| ә қ | ққ ә қ құ | ққ ә қ құ | Ә | |
| қ құ ұғ. . үң ү | 1. . . . ., , . 1., ( 1973) 2. . ., . . . ., , 1976, . 1. 3. . ., . . . ., , 1973,. 1. ( ) 1. . . . ., , . 1., ( 1973) 2. . ., . . . ., , 1976, . . 3. . ., . . . ., , 1973,. 1. ( ) | |||
| үң қ-ққғ, ә ә қғ. | ||||
| Ү ө ң ү ң қ-ққғ ә қғ. | ||||
| үң, ққң, ә, ң, ұң қ. | ||||
| ә ң ү ә ң | ||||
| . . ү . V- | ||||
| ң ү | ||||
| .. ә ң . . | ||||
| қғң ң . қғң үң ққғ | 1. . . . ., , . 1., ( 1973) 2. . ., . . . ., , 1976, . . 3. . ., . . . ., , 1973,. 1. ( ) | |||
| қ ңң қ. , қ, қ. . Ү ә . | ||||
| қ ө. ғ ққң қ қ. | ||||
| ң . қ ұғ. өқ ү . | 1. . . . ., , . ., ( 1973) 2. . ., . . . ., , 1976, . . 3. . ., . . . ., , 1973,. 1. ( ) | |||
| қ ұғ. қ ққ. . Ққң ұғ. ȳ ә ұ. | ||||
| ң қ . қ қ ұғ. ң қ . ȳ ұқ . |
Ө-ө ғғ ғ ұқ////ғ:
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1. i қ (1,2) үi үi ң.
A) (-1,2)
B) (1,-2)
C) (-1.-2)
D) (1,2)
E) (1,3)
2.() қ ққ қ (1,2,3) үi үi ң.
A) (-1,-3,-2)
B) (1,3,-2)
C) (-1,3,2)
D) (-1,-3,2)
E) (1,-3,2)
3. (1,2,3) ә (5,6,3) үiң ққғ ң.
A) 2 
B) 4 
D) 5 
C) 6
E) 4
4. iiiң үi ң, (4,1,5), (4,-1,1) .
A) (-4,0,-3)
B) (4,0,3)
C) (-4,0,3)
D) (4,0,-3)
E) (0,0,3)
5. 
{2,0,1} ә 
{-1,5,6} i. 
ң ң.
A) (- 
)
B) (
)
C) (
, 5,7)
D) (1,5,7)
E) (-3,5,6)
6. 
i. 
ң
A) 11
B) 10
C) 12
D) 8
E) 16
7. (1,2) ү қ өi ә 
(3,4) үiң ңi ң.
A) 4+3-2=0
B) 4-3+2==0
C) 4-3-2=0
D) 5-2+7=0
E) 6+2-3=0
8. (2,3) үi 2+3+7=0 үi ii қққ ң.
A) 20
B) 
C) 
) 13
) 
9.(1,2,0) ү қ өi ә ғ 
ққң ңi ң.
A) 4+3+2z-2=0
B) 4x-3y-2z+2=0
C) 4x+3y-2z-2=0
D) 4x-3y+2z+2=0
E) 4x-3y-2z-2=0
10. 2x-2y+z-18=0 ңi қ ү i.
A) x+y-z+6=0
11. (1,2,3) (2,4,6) үi қ өi үiң қ ңi ң.
) 
) 
) 
) 
) 
12. 42+252-100=0 iң ң.
A) 
B) F1(21,0), F2(-21,0)
C) 
, F2(21,0)
D) F1(-21,0) 
E) F1(10,0) F2(-10,0)
13. 92-42-36=0 ң ң.
A) y= 
x
B) y= 
x
C) y= 
x
D) y=x
E) y= 
x
14. x2+z2=2z ңi ңiii қ үi қ қ қ.
) () өi i .
B) () өi i .
C) қ . D) E)
15.(1,- ) үiiң қ ң, қ үiiң үi , i қ .
