UBND HUYN THU NGUYN

MN: TON 8Thi gian: 90pht (Khng k thi gian giao )Cu 1(1.5 im): Thc hin php tnh a) 98.28 ( 184 - 1)(184 + 1)

b) (2x - 1)2 + 2(2x - 1)(x + 1) + (x + 1)2 c)

Cu 2(1.5 im): Phn tch cc a thc sau thnh nhn t a) x3 9x

b) 4x2 3x 1

c) ab( a - b) + bc( b- c) + ca( c- a)

Cu 3. ( 1.5 im):

a) Chng minh rng: Nu aN, a > 1 th A = (a2 + a +1)(a2 + a + 2) 12 l hp s b) Cho 10a2 = 10b2 c2. Chng minh rng: (7a 3b 2c)(7a 3b + 2c) = ( 3a 7b)2 Cu 4(1.5 im): Cho A =

a) Rt gn A

b) Tm s nguyn a A l s nguyn

Cu 5(3.25 im): Cho tam gic ABC vung ti A (AC > AB), ng cao AH. Trong na mt phng b AH c cha C, v hnh vung AHKE. Gi P l giao im ca AC v KE a) Chng minh vung cnb) Gi Q l nh th t ca hnh bnh hnh APQB, gi I l giao im ca BP v AQ. Chng minh H, I, E thng hngc) T gic HEKQ l hnh g? Chng minh Cu 6(0.75 im): Tnh din tch hnh thang ABCD ( AB // CD), bit AB = 42cm, ; v chiu cao ca hnh thang bng 18m --------------- HT ---------------

UBND HUYN KIM SNPHNG GIO DC V O TO

HNG DN CHM THI CHN HSG

MN: TON 8

Cup nim

1a/ = 188 (188 1)

= 188 188 + 1 = 10.25

0.25

b/ =

= (3x)2 = 9x2 0.25

0.25

c/ =

= 0.25

0.25

2a/ = x(x2 - 9)

= x(x + 3)(x -3)0.25

0.25

b/ = 4x2 + 4x x 1 = (4x2 + 4x) (x + 1)

= 4x(x + 1) (x + 1) = (x + 1)(4x - 1)0.25

0.25

c/ = ab( a - b) + b2c bc2 + ac2 a2c

= ab( a-b) + ( b2c a2c) + (ac2 bc2)

= ab( a - b) + c( b2- a2) + c2(a - b)

= ( a - b)

= (a - b)( b - c)( a - c) 0.25

0.25

3a/t a2+ a + 1 = x (1)

A = x(x + 1) 12 = x2 + x 12= x2 3x + 4x 12

= (x2 3x) + (4x 12) = x(x - 3) + 4(x - 3)

= (x - 3)(x + 4)

Thay (1) vo biu thc A, ta c

A = (a2 + a - 2)(a2 + a + 5)

= (a2 + 2a a - 2)(a2 + a + 5)

= (a - )( a + 2)(a2 + a + 5)

Ta thy

Vy A l hp s

b/ VT = (7a 3b)2 4c2 = 49a2- 42ab + 9b2 4c2m 10a2 = 10b2 + c2 nn c2 = 10a2 10b2

nn VT = 49a2 42ab + 9b2 4(10a2 10b2)

= 49a2 42ab + 9b2 40a2 + 40b2

= 92 42ab + 49b2 = (3a 7b)2 = VP0.25

0.25

0.25

0.25

0.25

0.25

4a/ A =

=

b/ Ann a 2 l c ca

Vi a 2 = 1 th a = 3

Vi a 2 = - 1 th a = 1.

Vy a th A l s nguyn0.25

0.5

0.25

0.5

5a/ CM c (g.c.g)

AB = AP m (gt)

Vy vung cn

b/Ta c: HA = HK

H nm trn ng trung trc ca AK

Ta c: AE = KE

E nm trn ng trung trc ca KA

vung c IB = IP (t/c /c hbh ABQP)

(*)

Ta c ABQP l hbh(gt), c BA= AP ( vung cn ti A)

EMBED Equation.DSMT4 l hnh thoi, m (gt)

l hnh vung nn PI = IA(**).

T (*) v(**) suy ra IK = IA nn I nm trn ng trung trc ca AK

Vy H, I, E thng hng.

c/ Ta c APQB l hnh vung (cmt) nn AP = BQ

m IK =

c AI = IQ(t/c /c hv)

M (cmt) vung K

m (EAHK l hv) QK // HE

Vy HEKQ l hnh thang 0.5

0.25

0.25

0.25

0.25

0.5

0.25

0.25

0.25

0.5

6Qua A v B k AA v BB vung gc vi CD.

T gic ABBAl hcn v AA = BB = 18m

Do AAD vung cn

AD = AA = 18m

v th trong tam gic vung BBC

ta c BC = . Theo nh l Pi ta go, ta c:

BC2 = BC2 BB2

BC2 = 4BC2 BB2

3BC2 = BB2 BC = (cm)

Suy ra:

CD = AB AD BC = 42 18 -(cm)

Vy SABCD =(cm2)0.25

0.25

0.25

--------------- HT ---------------

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