pat 15803
DESCRIPTION
mathTRANSCRIPT
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PAT 1 (.. 58) 1
PAT 1 (.. 58) 71 (PAT 1) 7 2558 13.00 - 16.00 .
1 1 - 30 6 1. { | 1 < < 2 } () 32 4 4 < 0 () 2 > |2 4| () [()] [() ()] () [()] [()] 1. () () 2. () () 3. () () 4. () ()
2. , () ( ) ( ) ( ) () ( ) [(~ ) ] ( ~) 1. () () 2. () () 3. () () 4. () ()
3 Jun 2015
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2 PAT 1 (.. 58)
3. < 6 + 2 + 1 < + 3 1. (1, 2) 2. (0, 3) 3. (1, 4) 4. (2, 5)
4. = { (, ) | 2 + |1 |2 = 4 } = { (, ) | = 1 4 } () () ( ) ( ) = 1. () () 2. () () 3. () () 4. () ()
5. 0 < < 1 ||+1
> 1 1. (, 1
) 2. (1, 1
1 ) 3. (1, 1
) 4. ( 1
1 , )
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PAT 1 (.. 58) 3
6. 0 90 () = 12 92 0 < < 1 sin = ()
(cot2 )(sec 1)
1+sin +
(sec2 )(sin 1)
1+sec
1. 1 + 5 2. 5 3. 1 5 4. 0
7. 18 36
1. 2. 12
3. 14
4. 116
8. arctan (2 cos 10cos 50sin 70cos 80
) 1. 15 2. 30 3. 45 4. 60
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4 PAT 1 (.. 58)
9. 7 4 3 6
() 11
42
()
1. () () 2. () () 3. () () 4. () ()
10. 162 92 + 36 + 32 + 124 = 0 (0, 0)
1. 25 2. 35 3. 45 4. 55
11. (, ) 2 + 6 = 0 (3, 1) (, ) 1. 2 + 2 8 + 2 + 16 = 0 2. 2 + 2 8 + 2 + 1 = 0 3. 2 + 2 4 + 2 + 16 = 0 4. 2 + 2 4 + 2 + 1 = 0
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PAT 1 (.. 58) 5
12. , + + = 0 135 105 120 5
1. 10+261+3
2. 10+361+3
3. 10+461+3
4. 10+561+3
13. 1 = + i 2 = + i , , , {0} i = 1 12 + 22 = 1 2 = () |1| = |2| () Im(12) = 0 1. () () 2. () () 3. () () 4. () ()
14. 0 < < < 90 tan( + ) = 5 tan( ) (sin 2)(cosec 2)
1. 56 2. 5
4 3. 3
2 4. 2
3
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6 PAT 1 (.. 58)
15. 160 55 70 40
1. 16 2. 20 3. 24 4. 28
16. () = log (1+1
) 1 < < 1
() = ( 21+2
) 1. 2 2. 2 3. 2 4. 2
17. 0
limx
|5+1||51|+
= 80
2 + + 58 1. 64 2. 78 3. 130 4. 330
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PAT 1 (.. 58) 7
18. 22 = [1 23 4
] = [1 21 4
]
() = [ 7 1022 32
]
() ( )( + ) 2 2 1. () () 2. () () 3. () () 4. () ()
19. (8, 0) (4, 1) (1, 1) (quardrant) 1
1. 2 8 + 4 + 13 = 0 2. 2 8 4 + 20 = 0 3. 2 8 + 6 12 = 0 4. 2 8 6 + 19 = 0
20. , () = 2 5 , (1 )() = 4 ( )() 1 21 ( ) = 3 32 2
() ( )() = 23 () ( + )() = 35 1. () () 2. () () 3. () () 4. () ()
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8 PAT 1 (.. 58)
21. 33 det() > 0 , det( adj ) 2(det )2 3 det = 0 = 33 () 7 det det < 0 () det(2 3 adj ) = 2 1. () () 2. () () 3. () () 4. () ()
22. . 150 200 10 300 12.5 . 40,000 1,850 1,500 2,000
1. 300,000 2. 10 140 295,000 3. 50 100 275,000 4. 110 40 245,000
23. log 2 + log 24
+ log 28
+ = 1
3
4log 2log 2 = 8 () + = 102 () log = 16 1. () () 2. () () 3. () () 4. () ()
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PAT 1 (.. 58) 9
24. (1, 1), (2, 2), , (5, 5) 5
5
1i
= 20 , 5
1i
= 45 , 5
1i
2 = 100 ,
5
1i
2 = 485 ,
5
1i
= 220
= + ,
() 2 + 2 = 5 () 1. () () 2. () () 3. () () 4. () ()
25. 60 40 0.125 . 40 34 .
