de thi va dap an tuyen sinh vao lop 10 nam 2013 2014

7/28/2019 De Thi Va Dap an Tuyen Sinh Vao Lop 10 Nam 2013 2014

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1000B Trn Hng o TP Quy Nhn Tnh Bnh nh Nguyn Thanh Tun : ton hc + ng dng

S GD&T NGH AN K THI TUYN SINH VO LP 10 THPTNM HC 2013 2014

Mn thi: TON.

Thi gian lm bi: 120 pht ( khng k thi gian giao )---------------------------------------------------

Cu 1.(2,0 im)

Cho biu thc P = 2 1 1:4 2 2x x x

a) Tm KX v rt gn Pb) Tm x P = 3

2

Cu 2. (1,5 im)

Mt mnh vn hnh ch nht c chu vi 100 m. Nu tng chiu rng 3 m v gimchiu di 4m th din tch gim 2 m2 . Tnh din tch ca mnh vn.

Cu 3. (2,0 im)Cho phng trnh bc hai: x2 2(m + 1)x + m2 + 4 = 0 (m l tham s)

a) Gii phng trnh khi m = 2b) Tm m phng trnh c hai nghim x1, x2 tha mn: x12 + 2(m+1)x2 3m2 + 16

Cu 4. (3,5 im)Cho tam gic ABC nhn (AB < AC) ni tip ng trn (O), hai ng cao BE, CF

ct nhau ti H. Tia AO ct ng trn (O) ti D.a) Chng minh t gic BCEF ni tip ng trnb) Chng minh t gic BHCD l hnh bnh hnh.c) Gi M l trung im ca BC, tia AM ct HO ti G. Chng minh G l trng tm

ca tam gic ABC.Cu 5.(1,0 im)

Cho cc s thc dng a, b, c tha mn a + b + c = 1.

Chng minh rng:2 2 2a b c 1

+ +a+b b+c c+a 2

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

chnh thc


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P NCu 1:

a) KX: x 0, x 4Rt gn: P = 2 1 1:

4 2 2x x x

P =

2 2 2

1 22 2

x x

xx x

a) Vi x 0, x 4 , P = 32

3 2 3 2 6 3622

xx x x x

x

(tha

mn). Vy vi x = 36 th P =32

Cu 2: Na chu vi ca mnh vn l: 50m.Gi chiu rng ca mnh vn l: x (m), K: 0 < x < 50

Suy ra chiu di ca mnh vn l: 50 - x (m).

Din tch mnh vn l: x( 50 - x) (m2)

Chiu rng ca mnh vn sau khi tng 3m l: x + 3 (m)Chiu di ca mnh vn sau khi gim 4m l: 50 - x - 4 = 46 - x (m)

Do khi tng chiu rng 3m v gim chiu di 4m th din tch gim 2 m2 nn ta c pt:x( 50 - x) = (x + 3 ).(46 - x) + 2

50 x - x2 = 43x - x2 + 140 7x = 140 x = 20 tha mn

Suy ra din tch ca mnh vn l: 20.( 50 - 20) = 600 (m2)

Cu 3: x2 2(m + 1)x + m2 + 4 = 0

a) Vi m = 2, Pt tr thnh: x2 6x + 8 = 0 = 9 - 8 = 1 => x1 = 2, x2 = 4

Vy vi m = 2 th pt c hai nghim phn bit: x1 = 2, x2 = 4

b) Xt pt (1) ta c: ' = (m + 1)2 (m2 + 4) = 2m 3phng trnh (1) c hai nghim x1, x2 Khi ' 0 2m 3 0 m 32

Theo h thc Vi-et: 1 22

1 2

2( 1)

4

x x m

x x m

Theo gi thit: x12 + 2(m+1)x2 3m

2 + 16 x12 + (x1 + x2)x2 3m

2 + 16

x12 + x2

2 + x1x2 3m2 + 16

(x1 + x2)2 - x1x2 3m

2 + 16

=> 4(m + 1)2 (m2 + 4) 3m2 + 16


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8m 16 m 2

Vy: 32

m 2 th pt c hai nghim x1, x2 tha mn: x12 + 2(m+1)x2 3m

2 + 16

Cu 4:

a) 0BEC = 90 v BE AC; 0BFC 90 v CF AB

T gic BCEF c: 0BEC BFC 90 (gt)

T gic BCEF ni tip v c nh E v F cng nhnCnh BC di hai gc bng nhau

b) Ta c BAD= 900 (gc ni tip chn na trn)=> BD AB m CH AB => BD // CH

C/m tng t: CD // BH

=> BHCD l hnh bnh hnhc) BHCD l hnh bnh hnh , M l trung im ca BC M l trung im ca HDMt khc O l trung im ca AD suy ra G l trng tm ca AHD.

AGAM

=23

Xt ABC c AM l ng trung tuyn,AGAM

=23

Suy ra G l trng tm ca ABC

Cu 5: p dng BT Cauchy cho hai s khng m ta c:2 2

2 .4 4

a a b a a ba

a b a b

Tng t: 2 2b c;b +c 4 c+ a 4

b c c ab c

2 2 2a b c

+ +a + b b +c c +a

+a + b

4+

b + c4

+c + a

4 a + b + c

2 2 2a b c

+ +a + b b +c c +a

+a + b + c

2 1

2 2 2a b c

+ +a + b b +c c +a

+12 1

2 2 2a b c

+ +a + b b +c c +a

12

(pcm)

G

M

H

E

F

D

O

A

BC

de thi va dap an tuyen sinh vao lop 10 nam 2013 2014

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