THI HC SINH GII : TON 8

THI HC SINH GII : TON 8 - 5Thi gian: 90

I. bi:Bi tp 1: Phn tch a thc sau thnh nhn t.

a) x2 - (a+b) xy + aby2b) a2- b2 2a + 1

c) a3 19a + 30

Bi tp 2:

a) Tm a,b,c sao cho a thc x4 + a x2 + bx + c chia ht cho a thc ( x-3)3 b) cho a + b + c = 2012

Chng minh rng : = 2012Bi tp3:

a) Chng minh rng biu thc sau khng ph thuc vo gi tr ca bin P =

b) Cho Q = Chng minh rng Q l s nguyn; bit rng xyz = 1Bi tp 4: Cho hnh vung ABCD.Ly im M tu trn BD.T M k ME AB; MF AD.Chng minha) CF = DE; CFDE

b) CM = FE ; CM FE

c) CM,BF,DE ng qui.III.p n:Bi tpp n im

Bi 1 (2,5im)a) = x2 a xy bxy aby2 = x(x-by) ay( x-by) = ( x- ay)(x by)

b) = (a2 2a + 1) b2 = ( a 1)2 b2 = ( a -1- b)( a 1 + b)

c)= a3-4a -15a -30

= a(a2-4)-(15a-30)

= a(a-2)(a+2)-15(a-2)= (a-2) (a2-2a-15)

= (a-2)( a2+3a-5a-15a)

= (a-2)(a+3)(a-5)0,250,250,250,250,250,250,250,250,250,25

Bi 2

(1,5im)a) = x4+a x2+bx+c=(x-3)3(x+d) = (x3-9x2+27x-27)(x+d)

= x4+(d-9)x2+(27-9d)x2+(27d-27)x-27dcn bng h s ta c d-9=0 d=9

-27d = cc=-243

27d-27=bb=216

27-9d=a a=-54

Vy a=-54;b=216;c=-243;d=9 th x4+a x2+bx+c chia ht cho (x-3)3b)Ta c a3+b3=(a+b)3-3a2b-3ab2

a3+b3+c3-3abc = (a+b)3-3a2b-3ab2+c3-3abc = (a+b)3+c3-3ab(a+b+c)= (a+b+c)(a2+b2+c2+2ab ac-bc)-3ab(a+b+c)

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

Vy

=

= a+b+c = 2013

0250,50,250,50,25

Bi 3 (2im) a) P=

b) Q =

= 2013() = 2013() = 20130,750,250,50,5

Bi 4 (4 im)a) AEMF l hnh ch nht AF=EM

EBM cn ti E v = 450 EB =EM

AF= EB m AB = AD AE=FD

EMBED Equation.DSMT4 ADE =DCF (c,g,c) FC=DE v =

m + =900

EMBED Equation.DSMT4 + =900

EMBED Equation.DSMT4 =900 CFDE

b) MEF =GMC(c.g.c) CM = FE v =

ta li c =(so le trong)m +

EMBED Equation.DSMT4 +=900

EMBED Equation.DSMT4 ++=900

EMBED Equation.DSMT4 =900 CM FE

c)Xt EFC c EI,CK l ng cao nn FB l ng cao th 3 n n CM,BF,DE ng qui.

0,5 0,5 0,25 0,25 0,25 0,25 0,5 0,25 0,25 0,5 0,5

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