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N TP HC K 2 Nm hc Mn TON Lp 10

Thi gian lm bi 90 pht

Cu 1: Gii cc bt phng trnh v h bt phng trnh sau:

a) x x

x

( 1)( 2)0

(2 3)

. b) x5 9 6 . c).

x x

xx

56 4 7

7

8 32 5

2

Cu 2: Cho bt phng trnh sau: mx m x m2 2( 2) 3 0 .

a) Gii bt phng trnh vi m = 1. b) Tm iu kin ca m bt phng trnh nghim ng vi mi x thuc R.

Cu 3: Tm cc gi tr lng gic ca cung bit: 1

sin

5

v 2

.

Cu 4: Trong mt phng Oxy, cho ba im A(1; 0), B(1; 6), C(3; 2). a) Vit phng trnh tham s ca ng thng AB. b) Vit phng trnh tng qut ca ng cao CH ca tam gic ABC (H thuc ng thng

AB). Xc nh ta im H.

c) Vit phng trnh ng trn (C) c tm l im C v tip xc vi ng thng AB. Cu 6 :

a) Cho cota = 1

3

. Tnh Aa a a a2 2

3

sin sin cos cos

b) Cho tan 3 . Tnh gi tr biu thc A 2 2sin 5cos --------------------Ht-------------------

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

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s 1

P N N TP HC K 2 Nm hc Mn TON Lp 10

Thi gian lm bi 90 pht

Cu 1: Gii cc bt phng trnh v h bt phng trnh sau:

a) x x x x

x x

x xx

( 1)(2 )(2 3) 0 1( 1)( 2)

0 3 32(2 3)

2 2

2

b) x

xx

5 9 65 9 6

5 9 6

x

x

3

5

3

c). x x x

xx

x x

5 226 4 7

77 7

8 3 7 42 5

2 4

Cu 2: Cho bt phng trnh sau: mx m x m2 2( 2) 3 0 .

a) Gii bt phng trnh vi m = 1.

Vi m = 1 ta c BPT: 2 2 2 0 ( ; 1 3) ( 1 3; )x x x

b) Tm iu kin ca m bt phng trnh nghim ng vi mi x thuc R.

TH1: m = 0. Khi ta c BPT: 4x 3 > 0 3

4 x m = 0 khng tho mn.

TH2: m 0. Khi BPT nghim ng vi x R 0

' 0

m

2

0(4; )

( 2) ( 3) 0 4 0

mm

m m m m

Kt lun: m > 4

Cu 3: Tm cc gi tr lng gic ca cung bit: 1

sin

5

v 2

.

V 2

nn cos 0 .

21 2

cos 1 sin 1

5 5

sin 1 1

tan ; cot 2

cos 2 tan

Cu 4: Trong mt phng Oxy, cho ba im A(1; 0), B(1; 6), C(3; 2). a) Vit phng trnh tham s ca ng thng AB.

11

(1;3) : ,32

x tAB PTTS t R

y t

b) Vit PTTQ ca ng cao CH ca ABC (H thuc ng thng AB).

ng cao CH i qua C(3; 2) v nhn AB (2;6)uur

lm VTPT

PTTQ: x y2( 3) 6( 2) 0 x y3 9 0

H l giao im ca AB v CH To im H l nghim ca h PT:

1

3

3 9 0

x t

y t

x y

x

y

0

3

H(0; 3)

c) Vit phng trnh ng trn (C) c tm l im C v tip xc vi ng thng AB.

2 2 2 2 2 2( 3) 1 10 ( ) : ( 3) ( 2) 10 R CH C x y

Cu 6 :

a) Cho cota = 1

3

. Tnh Aa a a a2 2

3

sin sin cos cos

3

V cota = 1

3

nn sina 0 2

2

13 1

3(1 cot ) 96

1 11 cot cot1

3 9

aA

a a

b) Cho tan 3 . Tnh gi tr biu thc A 2 2sin 5cos

22

4 4 71 4cos 1 1

1 tan 1 9 5

A

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