1. 30 2. 33 3. 37 4. 39
26. , (1) 2 + 2 90 (2) + = 5 + (3) > 8 () + 2 + 3 36 () 3 + 3 + 3 1085 1. () () 2. () () 3. () () 4. () ()
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10 PAT 1 (.. 58)
27. 60 55.5 18.41 64
0
1. 21.19 2. 24.20 3. 25.80 4. 28.81
28. 3 45 2 2 : 3 3 50 5
1. 90 2. 90.4 3. 90.6 4. 92
29. = + i > 0 i = 1
3 = i |i5 + 2|2 ( || (absolute value) ) 1. 5 + 23 2. 7 3. 5 23 4. 3
0.7 0.8 0.9 1.0
0.2580 0.2881 0.3159 0.3413
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PAT 1 (.. 58) 11
30. 2 + 2 + 9 = 2(2 + 2) () < () (2 ) = ( + 32) 1. () () 2. () () 3. () () 4. () ()
2 31 - 45 8 31. () , , , () = { , {1}, , } , = , {2,3,4,5} 2
32. sin2 0+sin2 10+sin2 20+ +sin2 170+sin2 180
cos2 0+cos2 10+cos2 20+ +cos2 170+cos2 180 =
... 1 2 + 2
() () ( ) ( ) 8 32 2 4
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12 PAT 1 (.. 58)
33. log 42 + 4 + 1 + log(62 + 11 + 4) = 4 = 3 + 4 = 2 + 1 = { 82 | }
34. 1 4 1, 2, 3, 4 1 3 18 15 2 5 1, 2, 3, 4, 5 3 18.5, 15, 12 8
9 1, 2, 3, 4, 1, 2, 3, 4, 5
35. :
( + ) = () + () + 32 + 32 0
limx
()
= 2
(1) + (5)
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PAT 1 (.. 58) 13
36. = { 1, 2, 3, 4, 5, 6, 7 } 2 > 1
37. (, ) 22 log14
= 1 + 241
9(22)log18
= 9 + log12
2
= {
| (, ) }
38. {} {} 1+2+ +1+2+ +
= +1
21 = 1, 2, 3,
2100100
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14 PAT 1 (.. 58)
39. + 33 2 2 = 3 + 2 1 22 25 + 58
40. () = 24
3 0
() = (1 + 2)() (1) = 2 2
1 3()
41. () = {2 + 2 , < 0
+ , = 01++521
, > 0
= 0 15 + 30
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PAT 1 (.. 58) 15
42. {} {} = 2
(+2) =
3
5+18 = 1, 2, 3,
11
+22
+33
+
43. 5 () 7
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16 PAT 1 (.. 58)
44. {} 1 = 1
= (1 1
4) (1
1
9) (1
1
2) = 2, 3, 4,
nlim
45. || + = 8 + || + = 10
20 + 15
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PAT 1 (.. 58) 17
1. 11. 21. 31. 41. 2. 12. 22. 32. 42. 3. 13. 23. 33. 43. 4. 14. 24. 34. 44. 5. 15. 25. 35. 45. 6. 16. 26. 36. 7. 17. 27. 37. 8. 18. 28. 38. 9. 19. 29. 39. 10. 20. 30. 40.
1.
. Tarm Chaidirek