1

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s 2

N TP HC K 2 Nm hc Mn TON Lp 10

Thi gian lm bi 90 pht

Cu 1:

a) Cho x, y > 0. Chng minh rng: x y

xy7 9

252

b) Gii bt phng trnh: x x x2(2 1)( 3) 9

Cu 2: Tm tt c cc gi tr ca m phng trnh sau c 2 nghim phn bit:

m x m x m2( 2) 2(2 3) 5 6 0

Cu 3: Cho tam gic ABC c A(1; 1), B( 1; 3) v C( 3; 1). a) Vit phng trnh ng thng AB.

b) Vit phng trnh ng trung trc ca an thng AC. c) Tnh din tch tam gic ABC.

Cu 4: Cho tan = 3

5

. Tnh gi tr biu thc : A = 2 2

sin .cos

sin cos

.

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

H v tn th sinh: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD :. . . . . . . . . .

DAP AN

Cu 1:

a) V x, y > 0 nn ta c xyx y

xy2 637 9

.

252 4.63

Du bng xy ra x

x y

y

97 9

7

(pcm).

2

b) x x x x x x x x2 2 2 2(2 1)( 3) 9 2 5 3 9 5 6 0 x ( ; 3] ( 2; )

Cu 2: Xt phng trnh: m x m x m2( 2) 2(2 3) 5 6 0

Phng trnh cho c hai nghim phn bit

m m

m

m m m m m2 2

2 0 2(1;3) \ 2

' (2 3) ( 2)(5 6) 0 4 3 0

Cu 3: Cho tam gic ABC c A(1; 1), B( 1; 3) v C( 3; 1). a) Vit phng trnh ng thng AB.

AB VTPT n( 2;2) 2( 1;1) (1;1)

Phng trnh AB: x y 2 0 .

b) Vit phng trnh ng trung trc ca an thng AC.

Trung im AC l M(1; 0)

AC VTPT n( 4; 2) 2(2;1) (2;1)

Phng trnh x y: 2 2 0 .

c) Tnh din tch tam gic ABC.

ABC

d C AB AB S2 23 1 2 1

( , ) 3 2; ( 2) 2 2 2 .3 2.2 2 6

22

Cu 4: Cho tan = 3

5

. Tnh gi tr biu thc : A = 2 2

sin .cos

sin cos

.

V tan = 3

5

nn cos 0 A2

3

tan 155

9 16tan 11

25

Cu 5: S tit t hc ti nh trong 1 tun (tit/tun) ca 20 hc sinh.

S tit

Tn s

ni

Tn sut

fi

8 1 5% 8 64

9 2 10% 18 162

10 2 10% 20 200

11 2 10% 22 242

12 3 15% 36 432

13 1 5% 13 169

14 2 10% 28 392

15 2 10% 30 450

16 3 15% 48 768

17 0 0% 0 0

18 2 10% 36 648

N 20 100% 259 3527

S trung bnh cng: 12,95

Phng sai: 8,65

lch chun: 2,94

i in x

i in x2

Biu gi t hc

0

0,5

1

1,5

2

2,5

3

3,5

8 9 10 11 12 13 14 15 16 17 18

S tit

S

h

c s

inh