高二数学选修2-1质量检测试题(卷)2



21 20XX.2 1 2 3 6 . 60 1 2

12 5 60
1. (4, 4)

A. y2 4x B. x2 4 y

C. y2 4x x2 4 y D. y2 4x x2 4 y

2.

.

(1) a (1, 2,1) , b (1, 2, 3) (2) a (8, 4, 6) , b (4, 2, 3)

3 a (0,1, 1) , b (0, 3,3) 4 a (3, 2, 0) , b (4, 3,3)
A. B. C. D.
3. n1 (3, 2,1) n2 (2, 0,1)


70
A.
14

70
B.
10

C. 70 D. 70

14

10

4." k 5 , k Z "" sin 2 1 "

12

2

A.

B.

C. D.

5." l a "" l a "

A

B

C

D



6. ABCD A1B1C1D1 E A1B1 A1B D1E

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A 5 10

B 10 10

C 5 5

D 10 5

7. F1(5, 0) F2 (5, 0) P F1 F2
6

A. x2 y2 1 B. x2 y2 1 C. x2 y2 1 D. y2 x2 1

9 16

16 9

25 36

25 36

8. l P(1,0,1) a (2,1,1) l

M(1,2,3)
A. (1,4,2)B. (1 , 1, 1) C. ( 1 ,1, 1) D. (0,1,1) 42 42
9." a b a c b c " A. a c b c a b B. a c b c a b C. a c b c a b D. a c b c a b

10 . x2 y2 1 y . 4 m 10 m m 2

A. 4 .

B. 5 .

C. 7 .

D. 8 .

11

1"m ""m "

(2) " a b "" a2 b2 "

(3) " x 3 "" x2 2x 3 0 "

4" A B B "" A ".

A. 0 B. 1

C. 2

D. 3

12

x2 a2



y2 b2

1 a

0 b 0 F1F2 F1

30 M MF2 x

A 6 B 5 C 3 D 2

2/7



6 5 30 13.

14 a (0, 1,1) b (4,1, 0) | a b | 29
0 = ____________.
15 M112 AB O, 021 M AB __________.
16 P F (3, 0) x 2 1 P

. 17"".
18. x2 4 y2 16 AB P21 AB

AB 1 AB . 2
21 20XX.2
19 20 21 22








5 6 30 . .

13;.

14._____.15..16.

17.________________.

18. __________________.



4 60



19. 15 """"""

.

20. 15 y2 x2 1 4 12
13 x . 5

O
21. 15 O ABCD

M
3/7

A

B

N

D C



ABCD 1 ABC , OA ABCD , 4
OA 2 , M OA N BC A

MN OCD

AB MD B OCD .

22. 15 x 4

5
.

5

(1) 2 l MN

MN 16 5 l . 9
21 20XX.2

12 5 60

1. C. p75 1

2. Bp38 3 3. Ap45

2

4. B. A 4 5. C08 136. B08

12

7. Ap80 12 8. D A 13 9. Cp5,

2

10 .D A 2 11 A A 1 12C08



6 5 30

13 3 2 .

14 3 08 13.15 8 21p50

16 y2 12x 21 p76 A 5 17

18. p96 A 8

4 60 19. 3 2 . 20. 21p96B 2

x2 a2

y2 b2

1 e

2 c

4/7



y2 4



x2 12

1

2 c1 e1

2



c12 4 12 16 c1 4 4

e1



c1 2



2

6

e 13 2 3 c 3

5

5 a5

8

b c1 4

10

a2 b2 c2

12

a2 25

x2 y2 1 15 25 16
21. 15 08 18
AP CD P,, AB,AP,AO x, y, z


A(0,0,0), B(1,0,0), P(0, 2 ,0), D( 2 , 2 ,0),O(0,0, 2), M (0, 0,1), N (1 2 , 2 ,0)

2

22

44

,3

(1) MN (1 2 , 2 , 1),OP (0, 2 , 2), OD ( 2 , 2 , 2) 5

44

2

22



OCD n (x, y, z) , n OP 0, n OD 0

zO







2 2

y 2z

0

M



2 x 2

2 y 2z 0 2

A

z 2 , n (0, 4, 2) 7

xB

N

D CP y

5/7



MN n (1 2 , 2 , 1) (0, 4, 2) 0 44
MNOCD 9

(2) AB MD , AB (1, 0, 0), MD ( 2 , 2 , 1)
22

cos AB MD 1 , , AB MD 13

AB MD 2

3

3

(3) B OCD d , d OB n (0, 4, 2)

,

OB (1, 0, 2) , d OB n 2 . B OCD 2 15

n3

3



22. p87 3

1

x2 a2



y2 b2

1

2

2b 4, e c 5 (4 ) a2 b2 c26 a5
a2 5,b 2, c2 1, c 1

x2 y2 18 54
2 l k MN M (x1, y1), N (x2 , y2 ) (1, 0) l y k(x 1) 10

x2 k 2 (x 1)2 1

5

4

11

(4 5k 2 )x2 10k 2x 5k 2 20 0

6/7





x1



x2





10k 2 4 5k 2

,

x1x2



5k 2 4

20 5k 2

13



MN

(x1 x2 )2

( y1

y2 )2

16 9

5



( x1



x2 )2 (1

k2)



16 9

5



( x1



x

2

)2



4x1x

2



(1



k

2

)



1280 81



(

10k 2 4 5k 2

)2



4(5k 2 20) 4 5k 2



(1



k

2

)



1280 81



100k

4



4(5k

2



20)(4



5k

2

)

(1



k

2

)



1280 81

(4



5k

2

)2

320(1 k 2 )2 1280 (4 5k 2 )2 81

1 k 2 2 (4 5k 2 ) k 2 1, k 1 9

l y x 1 y x 115





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