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1. www.schoolDD.com
1
SchoolDD.com  

2. – F ˆ F www.schoolDD.com 1
1
ˈ F ʽ F F
F F F F F F
F F F F F
F F F F F ˈ F ʽ F
1.1 ʽ F F
ʽ F F F
F ʽ F ˈ F
F F F F F F F ˈ F
F
F F F F F F
F F F F F
F F F F F
ʽ F ˈ F F F
1.2 F SI
F 7 F F F (m), (kg), (s), F (A), (K),
(mol) (cd)
F F F F F F (N) = kg.m/s2
, (J) = N.m = kg.m2
/s2
1.3 F F (Prefix)
F F F F F F F F
F F 1 F F 1000 ˈ F F
F F 1000 103
F F F F F F F
(1012
), (10-12
), (109
), (10-9
), (106
), (10-6
)
(103
), (10-3
), (102
), (10-2
), (101
), (10-1
)
F F F F F ˈ F ˈ F F , ,
, , , F F F

3. – F ˆ F www.schoolDD.com 2
F F F F 103
F F 103
F 106
109
1012
F F F 101
F
102
101
F F ˈ F F ... F ˈ ....
1012
10-12
109
10-9
106
10-6
103
10-3
102
10-2
101
10-1
F 1
F
. 4,700,000,000 F ˈ
F F F 1 = 106
F ˈ (10-6
x 106
) F
F 1 F F F ...
∴ 4,700,000,000 x (10-6
x 106
) = 4,700 x 106
= 4,700 Mm Ans
. F F F F 0.0004 F
1 = 10-3
∴ 0.0004 x (103
x 10-3
) = 0.4 x 10-3
= 0.4 mm Ans
. 0.5
1 = 103
∴ 0.5 = 0.5 x 10-3
= 0.5 x 10-3
x (10-3
x 103
)
= 0.5 x 10-6
x 103
= 0.5 x 10-6
kg Ans
. 1 ,
1 = 10-2
∴ (1 )2
= (10-2
)2
= 10-4 2
1 = 10-4
Ans

4. – F ˆ F www.schoolDD.com 3
1 F F 101
(1 )2
= (101
)2
= 102 2
1 = 102
Ans
F F F Hard Disk F , F F
?
1.4 F
1.
F F F F F F F F F F
s = ut +
ଵ
ଶ
at2
F F m =
୫
ୱ
x s +
୫
ୱమ
x s2
F m = m + m
2.
F F F ˈ F F F F
F F
F a =
୴ି୳
୲
F F
୫
ୱమ
=
ౣ
౩
ି
ౣ
౩
ୱ
F
୫
ୱమ
=
୫
ୱమ
F F F F T = 2πට
ℓ
୥
F F s = ට
୫
ౣ
౩మ
= √sଶ
F s = s
1.5 F F
(error) F F
F F
F A ˈ F F A ˈ F + A
ˈ A + A
F F F F F 70 + 0.2 F F
ˈ F F F 69.8 70.2

5. – F ˆ F www.schoolDD.com 4
- F
F R = A +/- B
R = A + B
F = ( A +/- B ) + ( A + B )
F R = A +/- 2B
R = A + 2 B
F = ( A +/- 2B ) + ( A + 2 B )
- F F (%) F F F (%)
F
F R = A x/ൊ B
R = (
୅
୅
x100 +
୆
୆
x100 ) %
F = ( A x/ൊ B ) + (
୅
୅
x100 +
୆
୆
x100 ) %
F R = A x/ൊ B2
R = (
୅
୅
x100 +
ଶ ୆
୆
x100 ) %
F = ( A x/ൊ B2
) + (
୅
୅
x100 +
ଶ ୆
୆
x100 ) %
F R = A x/ൊ √B
R = (
୅
୅
x100 +
୆
ଶ୆
x100 ) %
F = (A x/ൊ √B ) + (
୅
୅
x100 +
୆
ଶ୆
x100 ) %
F 2
F 12.44 + 0.01 . F ˈ 2 F F 4.52 + 0.02 F
F
F F R = A B
F F R = ( A B ) + ( A + B )

