SMART EDUCATIONS 1
1. ′ ℎ:−
= +
2. × = ×
3. ℎ ℎ ∶ −
=
4. ℎ :−
ℎ = 2
× 5
5. =
+ + ; ≠ 0
= /
= /
=
6. ℎ = ℎ( )
7.
8.
(
+
)
=
9.
(
×
)
=
10. =
−
(
+
)
+ ×
11. :−
+ + = 0
(
, ; ≠ 0
)
12. ℎ ℎ .
13. ℎ :−
/ / →
≠
SMART EDUCATIONS 2
/ / →
=
≠
/ / →
=
=
14. ℎ :−
ℎ ℎ
ℎ
ℎ
ℎ
15. :−
++ = 0 ; ≠ 0
16. ℎ :−
ℎ
ℎ
17. :−
=
− ± √
−4
2
18. () =
−4
19. :−
> 0 ( )
< 0 ( )
= 0 ( )
20. :−, +, + 2, + 3, + 4........
21. ℎ :−
22. :−
23. :−
24. =
,
=
,ℎ =
ℎ =
25. ℎ →
= +
(
−
)
; =
=
SMART EDUCATIONS 3
26. ℎ →
= −
(
−1
)
; =
27. → =
−
(
−
)
28. →
=
{
2 +
(
−1
)
}
29. →
=
{
2−
(
−1
)
}
30. ℎ →
=
(
+
)
31. ℎ = − , , +
32. = −3, −, + , +3
33. = − 2, −, , + , +2
34. ℎ ℎ ℎ :−
35. ℎ , ℎ:−
) .
) .
36. ℎ :−
, , ()
37. ∆ ~ ∆,ℎ:−
=
=
& ∠A = ∠R, ∠B = ∠P, ∠C =∠Q
38. ℎ ℎ
(
∆ ~ ∆
)
=
∆
∆
=
=
=
39. ℎ :−
A
B
C
D
E
=
=
=
SMART EDUCATIONS 4
ℎ
=
+
40. :−
=
(
,
)
;
=
(
0,0
)
ℎ −
(
,0
)
ℎ − =
(
0,
)
41. =
(
−
)
+
(
−
)
42. ℎ =
+ y
43.
(
,
)
=
,
44.
(
,
)
=
,
45. ℎ =
,
46. ∆ =
|
(
−
)
+
(
−
)
+
(
−
)
|
47. ℎ = 0
48. =
; =
; =
; =
; =
; =
49.
0
30
45
60
90
0
1
2
1
√
2
√
3
2
1
1
√
3
2
1
√
2
1
2
0
0
1
√
3
1
√
3
2
√
2
2
√
3
1
1
2
√
3
√
2
2
0
√
3
1
1
√
3
SMART EDUCATIONS 5
50. :−
(
90−
)
= cosθ
(
90−
)
=
(
90−
)
=
(
90−
)
=
(
90 −
)
=
(
90 −
)
=
51. :−
× = 1
× = 1
× = 1
× = 1
θ+cos
θ = 1
θ−tanθ = 1
θ−cot
θ = 1
=
=
52. :−
(
+
)
=
+
+ 2
(
−
)
=
+
−2
−
=
(
−
)(
+
)
SMART EDUCATIONS 6
+
=
(
+
)
−2
(
−
)
+ 2
(
+
)
=
+
+ 3
+ 3
+
=
(
+
)(
+
−
)
(
−
)
=
−
−3
+ 3
−
=
(
−
)(
+
+
)
53.
54. ℎ ℎℎ ℎ =
55. ℎ:−
ℎ ℎ
56. ℎ = 90
SMART EDUCATIONS 7
57. ℎ
58. ℎ ℎ 180
ℎ ℎ .
59. :−
=
=
1
2
=
(
−
)
() = 2
=
= +
Radius
Tangent
90
o
A
B
C
=
∠+∠=
∠= ∠
∠= ∠
∠ = ∠ =
∠
O
SMART EDUCATIONS 8
=
360
×
=
1
4
ℎ =
360
×2
=
360
×2 +2
=
360
−
1
2
×
=
360
× 2 + ℎ
60. ℎ 3 :−
61. :−
6 () = 2
(
+ ℎ + ℎ
)
5 = 2
(
+
)
ℎ +
4 () = 2
(
+
)
ℎ
=
+
+ ℎ
= ℎ
62. :−
ℎ
SMART EDUCATIONS 9
6 () = 6
5 = 5
4 () = 4
= √3
=
63. :−
ℎ 2 = 2
(
+ ℎ
)
ℎ 1 =
(
2ℎ +
)
ℎ 0 = 2ℎ
=
ℎ
64. :−
ℎ 1 = (+)
ℎ 0 =
SMART EDUCATIONS 10
=
1
3
ℎ
= ℎ
+
65. ℎ:−
ℎ = 4
ℎ =
4
3
66. ℎ:−
ℎℎ ℎ ℎ = 3
ℎℎ ℎ = 2
ℎ ℎ =
2
3
67. :−
ℎ ℎ 2 =
(
+
)
+
(
−
)
ℎ ℎ 1 =
(
+
)
+
/
l
SMART EDUCATIONS 11
ℎ ℎ 0 =
(
+
)
=
1
3
ℎ
(
+
+
)
= ℎ
+
(
−
)
68.
(
)
:−
69. =
∑
∑
70. ℎ = +
∑
∑
;
(
=
−
)
71. ℎ = +
∑
∑
ℎ ;
=
72. = +
ℎ
73. = +
ℎ
74. →
(
)
=
(
)
(
)
75. 0 ≤
(
)
≥ 1
76. ℎ →
(
)
77.
(
)
+
(
)
= 1
