C

PHNG GIO DC & O TO

LC NAM KHO ST LN I NM HC 2013 - 2014MN: TON 9Thi gian lm bi: 90 pht

(Khng k thi gian giao )

Cu 1: (2,0 im)

1. Tnh

2. Tm gi tr ca tham s ng thng (1) i qua im A(1; 5)Cu 2: (2.5 im)

1. Gii h phng trnh:

2. Cho biu thc (vi). a/ Rt gn A.

b/ Tm gi tr ca .Cu 3: (2,0 im)

Hai lp 9A v 9B c phn cng trng 78 cy xanh. Tnh s cy m mi lp c phn cng trng bit rng lp 9A c 30 hc sinh, lp 9B c 35 hc sinh v s cy c chia t l vi s hc sinh ca mi lp.Cu 4: (3,0 im) Cho tam gic nhn ABC c . V ng trn ng knh AC c tm O, ng trn ny ct BA v BC ti D v E. 1. Chng minh AE = EB.

2. Gi H l giao im ca CD v AE. Chng minh rng ng trung trc ca on HE i qua trung im I ca BH.

3. Chng minh OD l tip tuyn ca ng trn ngoi tip BDE.

Cu 5: (0,5 im) Cho tha mn:

EMBED Equation.3 Hy tnh gi tr ca biu thc : M = + (x8 - y8)(y9 + z9)(z10 - x10) .

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

Cn b coi thi khng gii thch g thm!

H v tn th sinh:................................................ S bo danh:...................PHNG GIO DC & O TO

LC NAMHNG DN CHM KHO ST LN I NM HC 2013 - 2014MN THI:TON

Bn hng dn chm c 03 trang

Lu khi chm bi:

Di y ch l s lc cc bc gii v thang im. Bi gii ca hc sinh cn cht ch,chi tit, hp logic ton hc. Nu hc sinh lm bi theo cch khc hng dn chm m ng th chm v cho im ti a ca bi . i vi bi hnh hc (cu 4), nu hc sinh v sai hnh hoc khng v hnh th khng c tnh im.

CuHng dn giiim

Cu 1

(2,0 im)(2 im)

1

(1 im)A =

.0,5

EMBED Equation.DSMT4 = -2. Vy A = - 2.0,5

2

(1 im) ng thng (1) i qua im A(1; 5) th to ca im A tho mn (1)0,25

Ta c: 5 = (2m + 1) .1+ 12m = 5 - 20,25

2m = 3m =

0,25

Vy vi ng thng (1) i qua im A(1; 5).0,25

Cu 2(3im)

2a (1im)Vi KX: . Ta c:

0,25

0,25

EMBED Equation.DSMT4 0,25

Vy vi .0,25

b

(0,5 im)Ta c:

0,25

Kt hp iu kin , ta c vi th .0,25

1(1,0 im)

0,25

0,25

EMBED Equation.DSMT4 0,25

Vy h phng trnh c nghim duy nht

0,25

Cu 3.(2,0 im)(2,0 im)

- Gi s cy m lp 9A c phn cng trng l x( cy), (0 < x < 78, x l s nguyn).

s cy m lp 9B c phn cng trng l y( cy) ( 0 < y < 78, y l s nguyn).0,25

- Do tng s cy phi trng l 78 cy ta c phng trnh:

x + y = 78 (1)0,25

s cy c chia t l vi s hc sinh ca mi lp ta c phng trnh: (2)0,25

T (1) v (2) ta c h phng trnh:

0,25

- Gii h tm c x = 36, y = 42 tha mn iu kin 0,5

- Kt lun s cy m lp 9A c phn cng trng l 36( cy), s cy m lp 9B c phn cng trng l 42( cy) 0,25

Cu 4(3,0 im)(3 im)

1)(1 im)1. ( (ni tip chn na ng trn )

=> 0,25

EMBED Equation.DSMT4 ( v l hai gc k b); Theo gi thit

0,25

(AEB l tam gic vung cn ti E0,25

=> EA = EB.0,25

2)(1 im) Gi K l trung im ca HE (1) ; I l trung im ca HB => IK l ng trung bnh ca tam gic HBE0,25

=> IK // BE0,25

m nn BE ( HE ti E IK ( HE ti K (2).0,25

=> T (1) v (2) => IK l trung trc ca HE . Vy trung trc ca on HE i qua trung im I ca BH.0,25

3)(1 im)theo trn I thuc trung trc ca HE => IE = IH m I l trung im ca BH => IE = IB.0,25

(ni tip chn na ng trn ) => (k b ) => tam gic BDH vung ti D c DI l trung tuyn (do I l trung im ca BH) => ID = 1/2 BH hay ID = IB => IE = IB = ID => I l tm ng trn ngoi tip tam gic BDE bn knh ID. 0,25

Ta c (ODC cn ti O (v OD v OC l bn knh ) => . (3)

(IBD cn ti I (v ID v IB l bn knh ) => . (4)

Theo trn ta c CD v AE l hai ng cao ca tam gic ABC => H l trc tm ca tam gic ABC => BH cng l ng cao ca tam gic ABC => BH ( AC ti F => (AEB c .

Theo trn (ADC c => ( cng ph ) (5).

T (3), (4), (5) => m => = => OD ( ID ti D => OD l tip tuyn ca ng trn ngoi tip tam gic BDE.0,5

Cu 5:(0,5 im)T : =>

=>

0,25

Ta c : x8 - y8 = (x + y)(x-y)(x2+y2)(x4 + y4).

y9 + z9 = (y + z)(y8 - y7z + y6z2 - .......... + z8)

z10- x10 = (z + x)(z4 - z3x + z2x2 - zx3 + x4)(z5 - x5)

Vy M = + (x + y) (y + z) (z + x).A =

0,25

im ton bi10,0

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