20 đề kiểm tra 1 tiết chương 3 hình học 12

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KIÓM TRA 1 TIÕT
Hä vµ tªn:..............................................................................
M«n: HÌNH HỌC 12, chương III
Líp 12…..….
Ngày kiểm tra:..............................

Trường THPT ............
Điểm

Nhận xét của Thầy, Cô giáo

Đề 1A: Trong không gian Oxyz, cho bốn điểm A(1; 0; 0); B(0; 3; 0); C(0; 0; 6); D(1; 1; 1) và hai
 x = 1 + 2t
x = 2 + t '


đường thẳng (d), (d’) lần lượt có phương trình: ( d1 ) :  y = 2 + t ; ( d 2 ) :  y = −3 + 2t '
 z = −3 + 3t
 z = 1 + 3t '



1) Viết phương trình mặt phẳng (ABC). Chứng tỏ A, B, C, D là 4 đỉnh của một tứ diện.
2) Tìm hình chiếu của điểm D lên (ABC).
3) CMR (d), (d’) chéo nhau.
4) Viết phương trình ( α ) chứa (d) và song song với (d’). Tính khoảng cách giữa (d) và (d’).
5) Viết phương trình đường thẳng ( ∆ ) chứa trong (ABC) và cắt hai đường thẳng (d), (d’).

Bài Làm:

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KIÓM TRA 1 TIÕT
Hä vµ tªn:..............................................................................
M«n: HÌNH HỌC 12, chương III
Líp 12…..….
Ngày kiểm tra:..............................

Trường THPT ............
Điểm

Nhận xét của Thầy, Cô giáo

Đề 1B: Trong không gian Oxyz, cho bốn điểm A(1; 0; 0); B(0; 3; 0); C(0; 0; 6); D(1; 1; 1) và hai
 x = 1 + 2t
 x = −2 + t '


đường thẳng (d), (d’) lần lượt có phương trình: ( d1 ) :  y = −2 + t ; ( d 2 ) :  y = −3 + 2t '
 z = −3 + 3t
 z = 1 + 3t '



1) Viết phương trình mặt phẳng (BCD). Chứng tỏ A, B, C, D là 4 đỉnh của một tứ diện.
2) Tìm hình chiếu của điểm A lên (BCD).
3) CMR (d), (d’) chéo nhau.
4) Viết phương trình ( α ) chứa (d) và song song với (d’). Tính khoảng cách giữa (d) và (d’).
5) Viết phương trình đường thẳng ( ∆ ) chứa trong (BDC) và cắt hai đường thẳng (d), (d’).

Bài Làm:

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KIÓM TRA 1 TIÕT
Hä vµ tªn:..............................................................................
M«n: HÌNH HỌC 12, chương III
Líp 12…..….
Ngày kiểm tra:..............................

Trường THPT ............
Điểm

Nhận xét của Thầy, Cô giáo

Đề 2A:

Bài 1 (2.0đ): Cho hình hộp ABCD.A’B’C’D’ có các đỉnh A ( 2;5; −3) , D ( 1; 0; 0 ) , D ' ( 3; 0; −2 ) , C ' ( −3; −1;2 ) .
a) Tìm tọa độ các đỉnh còn lại.
b) Tính thể tích khối hộp?
Bài 2 (4.0đ): Trong không gian Oxyz, cho các điểm A ( 5;3;1) , B ( 2;3; −4 ) , C ( 1;2; 0 ) . Viết pt mp α biết:
a. α qua A và vuông góc với đường thẳng AB.
uur
b. α chứa đường thẳng AB và cùng phương với giá của vecto a = ( 3; −1; −2 ) .
c. α qua A và chứa đường thẳng OB.
Bài 3 (2.0đ): Trong không gian Oxyz, cho mp (P): mx + y + z − 1 = 0 , mp (Q): 2 x + ( 3 + m ) y + 6mz + 21 = 0
a. Tìm m để mp (P) song song với mp ( R): x + my + m ( 2m + 1) z + 3 = 0 ?
b. Tìm m để mp (Q) vuông góc với mp (Oxz)?
Bài 4 (2.0đ): Cho hình chóp S.ABC có tọa độ các đỉnh là: A ( 2;3;1) , B ( 4;1; −2 ) , C ( 6;3; 7 ) , S ( −4; −5;8 ) .
Viết pt mp (ABC)? Suy ra độ dài đường cao của hình chóp vẽ từ S?

Bài Làm:

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KIÓM TRA 1 TIÕT
Hä vµ tªn:..............................................................................
M«n: HÌNH HỌC 12, chương III

Líp 12…..….
Ngày kiểm tra:..............................

