Đề thi học kì 2 (HK2) lớp 10 môn Toán năm 2020 2021 trường THPT Thị xã Quảng Trị

90

2

a) Cho 3, ; . 5 2 cosa a . sina

6 2 4 4 2 4 sin 2sin cos 3sin cos cos P x x x x x x

.x

2 ( 1) 2( 1) 2 0 m x m x .

4 (2

ho A(1; -2), B(5;-4), C(-3; 2).

d BC .

, B, C.

5 (1

ho 2 2 2 4 5 0 x y x y

A(0;-1), M(3; 2).

B

2 2 1 1 OP OQ

----------------- ---------------------

sinh: danh:

01 trang)

2021 L

a) 2 2 1. x x

b) 2 6 0 x x

c) 2 2 1 x x

d) 2 x x

1 a 2x 2 x 1 x 3 1.0

1b 2 3 6 0 2 x x x x

1.0

1c 3 3 2 2 1 2 1 2 2 1 1 1 x x x x x x x x 0.5

0.25+0.25

1d

2 2

0 0

2 0 2 2 2 1 1 2 2 0 2

(2 ) 5 4 0

x x

x x x x x x x x x

x x x x

0.25+0.25+

0.25+0.25

2a 2 2 3 3 16 4 cos sin 1 sin . 5 5 25 5 a a a

4 ; sin . 2 5 a a

0.5+0.25

0.25

2b 6 2 4 4 2 4 sin 2sin cos 3sin cos cos P x x x x x x

=

6 4 2 4 2 2 4 4 sin sin cos 2sin cos 2sin cos cos x x x x x x x x

=

2 2 4 2 2 2 2 4 cos sin sin 2sin cos sin cos cos x x x x x x x x

=

2 4 2 2 4 2 2 cos 2sin cos sin sin cos 1 x x x x x x

0.5

0.5

3 2 ( 1) 2( 1) 2 0, m x m x x

TH1: m = 1

TH2: m 2 2 1 0 1 1. 4 3 0 1 2( 1) 0

m m Ycbt m m m m

1 3 m

1 3 m

0.25

0.25

0.25

0.25

4a A 1; 2 :4 3 10 0 8;6 2(4; 3)

qua d d x y VTPT BC 0.5 + 0.5

4b 2 2 2 2 ( ): 2 2 0, 0 C x y ax by c a b c

A, B, C 1 4 2 4 0 ( ) 25 16 10 8 0 9 4 6 4 0

a b c C a b c a b c

0.25

0.25

2 2 10 11 ( ) ( ) : 20 22 29 0 29

a b tm C x y x y c

0.25 + 0.25

5a

I

3 3 7 ; 2 2 2 AH AI H

(1;3) AI

3 12 0 x y

3 3 95 7 95 3 3 95 7 95 ; ; ; 2 2 2 2

0.25

0.25

5b

2 2 2 2 1 1 1 1 ( ) const OP OQ OH OM

khi M :3 2 13 0 H x y

0.25

0.25

90

a) Cho 12 , ; . 13 2 sina a . cosa

6 4 2 2 4 4 cos 2sin cos 3sin cos sin P x x x x x x

.x

2 ( 2) 2( 2) 2 0 m x m x .

4 (2

ho A(-1;2), B(5;-4), C(-3; 2).

d BC .

B, C.

5 (1

ho 2 2 2 4 5 0 x y x y

A(0;-1), M(1;4).

2 2 1 1 OP OQ

----------------- ---------------------

sinh: danh:

01 trang)

2021 L

a) 2 1 2. x x

b) 2 5 6 0 x x

c) 2 2 1 x x

d) 2 1 x x

1 a 2x 1 x 2 x 3 1.0

1b 2 3 5 6 0 2 x x x x 1.0

1c 3 1 2 2 1 2 1 2 2 1 3 3 x x x x x x x x 0.5

0.25+0.25

1d

2 2

0 1 0 1 2 2 1 2 1 0 1 1 2 1; 2 1 4 5 1 0 4

x x x x x x x x x x x x x x

0.25+0.25+

0.25+0.25

2a 2 2 12 12 25 5 cos 1 cos . 13 13 169 13 sin a a a

5 ; cos . 2 13 a a

0.5+0.25

0.25

2b 6 4 2 2 4 4 cos 2sin cos 3sin cos sin P x x x x x x

=

6 2 4 4 2 2 4 4 cos sin cos 2sin cos 2sin cos sin x x x x x x x x

=

2 2 4 2 2 2 2 4 cos sin cos 2sin cos sin cos sin x x x x x x x x

=

2 4 2 2 4 2 2 cos 2sin cos sin sin cos 1 x x x x x x

0.5

0.5

3 2 ( 2) 2( 2) 2 0, m x m x x

TH2: m 2 2 2 0 2 2. 6 8 0 2 2( 2) 0

m m Ycbt m m m m

2 4 m

2 4 m

0.25

0.25

0.25

0.25

4a A 1;2 :4 3 10 0 8;6 2(4; 3)

qua d d x y VTPT BC 0.5 + 0.5

4b 2 2 2 2 ( ): 2 2 0, 0 C x y ax by c a b c

A, B, C 1 4 2 4 0 ( ) 25 16 10 8 0 9 4 6 4 0

a b c C a b c a b c

0.25

0.25

2 2 2 5 ( ) ( ): 4 10 21 0 21

a b tm C x y x y c

0.25 + 0.25

5a

I

3 3 7 ; 2 2 2 AH AI H

(1;3) AI t:

3 12 0 x y

3 3 95 7 95 3 3 95 7 95 ; ; ; 2 2 2 2

0.25

0.25

5b

2 2 2 2 1 1 1 1 ( ) const OP OQ OH OM

khi M : 4 17 0 H x y

0.25

0.25