A) (4, 
)
B) (2, 
)
C) (-2, )
D) (5, )
E) (2, 
)
16. 
i. 
қ өiii ң.
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|
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A) (1,2,-7)
B) (-1,-2,7)
C) (1,2,7)
D) (-1,2,-7)
E) (1-2, 7)
17. (0,0,0), (1,2,3) C(3,4,5) D(5,-1,0) үi i. iң өi ң.
A) 
B) 
C) 
D) 
E) 
18. m қ ғ 
үi ә 
қғ ?
)1
)- 
)
)-1
)- 
.
19.i i қң.
2+22-3z2+2+4-6z=0
)қ , ).
)ii i , ) .
)қ ,
21. i қ (1,2) үi үi ң. A) (-1,-2)
B) (-1,2)
C) (1,2)
D) (2,1)
E)(-2,1)
22.(z) қ қққ қ (1,2,3) үi үi ң.
A) (-1,-2,-3)
B) (1,-2,3)
C) (-1,-2,3)
D) (1,-2,-3)
E) (-1,2,-3)
23.(1,2,3) ә (3,2,4) үiң ққғ ң.
A) 
B) 
C) 
D) 6
E) 5
24. iiiң үi ң, (2,3,1), (-2,1,3) .
A) (0,-2,-2)
B) (0,2,2)
C) (0,2,-2)
D) (0,-2,2)
E) (2,0,2)
25. (5,0,6) ә (1,3,3) i. 1/3(+) ң ң.
A) (-2,-1,3)
B) (2,1,3)
C) (-2,1,-3)
D) (-2,1,3)
E) (-2,-1,-3)
26. (5,0,-2) (1,7/2,-3) i. ң.
A) 12
B) 11
C) 10
D) 29/2
E) 7/2
27. (2,3) ү қ өi ә (1,5) үiң ңi ң.
A) x-5y+17=0
B) x+5y-17=0
C) x-5y-17=0
D) x+2y-6=0
E) x-2y+3=0
28. (5,6) үi 4+3-2=0 үi ii қққ ң. A) 8
B) 36/5
C) 5/36
D) 10
E) 7
29.(1,0,0), (0,0,3) үi қ өi ққң ңi ң.
A) 6x-3y-2z-6=0
B) 6x+3y+2z-6=0
C) 6x-3y+2z+6=0
D) 6x+3y-2z+6=0
E) 6x-3y-2z+6=0
30. m қ ғ 2+3-z+2=0 ә m x-6y+2+7=0 ққ .
A) 4
B) -4
C) 3
D) -3
E) 5
31. (1,-1,-3) үi қ өi ә (x-1)/2=(y+2)/4=(z-1)/3 үi үiң i ңi ң.
A) x=2t-1, y=4t-1, z=3t-3
B) x=2t+1, y=4t-1, z=3t-3
C) x=2t-1, y=4t-1, z=3t+3
D) x=2t+1, y=4t+1, z=3t+3
E) x=2t-1, y=4t+1, z=3t+3
32. i ң i ә ң
x²+y²+z²-12x+4y-6z=0
A) (-6,2,3), R=6
B) (6,-2,3), R=7
C) (-6,2,-3), R=7
D) (6,-2,-3), R=6
E) (-6,2,-3), R=7 
33. {2,3,4,} ә {1,2,1} i.[ ] қ өiii ң.
A) (5,2,1)
B) (-5,2,1)
C) (5,-2,1)
D) (-5,-2,1)
E) (5,-2,-1)
34. (0,0,0), (1,2,3), (3,4,5) D(5,-1,0) үi i AB, AC, AD құғ iң өi ң.
)18
B) 14
C) 16
D) 10
E) 14/3
35. 22-4-z2=0 ii i i қң.
)i , ) i қ )
)
) қ қ .
36. ққң ғ өi iii i қғ:
) i . ) i ..
) ғ . ) .
) .