6. – F ˆ F www.schoolDD.com 5
= ( 12.44 - 4.52 ) + ( 0.01 + 0.02 )
R = 7.92 + 0.03
∴ F F = 7.92 + 0.03 . Ans
F 3
F ˈ F F 1.20 + 0.01 ˈ F F
ˈ F F
V = W x L x H
F F V = (W x L x H ) + (
୛
୛
x100 +
୐
୐
x100 +
ୌ
ୌ
x100 ) %
= (1.20 x 1.20 x 1.20) + (
଴.଴ଵ
ଵ.ଶ଴
x100 x 3 )%
= 1.73 + 2.5 %
V = 1.73 + (
ଵ.଻ଷ ୶ ଶ.ହ
ଵ଴଴
)
F V = 1.73 + 0.043 3
Ans
+ 0.043 ˈ 2.5 % Ans
F 4
F F F (ℓ) ˈ 40.0 + 0.2 . F F F
T = 2πට
ℓ
୥
F F ( g = 10 m/s2
)
T = 2πට
ℓ
୥
F F T = 2πට
ℓ
୥
+ (
ℓ
ଶℓ
x 100 ) %
= 2 x (22/7) x ට
଴.ସ଴
ଵ଴
+ (
଴.ଶ
ଶ୶ସ଴
x 100 ) %
= 1.256 + 0.25 %
T = 1.256 + (
ଵ.ଶହ଺ ୶ ଴.ଶହ
ଵ଴଴
)
F F T = 1.256 + 0.003 s Ans

7. – F ˆ F www.schoolDD.com 6
F 5
F F F 1.00 + 0.01 F F ˈ
F F
V = 4/3 x π x (d/2)3
F F V = 4/3 x π x (d/2)3
+ (
ଷ ୢ
ୢ
x 100 ) %
= 4/3 x (22/7) x (1.00 /2 )3
+ (
ଷ ୶ ଴.଴ଵ
ଵ.଴଴
x 100 ) %
= 0.523 + 3 %
V = 0.523 + (
଴.ହଶଷ ୶ ଷ
ଵ଴଴
)
V = 0.523 + 0.02 m3
Ans
ˈ 3 % Ans
1.6
F
. + .
F F F
F 6 F 4.25 + 0.01 .
F F 4.2
( ) 5
0.1 .
F 0.01 .
F ˈ F F F 4.24 . 4.26 .
1 2 3 4 5 6
F F 4.2 + F 0.05
= 4.25

8. – F ˆ F www.schoolDD.com 7
1. F F F F F 0 F F
F 0.671 , 4.03 , 0.043 , 20.00 , 0.40 , 0.0003 3 , 3 , 2 , 4 , 2
1
2. F F F F F F 0 F F 15 , 136 , 4245 , 70324 ,
2001 2 , 3 , 4 , 5 4
3. F F F F 0 F A x 10n
1൑ A ൏ 10 10n
F ˈ F 12000 F ˈ 1.2 x 104
, 1.20 x 104
, 1.200 x 104
, 1.2000
x 104
2, 3, 4, 5
F F F
F F
3.21 + 4.156 = 7.366 ˈ 7.37 ( F 3 5
ˆ F F 5 ˆ )
5354 - 21.6 = 5332.4 ˈ 5332
F F F
F F
2.34 x 100.9 = 236.106 ˈ 236
7.3 ÷ 874 = 0.0083524 ˈ 0.0084
537.13 x 4.5 = 2417.085 ˈ 2.4 x 103
1.7 F
F F F F ˈ F
F F y = mx + c x ˈ y ˈ
ˈ y ˈ x F m = y/ x c ˈ y (y x
F y2
, y½
, 1/y x2
, x ½
, 1/x F )
F F F F F ˈ F F F
F F F F F F
c
x
y = mx + c
y
F
y = mx + c
x
xy = k y =
୩
୶
y
F
y =
௞
௫
k F

9. – F ˆ F www.schoolDD.com 8
1.8 F ʽ F
ʽ F F F F F F ʽ F F F
F ˈ ˈ F F F ˆ F ʽ F F F F
ˈ ʽ F
1.8.1 F F F F F F F
F
F
C
c
F 2 F ോോ F F F
a
a
a
∆ F F = 180/3=60°
a/b = A/B
a/c = A/C
b/c = B/C
B
A
θ
b
a
θ
θ
θ
θ
θ
α
α
α
α
∆ F 180°
‫׵‬ θ
90-θ
θ
θ
θ
θ