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Điểm

Nhận xét của Thầy, Cô giáo

Đề 2B:

Bài 1 (2.0đ): Cho hình hộp ABCD.A’B’C’D’ có các đỉnh A ( 1; 0;1) , A ' ( 3;5; −6 ) , C ( 2; 0;2 ) , D ' ( 3; 4; −6 ) . Tìm tọa
độ các đỉnh còn lại.
Bài 2 (4.0đ): Trong không gian Oxyz, cho các điểm A ( 2; −3;1) , B ( −3;2; −6 ) , C ( 1; 4; −3 ) . Viết pt mp α biết:
a. α qua B và vuông góc với đường thẳng AC.
b. α là mặt phẳng trung trực của đoạn thẳng
uurBC.
uur
c. α qua A và cùng phương với các vecto a = ( −2;1;3 ) vaø b = ( 2; −1; −4 ) .
Bài 3 (2.0đ): Trong không gian Oxyz, cho mp (P): mx + y + ( m + 1) z − 1 = 0 , mp (Q): 2 x + 3y + 6mz + 21 = 0
a. Tìm m để 2 mp (P) và (Q) song song với nhau?
b. Tìm m để mp (P) vuông góc với mp (Oxy)?
Bài 4 (2.0đ):
Tính độ dài đường cao của h.chóp S.ABC biết tọa độ các đỉnh là: A ( 5;3;1) , B ( 2;3; −4 ) , C ( 1;2; 0 ) , S ( 3;1; −2 ) .

Bài Làm:

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KIÓM TRA 1 TIÕT
Hä vµ tªn:..............................................................................
M«n: HÌNH HỌC 12, chương III
Líp 12…..….
Ngày kiểm tra:..............................

Trường THPT ............

Điểm

Nhận xét của Thầy, Cô giáo

Đề 3A:
Trong không gian tọa độ Oxyz, cho D(-3;1;2) và mặt phẳng ( α ) đi qua ba điểm A(1;0;11) ,
B(0;1;10) , C(1;1;8) .
a. Viết phương trình đường thẳng AC.
b. Viết phương trình tổng quát của mặt phẳng ( α ).
c. Viết phương trình mặt cầu (S) tâm D, bán kính R = 5 . Chứng minh mặt phẳng ( α ) cắt
mặt cầu (S).
d. Xác định tọa độ tâm và bán kính của đường tròn ngoại tiếp tam giác ABC.
e. Tìm tọa độ hình chiếu của gốc tọa độ O lên mặt phẳng ( α ).
Bài Làm:

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c. Viết phương trình mặt cầu (S) tâm A, bán kính R = 5 . Chứng minh mặt phẳng (P) cắt
mặt cầu (S).
d. Xác định tọa độ tâm và bán kính của đường tròn ngoại tiếp tam giác BCD.
e. Tìm tọa độ hình chiếu của gốc tọa độ O lên mặt phẳng ( α ).
Bài Làm:
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Viết phương trình mặt phẳng ( α ) tiếp xúc với mặt cầu (S) và song song với mặt phẳng
(ABD).
e. Tìm tọa độ hình chiếu của điểm A lên mặt phẳng (BCD).
Bài Làm:

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KIÓM TRA 1 TIÕT
Hä vµ tªn:..............................................................................

M«n: HÌNH HỌC 12, chương III
Líp 12…..….
Ngày kiểm tra:..............................

Trường THPT ............
Điểm

Nhận xét của Thầy, Cô giáo

Đề 5A:
Bài 1 (4điểm): Trongrkhông
gian Oxyz cho 3 điểm A(3; 1; 0), B(-2; 4; 1),C(1;-1;3)
uuur uuur
a)Tính tọa độ véc tơ u = 2 AC − 3CB .
b)Tìm tọa độ điểm M trên trục Oy cách đều hai điểm A và B.
Bài 2(2 điểm):
a) Tìm tâm và bán kính của mặt cầu có phương trình 2 x 2 + 2 y 2 + 2 z 2 − 4 x + y − 2 = 0 .
b) Lập phương trình mặt cầu đi qua điểm A ( 4;3;0 ) và có tâm là gốc toạ độ.
Bài 3(4 điểm): Cho hai điểm A(-1;1;2), B(0;-1;3) và mặt phẳng (α ) : 3 x − 2 y + z − 7 = 0
a)Viết phương trình mặt phẳng ( β ) đi qua A và song song với mặt phẳng (α ) .
b)Viết phương trình mặt phẳng (γ ) đi qua A,B và vuông góc với (α ) .
c)Tính khoảng cách giữa hai mặt phẳng ( α ), ( β ) .

