

0,25

0,25

Theo nh l pitago cho tam gic vung BKD ta c: (Do

0,25

HS lm cc cch khc ng vn chm im ti a

PAGE

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