37. i қ (2,3) үi үi ң.
A) (-2,-3)
B) (-2,3)
C) (-3,2)
D) (3,-2)
E) (-3,-2)
38. (Oyz) қ ққ қ (1,2,3) үi үi ң.
A)(- 1, - 2, -3)
B) (- 1, 2, 3)
C) (- 1, - 2, 3)
D)(1, 2, - 3)
E)(1, -2, 3)
39. (1,2,3) ә (1,5,4) үiң ққғ ң.
) 
) 
|
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) 10
) 5
) 2 
40. iiiң үi ң, (1,2,3), (4,2,1) .
)(- 
, 2, 2)
) (, 2,2)
) (- , -2, -2)
) (5, 
, 2)
) (5, 2, )
41. 
i. 
ң ң.
) (2,0, - 
)
) (2,0, )
) (-2,0, )
) (-2,0, - )
)(2,0,2)
42. 
i. 
ң.
)12;
)11;
)10;
)9;
)8.
43. (1,2) ә (5,3) үi қ өi үiң ңi ң
) +4-7=0;
) -4+7=0;
) -4-7=0;
) 2-3+7=0;
) 5+3-3=0;
44. (2,1) үi 4+3-1=0 үi i қққ ң.
)3;
)2;
)4;
) 
;
) 
.
45. (1,2,3), (-1,2,4), (0,2,5) ү қ өi ққң ңi ң.
) -2=0;
) -2=0;
) 2+3-1=0;
)2-3+1=0;
)+2=0.
46.m қ ғ 3-5+mz-3=0 ә +3+2z+5=0 ққ ?
)7;
)6;
)4;
)5;
)8.
47. (2,3,1) үi қ өi ә 
үi үiң қ ңi ң.
) 
) 
) 
) 
;
) 
48. 
қ ii ә 
үi ң.
) 
) 
) 
) 
) 
49. 
ғ (10,4) үi үiiң.
) +2+2=0
) -2-2=0
) -2+2=0
) +2-2=0
) -2-1=0
50.i ii i қң үi қң. 2+2-2+6+9=0
)
)
)
)ң
)қ қ ү.
51. өi (2,1,-1) үi 1 (1,-1,0) үi . үiiң үi қ ү ?
)(-1,-2,1)
) (1,2,-1)
) (-1,2,-1)
) (1,-2,1)
) (1,2,1)
52. (1,2,3) ә (3,1,2) ң қ өiii ң.
)(-1,7,5)
) (1,7,-5)
) (-1,-7,-5)
) (1,-7,5)
) (1,7,5)
53. (1,2,3), (3,4,5) ә (5,-1,0) i. құғ iң өi ң.
.
)16
)14
)18
) 
) 
54. қ ғ i ү
.
)6.
)7.
)-4.
)5.
)3.
55. i ii i iң үi қң.
42+42-z2-16+20=0
) i ) i қ
) қ қ )
)
56. ққң қғ
) қ
) ққ қ
) ү үi ү ү
) ү қ ү қ ү ғ
) үi қ
57. i қ (2,3) үi үi ң. A) (-2,-3)
B) (2,-3)
C) (3,2)
D) (-3,-2)
E) (-3,2)
58. () қ ққ қ (1,2,3) үi үi ң.
A) (-1,-2,-3)
B) (1,2,-3)
C) (-1,-2,3)
D) (-1,2,-3)
E) (1,-2,3)
59. (1,2,3) (6,2,4) үiң ққғ ң,
) 
D) 
E) 26
60. iiiiң үi ң, (4,1,5), (4,-1,1) .
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A) (2,-3,7)
B) (2,3, 
)
C) (2,3, - )
D) (-2,-3,7)
E) (2,3,7).
61. 
(4,6,-2), 
(3,-6,5) i, 
ң ң.
A) (- 
,0,-1)
B) (,0,1)
C) (- ,0,1)
D) (,0,-1)
E) (,0, 
)
62. {1,2,3} (5,6,7) i. ң.