Bài Làm:

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KIÓM TRA 1 TIÕT
Hä vµ tªn:..............................................................................
M«n: HÌNH HỌC 12, chương III
Líp 12…..….
Ngày kiểm tra:..............................

Trường THPT ............
Điểm

Nhận xét của Thầy, Cô giáo

Đề 5B:
Bài 1 (4điểm): Trongr không
gian Oxyz cho 3 điểm A(1;-1;3), B(3; 1; 0), C(-2; 4; 1).
uuur uuur
a)Tính tọa độ véc tơ u = 2 BA − 3 AC .
b)Tìm tọa độ điểm M trên trục Oy cách đều hai điểm B và C.
Bài 2(2 điểm):
a) Tìm tâm và bán kính của mặt cầu có phương trình x 2 + y 2 + z 2 − 4 x − 2 y − 2 z + 1 = 0 .
b) Lập phương trình mặt cầu đi qua điểm M ( −1; 2; 4 ) và có tâm là gốc toạ độ.
Bài 3(4 điểm): Cho hai điểm A(-3;2;-2), B(1;1;-3) và mặt phẳng (α ) : 2 x − y + 2 z − 7 = 0
a)Viết phương trình mặt phẳng ( β ) đi qua A và song song với mặt phẳng (α ) .
b)Viết phương trình mặt phẳng (γ ) đi qua A,B và vuông góc với (α ) .
c)Tính khoảng cách giữa hai mặt phẳng ( α ), ( β ) .

Bài Làm:

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Đề 6A:
Câu 1 (4 điểm):
a) Viết phương trình mặt cầu đường kính AB biết A ( 3; −1; −2 ) ; B ( 1;1; −2 )

b) Viết phương trình mặt cầu tâm C ( 3; −5; −2 ) và tiếp xúc mặt phẳng 2x − y − 3z + 11 = 0

Câu 2 (3 điểm): Cho bốn điểm M ( 5;1;3) ; N ( 1;6;2 ) ; P ( 2;0;4 ) ; Q ( 4;0;6 )
a) Viết phương trình mặt phẳng (α) đi qua 3 điểm M; N;P .
b) Viết phương trình mặt phẳng trung trực của đoạn thẳng PQ.
Câu 3 (3 điểm):
r
a) Viết phương trình đường thẳng đi qua điểm M ( 3;1; −2 ) và nhận vectơ n = (3; −1; −1) làm vectơ chỉ
phương.
b) Viết phương trình đường thẳng đi qua hai điểm A ( 1; −1; −2 ) ; B ( 3;1; −2 )

Bài Làm:

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b) Viết phương trình mặt cầu tâm C ( 2; −4; −1) và tiếp xúc mặt phẳng −2x + y − 3z + 1 = 0

Câu 2 (3 điểm): Cho bốn điểm M ( 2; −1;3) ; N ( −3; −2;2 ) ; P ( 2; −1;4 ) ; Q ( −4;0;6 )
a) Viết phương trình mặt phẳng (α) đi qua 3 điểm M; N;P .
b) Viết phương trình mặt phẳng trung trực của đoạn thẳng PQ.
Câu 3 (3 điểm):
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a) Viết phương trình đường thẳng đi qua điểm M ( 2;3; −1) và nhận vectơ n = (2; −3; −3) làm vectơ chỉ
phương.
b) Viết phương trình đường thẳng đi qua hai điểm A ( 1;3; −2 ) ; B ( −3;4; −2 )

Bài Làm:

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Bài Làm:

1
2

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a. Tìm tâm và bán kính mặt cầu (S).
b. Viết phương trình mặt phẳng (P) tiếp xúc với mặt cầu (S) và song song với hai đường thẳng
x + 5 y − 1 z + 13
d1 :
=
=
và d 2
2
−3
2

 x = −7 + 3t

:  y = −1 − 2t
z = 8


Bài Làm:

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=
=
trình là d :
và (α ) : x − y + 2 z − 2 = 0
2
3
−1
a. Tìm tọa độ giao điểm I của đường thẳng d với mặt phẳng (α ) . Viết phương trình mặt phẳng
( β ) qua điểm I và vuông góc với đường thẳng d .
b.Cho điểm A(1;0;1). Hãy tìm tọa độ của điểm B sao cho (α ) là mặt phẳng trung trực của đoạn
thẳng AB.
Câu 2: Cho mặt cầu ( S ) : x 2 + y 2 + z 2 + 26 x − 10 y + 2 z − 30 = 0
a. Tìm tâm và bán kính mặt cầu (S).
b. Viết phương trình mặt phẳng (P) tiếp xúc với mặt cầu (S) và song song với hai đường thẳng
x = 8

x − 1 y + 13 z + 5
d1 :
=
=
và d2 :  y = −7 + 3t
−3
2
2
 z = −1 − 2t


Bài Làm:

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KIÓM TRA 1 TIÕT
Hä vµ tªn:..............................................................................
M«n: HÌNH HỌC 12, chương III
Líp 12…..….
Ngày kiểm tra:..............................

Trường THPT ............
Điểm

Nhận xét của Thầy, Cô giáo

Đề 9A:
Câu 1: (2đ) Cho ∆ABC có A(2; 1; 4), B(-2; 2; -6), C(6; 0; -1). Tìm toạ độ trọng tâm G của ∆ABC.
Câu 2: (5đ) Cho A(4; -3; 2), B(-2; 1; -4)
a. Viết PT mặt phẳng trung trực của đoạn thẳng AB
b. Viết PT mặt phẳng quá A, B và song song với ox.
x = 1− t

Câu 3: (3đ). Cho A:  y = −1 + t
 z = 1 + 2t


và (P): x + 2y + z - 5 = 0

Viết phương trình hình chiếu vuông góc d của A lên (P).

Bài Làm:

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KIÓM TRA 1 TIÕT
Hä vµ tªn:..............................................................................
M«n: HÌNH HỌC 12, chương III
Líp 12…..….
Ngày kiểm tra:..............................

Trường THPT ............
Điểm

Nhận xét của Thầy, Cô giáo

Đề 9B:
Câu 1: (2đ) Cho ∆ABC có A(-2; 2; 6), B(-1; 0; -4), C(3; 3; -2). Tìm toạ độ trọng tâm G của ∆ABC.
Câu 2: (5đ) Cho A(0; -5; 2), B(-4; 3; -2)
a. Viết PT mặt phẳng trung trực của đoạn thẳng AB
b. Viết PT mặt phẳng quá A, B và song song với ox.
 x = 2 − 2t

Câu 3: (3đ). Cho đường thẳng d:  y = 1 + 3t
 z = −2 − t


và (P): 2x + y - z - 3 = 0

Viết phương trình hình chiếu vuông góc d' của d lên (P).

Bài Làm:

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Đề 10A:
BÀI 1: (7 điểm) Trong không gian Oxyz , cho 4 điểm: A(-1;1;2), B(0;2;1), C(2;-1;3) và D(1;0;1).
a/ Chứng minh rằng 4 điểm A,B,C,D tạo thành 1 tứ diện.
b/ Viết phương trình mặt phẳng (P) chứa đường thẳng AC và song song với BD. Tính khoảng cách
giữa hai đường thẳng AC và BD.
c/ Tìm tọa độ trực tâm H của tam giác ACD.
BÀI 2: (3 điểm) Trong không gian (Oxyz), cho mặt cầu (S): (x-1) 2+(y-2)2+(z-3)2=16 và mặt phẳng
Q):2x - 2y + z + m = 0
a/ Xác định tâm và tính bán kính của mặt cầu (S). Tìm m để mặt phẳng (Q) tiếp xúc với mặt cầu (S).
b/ Cho điểm B(2;2;2), mặt phẳng (P) qua A(1;1;1) và cắt mặt cầu (S) theo giao tuyến là đường tròn
có bán kính bé nhất. Tìm M trên mặt phẳng (P) sao cho tam giác ABM vuông cân tại A.

Bài Làm:

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c/ Tìm tọa độ trực tâm H của tam giác ABD.
BÀI 2: (3 điểm) Trong không gian (Oxyz), cho mặt cầu (S): (x-2) 2+(y-1)2+(z-3)2=16 và mặt phẳng
(P):2x+y-2z+m=0
a/ Xác định tâm và tính bán kính của mặt cầu (S). Tìm m để mặt phẳng (P) tiếp xúc với mặt cầu (S).
b/ Cho điểm A(2;2;2), mặt phẳng (Q) qua B(1;1;1) và cắt mặt cầu (S) theo giao tuyến là đường tròn
có bán kính bé nhất. Tìm N trên mặt phẳng (Q) sao cho tam giác ABN vuông cân tại B.

Bài Làm:

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20 đề kiểm tra 1 tiết chương 3 hình học 12

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