10. – F ˆ F www.schoolDD.com 9
1.8.2 F
α
θ
b
a
c
F sin , cos , tan
sinθ =
ୟ
ୡ
sinα =
ୠ
ୡ
cosθ =
ୠ
ୡ
cosα =
ୟ
ୡ
tanθ =
ୟ
ୠ
tanα =
ୠ
ୟ
tanθ =
ୱ୧୬ ஘
ୡ୭ୱ ஘
sin2
θ + cos2
θ = 1
√2
60
30
√3
1
2
45
1
1
53
37
4
3
5
(slope) =
୷మି୷భ
୶మି୶భ
= tan θ
x
y
(+)
x
y
(-)
x
y
x
y
1>2>3
3 =0
4 ˈ -
4
3
2
1
x
y
x
y
F =(k)xy
c2
= a2
+b2
c = √aଶ ൅ bଶ
x
y
y =mx + c F
c
y
θ
(x1 , y1)
(x2 , y2)
x
y

11. – F ˆ F www.schoolDD.com 10
1.8.3 F
1.
ଵ
ୟ౮
= a-x
, ax
.ay
= a(x + y)
,
ୟ౮
ୟ౯
= ax
.a- y
= a(x - y)
, a0
= 1
2. F log a = x F a = 10x
F ln a = x F a = ex
log(a.b) = log a + log b
log(a/b) = log a - log b
1.8.4
1. F ax2
+ bx + c = 0 F x =
ିୠേ√ୠమିସୟୡ
ଶୟ
2. F x2
a2
= 0 (x a)(x + a) = 0 F x = +a x = -a
3. F (x a)2
= 0 x2
2ax + a2
= 0 (x a)(x - a) = 0 F x = +a
4. F (x + a)2
= 0 x2
+ 2ax + a2
= 0 (x + a)(x + a) = 0 F x = -a
5. F x2
- 4 x - 12 = 0 (x - 6)(x + 2) = 0 F x = 6 , -2
1.8.5 F
1. 5 = (3+t)2
5-3 = 2t or
2. y = 3x + 2√3 x
y = 5√3 x or
3. 2x3
= 4x2
- (3x + x2
)x x F ?
4. y = 3x + 2 x y F ?
1.8.6 F F
1. F a ‫ן‬ b
ୟభ
ୟమ
=
ୠభ
ୠమ
2. F a ‫ן‬
ଵ
ୠ
ୟభ
ୟమ
=
ୠమ
ୠభ
3. F A x B = C x D A < C F B > D
4. D
ଡ଼
୐
= P F F F X F F F F ?
5. A
ହ୆మ
େିଵ
= (N
ଵ
ଶ
) X A
ଷ୆మ
େିଵ
= (6 - N) Y F N = 3 F X ˈ F Y ?

12. – F ˆ F www.schoolDD.com 11
1.8.7 F F F ˈ F
F ˆ F F F F F F F F ˆ
F F F F ˈ F ʾ F ˈ 44 ʾ
F F F 5 ʾ F F 2 ʾ F ˆ F F
F ˆ = A ʾ
F = B ʾ
= C ʾ
ʾ F ˈ 44 ʾ F ˆ ˈ
44+1+1+1 = 47 ʾ
F F F A + B + C = 47 ----(1)
F F F 5 ʾ
F F F B - A = 5 ----(2)
F F 2 ʾ
F F F B - C = 2 ----(3)
F F F F F 3 3 F F F F
F F 3 A C F B
(1) + (2) + (3) , (A+B+C) + (B-A) + (B-C) = 47 + 5 + 2
3B = 54
‫׵‬ B = 18
F B (2) F A F B - A = 5
18 - A = 5
18 - 5 = A
‫׵‬ A = 13
F B (3) F C F B - C = 2
18 - C = 2
18 - 2 = C
‫׵‬ C = 16
‫׵‬ ˆ F 13, 18 16 ʾ Ans
F F F F F F F ˇ F ʽ F F
! F F F F F F F F F F ˆ
ʽ F F