A) 36
B) 38
C) 30
D) 0
E) 40
63. i 450 құ ә (1,2) үi қ өi үiң ңi ң.
A) +-1=0
B) - +1=0
C) ++1=0
D) 3-2+5=0
E) 
+-7=0
64.(3,-2) үi 3+4-5=0 үi ii қққ ң.
A) 
)0,8
C) 
D) 5
E)-0,8
65. (1,2,3) ү қ өi қ 
(2,1,4) ққң ңi ң.
A) 2--4z+16=0
B) 2++4z-16=0
C) 2+-4z+16=0
D) 2-+4z+16=0
E) 2++4z+16=0
66. +2-3z-6=0 ққң ң i үi ң.
) 
;
) 
) 
;
) 
;
) 
67. (1,2,3) үi қ өi ә (3,2,4) үiң қ ңi ң.
) 
) 
) 
) 
) 
68. 
ii ә 
үi ң.
) 
) 
)
)
)
69. 2=8 ғ (2,4) үi үiiң.
)2+-4=0
)2--4=0
)2-+4=0
)2 + +4=0
) y+2 -3 =0
70. 2+2-2+6+9=0 ii i қң үi қң.
)
) ң
)
)
) қ қ ү
71. (3, 
) үiiң қ iұ ң, қ үiiң үi , қ i i . )(
)
)(
)
)(
)
)(
)
)(
)
72. 
i. 
ң.
) 3 
) 5 
) 10
) 5
) 15
73. (1,2,3), (3,2,0), (4,5,6),(0,0,1) үi i. iң өi ң.
) 
) 
) 
) 
)7
74. (2,-3,-5) үi қ өi ә 6-3-5z+2=0 қғ үiң ңi ң.
) 
) 
) 
) 
) 
75. i ii i iң үi ң: 2+22-3z2+2+4+6z=0
)
) қ
)қ
)
)
76.i үi
)ү ң ,
)ү ү , ) ү қ ү ,
) қ , ) ғ өi.
77. (3, 
) үiiң қ iұ ң, қ үiiң үi , қ i i .
) 
) 
) 
) (3,-4) ) 
78.(2,3) ү қ өi ә b(3,-5) ғ үiң i ңi ң.
79. ү i үi i: 
.ң ғ ң.
) 
) (3,-1) ) (6,2) ) (5,0) ) (7,-4)
80. (0,2), (3,1), (-1,4), (-5,8), (11,5) үi i. ң =-1+t, y=4-2t ү ii.
) , ) , ) , ) , )
81. i үiң 11-5-3=0 ңi қ ү iiң.
.
82. 
ңi қ ү iiң. 
83. (2,1,-1) ү қ өi ә 
ққң ңi ң.
) 2--z-7=0 ) -2+3z+3=0 )3-2z+5=0
) 3+-2z=0 ) 2+5+7z=0
84. үiiң үi қ өi ә 
ққң ңi ң.
) 5-3=0 )5-3z=0 C)5z-3x=0 )2-8+z=0 E)3x-2y-5z=0
85. ққң ңi i: x+2y-3z-6=0. ң ii үii ңi ң.
86. 3-z=0 ә 2+z=0 ққң ғ ұ ң.
) 300 ) 450 ) 1500 ) 600 ) 900
87. l қ ғ 2+3+3z-5=0 ә lx-6y-6z+2=0 ққ . ) 5 ) -4 ) 7 ) 2 ) -3
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88. l қ ғ 3x-5y+lz-3=0 ә x+3y+2z+5=0 ққ ?
) 7 )6 ) 4 ) 5 ) 8
89. (3,-1,2),(4,-1,-1),(2,0,2) ү қ өi ққң ңi ң.
) 2-+3z-5=0 B)3x+3y+z-8=0 C)x+4y-z+6=0 )x-5y=0
E)4y-z=0
90. 2x-2y+z-18=0 ққң ңi қ ү iiң. 
91. (3,-6,7) үi 4-3-1=0 қғ ii ққ ң
) 3 ) 2 ) 5 ) 2,5 ) 1,6
92. үiiң үi қ өi ә 4-+3z-1=0, x+5y-z+2=0 ққң қ қ өi ққң ңi ң.
) 6--z+5=0 )9+3+5z=0 )9++5z-6=0
)7+2+5z-3=0 )4-z-5=0
93. (2,0-3) үi қ өi ә 
үiң қ ңi ң.
94. i (1,2,-4) ә (-1,3,-5) үi қ өi үiң қ ңi ң. 
95. i (1,-1,-3) ү қ өi ә i
үi үiң i
ңi ң.
96. i 
ә 
үiң ғ үi ұ ң.
97. k қ ғ 
ә x=6t, y=-4t-1, z=2t+1 үi ?
)2 ) 1 ) -5 ) 0,6 ) -2
98. қ ғ 
ә 
үi ?
) 6 ) 7 ) -4 ) -3 ) 5
99. x=1+11t, y=2-7t, z=5-8t үiң ә 7x-8y+2z-10=0
ққң ғ ұ ң.
100. қ ғ x=-1+3t, y=2+t, z=-3-2t ү ә
x+3y+3z-2=0 ққ қ?
) 2 ) 1 ) -6 ) 0,4 ) -0,5
101. ә қ ғ 
ү x+8y+z+2=0
қғ ?
) =2,=4 ) =5, =1 )=-5, =-4 )=1, =-2 )=0,5 =4
102. ә қ ғ 
ү
x+y-2z+=0 қғ ii ?
) =3,=6 ) =-2, =11 )=-7, =8 )=9, =12 )=-5, =-8
103. (2,-3,-5) ү қ өi ә 6x-3y-5z+2=0
қғ үiң ңi
ң.
104. (1,-1,2) ү қ өi ә +-z+7=0 қғ ққң ңi ң.
) x-y-z-2=0 B) x+y-z+2=0 C) x-y+z-1=0
) x-y-z+9=0 ) x-y-z-1=0
105. (1,-1,-1) ү қ өi ә 
үi ққң ңi ң.
) 3x-2y-4z+1=0 B) 2x-3y+4z-1=0 C) 4x+y-2z-5=0
) x-y+6=0 ) 2x-y+9z-2=0
106. =2t+1, y=-3t+2, z=2t-3 ү қ ә (2,-2,1) үi
қ өi ққң ңi ң.
) 4xy+5z-3=0 B) 4x+6y+5z-1=0 C) 2x-2y-z-10=0
) x-4y-z+5=0 ) x-y+z-4=0
107. z i қ өi ә x=2+t, y=2t, z=1+3t үi ққң ңi ң.
) 3x-y=0 B) 2x-y=0 C) x-3y-5=0
) 2x-2y+2=0 )6x-5y-6=0
108. i 
ү қ өi ә
3x+2y-z-5=0 қғ
ққң ңi ң.
) x-y-3z-9=0 B) x-8y-13z+9=0 C) x-y=0
) 3x-4y=0 ) -4x-y+z-7=0
109. (1,-1,-2) үi i 
ү ii
ққ ң.
) 5 ) 7 ) 6 ) 2 ) 1
110.i 
ә 
үiң
ққ ң.
) 7 ) 17 ) 2 ) 13 ) 8
111. i 
ә 
үi ii ққң қ 16 ү қң.
112. 
iң ң.
113. өiiң қғ 8, ң қғ 10 ң қ ңi ң.
78. 114. ң ңi -20=0 ң
қ ңi ң.
115.ii i қ 
ң i. ң 
i ң.
116. i 
Ү iiң i ң ii ii ққ ң.
117. l қ ғ 2+3+3z-5=0 ә lx-6y-6z+2=0
ққ ?
) 5 ) -4 ) 7 ) 2 ) -3
